FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force...
Transcript of FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force...
![Page 1: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/1.jpg)
FORCE DEVELOPMENT DURING AND AFTER MUSCLE
LENGTH CHANGES
© Fábio Carderelli Minozzo, 2013
Department of Kinesiology and Physical Education
Faculty of Education
McGill University, Montreal
July 23rd
, 2013
A thesis submitted to McGill University in partial fulfillment of the requirements
of the degree of Doctor of Philosophy in Kinesiology
![Page 2: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/2.jpg)
2
Table of Contents
ACKNOWLEDGEMENTS ................................................................................. 5
CONTRIBUTION OF AUTHORS ..................................................................... 7
List of figures ......................................................................................................... 8
Abstract ................................................................................................................ 16
Résumé ................................................................................................................. 18
PART I – LITERATURE REVIEW ................................................................. 20
1 Introduction ................................................................................................ 21
2 Muscle force development during length changes ................................... 22
2.1 Force during muscle stretch .................................................................. 22
2.2 Force during muscle shortening ............................................................ 28
3 History dependence of muscle contraction ............................................... 31
3.1 Residual force enhancement after stretch .............................................. 33
3.2 Residual force depression after shortening ........................................... 41
4 Relations between force development during and after length changes 46
5 Rationale ...................................................................................................... 48
PART II – EXPERIMENTAL STUDIES ......................................................... 51
1 Force development during muscle stretch ................................................ 52
1.1 Preface ................................................................................................... 52
1.2 Effects of blebbistatin and Ca2+
concentration on force produced during
stretch of skeletal muscle fibres ............................................................................... 54
1.2.1 Abstract ..................................................................................................... 55
1.2.2 Introduction ............................................................................................... 56
1.2.3 Methods .................................................................................................... 58
1.2.3.1 Preparation of muscle fibres ............................................................................ 58 1.2.3.2 Solutions .......................................................................................................... 59 1.2.3.3 Experimental protocol ..................................................................................... 60
![Page 3: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/3.jpg)
3
1.2.3.4 Data analysis.................................................................................................... 62 1.2.4 Results ....................................................................................................... 64
1.2.4.1 Experiments using different calcium concentrations ....................................... 64 1.2.4.2 Effects of blebbistatin ...................................................................................... 67
1.2.5 Discussion ................................................................................................. 71
1.2.5.1 Comparison with other studies ........................................................................ 71 1.2.5.2 Effects of different calcium concentrations .................................................... 72 1.2.5.3 Effects of blebbistatin ...................................................................................... 75 1.2.5.4 Additional mechanisms ................................................................................... 78 1.2.5.5 Conclusion ....................................................................................................... 79 2. Force development during muscle shortening ........................................ 81
2.1 Preface ................................................................................................... 81
2.2 Pre-powerstroke crossbridges contribute to force transients during
imposed shortening in isolated muscle fibres ........................................................... 82
2.2.1 Abstract ..................................................................................................... 83
2.2.1 Introduction ............................................................................................... 84
2.2.3 Methods .................................................................................................... 86
2.2.3.1 Muscle fibre preparation .................................................................................. 86 2.2.3.2 Solutions .......................................................................................................... 87 2.2.3.3 Experimental protocol ..................................................................................... 88 2.2.3.4 Data analysis.................................................................................................... 90 2.2.3.5 Model development ......................................................................................... 92
2.2.4 Results ..................................................................................................... 100
2.2.4.1 Experimental results ...................................................................................... 100 2.2.4.2 Model results ................................................................................................. 105
2.2.5 Discussion ............................................................................................... 108
2.2.5.1 Experiments with different Ca2+
concentrations ............................................ 109 2.2.5.2 Modelling crossbridge kinetics ...................................................................... 110 2.2.5.3 Mechanism of blebbistatin inhibition ............................................................ 112 2.2.5.4 Indications for a load-dependent ADP-release step ....................................... 114 3 Force development during and after muscle length changes ................ 115
3.1 Preface ................................................................................................. 115
3.2 The effects of Ca2+
and MgADP on force development during and after
muscle length changes ............................................................................................ 116
3.2.1 Abstract ................................................................................................... 117
3.2.2 Introduction ............................................................................................. 118
3.2.3 Methods .................................................................................................. 119
![Page 4: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/4.jpg)
4
3.2.3.1 Fibre preparation ........................................................................................... 119 3.2.3.2 Solutions. ....................................................................................................... 120 3.2.3.3 Experimental protocol. .................................................................................. 121 3.2.3.4 Data analysis.................................................................................................. 122 3.2.3.5 Statistics ........................................................................................................ 123
3.2.4 Results ..................................................................................................... 124
3.2.4.1 Transient forces during length changes ......................................................... 124 3.2.4.2 Residual force enhancement and depression ................................................. 131
3.2.5 Discussion ............................................................................................... 139
3.2.5.1 Transient forces during length changes ......................................................... 139 3.2.5.2 Residual force enhancement .......................................................................... 141 3.2.5.3 Residual force depression .............................................................................. 143 3.2.5.4 Relation between the transient force and the residual forces ......................... 144 4 Muscle residual force enhancement ........................................................ 146
4.1 Preface ................................................................................................. 146
4.2 Force produced after stretch in sarcomeres and half-sarcomeres isolated
from skeletal muscles ............................................................................................. 147
4.2.1 Abstract ................................................................................................... 148
4.2.2 Introduction ............................................................................................. 149
4.2.3 Results ..................................................................................................... 150
4.2.4 Discussion ............................................................................................... 154
4.2.5 Methods .................................................................................................. 158
4.2.5.1 Preparation of the single and half-sarcomeres ............................................... 158 4.2.5.2 Micro-needle production and calibration ....................................................... 159 4.2.5.3 Mechanical isolation, visualization, and force measurement of single and half-
sarcomeres ................................................................................................................. 159 4.2.5.3 Solutions ........................................................................................................ 161 4.2.5.4 Protocol ......................................................................................................... 161 4.2.5.3 Data analysis.................................................................................................. 163 5 Final considerations .................................................................................. 165
5.1 Summary and conclusion .................................................................... 165
5.2 Future directions .................................................................................. 167
Reference list ..................................................................................................... 170
APPENDICES ................................................................................................... 196
![Page 5: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/5.jpg)
5
ACKNOWLEDGEMENTS
First and foremost, I would like to thank my thesis supervisor, Dr. Dilson
E. Rassier, for whom I was very fortunate in being the first Ph.D student. Dilson
represented and still represents to me much more than a supervisor: he has been a
great teacher, mentor, and friend. He taught me not only to be a meticulous, hard-
working and rigorous scientist, but also how to behave and interact with people
more professionally in an academic environment. For all of this, I will be eternally
grateful to him.
Secondly, I would like to express my appreciation to the Fonds de
recherche du Québec – Nature et Technologies (FQRNT), the WYNG trust
Foundation (WYNG trust Fellowship), the J.W. McConnel Foundation (Memorial
award), Herschel and Christine Victor Foundation (Fellowship in Education), and
the family of Mr David L. Montgomery (Memorial award) for their financial
support.
Thirdly, I would like to thank Lennart Hilbert, Clara Pun, Sara
Sigurðardóttir, Albert Kalganov, Ivan Pavlov, Rowan Novinger, Paula Ribeiro,
Anabelle Cornachione, Bruno Baroni, and Felipe Leite for their direct and indirect
collaboration in my research or simply for the pleasure of working with them.
Fourthly, I could not forget to thank my friends Mateus Cordeiro, and
Marilee Nugent for their emotional and psychological support during this
endeavour.
Fifthly, I wish to thank my beloved wife, Renata Minozzo, for her love,
support, kindness, and understanding throughout my degree. I remember the cold,
![Page 6: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/6.jpg)
6
dark winter days when I first arrived in Montreal in 2009. At that time, when
Renata was not yet a part of my life, everything seemed so difficult and looked so
grey. All of that changed the moment I met her, as Renata brought new colour and
meaning to my life!
Lastly, I would like to give special thanks to my family who has loved and
supported me in every way since I was born, through every step, every challenge,
every victory, every defeat. I thank my little sister, Carla Minozzo, for being the
“greatest cheerleader” I ever had; my mother, Angela Minozzo, for her
unconditional love and dedication to her children. It is impossible to hide anything
from her: she feels whatever I go through even when I do not tell her, and she is
always there, ready to listen to my problems. Finally, I would like to dedicate this
thesis to my father, Marcio Minozzo, whose commitment to work and passion for
life has always inspired me. He never gives up, he does not accept defeat, and at
the same time he is always ready to support whoever needs help. My father has
never lost faith in me, even when I lost my confidence in myself. My father’s
example not only inspired me to become the person I am but also helped to me to
get to where I am now.
![Page 7: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/7.jpg)
7
CONTRIBUTION OF AUTHORS
This thesis incorporates four manuscripts that are primarily the work of
Fábio Carderelli Minozzo, including data collection and analysis, writing, and
preparation for publication. The work for all the manuscripts was performed
under the supervision of Dr Dilson Rassier, who participated in their conception,
data analysis and writing. The second manuscript (part II, chapter 2), had the
collaboration of Lennart Hilbert, who conceived and wrote a mathematical model
(v. appendices) after several months of data analysis and discussion amongst the
three authors. The fourth manuscript (part II, chapter 4), was a result of a data
collection in conjunction with Dr. Bruno Baroni, who was visiting student in Dr.
Rassier’s laboratory. His supervisor, Dr. Marco Vaz also contributed to the
manuscript writing. Dr José Correa was invited later for statistical advice on the
required approach.
![Page 8: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/8.jpg)
8
List of figures
PART I – LITERATURE REVIEW
Figure 1 ¬ Schematic representation of the main molecular states during the crossbridge
cycle. “A” – actin; “M” – myosin; Pi – inorganic phosphate; ADP - adenosine diphosphate, ATP -
adenosine triphosphate. Step 1 – actomyosin + ATP complex is formed allowing ATP to be split
into ADP + Pi on the head of the myosin, this conformation, called pre-powerstroke molecular
state (AM.ADP.Pi) will use energy from ATP breakage to undergo powerstroke, releasing Pi, and
moving to the more stable post-powerstroke state (AM.ADP). Step 2 – AM.ADP complex will
release ADP when a new ATP comes into the myosin nucleotide binding region, causing myosin
to detach from actin. Step 3 – the M.ATP complex will eventually attach to actin due to affinity,
allowing the cycle to re-start……………………………………………………………………....22
Figure 2 – Comparison of Huxley’s predition to experimental data. The force-velocity
relationship predicted by Huxley’s (1957) crossbridge model (solid line) as opposed to the
experimental data (open circles). Note that the model fits well only the shortening limb
(rightwards) of the experimental data. Figure adapted from Harry et al (1990)…………...……...24
Figure 3 – Typical fibre stretch traces. Top trace – force traces from a muscle fibre that was
isometrically activated and subsequently stretched. Bottom trace – fibre length variation. The
red-dashed rectangle corresponds to the moment when the stretch was applied (data from personal
archive)…………………………………………………………………………………………….26
Figure 4 – Force transients during stretch. Schematic representation of muscle force (upper
traces) and length (lower traces) during stretch. Number 1 and 2 correspond to the first and second
phases respectively. Pc stands for critical force, and Lc critical length……………………….…...27
Figure 5 – Typical fibre shortening traces. Top trace – force traces from a muscle fibre that was
isometrically activated and subsequently shortened. Bottom trace – fibre length variation. The red-
dashed rectangle corresponds to the moment when the shortening was applied. Figure adapted
from Josephson and Stokes (1999)………………………………………………………………...29
Figure 6 – Force transients during shortening. Schematic representation of muscle force (upper
traces) and length (lower traces) during stretch. Number 1, 2, and 3 correspond to the first, second,
and third phases respectively. P1 and P2 represent the changes in slope from phase 1 to 2, and 2 to
3, respectively, being L1 and L2 their correspondent critical lengths………………………...……29
Figure 7 – Force and length relationship. Top: Force-length relationship diagram based on
isometric contractions from isolated muscle fibres at different average sarcomere lengths (striation
pattern). Bottom: Representation of two sets of filament (thin – actin, and thick – myosin)
corresponding to the average sarcomere length at specific points of the force-length relationship
(i.e. numbers 1-6). Adapted from Gordon et al (1966)……………………………………………33
Figure 8 – Muscle residual force enhancement. Upper panel – superimposed force traces from a
muscle fibre that was first isometrically activated, then stretched, and second simply isometrically
activated at the same final length. Lower panel – corresponding fibre lengths. In read, the amount
of “force enhancement” (FE). Figure adapted from Peterson et al (2004)………………………..34
Figure 9 – Graphical explanation for force enhancement using sarcomere-length non-
uniformity. Straight lines: from left to right, theoretical ascending, plateau, and descending limb
of the force-length relationship. Curved line (exponential): theoretical passive force component of
the force-length relationship. White circles: mean fibre sarcomere length (SL). Red circles:
different populations of sarcomeres. When a fibre is stretched from the mean SL A to B, some
sarcomeres are less stretched (C), while other sarcomeres (D) are more stretched than the mean SL
![Page 9: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/9.jpg)
9
(B). Crossbridges from the longer and “weaker” sarcomeres eventually yield, leaving these
structures to be supported only by passive elements (E), conveying the force produced by the
stronger sarcomeres. At equilibrium, the total force is given by the stronger sarcomeres (C), being
therefore greater than the isometric force predicted by the mean final SL (B). Figure adapted from
(Rassier & Herzog, 2004b)………………………………………………………………………...36
Figure 10 – A-band displacement and half-sarcomere non-uniformity. Left panel:
displacement of the A-band in relation to the centre of a sarcomere that was activated and
subsequently stretched. Right panel: correspondent behaviour of each of the halves from the same
sarcomere during and after stretch; notice that one half is losing overlap (black line), while the
other is gaining overlap (red line). Adapted from Rassier and Pavlov (2012)…………………….38
Figure 11 – Relation between force enhancement and A-band displacement. The relation
between the maximum amounts of A-band displacement observed after stretch and the level of
force enhancement compared with isometric contractions. Values for A-band displacements were
calculated as the averages of the absolute displacements among all half-sarcomeres in a given
preparation. Adapted from Rassier and Pavlov (2012)……………………………………………39
Figure 12 – Half-sarcomere non-uniformity schema. Schematic representation of a sarcomere
in three possible conditions: A – sarcomere isometrically activated before stretch; B – same
sarcomere after being uniformly stretched; C – same sarcomere, stretched by the same amount, but
undergoing a rightward A-band displacement. Noticed that one of the halves gained overlap, while
the other half tensioned titin from the same side of the sarcomere………………………………..40
Figure 13 – Muscle residual force depression. Upper panel – superimposed force traces from a
muscle that was first isometrically activated, then shortened, and second simply isometrically
activated at the same final length. Lower panel – corresponding lengths. In read, the amount of
“force depression” (FD). Figure adapted from (Josephson & Stokes, 1999)……………………...42
Figure 14 – Graphical explanation for force depression using sarcomere-length non-
uniformity. Straight lines: from left to right, theoretical ascending, plateau, and descending limb
of the force-length relationship. Curved line (exponential): theoretical passive force component of
the force-length relationship. White circles: mean fibre sarcomere length (SL). Red circles:
different populations of sarcomeres. When a fibre is shortened from the mean SL A to B, some
sarcomeres are less shortened (C), while other sarcomeres (D) are much more shortened than the
mean SL (B). After reaching equilibrium, the resultant force is lower than the isometric force
predicted by the force-length relationship (B), leading to force depression (FD). Figure adapted
from (Rassier & Herzog, 2004b)…………………………………………………………………..43
Figure 15 – Schematic representation of crossbridge inhibition due to actin deformation
during shortening. A – initial mean SL when a muscle is isometrically activated; notice that part
of the actin filament (continuous line) that is not overlapped by the myosin filament is strained and
deformed during activation. B – final SL when the same muscle is shortened; notice the newly
formed overlap zone containing the part of the actin previously deformed, hindering the
corssbridge formation in that zone (red shade)……………………………………………………45
Figure 16 – Relation between slow component of force enhancement during stretch and
residual force enhancement after stretch. inset: tetanus with force enhancement by stretch
superimposed on control tetanus to illustrate the approach used for measuring the slow component
of force enhancement during stretch (slow) and the residual force enhancement after stretch
(residual). Values from a given fibre denoted by the same symbol. Line, linear regression based on
all data points (P < 00001, n = 53). Adapted from Edman and Tsuchiya (1996)………………….47
Figure 17 – Schematic illustration of the functional arrangement of elastic passive structures
and the contractile elements in a muscle fibre. Stronger sarcomeres (SS) here act in series with
![Page 10: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/10.jpg)
10
weaker sarcomeres (WS). The latter is supported by an elastic passive structures (PS) that act in
series with SS. Adapted from Edman and Tsuchiya (1996)……………………………………….48
PART II EXPERIMENTAL STUDIES
1 Force development during muscle stretch
Figure 1 – Method for measuring critical force (Pc) and critical length (Lc) during stretch in
activated fibres. A: force and sarcomere length (SL) measured just before and during stretch and
during the early isometric phase of a contraction in a fibre activated in a pCa2+
of 4.5 (blue line).
Piecewise regression (black line) was used to find the transition between the 2 slopes and was used
to define Pc and Lc. B: closer image of the stretch phase recorded in the same contraction. Figure
also shows the 95% confidence interval (CI) for the regression (dashed lines; r2 = 0.99). Note that
the data are within the 95% CI…………………………………………………………………….64
Figure 2 – A: superimposed contractions produced by a fibre activated in pCa2+
of 4.5 (higher
force) and 6.0 (lower force). Force (top) and length (bottom) changes during the experiment are
shown; Lo, optimal length. Force rises during activation and then stabilizes to attain a steady-state
level. During stretch the force increases substantially, and afterward the stretch force decreases
slowly. Changes in solution during activation and relaxation create noise in the system, which is
reflected in the force transducer, but it quickly dissipates. B, top: superimposed contractions of the
experiment in A, showing the force produced during the stretch phase in the contractions
performed with different Ca2+
concentrations. Bottom: corresponding length change. The forces
produced during stretch and Pc were higher at increasing Ca2+
concentrations. The traces obtained
at pCa2+
of 9.0 before the stretch represent the force at rest (i.e., zero force). C: same experiment as
in B, but with forces normalized for the isometric contractions produced before stretch. Po,
maximal force before stretch………………………………………………………………………66
Figure 3 – Mean ± SE values of Pc (A) and Lc (B) in experiments performed with different Ca2+
concentrations. Changing the pCa2+
significantly altered Pc but not Lc. *Significantly different
from all other conditions (P < 0.05); # significantly different from pCa
2+ of 6.0 and 4.5 (P < 0.05).
HS, half-sarcomere………………………………………………………………………………...67
Figure 4 – Superimposed contractions produced by a fibre activated in pCa2+
of 4.5 before (higher
force) and after (lower force) blebbistatin (+/−) treatment. Force (top) and length (bottom) changes
during the experiment are shown. During the stretch force increases significantly, and afterward
the stretch force decreases slowly. The force produced during stretch after blebbistatin treatment
increases such that it virtually overlaps with the force produced before blebbistatin. Inset, changes
in sarcomere length (SL): note that we only measured SL during activation and stretch after the
noise produced by the solution exchange was totally cleared and we stopped measuring when just
before the solution was exchanged again for fibre relaxation…………………………..…………68
Figure 5 – Superimposed contractions of 3 experiments performed with blebbistatin (+/+) (A) or
blebbistatin (+/−) (B and C) at pCa2+
of 4.5. Blebbistatin (+/+) does not produce significant
changes in the isometric force and produces only a small change in force during stretch.
Blebbistatin (+/−), on the other hand, significantly decreases the isometric forces. The force
produced during stretch also decreases, but by a smaller magnitude that increases the stretch-to-
isometric force ratio. Note that Lc also increases after blebbistatin (+/−), as shown by the arrows
intercepting the length traces - the arrows start exactly at the transition between the slopes as
detected by piecewise regression - shown with the thick line. D: superimposed contractions of the
stretch performed by the fibre treated with blebbistatin (+/+) in A and blebbistatin (+/−) in B,
respectively. Force is normalized for the isometric force produced before the stretch. Note that Pc
and Lc are higher in the fibre treated with blebbistatin (+/−)……………………………………...70
Figure 6 – Mean ± SE values of Pc (A) and Lc (B) in the 2 sets of experiments performed with
blebbistatin (BB)(+/+) and respective control (control 1) and blebbistatin (+/−) and respective
control (control 2). Blebbistatin (+/−) changed Pc and Lc significantly. *Significantly different
![Page 11: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/11.jpg)
11
from all other conditions (P < 0.05). C: linear relation between stiffness (ΔSL/Δforce) and Pc
during the experiments conducted with fibres treated with blebbistatin (+/−). Pc values were
normalized for the maximal Pc (Pcmax) produced during these experiments……………………….70
2 Force development during muscle shortening
Figure 1 – Overview of mathematical model. The mathematical model comprises a load-
sensitive active crossbridge component adjusting the molecular contractile apparatus length Lmol,
and a passive element with a linear force response to differences between the externally set fibre
length L and Lmol. A three-state crossbridge kinetic cycle with a load-dependent powerstroke
transition from the pre to the post powerstroke state is assumed…………………………………94
Figure 2 – Simulated force during ramp shortening protocol with detected critical points.
Top row (A, B, C) shows measured force P vs. time, bottom row (D, E, F) shows fibre length L vs.
time. Triangles and circles represent P1 and P2 critical points, respectively. Negative times
correspond to times before start of shortening ramp, fibre activated at time -150t0 in simulation and
held isometrically up to time 0. Grey background rectangles indicate regions which are displayed
at higher time resolution in the next graph to the right. Five traces are simulated with ramp
velocities 0.125L0/t0, 0.25L0/t0, 0.5L0/t0, 1L0/t0 and 2L0/t0. Simulation parameters are presented in
Supplementary Material…………………………………………………………………………...95
Figure 3 – Typical experiment overview – pCa2+
4.5 and 6.0. Sample records from a typical
experiment showing the force produced by a muscle fibre activated in pCa2+
4.5 (upper trace) and
pCa2+
6.0 (lower trace). Force rises during activation and then stabilizes to achieve a plateau.
During shortening the force decays rapidly. After the shortening, the forces recover slowly to
achieve a new steady-state…………………………………………………………………………96
Figure 4 – Experimental detection of critical points at different Ca2+
concentrations. (A)
Superimposed contractions showing the force decrease during shortening while the fibre was
activated at different Ca2+
concentrations (top), with the corresponding length change (bottom).
All forces were normalized by their respective isometric forces (Po) before the ramp shortening.
P2 and L2 did not change at increasing Ca2+
concentrations. (B) Closer view from the initial
shortening phase of the experiment with another fibre, showing clearly that P1 and L1 do not
change with different Ca2+
concentrations. The critical points in this figure were detected with
regression analyses; the regression lines are shown in blue (pCa2+
4.5) and green (pCa2+
5.5)
traces……………………………………………………………………………………………….97
Figure 5 – Mean critical values for different Ca2+
concentrations. Mean values (+ S.E.M) of
P1 and P2 (A), and L1 and L2 (B) in experiments performed with different Ca2+
concentrations.
Changing the pCa2+
did not change any of the variables…….…………………………………....98
Figure 6 – Typical experiment overview – pCa2+
4.5 and blebbistatin. Sample records from a
typical experiment showing the force produced by a muscle fibre activated in pCa2+
4.5 (upper
trace) and then treated with blebbistatin (lower trace). Force rises during activation and then
stabilizes at a steady-state level. During shortening the force decreases. After the shortening, the
forces recover slowly to achieve a new steady-state……………………………………………....98
Figure 7 – Experimental detection of critical points in fibres treated with blebbistatin. (A)
Superimposed contractions, showing the force decay during shortening while the fibre was
activated with pCa2+
4.5 - (solid line), and then treated with blebbistatin (dashed line), with the
corresponding fibre length changes. All forces were normalized by their respective isometric
forces (Po) before shortening. P2 and L2 did not change with blebbistatin. (B) Closer view from
the initial shortening phase of the experiment with another fibre, showing that blebbistatin induced
a higher force decrease before P1. It also shows that blebbistatin induced greater P1 amplitude
when compared the contraction produced before blebbistatin. L1 was not changed by blebbistatin.
![Page 12: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/12.jpg)
12
The critical points in this figure were detected with regression analyses, the regression lines are
shown in blue (pCa2+
4.5) and red (pCa2+
4.5 + blebbistatin) traces……………...…………….....99
Figure 8 – Mean critical values of fibres treated with blebbistatin. Mean values (+ S.E.M.) of
P1 and P2 (A), and L1 and L2 (B) in experiments where fibres were treated with blebbistatin (+/-).
Blebbistatin changed P1 significantly. None of the other variables were changed. * Significantly
different from all other conditions (P < 0.05)…………………………………………………….101
Figure 9 – Critical points behaviour at different velocities. (A) Force responses (upper traces)
to ramp shortenings (lower traces) in a range of velocities (0.125 – 2 Lo.s-1
) from one set of
experiments performed with one fibre activated with a pCa2+
4.5. The rate of force decay
increased with shortening velocities. (B) Closer view from the same traces, showing increasing P1
amplitude (upper traces) and L1 (lower traces) with increasing velocities. (C) and (D) Same as in A
and B, now showing traces of another fibre treated with blebbistatin (3 velocities
displayed)………………………………………………………………………………………...104
Figure 10 – Mean critical values at different velocities. Mean (+ S.E.M.) of the P1 values at five
different velocities in a fibre activated with Calcium pCa2+
4.5 (dotted line), 6.0 (solid line) and
treaded with blebbistatin (solid line with inverted triangles). Blebbistatin changed P1 significantly
at all five velocities. *Significantly different from all other conditions (P < 0.05)……………...105
Figure 11 – Blebbistatin effect on ramp shortening critical points in experiment and model
simulation. A) Experimentally measured P1 for different ramp velocities. Solid line: pCa2+
4.5
with blebbistatin, dotted and dashed line: pCa2+
4.5 and pCa2+
6.0 without blebbistatin,
respectively. B) P1 detected in simulation for different ramp velocities. Solid line: blebbistatin
inhibition modeled by lowering of myosin actin tight binding energy by ΔE=0.35kBT. Dashed
line: no blebbistatin inhibition. C, D, E) Experimentally determined L1, P2, L2, respectively; same
conditions as in A). F, G, H) L1, P2, L2 detected in simulated ramp shortening, respectively; same
conditions as in B). Simulation parameters see Supplementary Material. ……………………….106
Figure 12 – Molecular mechanism of blebbistatin inhibition visualized in the crossbridge
cycle potential profile. We display here the two suggested mechanisms of blebbistatin inhibition,
each with its specific effect on the potential profile. The solid curve represents the free energy
profile without blebbistatin inhibition; the dashed curve represents the qualitative change from
blebbistatin addition. A progression through states 1, 2, 3 and finally back to 1 (from left to right)
corresponds to completion of one actomyosin crossbridge cycle by sequential transition through
the kinetic states. The elevations between the kinetic states correspond to reaction barriers; these
transitions require activation energy, so a higher barrier lowers the transition rates across this
barrier. A) Reduction of binding energy of myosin tight-binding to actin, manifesting itself as an
increase of the post-powerstroke energy level. Our model analysis indicates that this is a necessary
mechanism of blebbistatin inhibition. B) Reduction of the powerstroke zeroth order rate constant.
Our model analysis indicates that this is a possible but not a necessary mechanism of blebbistatin
inhibition. Potential profiles are only qualitative illustrations and not drawn to scale………..…109
Figure 13 – Simulated crossbridge dynamics during ramp shortening protocol with ramp
velocity 2L0/t0. A logarithmic time scale was used for all positive times; time 0 indicates start of
ramp shortening, negative times indicate isometric contraction phase before ramp shortening. A,
B) Force production, triangle and circle represent critical points P1 and P2, respectively. C, D)
Percentage of actively cycling crossbridges in the different kinetic states. Note logarithmic scaling
of vertical axis. E, F) Effective flux of crossbridges from pre- to post-powerstroke-state and from
post-powerstroke state to detached state. The effective flux is the rate at which crossbridges go
from a state xi to a state xj minus the rate at which crossbridges go from xj to xi. Note logarithmic
scaling of vertical axis. See also Discussion section and Supplementary Material. Simulation
parameters are included in the Supplementary Material…………………………..……..............113
3 Force development during and after muscle length changes
![Page 13: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/13.jpg)
13
Figure 1 – Detection of force transients during stretch and shortening of activated muscle
fibres. Left-to-right: P2 and L2 detection during stretch and shortening, respectively. Force traces
are on the top and fibre length variation at the bottom (Po = isometric force; Lo = initial length).
The force rise during stretch and the force decay during shortening can be fitted by two linear
functions: y1= a1 + b1 × xi (restriction: xi ≤ xo) and y2 = a2 + b2 × xi (restriction: xi > xo), where
(xo, yo) represents coordinates of the critical transitions (coordinates for P2 in this case), a1 and a2
are the intercepts of the two regression lines, and b1 and b2 are the slopes of the two regression
lines. The red traces in the graphs show the two-segmented piecewise regressions. The residual
sum of squares (RSS) is based on the sum of the squares of each regression line:
2
22
2
11
00
)()(
xx
ii
xx
ii
ii
xbayxbayRSS . RSS is used as a criterion to
determine the optimal values of a1, a2, b1, b2, and xo - those belonging to the minimal RSS are
considered optimal. The blue trace displayed on the inset correspond to a simple linear regression,
based on the best fit for the force coordinates (xo, yo) during the first 2-3 ms, and P1 corresponds to
the first data point where the regression does not follow the force trace. In both cases the statistic
F-value and confidence intervals are calculated according to standard methods for regression
analyses. L1 and L2 are extrapolated by crossing a perpendicular line passing by P1 and P2,
respectively, until reaching the length traces…………………….………………………………123
Figure 2 – Superimposed isometric contractions in different Ca2+
concentrations. Sample
records from typical isometric contractions produced in pCa2+
4.5 and pCa2+
6.0 (top), and
corresponding length traces (bottom). The average sarcomere lengths in each contraction were
2.82m, and 2.83m, respectively. ……………………………………………………………...125
Figure 3 – Force transients during length changes in different Ca2+
concentrations. (A)
Superimposed contractions showing the force increase during stretch while the fibre was activated
in pCa2+
4.5 (solid line) and pCa2+
6.0 (dashed line) (top), with corresponding changes in fibre
length (bottom). All forces were normalized by the isometric forces (Po) before the stretch. The
regression lines for the contractions produced in pCa2+
4.5 and pCa2+
6.0 are shown in blue and
red, respectively. (B) Superimposed contractions showing the force decrease during shortening
when a fibre was activated in pCa2+
4.5 (solid line) and pCa2+
6.0 (dashed line) (top), with the
corresponding length changes (bottom). (C) Closer view from the initial shortening phase,
showing that decreasing Ca2+
concentration induced an increase in L1 and P1 amplitudes. All
forces were normalized by the isometric forces (Po) before the shortening. The regression lines for
the contractions produced in pCa2+
4.5 and pCa2+
6.0 are shown in blue and red, respectively.
Decreasing Ca2+
concentration increased L1 and P1 amplitude………….………..……………...127
Figure 4 – Mean stiffness values during length changes. Mean stiffness values (+ S.E.M)
during isometric contractions (black bar), shortening (light grey bar) and stretch (dark grey bar)
from experiments performed in pCa2+
4.5 and pCa2+
6.0 (n = 13). Decreasing Ca2+
concentration
significantly decreased the stiffness in all conditions. In both pCa2+,
stiffness increased during
stretch and decreased during shortening. *Significantly different from isometric, #significantly
different from shortening, groups significantly different from each other………….…………128
Figure 5 – Force transients during length changes in fibres treated with MgADP. (A)
Superimposed contractions showing the force increase during stretch (top) when the fibre was
activated in pCa2+
4.5 (solid line) and treated with MgADP (dashed line). The corresponding
length changes are show in the bottom panels. All forces were normalized by the isometric forces
(Po) before the stretch. The regression lines for the contractions produced in pCa2+
4.5 and in
presence of MgADP are shown in blue and red, respectively. (B) Superimposed contractions
showing the force decrease during shortening (top) when a fibre was activated at pCa2+
4.5 (solid
line) and treated with MgADP (dashed line). The corresponding changes in fibre length are shown
in the bottom. (C) Closer view from the initial shortening phase showing that MgADP activation
induced an increase in L1. All forces were normalized by the isometric forces (Po) before the
![Page 14: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/14.jpg)
14
shortening. The regression lines for the contractions produced in pCa2+
4.5 before and after
MgADP treatment are shown in blue and red, respectively. MgADP treatment increased L1
significantly, while it did not change the other variables………………………………………...130
Figure 6 – Mean stiffness values during length changes. Mean stiffness values (+ S.E.M)
during isometric contraction (black bar), shortening (light grey bar) and stretch (dark grey bar)
obtained in experiments performed in pCa2+
4.5 before and after MgADP treatment (n = 7).
MgADP did not affect stiffness, but in stiffness was always increased during stretch and decreased
during shortening. * Significantly different from isometric contractions, # significantly different
from shortening…………………………………………………………………………………..131
Figure 7 – Typical experiment for analysis of residual force enhancement and force
depression performed in pCa2+
4.5. Superimposed force traces (upper panel), SL traces (mid
panel), and length traces (lower panel) from a fibre activated in pCa2+
4.5 and kept isometric (in
black), stretched (in red), or shortened (in blue)…………………………………………………132
Figure 8 – Residual force changes in different Ca2+
concentrations. (A) Sample records from a
typical experiment showing superimposed contractions produced by a fibre activated in pCa2+
4.5
and pCa2+
6.0. Black: isometric contraction at SL of 2.8μm. Red: isometric contraction at SL of
2.65μm followed by a 5% stretch. The corresponding length changes are shown in the lower
panels. (B) Mean (+ S.E.M.) relative forces from fibres activated in pCa2+
4.5 and pCa2+
6.0 (n =
13) in three conditions: isometric (black bar), shortened (light grey bar) and stretched (dark grey
bar). P = forces recorded 10s after length changes; Piso = force at the respective isometric
condition. *Significantly different from isometric, #significantly different from shortening,
significantly different from the same condition (shortened) in pCa2+
6.0...................................133
Figure 9 – Mean stiffness after length changes. Mean stiffness values (+ S.E.M) measured
during isometric contractions (black bar), and when forces reach a new steady state after
shortening (light grey bar) and stretch (dark grey bar) in experiments performed in pCa2+
4.5 and
pCa2+
6.0. Decreasing Ca2+
concentration decreased the stiffness in all conditions. In both pCa2+
,
the stiffness during stretch and shortening was higher and lower, respectively, than during
isometric contractions. *Significantly different from isometric, #significantly different from
shortening, significantly different from each other.........…………………...………………….134
Figure 10 – Residual force changes after MgADP treatment. (A) Sample records recorded
during a typical experiment in a fibre activated in pCa2+
4.5 with 10mM MgADP. Black:
isometric contraction at SL of 2.8μm. Red: isometric contraction at SL of 2.65μm followed by a
5% length stretch. Blue: isometric contraction at SL 2.95μm followed by a 5% length shortening.
Lower panel: correspondent fibre length changes. (B) Mean (+ S.E.M.) forces produced by fibres
(n = 7) activated in pCa2+
4.5 and pCa2+
4.5 + 10mM MgADP during isometric contractions (black
bar), after shortening (light grey bar) and after stretch (dark grey bar). P = forces 10s after length
changes. Piso = force produced during the respective isometric condition. *Significantly different
from isometric, # significantly different from shortening………………………………………...135
Figure 11 – Mean stiffness after length changes. Mean stiffness values (+ S.E.M) measured
during isometric contractions (black bar), and when forces reach a new steady state after
shortening (light grey bar) or stretch (dark grey bar) during experiments performed in pCa2+
4.5
with and without MgADP (n = 7). *Significantly different from isometric, #significantly different
from shortening…………………………………………………………………………………..136
Figure 12 – Relation between force and stiffness after length changes. Mean forces (P/Piso +
S.E.M.) plotted against the mean stiffness (S/Siso + S.E.M.). Relative stiffness in MgADP after
stretch does not follow the same trend as in Ca2+
solutions. P = force measured 10s after length
changes. Piso = force at the respective isometric condition; S = stiffness measured 10s after length
changes in every condition, Siso = stiffness at the respective isometric condition…….…………137
![Page 15: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/15.jpg)
15
Figure 13 – Difference between P2 and forces at the end of length changes (peak for
stretching and valley for shortening). Left panel: experiments performed in different pCa2+.
Right panel: experiments performed with MgADP. ST = P/Po during stretch (light gray bar), SH =
P/Po during shortening (black bar). * Significant difference between two groups…...………….138
4 Muscle Residual Force Enhancement
Figure 1 – Typical experiment overview. A - Superimposed force traces (upper panel) and
length traces (lower panel), from a single sarcomere activated in pCa2+
4.5 and kept isometric (in
black) or stretched during activation (in red). B - Superimposed force traces (upper panel) and
length traces (lower panel), from a half-sarcomere activated in pCa2+
4.5 and kept isometric (in
black) or stretched (in red). In both cases, force enhancement (FE) was calculated as the difference
between the isometric (in black) and steady state force (in red) achieved after stretch. Note that for
the actual FE calculation, the passive component was also taken into account………………….151
Figure 2 – Mean force values (±SD) produced by single and half-sarcomeres. Predictive force-
length relationship, constructed based on the filament lengths of rabbit psoas (Sosa et al, 1994)
Mean isometric forces (±SD) produced by single (black closed symbols) and half-sarcomeres
(black open symbols). The dashed line corresponds to exemplary passive force curves derived
from two sets of experiments with relaxed sarcomeres (small crosses), the dash-dotted line
corresponds to the descending limb of the force-length relationship, the continuous line
corresponds to the sum of the predictive force-length relationship to the passive curve. The mean
forces after a stretch are shown in red for single sarcomeres (closed-triangle) and half sarcomeres
(opened-triangle). The circles represent mean force values (±SD) from isometric contractions
performed close to the plateau of the force-length relation, while the squares represent mean (±SD)
values from isometric contractions performed at longer SL and HSL………………………...…154
Figure 3 – Needle dimensions. Tip of a glass micro-needle piercing a myofibril (on the left)
externally adjacent to the Z-line from one if its sarcomeres. The figure shows representative
measurements (on the top-left, yellow arrows) of five arbitrary cross-sectional areas of the conical-
shaped tip of the needle. The red arrow represents how much of this tip was inserted in the
myofibril; this value was never higher than 1.5μm. Magnification = 150X……………………..160
Figure 4 – Half and single sarcomere isolation. A - Glass micro-needles approaching a single
myofibril on the microscope coverslip (magnification = 90X). B - Half-sarcomere being caught
between the micro-needles. The myofibril is still on the coverslip (magnification = 90X). C - Half-
sarcomere isolated and lifted (~2μm) from the coverslip (magnification = 150X). D - Single
sarcomere caught by the two micro-needles (magnification = 150X)…………………………...163
![Page 16: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/16.jpg)
16
Abstract
Muscles are the motors of human movement. The most commonly
accepted theory of muscle contraction, the “crossbridge theory”, was postulated
by A.F Huxley in 1957, and since then it has been widely accepted to model and
explain how a muscle contracts. However, some phenomena are still not fully
understood in the framework of the crossbridge theory, including the effects of
muscle stretching and shortening on force production. More specifically, there is
still controversy in the literature about the mechanisms responsible for the
increase in force observed during and after stretch, and the decrease in force
observed during and after shortening. The goal of the studies presented in this
thesis was to investigate the mechanisms responsible for changes in force during
and after length changes to test the following hypotheses: (i) force development
during stretch is caused by crossbridges in a pre-powerstroke state, (ii) force
development during shortening is affected by biasing crossbridges into pre-
powerstroke, (iii) force enhancement after stretch is due to an increase in the
number of attached crossbridges, (iv) force enhancement after stretch is caused by
half-sarcomere non-uniformities, (v) force enhancement after stretch is caused by
stiffening of non-contractile proteins induced by Ca2+
, and (vi) force depression
after shortening is caused by a decrease in the number of attached crossbridges.
In order to achieve this goal, we developed four studies. First we
investigated the mechanisms of force development (i) during stretch, and (ii)
during shortening separately. We then investigated the link between the changes
in force during length changes with the changes observed after length changes
(iii). These three studies were performed with skinned muscle fibres from the
![Page 17: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/17.jpg)
17
rabbit psoas muscle. Finally, we investigated in details a potential mechanism for
the residual force enhancement observed after stretch using a new preparation that
we developed in our laboratory – isolated half-sarcomeres (iv).
Our results suggest that (i) the force increase during stretch is largely
caused by crossbridges in a pre-powerstroke state, (ii) the force decrease during
shortening is related to the engagement of pre-powerstrokes only at the initial,
rapid phase of force change, (iii) force enhancement after stretch is caused by an
increase in the number of crossbridges attached to actin, half-sarcomere non-
uniformities, and titin stiffening upon Ca2+
activation, and (iv) force depression
after shortening is caused by myosin crossbridge deactivation.
![Page 18: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/18.jpg)
18
Résumé
Les muscles sont les moteurs du mouvement humain. La théorie la plus
communément reconnue de la contraction musculaire, “théorie des pontages
croisés”, mis en avant par AF Huxley en 1957, est depuis largement utilisée
comme model d’explication afin de démontrer comment un muscle se contracte.
Toutefois, certains phénomènes ne sont pas encore entièrement compris dans la
structure de cette théorie, notamment les effets d’étirement et de raccourcissement
du muscle sur la production de la force. D’ailleurs, il existe toujours une
controverse dans la littérature sur les mécanismes responsables de l'augmentation
de la force observée pendant et après l’étirement, et la diminution de la force
observée pendant et après le raccourcissement. L'objectif des travaux présentés
dans cette thèse est d'étudier les mécanismes responsables des changements au
niveau de la force pendant et après une modification de la longueur du muscle
afin de tester les hypothèses suivantes: (i) le développement de la force au cours
de l’étirement est causé par les pontages croisés en pré-course de puissance, (ii) le
développement de la force au cours du raccourcissement est affecté par la
polarisation des pontages croisés en pré-course de puissance, (iii) l'augmentation
de la force après étirement est due à une augmentation du nombre de pontages
croisés attachés, (iv) l'augmentation de la force après étirement est causée par les
non-uniformités du demi-sarcomère, (v) l'augmentation de la force après
étirement est causée par le raidissement des protéines non contractiles induites par
le Ca2+
, et (vi) la diminution de la force après raccourcissement est provoquée par
une diminution du nombre de pontages croisés attachés.
![Page 19: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/19.jpg)
19
Dans le but d’atteindre cet objectif, nous avons élaboré quatre études.
D'abord, nous avons étudié séparément les mécanismes de développement de la
force (i) au cours de l’étirement, et (ii) au cours du raccourcissement. Ensuite,
nous avons étudié le lien entre les changements de la force observés pendant et
après une modification de la longueur du muscle. (iii). Ces trois études ont été
réalisées à l’aide de fibres musculaires provenant du psoas du lapin. Enfin, nous
avons étudié en détail un mécanisme potentiel pour l'augmentation de la force
résiduelle observée après étirement en utilisant une nouvelle préparation
développée en laboratoire - demi-sarcomères isolés (iv).
Nos résultats nous amènent à penser que (i) l'augmentation de la force
durant l’étirement est en grande partie causée par les pontages croisés dans un état
de pré-course de puissance, (ii) la diminution de la force au cours du
raccourcissement du muscle est lié à l'engagement de la pré-course de puissance,
seulement au moment de la phase initiale rapide du changement de la force, (iii)
l'augmentation de la force après étirement est provoquée par une augmentation du
nombre de ponts fixés à l'actine, des non-uniformités du demi-sarcomère et du
durcissement de la titine sur l’activation du Ca2+
, et (iv) la diminution de force
après raccourcissement est causée par la désactivation du pontage croisé de
myosine.
![Page 20: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/20.jpg)
20
PART I – LITERATURE REVIEW
![Page 21: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/21.jpg)
21
1 Introduction
Muscles are the motors of all vertebrates. The musculoskeletal system
functions much like a system of levers and pulleys via the bones and muscles,
respectively. At the molecular level, muscle contraction happens due to a
chemical process regulated by Ca2+
, which allows the interaction between two sets
of protein filaments (i.e. myosin and actin). This interaction uses energy from
Adenosine Triphosphate (ATP) to cause muscle to shorten, hence generating
tension. According to the most accepted mechanisms of muscle contraction,
“crossbridges” are formed between myosin and actin filaments, which drive the
sliding of actin and myosin past each other. The “crossbridge model”, first
proposed by Andrew F. Huxley in 1957, and later modified by the same author
and collaborators (Huxley & Simmons, 1971), is considered the best predictor of
how muscle force is developed upon contraction. It also explains well the features
of the force-velocity relationship observed during muscle shortening proposed
initially by Hill (1938).
![Page 22: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/22.jpg)
22
Figure 1 - Schematic representation of the main molecular states during the crossbridge
cycle. “A” – actin; “M” – myosin; Pi – inorganic phosphate; ADP - adenosine diphosphate, ATP -
adenosine triphosphate. Step 1 – actomyosin + ATP complex is formed allowing ATP to be split
into ADP + Pi on the head of the myosin, this conformation, called pre-powerstroke molecular
state (AM.ADP.Pi) will use energy from ATP breakage to undergo powerstroke, releasing Pi, and
moving to the more stable post-powerstroke state (AM.ADP). Step 2 – AM.ADP complex will
release ADP when a new ATP comes into the myosin nucleotide binding region, causing myosin
to detach from actin. Step 3 – the M.ATP complex will eventually attach to actin due to affinity,
allowing the cycle to re-start.
Since Huxley’s first manuscript on the crossbridge theory (1957), several
models have been proposed (e.g. Eisenberg et al, 1980; Harry et al, 1990; Hill et
al, 1975; Julian et al, 1974), mainly complementing and strengthening the original
model. In general, the crossbridge cycle assumes three molecular states: (i) a pre-
powerstroke state - where crossbridges are attached to actin but still weakly
bound, (ii) a post-powerstroke state - where crossbridges strongly attach to actin,
and (iii) a detached state (Roots et al, 2007) (see details in Figure 1). However,
there are certain phenomena that are either not readily incorporated or not taken
into account by the original crossbridge theory. First, forces produced during
stretch of activated muscles are not well predicted and generally overestimated by
the crossbrige model (Harry et al, 1990). Second, there is a long-lasting increase
or depression in force after stretch or shortening of muscle fibres, respectively.
These phenomena challenge the established force-length relationship (Gordon et
al, 1966), and Huxley’s original model, which had no provisions to account for
changes in force depending on the history of contraction.
2 Muscle force development during length changes
2.1 Force during muscle stretch
![Page 23: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/23.jpg)
23
When a muscle is activated several interactions between actin and myosin
take place fuelled by ATP hydrolysis, which drives a series of conformational
changes on the S1-subfragment of each myosin head (Houdusse et al, 2000).
These conformational changes are amplified by the rotation of the myosin head
and tilting of the “lever arm” of myosin (powerstroke) and transmitted to elastic
component of the S2-myosin-subfragment (Holmes, 1997; Rayment et al, 1993).
Such force transmission in turn will make the filaments slide past each other,
leading to muscle shortening.
If muscles are prevented from shortening, they will generate an isometric
contraction. However, if muscles are stretched while activated, there is a notable
increase in force (Bickham et al, 2011; Edman et al, 1978; Getz et al, 1998;
Lombardi & Piazzesi, 1990; Pinniger et al, 2006; Stienen et al, 1992) without
concomitant increase in ATP hydrolysis (Abbott et al, 1951; Bickham et al, 2011;
Linari et al, 2003; Woledge et al, 2003); this phenomenon is called hereupon force
enhancement during stretch.
Interestingly, most of the crossbridge models of muscle contraction
(Eisenberg et al, 1980; Huxley, 1957; Huxley & Simmons, 1971) do not predict
well force development during muscle stretch. Huxley’s original model (1957)
does not clearly attribute a maximum crossbridge strain during stretch, which
leads to an overestimation (Figure 2) of the predicted forces when compared to
experimental values. The addition of a maximum crossbridge strain to the model
does not overcome this limitation because it invariably underestimates the
experimental values (Harry et al, 1990)
![Page 24: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/24.jpg)
24
Figure 2 – Comparison of Huxley’s predition to experimental data. The force-velocity
relationship predicted by Huxley’s (1957) crossbridge model (solid line) as opposed to the
experimental data (open circles). Note that the model fits well only the shortening limb
(rightwards) of the experimental data. Figure adapted from Harry et al (1990).
Although extensively investigated, the exact mechanisms responsible for
force enhancement during stretch are still unclear, becoming a matter of intense
debate (Bickham et al, 2011; Brunello et al, 2007; Colombini et al, 2007b; Edman
& Tsuchiya, 1996; Julian et al, 1978; Linari et al, 2000a; Lombardi & Piazzesi,
1990; Pinniger et al, 2006; Ranatunga et al, 2010; Rassier, 2008). In general,
studies do not agree if force during stretch is caused by an increase in the number
of cycling crossbridges (Brunello et al, 2007; Fusi et al, 2010; Linari et al, 2000a),
or by the an increase in the mean force exerted per crossbridge (Bickham et al,
2011; Colombini et al, 2007a; Colombini et al, 2008; Lombardi & Piazzesi,
Huxley’s model
Experimental data
![Page 25: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/25.jpg)
25
1990). Therefore, it is important to characterize force development during stretch
in order to better understand the different suggested mechanisms.
Normally, when a muscle is stretched using a ramp-protocol, force rises in
two phases (Figure 3 and 4). The first phase of force increase is very steep, while
the second is less steep (Figure 3) or absent (Edman & Tsuchiya, 1996; Rassier,
2008; Roots et al, 2007). The first phase has been normally attributed to
crossbridge kinetics, while the second phase is less understood. The transition
between the first and second phases has been attributed to the force at which the
attached crossbridges reach their maximum extension (also referred as critical
force, Pc), which occurs at a critical sarcomere length (Lc) before detaching from
actin (Edman et al, 1981; Getz et al, 1998; Rassier, 2008; Stienen et al, 1992).
When the stretch speeds are fast enough ( 2.0 Lo.s-1
) to overcome the
crossbridge cycling rate, this transition becomes independent of the stretch
velocity, happening at relatively constants Pc and Lc (Piazzesi et al, 1997; Pinniger
et al, 2006; Roots et al, 2007). These observations strengthen the hypothesis that
the force enhancement in this phase 1 during stretch is due to an increase in the
force produced per crossbridge.
Another study (Getz et al, 1998) attributed an increase in stiffness during
stretch to crossbridges in a “weakly-bound” molecular state, preceding the myosin
powerstroke, and therefore called pre-powerstroke state. Crossbridges in this state
would not contribute to isometric force production, but would resist to stretch,
leading to an increase in force during lengthening (Getz et al, 1998; Rassier,
2008). Studies that used different substances to bias crossbridges into the pre-
powerstroke state invariably show an increase in force during phase 1 relatively to
![Page 26: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/26.jpg)
26
the isometric force (Chinn et al, 2003; Getz et al, 1998; Pinniger et al, 2006;
Rassier, 2008; Roots et al, 2007).
Figure 3 – Typical fibre stretch traces. Top trace – force traces from a muscle fibre that was
isometrically activated and subsequently stretched. Bottom trace – fibre length variation. The red-
dashed rectangle corresponds to the moment when the stretch was applied (data from personal
archive)
However, studies also observed an increase in fibre stiffness and changes
in the crossbridge X-ray diffraction pattern during stretch compared to the
isometric conditions. Since stiffness is a putative measurement of the number of
crossbridges attached to actin, and X-ray diffraction is a technique that reveals the
crystalline pattern of muscle fibres and thus their mean crossbridge orientation
(Brunello et al, 2007; Linari et al, 2000a), these studies suggest that an increase in
force is associated with an increase in the number of crossbridges during phase 1.
A more recent study (Fusi et al, 2010) that showed an increase in stiffness during
stretch only when fibres were activated, but not when they were stretched in rigor
(where several crossbridges are also attached to actin), strengthens the notion that
the stiffness increase in activated fibres is likely attributed to the attachment of
Force
Length
![Page 27: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/27.jpg)
27
new crossbridges during stretch, as opposed to a mean increase in force of the
attached crossbridges. Clearly, there is still debate regarding stiffness behaviour
during stretch
Figure 4 – Force transients during stretch. Schematic representation of muscle force (upper
traces) and length (lower traces) during stretch. Number 1 and 2 correspond to the first and second
phases respectively. Pc stands for critical force, and Lc critical length.
The reason for a slower tension rise in phase 2 (Figure 4) is not clear. If
the transition in the force traces observed between phase 1 and 2 is caused by the
detachment of crossbridges, it is hard to grasp why and how force still rises after
this event. In fact a few studies did not see any force rise in phase 2 (Bagni et al,
2005; Edman et al, 1978; Stienen et al, 1992). Different from phase 1, this phase
is velocity dependent; the faster the stretch the lesser the force rises (Ranatunga et
![Page 28: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/28.jpg)
28
al, 2010; Roots et al, 2007), being absent when the stretch velocities are > 9 SL.s-1
(Bagni et al, 2005).
It remains unclear if phase 2 can be attributed to new crossbridges
attaching to actin during stretch (Pinniger et al, 2006; Roots et al, 2007) or to
another phenomenon not related to crossbridges. Edman and Tsuchiya (1996)
credited the continued rise in tension after the first transition to a non-uniform
distribution of the sarcomere lengths within the fibre. Accordingly, the stress
imposed by the stretch would lead to a non-uniform behaviour of the sarcomeres,
which in turn would strain the non-contractile elastic structures inside some
sarcomeres (i.e. titin and nebulin) as well as the links between adjacent myofibrils
leading to a steady increase in force.
2.2 Force during muscle shortening
When activated and not held against any load muscles naturally shorten
since their thick and thin filaments will slide past each other while their A-bands
keep constant (Huxley & Niedergerke, 1954; Huxley & Hanson, 1954). ATP
usage is matched to force when muscles are able to shorten against external loads
that are lower than their internal force. In this case, ATPase activity is directly
propositional to the speed of muscle shortening, reaching its maximum when
there is no load applied, and shortening velocity is maximal (Barany, 1967). This
is one of the reasons why the traditional crossbridge models of contraction
(Huxley, 1957; Huxley & Simmons, 1971) are able to well explain the established
force-velocity relationship during muscle shortening (i.e. Hill, 1938).
![Page 29: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/29.jpg)
29
Figure 5 – Typical fibre shortening traces. Top trace – force traces from a muscle fibre that was
isometrically activated and subsequently shortened. Bottom trace – fibre length variation. The red-
dashed rectangle corresponds to the moment when the shortening was applied. Figure adapted
from Josephson and Stokes (1999).
Figure 6 – Force transients during shortening. Schematic representation of muscle force (upper
traces) and length (lower traces) during stretch. Number 1, 2, and 3 correspond to the first, second,
and third phases respectively. P1 P2 represent the changes in slope from phase 1 to 2, and 2 to 3,
respectively, being L1 and L2 their correspondent critical lengths.
Force
Length
![Page 30: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/30.jpg)
30
However, some features of the force changes observed during shortening
are still unclear. At first glance, the force trace during muscle shortening
resembles the trace during stretch, but in the opposite direction (Figure 5).
Nevertheless both traces have dissimilarities that are attributed to different strain-
dependences of the crossbridge kinetics during stretch and shortening (Roots et al,
2007). During shortening, force normally decreases steeply (phase 1), then it
decreases less rapidly (phase 2). Finally, the force decrease becomes even slower
(phase 3) (see Figure 6). the transition in the force trace from phase 1 to phase 2 is
normally referred to as the first critical point (P1), which occurs at specific
sarcomere lengths (L1), while a transition in the force trace from phase 2 to phase
3 is referred to as the second critical point (P2), which occurs at a corresponding
sarcomere length (L2) (Ranatunga et al, 2010; Roots et al, 2007; Roots &
Ranatunga, 2008). Phase 1 is commonly associated with a pure elastic response
(Ford et al, 1977), while the force behaviour during phase 2 is attributed to a
transition from the initially to the newly attached crossbridges, after they undergo
the powerstroke (Ranatunga et al, 2010; Roots et al, 2007).
The first rapid drop in tension during ramp shortening was first attributed
to the unloading of an elastic element within the crossbridges attached previous to
the shortening (Ford et al, 1977). This interpretation is consistent with the model
proposed by Huxley and Simmons (1971), which attributes the linearity of T1 (the
first lowest drop during a length step) to a release of elastic energy residing within
the crossbridges. Later, another study (Bressler, 1985) cast doubt on the idea that
the first drop during a ramp shortening corresponds to T1, since the same
behaviour was not detected either in an artificial elastic structure, or in a small
![Page 31: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/31.jpg)
31
piece of tendon. Bressler (1985) interpreted the first phase of the force drop to the
head rotation of the crossbridge, represented by the transition from T1 to T2 in the
study of Huxley and Simmons (1971). Recently when the first phase of force
decrease was reinvestigated in different velocities (Roots et al, 2007) and
temperatures (Roots & Ranatunga, 2008), changes in P1 were also attributed to
changes in kinetics of the crossbridge powerstroke.
Similarly to stretch, the P2 transition during shortening represents the point
at which the originally attached crossbridges detach, but in this case undergoing a
forward powerstroke. These crossbridges would be negatively strained throughout
muscle shortening finally detaching at L2 (Roots et al, 2007). After P2 (phase 3)
most of the previously attached crossbridges would be replaced with an increasing
number of newly formed cycling crossbridges until shortening is over, and the
equilibrium is re-established (Ranatunga et al, 2010). However, the mechanisms
of the continuous slower tension decline after P2 are less clear; there is some
evidence it could be caused by actin filament deactivation induced by shortening
(Colomo et al, 1986; Edman, 1975). Recent studies (Ranatunga et al, 2010; Roots
et al, 2007) suggest it is caused by a combination of i) changes in filament
overlap, since the decline is more prominent on the ascending limb of the force-
length relation, and ii) release of stored elastic tension from non-crossbridge
structures (i.e. titin).
3 History dependence of muscle contraction
![Page 32: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/32.jpg)
32
If skeletal muscles are stretched or shortened while activated, the steady-
state force obtained after these length changes is always higher or lower,
respectively, than the corresponding isometric force at the same final length
(Abbott & Aubert, 1952). This history dependence of muscle contraction
challenges the well-established force-length relationship, which experimentally
demonstrated that muscle isometric force was dependent on the average
sarcomere length, and therefore the amount of overlap between actin and myosin
filaments (Gordon et al, 1966), independent of the history of contraction (Figure
7).
Z-line
![Page 33: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/33.jpg)
33
Figure 7 – Force and length relationship. Top: Force-length relationship diagram based on
isometric contractions from isolated muscle fibres at different average sarcomere lengths (striation
pattern). Bottom: Representation of two sets of filament (thin – actin, and thick – myosin)
corresponding to the average sarcomere length at specific points of the force-length relationship
(i.e. numbers 1-6). Adapted from Gordon et al (1966).
History dependence of force production is not predicted by the traditional
crossbridge models of contraction either (i.e. Huxley, 1957; Huxley & Simmons,
1971); according to these models muscle force is a function of the number of
cycling crossbridges that are governed by rates of attachment and detachment, not
previous history of contraction.
Although several explanations for the history dependence of force
production have been provided (Abbott & Aubert, 1952; Marechal & Plaghki,
1979; Morgan, 1994; Morgan et al, 2000; Roots et al, 2007), the underlying
mechanisms are still a matter of intense debate (Edman, 2012; Herzog et al, 2006;
Herzog & Leonard, 2006; Morgan & Proske, 2007; Ranatunga et al, 2010;
Rassier, 2012; Rassier & Herzog, 2004b).
3.1 Residual force enhancement after stretch
An example of residual force enhancement is shown on Figure 8, which
depicts force traces from a muscle fibre that was first activated and subsequently
stretched. After the stretch, the transient force increase ceases, but force remains
elevated in relation to the isometric reference at the same final length. This
phenomenon has been observed in human muscles during voluntary and electrical
stimulation (Lee & Herzog, 2002; Pinniger & Cresswell, 2007; Power et al,
2012a; Power et al, 2012b), isolated muscles in vitro (Abbott & Aubert, 1952;
![Page 34: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/34.jpg)
34
Ettema et al, 1992) and in situ (Brown & Loeb, 2000; Herzog & Leonard, 2002;
Morgan et al, 2000), single muscle fibres (Edman et al, 1978; Edman & Tsuchiya,
1996; Peterson et al, 2004; Pinniger et al, 2006; Roots et al, 2007), myofibrils
(Joumaa et al, 2008; Leonard & Herzog, 2010; Pun et al, 2010), and recently
mechanically isolated single sarcomeres (Rassier & Pavlov, 2012).
Figure 8 – Muscle residual force enhancement. Upper panel – superimposed force traces from a
muscle fibre that was first isometrically activated, then stretched, and second simply isometrically
activated at the same final length. Lower panel – corresponding fibre lengths. In read, the amount
of “force enhancement” (FE). Figure adapted from Peterson et al (2004) .
Force enhancement shows similar characteristics throughout most of the
preparations: it is long lasting, positively correlated with the stretch amplitude
(Abbott & Aubert, 1952; Edman et al, 1982; Herzog & Leonard, 2002), and
independent of stretch velocity (Edman et al, 1982; Rassier et al, 2003c).
Furthermore, it can be decreased or even fully supressed by shortening (Herzog &
Leonard, 2000; Rassier & Herzog, 2004c), but only partially abolished by
![Page 35: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/35.jpg)
35
deactivation (Abbott & Aubert, 1952; Herzog & Leonard, 2002; Herzog et al,
2003).
The theory of sarcomere length non-uniformity (Morgan, 1990; Morgan,
1994) was the first attempt to explain this phenomenon based on the observations
of a non-uniform behaviour in the sarcomere lengths during muscle activation
(Julian & Morgan, 1979b; Julian et al, 1978) and after stretch (Julian & Morgan,
1979a). According to this theory (Morgan 1990, 1994) the descending limb of the
force-length relationship (Figure 7) is unstable. As a result, a stretch inflicted
when a muscle is activated would elicit differences in lengths among its
individual sarcomeres in series: part of these sarcomeres would lengthen more,
getting weaker (Figure 9; mean SL – D) due to a decrease in filament overlap,
while the other part would lengthen less, getting stronger (Figure 9; SL – C) since
they keep relatively more filament overlap. The “weaker” sarcomeres would
continually yield, losing overlap (Figure 9; SL - D to E) and eventually “popping”
when the tension borne by passive elements equals the tension of the “stronger”
sarcomeres. At this point the average sarcomere force is higher than that produced
during isometric contractions (Figure 9; SL – B).
![Page 36: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/36.jpg)
36
Figure 9 – Graphical explanation for force enhancement using sarcomere-length non-
uniformity. Straight lines: from left to right, theoretical ascending, plateau, and descending limb
of the force-length relationship. Curved line (exponential): theoretical passive force component of
the force-length relationship. White circles: mean fibre sarcomere length (SL). Red circles:
different populations of sarcomeres. When a fibre is stretched from the mean SL A to B, some
sarcomeres are less stretched (C), while other sarcomeres (D) are more stretched than the mean SL
(B). Crossbridges from the longer and “weaker” sarcomeres eventually yield, leaving these
structures to be supported only by passive elements (E), conveying the force produced by the
stronger sarcomeres. At equilibrium, the total force is given by the stronger sarcomeres (C), being
therefore greater than the isometric force predicted by the mean final SL (B). Figure adapted from
(Rassier & Herzog, 2004b)
According to the original sarcomere length non-uniformity theory
(Morgan, 1990; Morgan, 1994) force enhancement should only happen on the
descending limb, as it is the sole “unstable” portion of the force-length curve.
Force enhancement should not exceed the plateau of the force-length relationship,
since the maximal overlap given by the “stronger” sarcomeres should at most
equal force at the plateau. All these conditions have been questioned: studies have
detected force enhancement above the plateau (Pun et al, 2010; Rassier et al,
2003c) or along the ascending limb (Pun et al, 2010) of the force-length
relationship. Moreover, although sometimes non-uniform after stretch, sarcomeres
![Page 37: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/37.jpg)
37
were neither observed to reach a length in which they would pop (Joumaa et al,
2008; Pun et al, 2010; Rassier et al, 2003b).
More recently, the engagement of passive elements (i.e. titin) upon Ca2+
activation followed by stretch, changes in the kinetics of crossbridges inducing an
increase in the number of attached motors, and dissimilarities in half-sarcomere
lengths, have been proposed to explain the force enhancement after stretch
(Rassier, 2012).
The stiffness of titin, the protein which is mainly responsible for the
development of passive force, increased in the presence of Ca2+
(Labeit et al,
2003). This result suggests that titin can change its characteristics with muscle
activation during contraction. In a subsequent study, it was observed that muscle
fibres presented ~10% force enhancement when fibres lacking myosin-actin
interactions were stretched in presence of Ca2+
(Cornachione & Rassier, 2012).
Hence, the mechanisms of force enhancement could rely on “non-contractile”
structures.
Alternatively, stretch after activation could be inducing changes in the
kinetics of crossbridges, leading to an increase in the crossbridges attached to
actin. This hypothesis finds support in studies that found an increase in fibre
stiffness in the force enhanced state (Herzog & Leonard, 2000; Rassier & Herzog,
2005). Nevertheless, the exact mechanisms by which the number of attached
crossbridges would be increased are unknown.
Recent studies, using new techniques that allowed mechanical isolation of
single sarcomeres (Pavlov et al, 2009a; Rassier & Pavlov, 2012), demonstrated
that force enhancement was also present in this preparation (Rassier & Pavlov,
![Page 38: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/38.jpg)
38
2012). At first glance, these findings were able to directly refute sarcomere length
non-uniformities as the cause of force enhancement after stretch. However, in the
same study (Rassier & Pavlov, 2012), the authors observed that during activation
and stretch, A-bands were displaced toward one of the sides of the sarcomeres
(Figure 10), showing that each half of the sarcomeres could produce a different
amount of overlap due to A-band displacements. This observation corroborated
previous findings that showed a non-uniform behaviour of half-sarcomeres in
single myofibrils (Telley et al, 2006b).
Figure 10 – A-band displacement and half-sarcomere non-uniformity. Left panel:
displacement of the A-band in relation to the centre of a sarcomere that was activated and
subsequently stretched. Right panel: correspondent behaviour of each of the halves from the same
sarcomere during and after stretch; notice that one half is losing overlap (black line), while the
other is gaining overlap (red line). Adapted from Rassier and Pavlov (2012)
Additionally, the levels of force enhancement were correlated to the
degree of A-band displacement (Figure 11), suggesting that half-sarcomere non-
uniformity as a possible mechanism for force enhancement in single sarcomeres
(Rassier & Pavlov, 2012) .
![Page 39: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/39.jpg)
39
Figure 11 – Relation between force enhancement and A-band displacement. The relation
between the maximum amounts of A-band displacement observed after stretch and the level of
force enhancement compared with isometric contractions. Values for A-band displacements were
calculated as the averages of the absolute displacements among all half-sarcomeres in a given
preparation. Adapted from Rassier and Pavlov (2012)
The suggested mechanism by which half-sarcomere non-uniformity would
generate force enhancement is, to some extent, similar to the explanation given
for non-uniformity between sarcomeres. One of the halves take up most of the
stretch, losing overlap and becoming weaker, while the other half is much less
elongated, keeping more overlap and getting stronger (Figure 12). In the
equilibrium, forces produced mainly by the crossbridges from the stronger half of
the sarcomere are counterbalanced by the passive structures together with the
crossbridges from the other half. This resultant force is therefore, higher than
what the sarcomere would produce if uniformly stretched (Rassier, 2012; Rassier
& Pavlov, 2012).
![Page 40: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/40.jpg)
40
Figure 12 – Half-sarcomere non-uniformity schema. Schematic representation of a sarcomere
in three possible conditions: A – sarcomere isometrically activated before stretch; B – same
sarcomere after being uniformly stretched; C – same sarcomere, stretched by the same amount, but
undergoing a rightward A-band displacement. Noticed that one of the halves gained overlap, while
the other half tensioned titin from the same side of the sarcomere.
Although there is evidence supporting half-sarcomere non-uniformity as a
possible mechanism for residual force enhancement (Campbell et al, 2011;
Rassier & Pavlov, 2012), it cannot exclusively explain this phenomenon since
some sarcomeres that did not present A-band displacement were still able to
generate significant amounts of force enhancement (Figure 11) (Rassier & Pavlov,
2012). Therefore, force enhancement could be caused by a combination of half-
![Page 41: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/41.jpg)
41
sarcomere non-uniformity, and a molecular mechanism - titin stiffening upon Ca2+
activation or crossbridge kinetics as mentioned earlier (Rassier, 2012).
3.2 Residual force depression after shortening
Figure 13 shows a typical experiment in which a muscle was activated and
subsequently shortened. After shortening, the force transient ceases, but force
remains decreased in relation to the isometric reference contraction at the same
final length. Ever since first observed (Abbott & Aubert, 1952), force depression
has been detected in several preparations, ranging from whole muscles (Abbott &
Aubert, 1952; Bullimore et al, 2007; Herzog & Leonard, 2000; Herzog et al,
2000; Morgan et al, 2000), to single fibres (Edman, 1975; Edman et al, 1993;
Granzier & Pollack, 1989; Lee & Herzog, 2009; Roots et al, 2007), and myofibrils
(Joumaa & Herzog, 2010; Pun et al, 2010). Force depression increases with
increasing shortening magnitudes (Abbott & Aubert, 1952; Bullimore et al, 2007;
Herzog & Leonard, 1997; Josephson & Stokes, 1999; Marechal & Plaghki, 1979),
increasing levels of activation (De Ruiter et al, 1998; Herzog & Leonard, 1997),
decreasing speeds of shortening (Abbott & Aubert, 1952; Herzog et al, 2000;
Josephson & Stokes, 1999; Morgan et al, 2000; Roots et al, 2007), and increasing
amount of mechanical work delivered during shortening (Abbott & Aubert, 1952;
Herzog & Leonard, 1997; Herzog et al, 2000; Josephson & Stokes, 1999; Morgan
et al, 2000; Van Noten & Van Leemputte, 2013). Additionally, force depression is
abolished after relaxation (Abbott & Aubert, 1952; Edman et al, 1993; Herzog &
Leonard, 1997; Joumaa & Herzog, 2010; Morgan et al, 2000), although some
studies found a small loss in force when a subsequent isometric activation is
![Page 42: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/42.jpg)
42
performed (Granzier & Pollack, 1989; Josephson & Stokes, 1999; Van Noten &
Van Leemputte, 2013). Force depression seems not to be affected by a previous
stretch (Herzog & Leonard, 2000).
Figure 13 - Muscle residual force depression. Upper panel – superimposed force traces from a
muscle that was first isometrically activated, then shortened, and second simply isometrically
activated at the same final length. Lower panel – corresponding lengths. In read, the amount of
“force depression” (FD). Figure adapted from (Josephson & Stokes, 1999) .
Sarcomere length non-uniformity has been also proposed to explain force
depression (Edman et al, 1993; Julian & Morgan, 1979a; Morgan et al, 2000)
based on the assumption of instability on the descending limb of the force-length
relationship (Morgan et al, 2000). Accordingly, if a muscle undergoes an imposed
shortening on the “unstable” descending limb of the force-length relationship,
some sarcomeres will shorten only a small amount (Figure 14; SL - C), while
others will take up most of the shortening. The latter may shorten so much that
they will end up on the ascending limb of the force-length relationship (Figure 13;
SL – D). Since both groups of sarcomeres (C and D) are in series, at equilibrium
![Page 43: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/43.jpg)
43
forces will be matched below the predicted force given by the average SL (Figure
14; SL – B).
Figure 14 - Graphical explanation for force depression using sarcomere-length non-
uniformity. Straight lines: from left to right, theoretical ascending, plateau, and descending limb
of the force-length relationship. Curved line (exponential): theoretical passive force component of
the force-length relationship. White circles: mean fibre sarcomere length (SL). Red circles:
different populations of sarcomeres. When a fibre is shortened from the mean SL A to B, some
sarcomeres are less shortened (C), while other sarcomeres (D) are much more shortened than the
mean SL (B). After reaching equilibrium, the resultant force is lower than the isometric force
predicted by the force-length relationship (B), leading to force depression (FD). Figure adapted
from (Rassier & Herzog, 2004b)
The non-uniform hypothesis proposed for force depression (Morgan et al,
2000) fails to explain force depression when fibres had their sarcomere lengths
controlled, which avoids non-uniformity (Granzier & Pollack, 1989).
Furthermore, force depression has been found on the “stable” ascending limb of
![Page 44: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/44.jpg)
44
the force-length relationship in several preparations (Granzier et al, 1989; Herzog
& Leonard, 1997; Herzog et al, 1998; Pun et al, 2010). Recently, studies that used
mechanically isolated myofibrils, which allows for tracking of individual
sarcomeres, observed that the sarcomere lengths were non-uniform, but never
unstable during and after shortening (Joumaa & Herzog, 2010; Pun et al, 2010).
It has been also suggested that force depression is associated with an
accumulation of metabolites, i.e. inorganic phosphate (Pi) and protons (H+)
(Granzier & Pollack, 1989) (Van Noten & Van Leemputte, 2013), and/or a
decrease in Ca2+
sensitivity (Edman, 1996) induced by shortening. (Van Noten &
Van Leemputte, 2013). Nevertheless, if force depression was solely caused by any
of these metabolic mechanisms, a brief period of deactivation should not be able
to eliminate the deficit in force, but studies show the opposite (Abbott & Aubert,
1952; Herzog & Leonard, 1997; Julian & Morgan, 1979a; Morgan et al, 2000).
Furthermore, in the light of recent studies (Joumaa & Herzog, 2010; Pun et al,
2010) that detected force depression in single myofibrils, which have to be fully
permeabilized and immersed in a chamber filled with solutions in continuous
flow, it is unlikely that force depression would be caused by an accumulation of
metabolites in such controlled environment.
More than 40 years ago, Marechal and Plaghki (1979) suggested that force
depression was caused by an inhibition of crossbridge attachments due to a
mechanical deformation of the actin filaments entering the overlap zone during
shortening. According to this hypothesis, during muscle activation the portion
from actin filaments that is not interacting with the myosin filaments would be
more strained than the portion that has cycling crossbridges (overlap zone),
![Page 45: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/45.jpg)
45
leading to a transient deformation on these filaments that could hinder their
myosin binding sites, ultimately inhibiting some of the crossbridge formation
when entering the new overlap zone during shortening (Figure 15).
Figure 15 – Schematic representation of crossbridge inhibition due to actin deformation
during shortening. A – initial mean SL when a muscle is isometrically activated; notice that part
of the actin filament (continuous line) that is not overlapped by the myosin filament is strained and
deformed during activation. B – final SL when the same muscle is shortened; notice the newly
formed overlap zone containing the part of the actin previously deformed, hindering the
corssbridge formation in that zone (red shade).
The hypothesis that crossbridge inhibition via actin deformation would
explain studies that showed a decrease in stiffness after shortening (Lee &
Herzog, 2003; Sugi & Tsuchiya, 1988), since the number of crossbridges should
decrease in proportion to the magnitude of shortening and force depression. It
also explains studies that correlate force depression to muscle work during
shortening (Abbott & Aubert, 1952; Herzog & Leonard, 1997; Herzog et al, 2000;
Josephson & Stokes, 1999; Van Noten & Van Leemputte, 2013).
![Page 46: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/46.jpg)
46
Finally, a recent study showed that force depression was decreased when
myofibrils were activated with MgADP (Pun et al, 2010). The authors attributed
this effect to ADP inducing strong-binding and activation via cooperativity, in
which Ca2+
regulation of the crosssbridge binding sites on the actin filament is not
necessary. Hence MgADP activation partially counteracted the inhibition of
crossbridge attachment to actin during shortening, probably because the “actin
deformation” was hindering the Ca2+
regulation of the crossbridge binding site on
actin (Pun et al, 2010).
4 Relations between force development during and after length
changes
There is one study that correlated the transient changes in force observed
during stretch with the residual force enhancement (Edman & Tsuchiya, 1996).
The authors found a strong relationship between the level of the slow increase in
force after Pc during stretch and the level of residual force enhancement (Figure
16). They attributed this increase in force to overstrained “passive structures” (PE)
working in parallel with the “weak sarcomeres” (WS), and these both structures
working in series with the “stronger sarcomeres” (SS) as depicted in figure 17.
According to the study (Edman & Tsuchiya, 1996) the reason why the
amount of force increase after the breaking point was always greater than the
residual force enhancement was due to a dampening effect elicited by the
crossbridges from the WS during stretch. This “extra” amount of force would
disappear as soon as the populations between WS and SS reached equilibrium
![Page 47: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/47.jpg)
47
after the transients cease. The remaining force enhancement was then only
attributed to the final non-uniform distribution of the sarcomeres.
Figure 16 - Relation between slow component of force enhancement during stretch and
residual force enhancement after stretch. inset: tetanus with force enhancement by stretch
superimposed on control tetanus to illustrate the approach used for measuring the slow component
of force enhancement during stretch (slow) and the residual force enhancement after stretch
(residual). Values from a given fibre denoted by the same symbol. Line, linear regression based on
all data points (P < 00001, n = 53). Adapted from Edman and Tsuchiya (1996)
Figure 17 – Schematic illustration of the functional arrangement of elastic passive structures
and the contractile elements in a muscle fibre. Stronger sarcomeres (SS) here act in series with
![Page 48: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/48.jpg)
48
weaker sarcomeres (WS). The latter is supported by an elastic passive structures (PS) that act in
series with SS. Adapted from Edman and Tsuchiya (1996).
Although the slow decrease after P2 was shown to be related to the level of
filament overlap before shortening and with the level of crossbridge inhibition
(Roots et al, 2007), the existence of a direct relationship between force behaviour
during shortening and the residual force depression has not been investigated thus
far.
5 Rationale
Notwithstanding the extensive amount of research in the field, the molecular
mechanisms behind muscle force development during and after imposed length
changes are not fully understood. Therefore, we decided to investigate these
phenomena in four separate studies:
1 – The first study investigated the effects of Ca2+
concentration and the myosin
inhibitor blebbistatin on force development during stretch. Changing Ca2+
concentrations changes the number of crossbridges attached to actin, and
blebbistatin biases crossbridge toward pre-powerstroke state. Therefore, we can
test the mechanisms of force enhancement associated with the number of
crossbridges attached to actin and the contribution of pre-powerstroke
crossbridges to the force increase during stretch.
Hypotheses:
![Page 49: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/49.jpg)
49
i) the level of Ca2+
activation affects force development during stretch of
muscle fibres.
ii) biasing crossbridges into pre-powerstroke state affects force development
during stretch of muscle fibres.
2 – The second study investigated the effects of Ca2+
concentration and
blebbistatin on force development during shortening. Similarly to the first study,
we used changes in Ca2+
concentrations and blebbistatin to investigate if
mechanisms of force development were associated with the number of
crossbridges attached to actin and/or to the amount of crossbridges in the pre-
powerstroke state.
Hypotheses:
i) the level of Ca2+
activation affects force decrease during shortening of
muscle fibres.
ii) biasing crossbridges into pre-powerstroke state affects force development
during shortening of muscle fibres.
3 – The third study investigated the effects of Ca2+
and MgADP activation on the
force development during and after length changes. MgADP activation induces
strong binding of myosin crossbridges to actin, and thus allows for testing
mechanisms related to crossbridges cooperativity. This study was aimed at
understanding the relations between force development during and after length
changes.
Hypotheses:
![Page 50: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/50.jpg)
50
i) the level of Ca2+
activation affects force development during stretch and/or
shortening of muscle fibres.
ii) inducing crossbridges strong binding to actin via MgADP activation
increases force during stretch.
iii) inducing crossbridges strong binding to actin via MgADP activation
attenuates force decrease during shortening.
vi) inducing crossbridges strong binding to actin via MgADP activation
attenuates force depression after shortening of muscle fibres.
v) inducing crossbridges strong binding to actin via MgADP activation
increases force enhancement after stretch of muscle fibres.
vi) there is a significant relationship between the level of force changes during
and after length changes.
4- The fourth study used a new technique that allowed for mechanically
isolation of half-sarcomeres from individual myofibrils, to investigate if half-
sarcomere length variability was associated with force enhancement after stretch.
Hypotheses:
i) there is force enhancement after stretch of single sarcomeres and half-
sarcomeres.
![Page 51: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/51.jpg)
51
PART II – EXPERIMENTAL STUDIES
![Page 52: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/52.jpg)
52
1 Force development during muscle stretch
1.1 Preface
Despite extensive research conducted in the field of muscle contraction,
the molecular bases for force development during stretch are still controversial
(Bickham et al, 2011; Brunello et al, 2007; Fusi et al, 2010; Getz et al, 1998;
Pinniger et al, 2006). Force enhancement during stretch has been attributed to: (a)
an increase in the number of crossbridges attached to actin (Brunello et al, 2007;
Fusi et al, 2010; Linari et al, 2000b); (b) an increase in mean crossbridge force
(Colombini et al, 2007b; Lombardi & Piazzesi, 1990); and (c) crossbridges
operating in pre-powerstroke state, which would not produce force during
isometric contractions, but would contribute to force when stretched (Chinn et al,
2003; Getz et al, 1998; Rassier, 2008). The later mechanism has received much
attention, as studies that used different non-specific myosin inhibitors, i.e.
vanadate (Vi) (Chinn et al, 2003; Getz et al, 1998), N-benzyl-p-tolune
sulphonamide (BTS) (Pinniger et al, 2006), and 2, 3-Butanedione monoxime
(BDM) (Rassier, 2008; Rassier & Herzog, 2004a), which bias crossbridges into
pre-powerstroke states, showed an enhanced force during stretch of activated
muscles.
Most of these myosin inhibitors are not specific for myosin II, and may
change the kinetics of ATP hydrolysis, creating confounding effects for a clear
interpretation of the experiments aimed at investigating the influence of pre-
powerstroke crossbridges in the forces produced during stretch. Thus, we
designed a study to investigate force enhancement during stretch of muscle fibres,
![Page 53: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/53.jpg)
53
testing mostly two hypotheses: (i) force increase is caused by an increase in the
number of crossbridges attached to actin, and (ii) force increase is caused by pre-
powerstroke crossbridges attached to actin during stretch. Force was controlled
either by altering Ca2+
concentration, which supposedly does not alter the
repartitioning of crossbridges into different molecular states, or via crossbridge
inhibition induced by blebbistatin, which is a highly specific myosin inhibitor
since it is not a phosphate analogue and therefore does not directly interfere with
the chemistry of ATP kinetics.
![Page 54: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/54.jpg)
54
1.2 Effects of blebbistatin and Ca2+
concentration on force produced during
stretch of skeletal muscle fibres
Fábio Carderelli Minozzo
Dilson E. Rassier
Reprinted from: American Journal of Physiology – Cell Physiology. 2010
Nov;299(5):C1127-35. doi: 10.1152/ajpcell.00073.2010.
![Page 55: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/55.jpg)
55
1.2.1 Abstract
When activated muscle fibres are stretched at low speeds (≤2 optimal
length Lo/s), force increases in two phases, marked by a change in slope [critical
force (Pc)] that happens at a critical sarcomere length extension (Lc). Some studies
attribute Pc to the number of attached crossbridges before stretch, while others
attribute it to crossbridges in a pre-powerstroke state. In this study, we
reinvestigated the mechanisms of forces produced during stretch by altering either
the number of crossbridges attached to actin or the crossbridge state before
stretch. Two sets of experiments were performed: 1) activated fibres were
stretched by 3% Lo at speeds of 1.0, 2.0, and 3.0 Lo/s in different pCa2+
(4.5, 5.0,
5.5, 6.0), or 2) activated fibres were stretched by 3% Lo at 2 Lo/s in pCa2+
4.5
containing either 5 μM blebbistatin(+/−) or its inactive isomer (+/+). All stretches
started at a sarcomere length (SL) of 2.5 μm. When fibres were activated at a
pCa2+
of 4.5, Pc was 2.47 ± 0.11 maximal force developed before stretch (Po) and
decreased with lower concentrations of Ca2+
. Lc was not Ca2+
dependent; the
pooled experiments provided a Lc of 14.34 ± 0.34 nm/half-sarcomere (HS).
Pc and Lc did not change with velocities of stretch. Fibres activated in blebbistatin
(+/−) showed a higher Pc (2.94 ± 0.17 Po) and Lc (16.30 ± 0.38 nm/HS) than
control fibres (Pc 2.31 ± 0.08 Po; Lc 14.05 ± 0.63 nm/HS). The results suggest that
forces produced during stretch are caused by both the number of crossbridges
attached to actin and the crossbridges in a pre-powerstroke state. Such
crossbridges are stretched by large amplitudes before detaching from actin and
contribute significantly to the force developed during stretch.
![Page 56: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/56.jpg)
56
1.2.2 Introduction
Stretch of skeletal muscle fibres has been commonly used to investigate
the mechanics and kinetics of myosin crossbridges. When activated muscle fibres
and myofibrils are stretched at low speeds [≤2 optimal length (Lo)/s], crossbridges
have to resist the opposing forces while attached to actin, which causes the force
to increase in two phases: 1) a fast increase that happens over the extension of a
few nanometers and subsequently 2) a slow increase or a stabilization of force
(Edman, 1999; Getz et al, 1998; Pinniger et al, 2006; Rassier, 2008; Roots et al,
2007). The transition between the two phases is marked by a change in slopes of
the force rise, called critical force (Pc) here, and is commonly associated with the
mechanical detachment of crossbridges from actin. The detachment happens after
the crossbridges reach a critical extension length (Lc), commonly observed in
lengths between 8 and 20 nm/half-sarcomere (HS), depending on the experimental
condition (Edman, 1999; Getz et al, 1998; Pinniger et al, 2006; Roots et al, 2007).
Rapid stretches (>10 Lo/s) produce a break in the force rise also associated with
the mechanical detachment of crossbridges and corresponding well to the
transition in force observed during slower stretches (Bagni et al, 2005; Colombini
et al, 2008; Colombini et al, 2009).
Although stretch-induced force enhancement has been investigated for
many years, the underlying mechanisms are still controversial. Some studies
attribute the force enhancement mainly to the number of crossbridges attached to
actin (Bagni et al, 2005; Colombini et al, 2008; Colombini et al, 2009), while
others attribute the force enhancement to a change in the mean crossbridge force
(Lombardi & Piazzesi, 1990; Sugi & Tsuchiya, 1988). Lately, it has been
![Page 57: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/57.jpg)
57
suggested that the force during stretch is caused or influenced by a population of
crossbridges weakly attached to actin in a pre-powerstroke state, preceding
inorganic phosphate (Pi) release during the ATPase cycle. These crossbridges
would not generate significant isometric forces but would have the potential to
generate a large force while strained during muscle stretch (Chinn et al, 2003;
Getz et al, 1998; Rassier, 2008). Studies using interventions that bias crossbridges
toward a pre-powerstroke state, including inorganic vanadate (Vi) (Chinn et al,
2003; Getz et al, 1998) and the myosin inhibitor 2,3-butanedione monoxime
(BDM) (Rassier, 2008; Rassier & Herzog, 2004a), show an increase in Pc relative
to the isometric force during the stretch, strengthening the latter mechanism.
However, there is a limitation inherent to these myosin inhibitors, which makes
the results controversial: they change the kinetics of ATP hydrolysis, interfering
with Pi release. Thus it is not clear whether the stretch forces are a result of pre-
powerstroke crossbridges due to their structure (which may vary according to the
myosin inhibitors) or whether this is associated mostly with the kinetics of
Pi release. Studies that have used the myosin inhibitor N-benzyl-p-toluene
sulfonamide (BTS) investigated the force produced during stretch without paying
special attention to the characteristics of the transitions in force (Pc, Lc) (Pinniger
et al, 2005; Roots et al, 2007). Unfortunately, the structure of the myosin-BTS
complex has not been described, and there are controversial results regarding the
effects of BTS on the force-stiffness relation (Moreno-Gonzalez et al, 2005;
Pinniger et al, 2005), which may relate to the effects of BTS on the number of
crossbridges attached to actin.
![Page 58: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/58.jpg)
58
In this study, we reinvestigated the mechanisms of the force produced
during stretch by altering either the number of crossbridges attached to actin or
the crossbridge configuration state without interfering with the ATP kinetics. To
achieve this goal we used 1) fibres activated with different Ca2+
concentrations
(i.e., varying pCa2+
) and 2) fibres treated with blebbistatin, a recently developed
1-phenyl-2-pyrrolidinone derivative that is highly specific; it inhibits certain
isoforms of myosin II without affecting the remaining contractile apparatus. The
structure of the myosin-actin-blebbistatin complex has been well defined
(Allingham et al, 2005). Blebbistatin biases crossbridges into myosin-actin-ADP
states, but it is not a Pi analog (Allingham et al, 2006; Kovacs et al, 2004; Straight
et al, 2003); therefore it does not directly influence ATP kinetics.
1.2.3 Methods
1.2.3.1 Preparation of muscle fibres
Small muscle bundles of rabbit psoas were dissected, tied to wood sticks,
and chemically permeabilized by standard procedures (Campbell & Moss, 2002).
Muscles were incubated in rigor solution (pH = 7.0) for ~ 4 h, after which they
were transferred to a rigor-glycerol (50:50) solution for 15 h. The samples were
subsequently placed in a fresh rigor-glycerol (50:50) solution with the addition of
a cocktail of protease inhibitors (Roche Diagnostics) and stored in a freezer
(−20°C) for at least 7 days. On the day of the experiment, a muscle sample was
transferred to a fresh rigor solution and stored in the fridge for 1 h before use. A
small section of the sample was cut (~ 4 mm in length), and single fibres were
carefully dissected in relaxing solution (see below). The fibres were gripped at
![Page 59: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/59.jpg)
59
their ends with T-shaped clips made of aluminum foil and were transferred to a
temperature-controlled chamber to be attached between a force transducer
(resonant frequency 1 kHz) (model 403A, Aurora Scientific, Toronto, ON,
Canada) and a length controller (model 312B, Aurora Scientific). The protocol
was approved by the McGill University Animal Care Committee and complied
with the guidelines of the Canadian Council on Animal Care.
1.2.3.2 Solutions
The rigor solution (pH 7.0) was composed of (in mM) 50 Tris, 100 NaCl,
2 KCl, 2 MgCl2, and 10 EGTA. The relaxing solution used for muscle storage
and dissection (pH 7.0) was composed of (in mM) 100 KCl, 2 EGTA, 20
imidazole, 4 ATP, and 7 MgCl2. The experimental solutions with pCa2+
of 4.5,
5.0, 5.5, and 6.0 (pH 7.0) contained (in mM) 20 imidazole, 14.5 creatine
phosphate, 7 EGTA, 4 MgATP, 1 free Mg2+
, free Ca2+
ranging from 1 nM
(pCa2+
9.0) to 32 μM (pCa2+
4.5), and KCl to adjust the ionic strength to 180
mM. The final concentrations of each metal-ligand complex were calculated with
a computer program (Fabiato, 1988) kindly provided by Dr. K. Campbell
(University of Kentucky). A preactivating solution (in mM: 68 KCl, 0.5 EGTA,
20 imidazole, 14.5 creatine phosphate, 4.83 ATP, 0.00137 CaCl2, 5.41 MgCl2 and
6.5 HDTA; pH 7.0, pCa2+
9.0) with a reduced Ca2+
buffering capacity was used
immediately before activation to minimize delays in diffusion.
Blebbistatin was dissolved in dimethylformamide (DMF) to reach a
concentration of 20 mM and was stored at −20°C before use. On the day of the
experiment, 1 μl of blebbistatin was diluted in 4 ml of activating (pCa2+
4.5) or
relaxing (pCa2+
9.0) solution to reach a final concentration of 5 μM. This
![Page 60: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/60.jpg)
60
concentration has been commonly used in the literature and allows for simple
comparisons with other studies (Farman et al, 2008; Stewart et al, 2009). When
performing pilot experiments, we noted that 5 μM blebbistatin consistently
decreased the force to levels between 40% and 50% of maximal force, enabling
comparisons with the experiments performed with different pCa2+
(i.e., we used a
pCa2+
range that would cover forces below and above 50% of the maximal force).
Moreover, higher concentrations of blebbistatin (15 μM and 20 μM) decreased the
force to levels below 20% of maximal force, but the variation between
experiments was substantial. The procedure was performed with both the active
(+/−) and the inactive (+/+) isomers of blebbistatin, the latter of which was used
as a negative control. Both blebbistatin isoforms were purchased from Sigma.
Care was taken to limit blebbistatin exposure to light, as it loses its effectiveness
in wavelengths between 365 and 490 nm (Kolega, 2004). A red filter (650 nm)
placed on the light source of the microscope was used to avoid exposure when the
use of light was necessary during the experiments.
1.2.3.3 Experimental protocol
The average sarcomere length (SL) was calculated in relaxing solution
with a high-speed video system (HVSL, Aurora Scientific 901A). Images from a
selected region of the fibres were used to calculate SL by fast Fourier transform
(FFT) analysis, based on the striation spacing produced by dark and light bands
of myosin and actin, respectively. The fibre diameter and length were measured
with a charge-coupled device (CCD) camera (Go-3, QImaging; pixel size: 3.2 μm
× 3.2 μm), and the cross-sectional area was estimated assuming circular
symmetry.
![Page 61: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/61.jpg)
61
Two separate sets of experiments were performed during this study,
using 1) fibres activated at different Ca2+
concentrations (n = 12) and 2) fibres
activated in the presence or absence of blebbistatin (n = 16). The initial SL was
adjusted to ~2.5 μm (optimal length, Lo) before fibre activation. All experiments
were performed at 5°C.
For the experiments with different Ca2+
concentrations, fibres were
activated at pCa2+
of 4.5, 5.0, 5.5, and 6.0 (random order). When force was fully
developed in each pCa2+
, a ramp stretch of 3% Lo was applied to the fibres, with
velocities ranging from 1.0 to 4.0 Lo·SL·s−1
. Control contractions at a pCa2+
of 4.5
were elicited through the experiments; at the end of the experiments the isometric
forces never decreased by >10% (actual range: 5.2–8.3%) from the maximal force
produced at the beginning of the experiment (Po). When the striation pattern of the
muscle fibres became unclear such that it did not allow measurements of SL, the
experiments were ended.
For the experiments with blebbistatin, the fibres were divided into two
subgroups, treated with either an active form of blebbistatin (+/−) (n = 11) or an
inactive (control) form of blebbistatin (+/+) (n = 5). The fibres were first activated
at a pCa2+
of 4.5 and stretched by 3% Lo, at a velocity of 2Lo·SL·s−1
. After that,
the fibres were incubated in relaxing solution (pCa2+
= 9.0) containing one of the
blebbistatin solutions. Since the rate of force decay after blebbistatin application
is reportedly slow (<0.3%/s) at the concentration used in this study (Farman et al,
2008; Kovacs et al, 2004; Limouze et al, 2004; Straight et al, 2003), we
performed pilot experiments with different times of blebbistatin incubation (5, 10,
15, 20, and 30 min). We observed that maximal isometric force decreased for the
![Page 62: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/62.jpg)
62
first 15 min after incubation, and then it stabilized at constant values. We thus
used a 15-min interval after blebbistatin application during the main experiments.
After blebbistatin incubation in relaxing solution, the fibre was immersed in
activating solution also containing blebbistatin (5 μM). After full force
development, a stretch of 3% Lo at 2 Lo·SL·s−1
was applied to the fibres, following
the same protocol used for the experiments with different pCa2+
.
1.2.3.4 Data analysis
The transition between the two phases of force rise during a stretch was
detected with a two-segment piecewise regression (Vieth, 1989), as shown in
Figure 1. The method assumes that the rise in force can be fitted by two linear
regression functions: y1 = a1 + b1 × xi (restriction: xi ≤ xo), and y2 = a2 + b2
× xi (restriction: xi > xo), where (xo, yo) represents coordinates of the critical
transition (Lc and Pc measured in this study), a1 and a2 are the intercepts of the
two regression lines, and b1 and b2 are the slopes of the two regression lines. At
the first iteration, the observations x1, x2,…x5 are included to estimate the
parameters of the first regression line, and the remaining observations x6,…xn are
used to fit the second regression line. At the next iteration, the
observations x1,…x6 are included to estimate the parameters of the first
regression line, and the remaining observations x7,…xn are used to fit the second
regression line; the same procedure is performed in each iteration. The residual
sum of squares (RSS) calculated is based on the sum of the squares of each
regression line:
2
22
2
11
00
)()(
xx
ii
xx
ii
ii
xbayxbayRSS
![Page 63: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/63.jpg)
63
RSS is used as a criterion to determine the optimal values of a1, a2, b1, b2,
and xo -those belonging to the minimal RSS are considered optimal. The F-test
statistic and confidence intervals (CIs) are calculated according to standard
methods for regression analyses (Vieth, 1989). The piecewise regression results
were accepted when 1) the method detected the transition between the two slopes,
with a clearly minimal RSS and a correlation coefficient of r2 ≥ 0.99, and 2) the
experimental data were fitted inside the 95% CI of the regression lines. When the
piecewise regression did not detect the transition point based on these criteria, we
extrapolated the two lines visually to detect the breakpoint, an approach most
commonly used in the literature (Pinniger et al, 2006; Ranatunga et al, 2007;
Stienen et al, 1992) with repeatable results. Visual inspection provided results
similar to regression analyses when both methods could be compared. The
intersection between the two slopes representing the fast and slow increases in
force was used to define Pc and Lc (Figure 1), which were compared among
different pCa2+
or blebbistatin conditions with a one-way ANOVA for repeated
measures (P < 0.05). Pc was calculated as the relative increase in force obtained
from the maximal isometric force developed before stretch (Po) in any given
condition. When significant changes were observed, post hoc analyses were
performed with Newman-Keuls tests (P < 0.05). All results are shown as means ±
SE.
![Page 64: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/64.jpg)
64
Figure 1 - Method for measuring critical force (Pc) and critical length (Lc) during stretch in
activated fibres. A: force and sarcomere length (SL) measured just before and during stretch and
during the early isometric phase of a contraction in a fibre activated in a pCa2+
of 4.5 (blue line).
Piecewise regression (black line) was used to find the transition between the 2 slopes and was used
to define Pc and Lc. B: closer image of the stretch phase recorded in the same contraction. Figure
also shows the 95% confidence interval (CI) for the regression (dashed lines; r2 = 0.99). Note that
the data are within the 95% CI.
1.2.4 Results
1.2.4.1 Experiments using different calcium concentrations
Figure 2A shows two contractions recorded during a typical experiment
performed with a single fibre used in this study. The fibre was initially activated
(in this case in pCa2+
of 4.5 and 6.0), and after a few seconds the force was fully
developed. The fibre was then stretched, and the force rose considerably. After
the end of stretch, the force decreased slowly until a steady-state level was
obtained—at this point, the fibre was deactivated. Figure 2B shows a closer view
of the stretch phase from the same contractions shown in Figure 2A and also
contractions performed during the same experiment in pCa2+
of 5.0, 5.5, and 9.0.
Fibres tested in pCa2+
of 9.0 did not show a significant increase in force during
stretch. In all other conditions, the increase in force was divided into two phases;
a clear force transition was observed, as previously shown (e.g., Refs. Edman,
B A
![Page 65: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/65.jpg)
65
1999; Getz et al, 1998; Pinniger et al, 2006; Roots et al, 2007). In this example,
the force continued to increase after the transition was detected and decreased
after the stretch. The force behavior after the transition was variable: sometimes
it increased, but in other experiments it was maintained at the same levels or even
decreased. The force after the transition in force or after the stretch is not the
main focus of this study, as we were interested in the kinetics of crossbridges
before and at the transition point. When stretches of 3% SL at 2 Lo·SL·s−1
were
applied during full force development at a pCa2+
of 4.5, Pc was 2.47 ± 0.11 × Po,
within the range observed in the literature (e.g., Refs. Roots et al, 2007; Stienen
et al, 1992).
A
B C
![Page 66: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/66.jpg)
66
Figure 2 - A: superimposed contractions produced by a fibre activated in pCa2+
of 4.5 (higher
force) and 6.0 (lower force). Force (top) and length (bottom) changes during the experiment are
shown; Lo, optimal length. Force rises during activation and then stabilizes to attain a steady-state
level. During stretch the force increases substantially, and afterward the stretch force decreases
slowly. Changes in solution during activation and relaxation create noise in the system, which is
reflected in the force transducer, but it quickly dissipates. B, top: superimposed contractions of the
experiment in A, showing the force produced during the stretch phase in the contractions
performed with different Ca2+
concentrations. Bottom: corresponding length change. The forces
produced during stretch and Pc were higher at increasing Ca2+
concentrations. The traces obtained
at pCa2+
of 9.0 before the stretch represent the force at rest (i.e., zero force). C: same experiment as
in B, but with forces normalized for the isometric contractions produced before stretch. Po,
maximal force before stretch.
The level of Ca2+
concentration considerably affected the absolute values
for the forces produced during stretch and also changed the stretch force relative
to Po (Pc) (Figures 2B and 2C), which was higher at high Ca2+
concentrations than
at low Ca2+
concentrations (Figure 3). These results, showing that Pc was
associated with the initial isometric force, suggest that Pc is dependent on the
number of activated crossbridges before the stretch. The stretch amplitude
necessary to attain the break in the force trace (Lc) observed at pCa2+
4.5 was
14.67 ± 0.26 nm/HS, higher than that obtained in studies that controlled the SL
during contractions (Getz et al, 1998) but within the range of studies performed
without SL control (Edman, 1999; Pinniger et al, 2006; Ranatunga et al,
2007). Lc was not affected by Ca2+
concentrations (Figures, 2B, 2C and 3) - when
all pCa2+
data are pooled, the Lc was 14.09 ± 0.27 nm/HS. In a few experiments,
stretches at different pCa2+
were performed at velocities of 1.0, 2.0, and
3.0 Lo·SL·s−1
. The velocity of stretch did not change Pc or Lc in any of the
pCa2+
investigated (data not shown).
![Page 67: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/67.jpg)
67
Figure 3 - Mean ± SE values of Pc (A) and Lc (B) in experiments performed with different Ca2+
concentrations. Changing the pCa2+
significantly altered Pc but not Lc. *Significantly different
from all other conditions (P < 0.05); #significantly different from pCa2+
of 6.0 and 4.5 (P < 0.05).
HS, half-sarcomere.
1.2.4.2 Effects of blebbistatin
Figure 4 shows two contractions recorded during a typical experiment
performed with a single fibre before and after blebbistatin (+/−) treatment. The
fibre was initially activated in pCa2+
of 4.5 and stretched after full force
development. Blebbistatin (+/−) significantly decreased the isometric force
production. Figure 5 shows the stretch phases of different fibres activated after
treatment with blebbistatin (+/+) or blebbistatin (+/−). When the fibres were
incubated in blebbistatin (+/+) isometric force and Pc were not changed
significantly, suggesting that it did not play a role in the results obtained with the
active form (+/−) of blebbistatin. When the fibres were activated in solution
containing blebbistatin (+/−), the isometric force decreased by 44.95 ± 6.37%
from the maximal isometric force exhibited without blebbistatin (+/−) treatment.
The decrease in force was smaller than observed in previous studies, which
reported an ~ 60% decrease in force with 5 μM blebbistatin (Farman et al, 2008;
A B
![Page 68: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/68.jpg)
68
Stewart et al, 2009). Although it is difficult to explain the difference, the
variability seems to be highly dependent on the experimental condition, and also
inherent to the drug effects; with 15 μM blebbistatin, decreases in force between
39% (Farman et al, 2008) and 80% (Stewart et al, 2009) have been reported in
apparently similar situations. In our experiments, the variability in the isometric
forces produced after drug administration is small among fibres, conferring a
high reproducibility to our results.
Figure 4 - Superimposed contractions produced by a fibre activated in pCa2+
of 4.5 before (higher
force) and after (lower force) blebbistatin (+/−) treatment. Force (top) and length (bottom) changes
during the experiment are shown. During the stretch force increases significantly, and afterward
the stretch force decreases slowly. The force produced during stretch after blebbistatin treatment
increases such that it virtually overlaps with the force produced before blebbistatin. Inset, changes
![Page 69: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/69.jpg)
69
in sarcomere length (SL): note that we only measured SL during activation and stretch after the
noise produced by the solution exchange was totally cleared and we stopped measuring when just
before the solution was exchanged again for fibre relaxation.
Figures 5B and 5C show superimposed contractions of two fibres that
were activated in the absence and presence of blebbistatin (+/−) and then stretched
by 3% SL at 2 Lo·SL·s−1
. The two phases of force increase observed in control
situations were observed with blebbistatin (+/−). Similar to a control situation, the
force produced after the break was variable: in some fibres the force continued to
increase during the remaining stretch, while in other fibres the force stabilized or
decreased after the break.
![Page 70: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/70.jpg)
70
Figure 5 - Superimposed contractions of 3 experiments performed with blebbistatin (+/+) (A) or
blebbistatin (+/−) (B and C) at pCa2+
of 4.5. Blebbistatin (+/+) does not produce significant
changes in the isometric force and produces only a small change in force during stretch.
Blebbistatin (+/−), on the other hand, significantly decreases the isometric forces. The force
produced during stretch also decreases, but by a smaller magnitude that increases the stretch-to-
isometric force ratio. Note that Lc also increases after blebbistatin (+/−), as shown by the arrows
intercepting the length traces—the arrows start exactly at the transition between the slopes as
detected by piecewise regression—shown with the thick line. D: superimposed contractions of the
stretch performed by the fibre treated with blebbistatin (+/+) in A and blebbistatin (+/−) in B,
respectively. Force is normalized for the isometric force produced before the stretch. Note that Pc
and Lc are higher in the fibre treated with blebbistatin (+/−).
Figure 6 - Mean ± SE values of Pc (A) and Lc (B) in the 2 sets of experiments performed with
blebbistatin (BB)(+/+) and respective control (control 1) and blebbistatin (+/−) and respective
control (control 2). Blebbistatin (+/−) changed Pc and Lc significantly. *Significantly different
from all other conditions (P < 0.05). C: linear relation between stiffness (ΔSL/Δforce) and Pc
during the experiments conducted with fibres treated with blebbistatin (+/−). Pc values were
normalized for the maximal Pc (Pcmax) produced during these experiments.
The decrease in stretch forces after blebbistatin (+/−) was not as large as
the decrease observed in isometric forces. As a result, the relative Pc was
significantly higher than that observed in the control fibre (Figures 5B and
5C). Figure 5D shows superimposed contractions produced by a fibre treated with
the inactive (+/+) and active (+/−) forms of blebbistatin. It should be noted that
the changes in Pc and Lc are clear—both increase with blebbistatin (+/−). This
result was confirmed when all experiments were analyzed; Figure 6 shows the
mean values obtained for the two sets of experiments using the active (+/−) and
inactive (+/+) forms of blebbistatin. The only statistical difference detected in
![Page 71: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/71.jpg)
71
these experiments was the increased Pc and Lc in blebbistatin (+/−)-treated fibres.
We thus plotted the stiffness (ΔSL/Δforce) against the Pc for these experiments
(Figure 6C). It should be noted that the Pc increases with the stiffness, suggesting
that crossbridges detach from actin after reaching a given strain during the stretch
in all conditions.
1.2.5 Discussion
The main findings of this study were that 1) increasing Ca2+
concentration
enhances Pc without changing Lc and 2) blebbistatin (+/−) increases both
Pc and Lc when activated muscle fibres are stretched. These results suggest that
forces during stretch are modulated by both the number of crossbridges attached
to actin and the state of crossbridges before the stretch. Furthermore, this study
provides significant new information about the action of a new, highly specific
myosin inhibitor (blebbistatin) on the mechanics of skeletal muscle fibres.
1.2.5.1 Comparison with other studies
When a 3% Lo stretch was performed at 2 Lo·SL·s−1
, the mean Pc of
2.47Po in fully activated fibres (pCa2+
= 4.5) observed in our study is comparable
to that observed by others who used velocities higher than
1.0 Lo·SL·s−1
(Pinniger et al, 2006; Roots et al, 2007; Stienen et al, 1992). Few
studies have been performed in mammalian muscles for direct comparisons. A
previous study performed in our laboratory (Rassier, 2008) used individual
myofibrils, also isolated from the psoas muscle. Myofibrils tested at ~10°C and
stretched at 0.4 Lo/s showed a Pc of 1.69Po. It is known that increasing
![Page 72: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/72.jpg)
72
temperatures decrease Pc (Colombini et al, 2008; Ranatunga et al, 2007), and thus
the difference between these two studies is expected. We used the stretch
amplitude necessary to cause the break in the force trace as an indication of the
critical extension of crossbridges before they detach from actin - a common
approach used by several investigators (Edman, 1999; Getz et al, 1998; Rassier,
2008). The Lc of 14.09 nm/HS is within the lower range observed in the literature
(14–28 nm/HS) in most experiments with intact cells in which SL is not
controlled during the experiments.
Our results are, however, significantly different from those reported by
Getz et al. (1998), who observed a Pc of 3.26Po, among the largest values reported
in the literature with any muscle. The main difference is that Getz et al. (1998)
controlled the average SL during the stretch by means of a feedback system. SL
nonuniformity may change the values for Pc and Lc and may be responsible for the
different results—a study performed in our laboratory with myofibrils (Rassier,
2008), a preparation that allows direct measurements of SL, observed a
small Lc (7.7 ± 0.1 nm/HS), suggesting that SL nonuniformity may in fact
influence the results.
1.2.5.2 Effects of different calcium concentrations
We used different pCa2+
to induce different levels of activation, thus
changing the number of crossbridges attached to actin before stretching the
fibres. We observed that the absolute force obtained during stretch (before the
force transition point) was lowered with decreasing Ca2+
concentrations. Our
findings corroborate previous studies suggesting that Pc is related to the number
of crossbridges formed before the stretch (>1 Lo/s) (Bagni et al, 2005; Colombini
![Page 73: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/73.jpg)
73
et al, 2008; Colombini et al, 2009). If we assume that the crossbridges arranged
in series and in parallel produce the same amount of force at any given time, and
that they all contribute to the total force generated by the fibre, then the force
during stretch would increase with an increased number of crossbridges. Such an
interpretation was suggested by Flitney and Hirst (1978) years ago when they
observed that the force response to stretch was directly proportional to both
muscle stiffness and degree of filament overlap. It is also in line with suggestions
that Pc can be used as an alternative to stiffness measurements to indirectly
evaluate the number of crossbridges attached to actin during contractions (Bagni
et al, 2005; Colombini et al, 2010).
Most intriguing in our results was the fact that Pc and isometric tension
were decreased by low levels of activation in disproportional magnitudes—the
relative Pc during contractions produced at low Ca2+
concentrations was smaller
than those produced at high pCa2+
concentrations; the difference was small but
still significant (Figure 3). The reason for the lack of proportionality is not clear,
and it may be caused by different factors: 1) The different levels of Ca2+
may have
caused changes in sarcomere stiffness that do not change linearly with force. If
the stiffness-to-force ratio decreased more at low Ca2+
than at high
Ca2+
concentration, the force response during stretch could be also lower. 2) The
attachment of more crossbridges at high Ca2+
concentrations may facilitate the
attachment of additional crossbridges during stretch (e.g., Ref. Fusi et al, 2010),
increasing Pc more significantly than what is observed at low Ca2+
concentrations.
With our present data we cannot define the reason for the discrepancy, which
needs to be investigated further.
![Page 74: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/74.jpg)
74
The interpretation based on the crossbridges is also consistent with the
observation that Lc does not change with different Ca2+
concentrations. If
Lc represents a critical strain of crossbridges, beyond which they detach from actin
(Bagni et al, 2005; Colombini et al, 2008; Colombini et al, 2009), cross bridges in
series will elongate to the same extent before detaching from actin (Lc). This
interpretation is strengthened by findings showing that the strain of crossbridges
attached to actin does not change with varying Ca2+
concentrations in rabbit psoas
muscles - and thus should not change the force produced per myosin heads (Linari
et al, 2007). The crossbridge extension would therefore not be affected by the
number of crossbridges strongly bound to actin before stretch. This interpretation
also lies on the assumption that filament compliance in a given Ca2+
concentration
is equally distributed along all myosin-actin attachment sites—an assumption
commonly used by investigators who use Lc as a putative measurement of
crossbridge extension (Bagni et al, 2005; Colombini et al, 2008; Colombini et al,
2009; Edman et al, 1978; Edman et al, 1981; Flitney & Hirst, 1978; Getz et al,
1998; Lombardi & Piazzesi, 1990; Stienen et al, 1992). This assumption may not
be valid in all cases (e.g., Ref Campbell, 2006) but in order to know the influence
of compliance in our results we would need to measure local differences in
filament and crossbridge compliances—not possible with our preparation.
Since 1) many crossbridges are undergoing attachment-detachment cycles during
the isometric phase of contraction (i.e., previous to stretch) across all filaments
and 2) the stretch is large enough to detach all crossbridges, we assumed that
individual cross-bridge deviations from the mean crossbridge elongation should
![Page 75: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/75.jpg)
75
be negligible and not responsible for potential differences among
Ca2+
concentrations.
1.2.5.3 Effects of blebbistatin
Blebbistatin (+/−) decreased the isometric force, but it increased the
relative Pc, suggesting that the force produced during the stretch has a component
not associated uniquely to the number of crossbridges attached to actin. Although
similar findings have been observed with the myosin inhibitor BDM (Chinn et al,
2003; Getz et al, 1998; Rassier, 2008; Rassier & Herzog, 2004a), our results add
important new information to the literature. Differently from BDM, blebbistatin
(+/−) does not compete with the nucleotide binding site in the molecule, avoiding
confounding effects of ATP kinetics during measurements. Blebbistatin (+/−)
binds to the hydrophobic pocket near the apex of the 50-kDa cleft of myosin,
close to the Pi binding site (Allingham et al, 2005). Studies have shown that
blebbistatin hinders the 50-kDa closure, which is necessary for Pi release and
strong binding formation. Hence during the myosin-ATPase cycle, ATP
hydrolyses is trapped in an intermediate state – ADP.Pi -, in which myosin can
only weakly attach to actin. As a result, blebbistatin causes both a reduction in
the number of crossbridges strongly attached to actin and a redistribution of
crossbridges toward a weakly bound state, stabilizing the complex
myosin·ADP·Pi into a pre-powerstroke state.
Two studies (Pinniger et al, 2006; Roots et al, 2007) have been performed
to evaluate the effects of stretch on intact fibres treated with BTS, another myosin
inhibitor with some characteristics that are similar to blebbistatin. The authors
noted that the slopes of force increase during stretch decreased after BTS
![Page 76: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/76.jpg)
76
treatment, but they did not evaluate the characteristics of force during stretch after
BTS treatment (Pc, Lc). Kinetic studies have shown that BTS decreases the steady-
state ATPase rate, likely because of the inhibition of Pi release and affinity of
myosin·ADP·Pi and myosin·ADP for actin (Shaw et al, 2003), but we cannot
predict that BTS would have provided results similar to ours, as the structure of
the myosin·BTS complex has not yet been described. Although BTS decreases the
force without altering significantly the shortening velocity in skeletal muscle
fibres (Cheung et al, 2002; Pinniger et al, 2005), there is controversy surrounding
the effects of BTS on muscle stiffness. Pinniger et al. (2005) observed that BTS
decreased muscle stiffness significantly less than force, suggesting that the
decrease in force is not caused uniquely by a decrease in the number of
crossbridges attached to actin. On the other hand, Moreno-Gonzalez et al. (2005)
observed a linear relationship between the BTS-induced decreases in force and
stiffness. Moreno-Gonzalez et al. (2005) used fibres isolated from the same
muscle that we used (permeabilized rabbit psoas) but have not evaluated the
effects of stretch on force kinetics. Given 1) the effects of Vi and BDM on
ATPase kinetics and Pi release, 2) some unknown characteristics of BTS, and 3)
the lack of studies evaluating in detail the effects of BTS on forces during stretch,
comparisons between our results and previous studies are complex.
The magnitude of force decrease after treatment with 5 μM blebbistatin
(+/−) was lower than that observed in all submaximal Ca2+
concentrations
investigated in this study, except when contractions were performed in a pCa2+
of
6.0, in which the force decreased by 68.21% ± 5.84 from maximal force. Thus it is
difficult to compare these two sets of experiments directly. Of particular interest
![Page 77: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/77.jpg)
77
was the fact that blebbistatin (+/−) treatment increased Pc to levels that were
higher than any pCa2+
tested in the present experiments. Therefore, the effects of
blebbistatin (+/−) on Pc cannot be associated purely to a decrease in the number of
crossbridges attached to actin. Taking into account the known mechanism of
blebbistatin (+/−), we suggest that the increase in Pc is largely due to crossbridges
in a pre-powerstroke state. Such crossbridges would not cause large forces during
isometric contractions, but they would resist the imposed stretch, producing
significant amounts of force, and a reversal of the powerstroke as suggested in
previous studies (Pinniger et al, 2006; Roots et al, 2007). This result also agrees
qualitatively with studies using isolated fibres tested at increasing temperatures,
which conceptually shift crossbridges toward a strongly bound state, showing that
the stretch-to-isometric force ratios decrease (Colombini et al, 2008; Coupland et
al, 2001; Piazzesi et al, 2003; Wang & Fuchs, 2001). In a recent study, Colombini
et al. (2010) showed that a direct relation between Po and Pc had a fitted line with
an intercept above zero (their Figure 9). The authors suggested that the deviation
from direct proportionality was caused by the presence of pre-powerstroke
crossbridges, which generate force only upon stretching - similar to our
interpretation.
The results showing that blebbistatin (+/−) increases Lc also fit our
proposed mechanism including pre-powerstroke crossbridges, and agree with
previous studies showing that Pi analogs increase Lc (Rassier, 2008; Stienen et al,
1992). Assuming that crossbridges detach from actin at a given strain/force,
crossbridges in fibres treated with blebbistatin (+/−) produce lower strain/force
than strongly bound crossbridges, and thus would be stretched to a greater Lc
![Page 78: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/78.jpg)
78
before detaching from actin. Such an assumption is supported by the linear
relation between Pc and stiffness (Figure 6C) observed in these experiments. With
a reduction of ~45% of force induced by blebbistatin (+/−), Lc increased by 1.16
nm/HS, suggesting that crossbridges were strained by 1.16 less after blebbistatin
treatment. This argument is also in line with kinetic models (e.g., Ref. Colombini
et al, 2009; Getz et al, 1998; Lombardi & Piazzesi, 1990; Pinniger et al, 2006),
suggesting that crossbridges in the myosin·ADP·Pi state attach to actin at low
strains and get carried to higher strains during lengthening, where they exert
increasingly higher forces before detaching from actin. A series of recent studies
show that interventions that reduce the strain of crossbridges, including increasing
temperature and ionic strength, consistently increase Lc (Colombini et al, 2007a;
Colombini et al, 2007b; Colombini et al, 2008).
1.2.5.4 Additional mechanisms
Pc and Lc values could be affected by SL nonuniformity (Julian &
Morgan, 1979a; Lombardi & Piazzesi, 1990), the stiffening of passive elements
(Bagni et al, 2002; Bagni et al, 2004), or compliance of the myofilaments
(Huxley et al, 1994; Wakabayashi et al, 1994). However, it seems unlikely that
these mechanisms would alter the interpretation of this study: 1) A previous
study using myofibrils showed that SL nonuniformity is small at the force
transition where Pc and Lc are measured (Rassier, 2008). Sarcomeres never
shortened during myofibril stretch and never stretched to a nonoverlap zone
(“popping sarcomeres” as suggested by Morgan, 1994), where passive forces
could be significantly high. Previous studies in which slow stretches were applied
to myofibrils (Joumaa et al, 2008; Telley et al, 2006b) also failed to observe
![Page 79: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/79.jpg)
79
“popping” sarcomeres. 2) It is suggested that passive elements contribute to force
during stretch of activated muscles through Ca2+
-induced changes in titin
molecules (Bagni et al, 2004; Pinniger et al, 2006; Rassier & Herzog, 2004a).
The persistence length of titin decreases with high Ca2+
concentrations, which
would increase forces beyond that produced during a passive stretch (Labeit et al,
2003). However, the optimal SL for the force produced by the activity-induced
engagement of titin is ~ 2.8 μm (Bagni et al, 2002; Bagni et al, 2004; Rassier &
Herzog, 2004a), while the present experiments were performed at shorter SLs
(2.5–2.6 μm). 3) If filament compliance would alter the rate at which myosin
crossbridges bind to actin filaments, as suggested in theoretical models
(Campbell, 2006; Daniel et al, 1998), it could influence the absolute values of Pc.
Although filament compliance may account for ~ 50% of the sarcomere
compliance (Huxley et al, 1994; Wakabayashi et al, 1994), its contribution to the
total strain-force relationship is unknown. When isolated thick and thin filaments
are stretched from zero tension to maximal physiological tensions, strains of
0.3% and 1.5% are observed, respectively (Liu & Pollack, 2002; Neumann et al,
1998), values that are too small to explain the changes observed in this study.
Even if the compliance affects our results and explains part of the stretch forces,
there is no evidence that blebbistatin affects the compliance of the filaments, and
therefore the comparisons made between the two situations remain valid.
1.2.5.5 Conclusion
Our results obtained with experiments using Ca2+
and blebbistatin, a non-
phosphate analog that does not interfere with ATP kinetics, suggest that critical
force (Pc) is proportional to the number of crossbridges attached to actin and also
![Page 80: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/80.jpg)
80
to the population of crossbridges in a pre-powerstroke state. Such a mechanism
can be explained by proposed models in which crossbridges attach to actin at low
strains, and are carried to high strains during stretch (Getz et al, 1998; Pinniger et
al, 2006). Increasing the number of crossbridges attached to actin before stretch
also increases the number of pre-powerstroke crossbridges, which will increase
the Pc.
![Page 81: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/81.jpg)
81
2. Force development during muscle shortening
2.1 Preface
The involvement of crossbridges in the early phase of force development
during muscle shortening remains a matter of debate. While early studies (Ford et
al, 1977; Stienen et al, 1978) have attributed this first quick drop in force to pure
elastic behaviour of the attached crossbridges, more recent studies (Bressler,
1985; Roots et al, 2007) associate the force inflexion during shortening as
crossbridge-cycle transitions comparable to the T1-T2 transitions proposed by
Huxley and Simmons (1971).
Motivated by our first study that found stretch forces were increased when
muscle fibres were activated in presence of blebbistatin, we designed a similar
experimental protocol to test if forces during shortening would be affected by
blebbistatin-induced changes in the repartitioning between different crossbridge
molecular states. We also developed a mathematical model based on three
crossbridge molecular states – i) pre-powerstroke, ii) post-powerstroke, and iii)
detached - to better understand the decrease in force observed during shortening.
![Page 82: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/82.jpg)
82
2.2 Pre-powerstroke crossbridges contribute to force transients during
imposed shortening in isolated muscle fibres
Fabio C. Minozzo
Lennart Hilbert
Dilson E. Rassier
Reprinted from: PloS One. 2012. 7(1):e29356. doi:
10.1371/journal.pone.0029356.
![Page 83: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/83.jpg)
83
2.2.1 Abstract
When skeletal muscles are activated and mechanically shortened, the force
that is produced by the muscle fibres decreases in two phases, marked by two
changes in slope (P1 and P2) that happen at specific lengths (L1 and L2). We tested
the hypothesis that these force transients are determined by the amount of myosin
crossbridges attached to actin and by changes in crossbridge strain due to a
changing fraction of crossbridges in the pre-powerstroke state. Three separate
experiments were performed, using skinned muscle fibres that were isolated and
subsequently (i) activated at different Ca2+
concentrations (pCa2+
4.5, 5.0, 5.5,
6.0) (n = 13), (ii) activated in the presence of blebbistatin (n = 16), and (iii)
activated in the presence of blebbistatin at varying velocities (n = 5). In all
experiments, a ramp shortening was imposed (amplitude 10 %Lo, velocity 1
Lo•sarcomere length (SL)•s-1
), from an initial SL of 2.5µm (except by the third
group, in which velocities ranged from 0.125 to 2.0 Lo•s-1
). The values of P1, P2,
L1, and L2 did not change with Ca2+
concentrations. Blebbistatin decreased P1, and
it did not alter P2, L1, and L2. We developed a mathematical crossbridge model
comprising a load-dependent powerstroke transition and a pre-powerstroke
crossbridge state. The P1 and P2 critical points as well as the critical lengths L1
and L2 were explained qualitatively by the model, and the effects of blebbistatin
inhibition on P1 were also predicted. Furthermore, the results of the model suggest
that the mechanism by which blebbistatin inhibits force is by interfering with the
closing of the myosin upper binding cleft, biasing crossbridges into a pre-
powerstroke state.
![Page 84: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/84.jpg)
84
2.2.1 Introduction
A long-standing scientific challenge resides in the explanation of how
characteristics of the molecular actin-myosin interaction give rise to
macroscopically observed phenomena in striated muscles, and how conditions
imposed on macroscopic scales affect actin-myosin kinetics. In early experiments
to connect macroscopic muscle mechanics to load-dependent crossbridge kinetics,
step shortenings were imposed to fully activated fibres isolated from amphibian
muscles (Ford et al, 1977). The force transients could be described in four
phases: 1) during the fast shortening step, there was a force decrease proportional
to the shortening amplitude, 2) during the next 3-5ms there was a rapid force
recovery, 3) during the next 10-50ms there was an extreme reduction of force
recovery, and 4) during the remainder of response, there was an asymptotic
recovery towards maximum isometric force. At the end of phase 1, a maximal
drop in force (T1) was observed and the beginning of phase 2 indicated a
transition into an increase of force. A following inflection or even a low peak in
the force time course at force (T2) indicated the transition into phase 3 (Ford et al,
1977).
Length ramps performed at constant velocities are now commonly used
for studying the molecular mechanisms of muscle contraction (Bressler, 1985;
Ford et al, 1977; Huxley & Simmons, 1971; Piazzesi et al, 2002; Roots et al,
2007), and show force responses that are qualitatively similar to early studies that
used step shortening: 1) the force decreases in proportion to shortening, 2) the
force decrease becomes less rapid, 3) the force decrease becomes even slower, 4)
and the force shows an asymptotic approach to a lowered but constant steady
![Page 85: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/85.jpg)
85
state. Some of these studies show a transition in the force trace from phase 1 to
phase 2 (hereafter called critical point P1) that occurs at a critical sarcomere length
(L1), and a transition in the force trace from phase 2 to phase 3 (hereafter called
critical point P2), that occurs at a critical sarcomere length (L2). While phase 1 in
force traces is commonly associated with a purely elastic response, the behaviour
during phase 2 is attributed to a repartitioning of crossbridges from the pre to the
post powerstroke state, due to an acceleration of the powerstroke step under
conditions of lowered mechanical load on myosin cycling (Ford et al, 1977;
Huxley & Simmons, 1971; Ranatunga et al, 2010; Roots et al, 2007).
In this study, we reinvestigated the mechanisms responsible for the force
transients during a shortening ramp. We examined fibres at different levels of
Ca2+
activation, and fibres treated with the highly specific myosin inhibitor
blebbistatin, which biases crossbridges into a pre-powerstroke state (Farman et al,
2008; Kovacs et al, 2004). Different Ca2+
concentrations allowed us to examine
the influence of the number of strongly-bound crossbridges on the force transients
during shortening, while blebbistatin allowed us to investigate the effects of
crossbridge partitioning into pre and post-powerstroke states before ramp
shortening. While changes in Ca2+
concentration did not significantly alter the P1
and the P2 transitions during shortening, blebbistatin decreased P1 significantly
during shortening.
We developed a mathematical crossbridge model with a load-dependent
powerstroke transition between pre and post-powerstroke crossbridge states,
which was based on general protein motor kinetics formalisms (Hill, 2004) and
single myosin experiments (Veigel et al, 2003). Three crossbridge kinetic states
![Page 86: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/86.jpg)
86
were derived in accordance with well-defined biochemical pathways (Eisenberg
& Hill, 1985; Eisenberg et al, 1980; Hill, 2004) and compatible with current
structural models of myosin (Rayment et al, 1993). Similar to what other models
investigating ramp stretches have suggested (Chinn et al, 2003; Getz et al, 1998;
Minozzo & Rassier, 2010; Ranatunga et al, 2010; Rassier & Herzog, 2004a), pre-
powerstroke crossbridges were found to be a major determinant of the force
transients during shortening. The model explained qualitatively the force
transients (P1 and P2) and the lengths at which they happen (L1 and L2,
respectively) observed in our experiments using different shortening velocities. It
also predicted the effects of blebbistatin inhibition on P1, further indicating that
the mechanism by which blebbistatin inhibits active force generation is by
preventing the closing of the myosin binding cleft, effectively biasing
crossbridges into a pre-powerstroke state.
2.2.3 Methods
2.2.3.1 Muscle fibre preparation
Small muscle bundles of the New Zealand White rabbit psoas were
dissected, tied to wood sticks, and chemically permeabilized following standard
procedures (Campbell & Moss, 2002; Minozzo & Rassier, 2010). The muscles
were incubated in rigor solution (pH = 7.0) for approximately 4 hours, after which
they were transferred to a rigor:glycerol (50:50) solution for 15 hours. The
samples were placed in a new rigor:glycerol (50:50) solution with the addition of
a mixture of protease inhibitors (Roche Diagnostics, USA) and stored in a freezer
(-20°C) for at least seven days. On the day of the experiment, a muscle sample
![Page 87: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/87.jpg)
87
was transferred to a fresh rigor solution and stored in the fridge for one hour
before use. A small section of the sample was extracted (~4 mm in length), and
single fibres were dissected in a relaxing solution (pH = 7.0). The fibres were
fixed at their ends with T-shaped clips made of aluminum foil, and were
transferred to a temperature controlled experimental chamber to be attached
between a force transducer (Model 400A, Aurora Scientific, Toronto, Canada)
and a length controller (Model 312B, Aurora Scientific, Toronto, Canada). The
protocol was approved by the McGill University Animal Care Committee
(protocol #5227, valid 2006-2016) and complied with the guidelines of the
Canadian Council on Animal Care.
2.2.3.2 Solutions
The rigor solution (pH 7.0) was composed of (in mM): 50 Tris, 100 NaCl,
2 KCl, 2 MgCl2, and 10 EGTA. The relaxing solution (pH 7.0) used for muscle
dissection was composed of (in mM): 100 KCl, 2 EGTA, 20 imidazole, 4 ATP
and 7 MgCl2. The solutions with pCa2+
of 4.5, 5.0, 5.5 and 6.0 (pH 7.0) were
composed of (in mM): 20 imidazole, 14.5 creatine phosphate, 7 EGTA, 4
MgATP, 1 free Mg2+
. These solutions had free Ca2+
ranging from 1 nM (pCa2+
9.0 relaxing) to 32 μM (pCa 4.5 maximum activation), and KCl to adjust the ionic
strength to 180 mM. A pre-activation solution (pH 7.0, pCa2+
9.0) was used
before activating the fibres, composed of (in mM): 68 KCl, 0.5 EGTA, 20
Imidazole, 14.5 PCr, 4.83 ATP, 0.00137 CaCl2, 5.41 MgCl2 and 6.5 HDTA (pH
7.0, pCa2+
9.0). The final concentrations of each metal-ligand complex were
calculated using a computer program (Fabiato, 1988) which takes into account the
![Page 88: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/88.jpg)
88
reaction between the buffers when forming chemical complexes to calculate the
final free ionic concentrations.
The solutions containing blebbistatin were prepared according to the
following procedures. 1 µL of blebbistatin (Sigma, USA) prepared at 20mM,
previously dissolved in dimethylformamide (DMF), was diluted in 4mL of
activating (pCa2+
4.5) or relaxing (pCa2+
9.0) solutions to reach a final
concentration of 5µM. Care was taken to limit blebbistatin exposure to light, as it
loses its effectiveness in wavelengths between 365nm and 490nm (Kolega, 2004).
A red filter (650nm) placed on the light source of the microscope was used to
avoid exposure when the use of light was necessary during the experiments.
Solutions were prepared with both the active and the inactive (+/+) isomers of
blebbistatin, which was used as a negative control.
2.2.3.3 Experimental protocol
After the fibres were set in the experimental chamber, the average
sarcomere length (SL) was calculated in relaxing solution using a high-speed
video system (HVSL, Aurora Scientific 901A, Toronto, Canada). Images from a
selected region of the fibres were collected at 1000-1500 frames.sec-1
, and the SL
was calculated by fast fourier transform (FFT) analysis based on the striation
spacing produced by dark and light bands of myosin and actin, respectively. The
fibre diameter and length were measured using a CCD camera (Go-3, QImaging,
USA; pixel size: 3.2µm X 3.2µm), and the cross-sectional area was estimated
assuming circular symmetry.
Three separate sets of experiments were performed during this study,
using (i) fibres activated at different Ca2+
concentrations and shortened at 1
![Page 89: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/89.jpg)
89
Lo•SL•s-1
(n = 13), (ii) fibres activated in the presence or absence of blebbistatin
and shortened at 1 Lo•SL•s-1
(n = 16), and (iii) fibres activated in pCa2+
4.5 and
pCa2+
6.0 in the presence of blebbistatin, shortened at varying velocities ranging
from 0.125 Lo•SL•s-1
to 2.0 Lo•SL•s-1
(n = 5). All experiments were performed at
5°C.
At the beginning of the experiments, the initial SL was adjusted to 2.5µm
(optimal length, Lo) before activation. (i) For the experiments with different Ca2+
concentrations, fibres were activated at pCa2+
of 4.5, 5.0, 5.5 and 6.0 (random
order). When force was fully developed in each pCa2+
, a ramp shortening of 10
%Lo was applied at a constant velocity of 1 Lo•SL•s-1
. (ii) For the experiments
with blebbistatin, the fibres were divided in two sub-groups, treated with either an
active form of blebbistatin (n = 12) or an inactive (control) form of blebbistatin
(+/+) (n = 4). The fibres were first activated at a pCa2+
of 4.5 and shortened by 10
%Lo, at a velocity of 1 Lo•SL•s-1
; this trial provided the control value for these
experiments. Following, the fibres were incubated in relaxing solution (pCa2+
=
9.0) containing blebbistatin. After the incubation period in relaxing solution, the
fibres were immersed in activating solution (pCa2+
= 4.5) containing blebbistatin
(5µM). After full force development, a shortening of 10%Lo at 1 Lo•s-1
was
applied to the fibres. (iii) For the experiments with different velocities of
shortening (n = 12), fibres were activated at pCa2+
of 4.5 or 6.0 (random order)
and then immersed into relaxing (pCa2+
9.0) and activating (pCa2+
4.5) solutions
containing blebbistatin (5µM), as previously described. When force was fully
developed, ramp shortenings of 10%Lo were applied at velocities of 0.125, 0.25,
0.5, 1.0, or 2.0 Lo•s-1
(random order).
![Page 90: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/90.jpg)
90
In all experiments, control contractions (pCa2+
of 4.5) were elicited
throughout the experiments; when isometric forces decreased by >10% from the
maximal force produced at the beginning of the experiment or when the striation
pattern corresponding to the SL was lost during activation, the experiment was
ended and data from this fibre was discarded from future analysis.
2.2.3.4 Data analysis
The changes in slope of force observed during shortening were detected
using a two-segment piecewise regression, in which the force trace can be fitted
by two linear regression functions: y1=a1+b1xi (restriction: xi≤x0), and y2=a2+b2xi
(restriction: xi>x0), where (x0,y0) represents the coordinates of the critical
transition (Lc and Pc measured in this study), a1 and a2 represent the intercepts of
the two regression lines, and b1 and b2 are the slopes of the two regression lines.
At the first iteration, the observations x1, x2, ... x5 are included to estimate the
parameters of the first regression line. The remaining observations x6, ... xn are
used to fit the second regression line. At the next iteration, the observations x1, ...
x6 are included to estimate the parameters of the first regression line, and the
remaining observations x7, ... xn are used to fit the second regression line. The
same procedure is performed in all iterations. The residual sum of squares (RSS)
is based on the sum of the squares of each regression line:
2
22
2
11
00
)()(
xx
ii
xx
ii
ii
xbayxbayRSS
The RSS is used to determine the optimal values of a1, a2, b1, b2, and x0 –
the values associated with the minimal RSS are considered optimal (Vieth, 1989).
The regression results were accepted when they presented a correlation coefficient
![Page 91: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/91.jpg)
91
(r2) > 0.99, and data points fitted inside a 95% confidence interval (CI) of the
regression lines, similar to procedures used previously in our laboratory (Minozzo
& Rassier, 2010). In cases in which these criteria were not fulfilled, we used two
approaches to detect the breakpoints, two single regression lines were fitted into
the two slopes, which were extrapolated visually to detect the breakpoint
(Minozzo & Rassier, 2010; Pinniger et al, 2006; Roots et al, 2007). Regression
lines were accepted when the correlation coefficient (r2) were >0.99 and data
points fitted inside a 95% confidence interval. The force produced during the first
and second changes in slope were calculated at the transition points (P1 and P2,
respectively). L1 and L2 were determined as the length change amplitudes
necessary to achieve the P1 and P2 transitions, measured from the beginning of
shortening. In a few experiments, the signal from the striation pattern arising
from the fibres became weak during shortening; in this case, the L1 and L2 were
calculated by extrapolating the percentage of change in fibre length (measured
during the experiments) based on the SL measured just before shortening. Both
methods provided similar results, as confirmed in experiments in which SL was
measured.
The values of P1, P2, L1, and L2 were compared among different pCa2+
or
blebbistatin conditions using a one-way ANOVA for repeated measures. When
significant changes were observed, post-hoc analyses were performed with
Newman-Keuls tests. For the third group of experiments a two-way ANOVA (3
conditions × 5 velocities) for repeated measures were used to compare the P1, P2,
L1 and L2. When significant interactions or main effects were found, post-hoc
comparisons using Newman-Keuls adjustment for multiple comparisons were
![Page 92: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/92.jpg)
92
performed to locate significant differences. The significance level for all
statistical tests was set at P < 0.05.
2.2.3.5 Model development
We developed a crossbridge model consisting of two major elements: (1)
an active molecular contractile element, consisting of crossbridges capable of
contraction and (2) a passive element with linear elasticity, which is placed
between the active contractile element and the external apparatus which controls
fibre length.
Crossbridge kinetics
We assumed that the number of crossbridges in the fibre is high enough to
support a treatment of crossbridge populations, instead of monitoring single
crossbridges. According to a simple Attach - Powerstroke - Detach scheme
(Figure 1), we monitored three general populations of crossbridges: x1 – Pre-
powerstroke, x2 – Post –powerstroke, x3 – Non-bound (Figure 1). Crossbridge
transition between these populations is regulated at rates kij; i=1,2,3 is the source
population where the crossbridge comes from, and j=1,2,3 is the sink population
which the crossbridge transits into. Based on these transition rates, we can
describe the crossbridge population dynamics in a set of two ordinary differential
equations (ODEs):
,xx=x
,xk+xk+)xk+(k=dtdx
,xk+xk+)xk+(k=dtdx
3212212
3121131
213
31223
32112
1
/
/
![Page 93: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/93.jpg)
93
where xi represent the fraction of the total crossbridges that can be found
in the kinetic state xi;. We used the normalization x1+x2+x3=1 to reduce the
system from three ODEs to two ODEs, because x3 can be calculated from x1 and
x2 as described in above expressions. All transition rates except those containing
the powerstroke transition were assumed to be constant. The transitions
containing the powerstroke have an exponential dependence on load F, which is
multiplied by the powerstroke step size Δd and enters as work into the exponent:
.
const.
2/2/
12
23
dF
21
dF
133132
ek,ek
=k,k,k,k
For exact expressions in terms of ATP, ADP, Pi (phosphate)
concentrations, myosin affinity for actin, and zeroth order transition rates, see
supplementary material (SM). Ionic strength, [Ca2+
] and pH are assumed to be
implicitly contained in the effective zeroth order rates for all transitions.
![Page 94: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/94.jpg)
94
Figure 1 - Overview of mathematical model. The mathematical model comprises a load-
sensitive active crossbridge component adjusting the molecular contractile apparatus length Lmol,
and a passive element with a linear force response to differences between the externally set fibre
length L and Lmol. A three-state crossbridge kinetic cycle with a load-dependent powerstroke
transition from the pre to the post powerstroke state is assumed
![Page 95: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/95.jpg)
95
Figure 2 - Simulated force during ramp shortening protocol with detected critical points.
Top row (A, B, C) shows measured force P vs. time, bottom row (D, E, F) shows fibre length L vs.
time. Triangles and circles represent P1 and P2 critical points, respectively. Negative times
correspond to times before start of shortening ramp, fibre activated at time -150t0 in simulation and
held isometrically up to time 0. Grey background rectangles indicate regions which are displayed
at higher time resolution in the next graph to the right. Five traces are simulated with ramp
velocities 0.125L0/t0, 0.25L0/t0, 0.5L0/t0, 1L0/t0 and 2L0/t0. Simulation parameters are presented in
Supplementary Material.
Table 1. Relative force decrease (%) when compared to contractions produced in
pCa2+
4.5 in each experiment.
Experiment
(i) (ii) (iii)
pCa
2+ 5.0 20 ± 15 - -
pCa2+
5.5 18 ± 17 - -
pCa2+
6.0 59 ± 5* - 55 ± 10*
Blebbistatin (+/-) - 60 ± 6* 72 ± 4*
Blebbistatin (+/+) - 13 ± 32 -
* Significantly different from contractions produced in pCa2+
4.5 (p ≤ 0.05)
Measured force
The measured force P is determined by the stretch of the passive elastic
element. This stretch, in turn, is determined by the difference between L, the
overall length of the fibre, and Lmol, the length of the molecular contractile
apparatus multiplied by the elastic modulusC .
.( )LLC=P mol
The fibre length L is externally set by the operator; we use the following
time course to model a shortening ramp
,L))vt,v(L(=L(t) rampmolrampmax 0/max0,min
![Page 96: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/96.jpg)
96
so that the ramp starts at time t=0, the length L(t=0)=0 is set equal 0 for
the maximum isometric contraction point at t=0 (see Figures 2 D, 2E, and 2F).
The fibre length L is changed at a constant velocity vramp up to a total shortening
length by Lmax. Note that in case of shortening vramp, Lmax<0.
Figure 3 - Typical experiment overview – pCa2+
4.5 and 6.0. Sample records from a typical
experiment showing the force produced by a muscle fibre activated in pCa2+
4.5 (upper trace) and
pCa2+
6.0 (lower trace). Force rises during activation and then stabilizes to achieve a plateau.
During shortening the force decays rapidly. After the shortening, the forces recover slowly to
achieve a new steady-state.
![Page 97: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/97.jpg)
97
Figure 4 - Experimental detection of critical points at different Ca2+
concentrations. (A)
Superimposed contractions showing the force decrease during shortening while the fibre was
activated at different Ca2+
concentrations (top), with the corresponding length change (bottom).
All forces were normalized by their respective isometric forces (Po) before the ramp shortening.
P2 and L2 did not change at increasing Ca2+
concentrations. (B) Closer view from the initial
shortening phase of the experiment with another fibre, showing clearly that P1 and L1 do not
change with different Ca2+
concentrations. The critical points in this figure were detected with
regression analyses; the regression lines are shown in blue (pCa2+
4.5) and green (pCa2+
5.5)
traces.
![Page 98: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/98.jpg)
98
Figure 5: Mean critical values for different Ca2+
concentrations. Mean values (+ S.E.M) of P1
and P2 (A), and L1 and L2 (B) in experiments performed with different Ca2+
concentrations.
Changing the pCa2+
did not change any of the variables.
Figure 6 - Typical experiment overview – pCa2+
4.5 and blebbistatin. Sample records from a
typical experiment showing the force produced by a muscle fibre activated in pCa2+
4.5 (upper
trace) and then treated with blebbistatin (lower trace). Force rises during activation and then
stabilizes at a steady-state level. During shortening the force decreases. After the shortening, the
forces recover slowly to achieve a new steady-state.
Connecting crossbridges and measured force
The active contractile element and the passive elastic element interact in
two ways:
(1) The force P on the fibre, which develops in the passive elastic element
in response to stretch, is divided by the number of attached myosin heads, and
thereby gives the load F experienced by a single attached myosin head
,)x+N(x
P=F
21
![Page 99: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/99.jpg)
99
which in turn influences the transition rates of the forward and reverse
powerstroke steps. N is the total number of crossbridges in the fibre.
(2) Crossbridges transitioning through the forward or reverse powerstroke
step decrease or increase Lmol (the length of the active molecular contractile
element), respectively. The change in Lmol can be calculated by multiplication of
the forward flux through the powerstroke state by the powerstroke step size
.( 112221 )xkxkdN=Ldt
dmol
Lmol, together with L, determines the stretch of the passive elastic element,
and thereby the measured fibre force.
Figure 7 - Experimental detection of critical points in fibres treated with blebbistatin. (A)
Superimposed contractions, showing the force decay during shortening while the fibre was
activated with pCa2+
4.5- (solid line), and then treated with blebbistatin (dashed line), with the
corresponding fibre length changes. All forces were normalized by their respective isometric
forces (Po) before shortening. P2 and L2 did not change with blebbistatin. (B) Closer view from
the initial shortening phase of the experiment with another fibre, showing that blebbistatin induced
a higher force decrease before P1. It also shows that blebbistatin induced greater P1 amplitude
![Page 100: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/100.jpg)
100
when compared the contraction produced before blebbistatin. L1 was not changed by blebbistatin.
The critical points in this figure were detected with regression analyses, the regression lines are
shown in blue (pCa2+
4.5) and red (pCa2+
4.5 + blebbistatin) traces.
Implementation of experimental protocol, measurement of critical points
To reproduce the experimental ramp shortening protocol in a simulation of
our model, we allowed the fibre to reach a force plateau (P0) before imposing a
ramp shortening (Figure 2A). Dependent on ramp velocity, the time of the ramp
shortening was adjusted in each contraction to reach the same ramp lengths
independent of ramp velocity (see figure 2D and 2E). We simulated our model
using the MatLab ode15s adaptive time step size integrator for stiff ODEs (for
resulting traces see Figure 2). We found regular ODE integrators to be inefficient
due to the rapid changes in force right after beginning of the ramp shortening.
The P1 and P2 transitions were detected based on the curvature Curv of the force
time course L(t). At P1, the linear force decrease transitions into a less steep
decrease, Curv at this “kink” has a prominent peak which we used to detect P1;
considering P1 as a transition from a phase with marked shifts in the crossbridge
populations to a phase of exponential approach to a new steady state, we detected
P2 as a characteristic transition in log10(Curv) from a curved decay to a linear
decay (exponential decay displays as a linear decay on a log-scale) (see Figure 2
and SM, Figure 2).
2.2.4 Results
2.2.4.1 Experimental results
![Page 101: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/101.jpg)
101
The isometric forces were altered by Ca2+
concentration changes as well as
by blebbistatin (Table 1). When contractions were produced in pCa2+
5.0 or 5.5, a
not statistically significant trend towards decreased force was visible, and
contractions in pCa2+
6.0 showed a significant decrease in force relative to
contractions produced at pCa2+
4.5. When fibres were treated with blebbistatin,
there was a significant force decrease, in accordance with previous studies that
reported a decrease of ~ 60% when using 5M of blebbistatin (Farman et al,
2008; Minozzo & Rassier, 2010; Stewart et al, 2009).
Figure 8 - Mean critical values of fibres treated with blebbistatin. Mean values (+ S.E.M.) of
P1 and P2 (A), and L1 and L2 (B) in experiments where fibres were treated with blebbistatin (+/-).
Blebbistatin changed P1 significantly. None of the other variables were changed. * Significantly
different from all other conditions (P < 0.05).
![Page 102: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/102.jpg)
102
The effects of blebbistatin are highly dependent on the experimental
conditions; differences of ~20% are observed in studies that use similar
blebbistatin concentrations (Farman et al, 2008; Stewart et al, 2009). Note that
the inactive isomer of blebbistatin (+/+) also decreased the force by a small
magnitude, a result that has been reported previously (Minozzo & Rassier, 2010;
Stewart et al, 2009). However, during shortening, we did not find any difference
between the inactive form of blebbistatin and the control experiments, as
previously observed (Minozzo & Rassier, 2010). For reasons of clarity we will
therefore report only the results of experiments using the active form of
blebbistatin.
Effects of Ca2+
concentrations: Figure 3 shows two contractions (pCa2+
4.5 and 6.0) recorded during a typical experiment performed in this study. In both
cases the force rose quickly during activation to reach different steady-state levels
– in this case the force produced at pCa2+
6.0 was 40% of the force produced at
pCa2+
4.5. Once full force development was obtained, the fibre was shortened and
the force rapidly decreased to zero. The force was then redeveloped to reach a
new steady state, after which the fibre was deactivated (deactivation not shown).
We were mostly interested in the transient force changes during
shortening. Figure 4A shows a zoomed image of the shortening phase during two
contractions produced in different pCa2+
. The force was normalized by the
maximum isometric force produced just before shortening. In this case the values
of P2 and L2 were not different among the different contractions. In Figure 4B we
changed the graph scale to show the P1 force transition, which was clearly
detected. The values of P1 and L1 did not change during the shortening with
![Page 103: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/103.jpg)
103
different pCa2+
. The results observed in this experiment were confirmed
statistically, and despite the increase in Po following the increase in Ca2+
concentrations, none of the variables investigated during shortening (P1, P2, L1
and L2) were affected by changes in pCa2+
(Figure 5). When all pCa2+
data were
pooled, P1 and P2 were 0.79 ± 0.003 and 0.27 ± 0.01 times Po, respectively, and L1
and L2 were 4.62 ± 0.16 and 24.17 ± 0.20 nm.HS-1
respectively.
Effects of blebbistatin: Figure 6 shows two contractions recorded during
the same experiment before and after blebbistatin treatment. Blebbistatin
substantially decreased the maximum isometric force, but the response to
shortening was similar to control experiments: the force decreased quickly to
almost zero to then redevelop towards a new steady-state level. Figure 7 shows a
zoomed image of the shortening phase in an experiment where the fibre was
activated at pCa2+
4.5 and treated with blebbistatin (+/-). The force was
normalized by the maximum isometric force. The values of P2 and L2 were not
different before and after blebbistatin treatment (Figure 7A). However, P1, also
detectable for this condition, decreased significantly after blebbistatin treatment,
while L1 was not changed (Figure 7B). The results shown in the experiment
depicted in Figure 7 were confirmed statistically (Figure 8). P2 and L2 were not
statistically different from the control group (pCa2+
4.5). The P1 amplitude
(absolute distance between the critical point and Po) was significantly higher after
blebbistatin treatment when compared with the control, as shown in a higher force
decrease, while L1 was not affected by blebbistatin (Figure 8B).
![Page 104: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/104.jpg)
104
Figure 9 - Critical points behaviour at different velocities. (A) Force responses (upper traces)
to ramp shortenings (lower traces) in a range of velocities (0.125 – 2 Lo.s-1
) from one set of
experiments performed with one fibre activated with a pCa2+
4.5. The rate of force decay
increased with shortening velocities. (B) Closer view from the same traces, showing increasing P1
amplitude (upper traces) and L1 (lower traces) with increasing velocities. (C) and (D) Same as in A
and B, now showing traces of another fibre treated with blebbistatin (3 velocities displayed).
Effects of shortening velocity: Figures 9A and 9C show records of
contractions in which ramp shortenings at different (constant) velocities were
applied in two fibres activated in pCa2+
4.5 and treated with blebbistatin,
respectively. The P2 amplitude and L2 were augmented with increasing velocities,
as previously shown (Roots et al, 2007). Figures 9B and 9D show a closer view
of the force records from panels A and C respectively in which the P1 transitions
![Page 105: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/105.jpg)
105
were detected. The amplitude of P1 increased with velocity, which was
accompanied by an increase in L1. The amplitudes of P1, P2, L1, and L2 increased
with velocities, in all conditions investigated. There was not a difference detected
in P2, L1, and L2 among the three conditions, although the P1 amplitude increased
in fibres treated with blebbistatin. Figure 10 shows the mean (± S.E.M) values for
P1 activated in pCa2+
4.5, 6.0 and after treatment with blebbistatin. The velocity-
P1 curve was shifted downward in fibres treated with blebbistatin.
Figure 10 - Mean critical values at different velocities. Mean (+ S.E.M.) of the P1 values at five
different velocities in a fibre activated with Calcium pCa2+
4.5 (dotted line), 6.0 (solid line) and
treaded with blebbistatin (solid line with inverted triangles). Blebbistatin changed P1 significantly
at all five velocities. *Significantly different from all other conditions (P < 0.05).
2.2.4.2 Model results
![Page 106: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/106.jpg)
106
Using our model (for parameter values see Table 1; Supplementary
Material), the dependence of P1, P2, L1, and L2 on ramp velocity observed in our
experiments without blebbistatin could be qualitatively explained (Figure 11); the
critical P1 and P2 decreased and the critical L1 and L2 increased with increasing
ramp velocity. We also observed the characteristic nonlinear dependencies of the
critical force transitions during the shortening; the monotonous upward and
downward tendencies observed in experiment for P1, P2, L1, and L2 are all
accounted for by our model results.
Figure 11 - Blebbistatin effect on ramp shortening critical points in experiment and model
simulation. A) Experimentally measured P1 for different ramp velocities. Solid line: pCa2+
4.5
![Page 107: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/107.jpg)
107
with blebbistatin, dotted and dashed line: pCa2+
4.5 and pCa2+
6 without blebbistatin, respectively.
B) P1 detected in simulation for different ramp velocities. Solid line: blebbistatin inhibition
modeled by lowering of myosin actin tight binding energy by ΔE=0.35kBT. Dashed line: no
blebbistatin inhibition. C, D, E) Experimentally determined L1, P2, L2, respectively; same
conditions as in A). F, G, H) L1, P2, L2 detected in simulated ramp shortening, respectively; same
conditions as in B). Simulation parameters see Supplementary Material.
Mechanism of blebbistatin inhibition: The powerstroke inhibitor
blebbistatin is believed to affect the tight binding of myosin to actin. Its
characteristic molecular structure targets the myosin-actin binding interface, and
the closing of the myosin’s actin-binding cleft is hindered. Conceptually, there
are two not mutually exclusive ways to incorporate this mechanism into
crossbridge kinetics: (1) as the establishment of inter-protein molecular bonds is
disturbed by the presence of blebbistatin, the binding energy of the tight-bound
postpower-stroke state is reduced, or (2) as the closing of the actin binding cleft is
hindered, the zeroth order transition rate of the powerstroke is reduced. In terms
of the molecular potential energy profile, these changes correspond to an increase
of the potential energy level of the post-powerstroke state, or the increase of the
reaction energy barrier of the transition between the pre and the post-powerstroke
state, respectively (see Figure 12). Intuitively, case (1) would be expected to
lower the effective affinity between actin's myosin binding sites and myosin
heads. Case (2) would be expected to slow down the powerstroke transition, but
not to change the effective myosin-actin affinity. Both alterations are in line with
findings from biochemical and structural studies of kinetic mechanism of
blebbistatin (Allingham et al, 2005; Kovacs et al, 2004; Limouze et al, 2004;
Ramamurthy et al, 2004). However, we can show that in case (2) no reduction in
the isometric maximum force Po is predicted with blebbistatin. In case (1), Po
![Page 108: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/108.jpg)
108
decreases monotonously with increasing concentration of blebbistatin. Thus, a
decreased binding energy of the strongly bound crossbridges as described under
(1) is the necessary mechanism of action and used for the following model
predictions of the blebbistatin effect.
Prediction of critical points with blebbistatin inhibition: We introduced
the kinetic influence of blebbistatin into our model as a reduction of the binding
energy by ∆E = 0.35kBT. This alteration predicts a prominent reduction of the P1
and P2 and minimal changes in L1 and L2. Applying the powerstroke inhibitor
blebbistatin in our experiment caused a significant decrease in P1 force and no
significant changes for P2, L1, and L2. Thus the predicted and measured
qualitative effects of blebbistatin are the same for P1, L1 and L2; the case of P2 is
unclear. Applying alternatively an increase in the zeroth order rate constant of the
powerstroke by a factor 1/1.75 predicts similar effects on the critical points
(Figure S5 in the Supplementary Material), thus a decrease in the energy of tight
binding of myosin to actin is a necessary mechanism to explain our results, the
reduction of the zeroth order powerstroke transition rate is a possible one.
2.2.5 Discussion
In this study we detected an early force transition during an imposed
shortening of activated muscle fibres (P1), depicted as a change in slope prior to
P2 during shortening (Bressler, 1985; Ford et al, 1977; Roots et al, 2007). In our
experiments, when different velocities (0.125 to 2 Lo•SL•s-1
) were applied, P1
amplitude (i.e. distance between Po and critical force) ranged between -0.03 and -
0.39 times Po and L1 amplitudes ranged between 0.5 and 7.0 nm•HS-1
; the higher
![Page 109: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/109.jpg)
109
the velocity the higher P1 and L1 amplitude; in agreement with previous studies
[5]. We also observed values for P2 and L2 that were within the range observed in
previous studies; when a 10%Lo shortening was performed at velocities ranging
from 0.125 to 2 Lo•SL•s-1
, the values of P2 and L2 ranged between ~ 0.65 and 0.20
times Po and ~15 and 27 nm•HS-1
.
Figure 12 - Molecular mechanism of blebbistatin inhibition visualized in the crossbridge
cycle potential profile. We display here the two suggested mechanisms of blebbistatin inhibition,
each with its specific effect on the potential profile. The solid curve represents the free energy
profile without blebbistatin inhibition; the dashed curve represents the qualitative change from
blebbistatin addition. A progression through states 1, 2, 3 and finally back to 1 (from left to right)
corresponds to completion of one actomyosin crossbridge cycle by sequential transition through
the kinetic states. The elevations between the kinetic states correspond to reaction barriers; these
transitions require activation energy, so a higher barrier lowers the transition rates across this
barrier. A) Reduction of binding energy of myosin tight-binding to actin, manifesting itself as an
increase of the post-powerstroke energy level. Our model analysis indicates that this is a necessary
mechanism of blebbistatin inhibition. B) Reduction of the powerstroke zeroth order rate constant.
Our model analysis indicates that this is a possible but not a necessary mechanism of blebbistatin
inhibition. Potential profiles are only qualitative illustrations and not drawn to scale.
2.2.5.1 Experiments with different Ca2+
concentrations
Despite the velocity dependence of P2, the values did not change with Ca2+
concentrations (pCa2+
4.5, 5.0, 5.5 and 6.0), suggesting that P2 values are
independent from the number of crossbridges attached to actin. Although
estimating the number of strongly-bound crossbridges in a given moment during
![Page 110: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/110.jpg)
110
contractions is challenging, there is evidence that the number does not exceed
40% at high Ca2+
concentrations. One study that experimented with
permeabilized fibres from the rabbit psoas muscle, and used stiffness
measurements, to calculate the relative proportion of crossbridges attached to
actin, found a value of ~ 33% of crossbridges attached to actin during isometric
contractions produced at saturating Ca2+
concentration (Linari et al, 2007). It is
likely that the number is similar to what we have in our experiments.
To our knowledge, no other studies evaluated the effects of Ca2+
concentrations on P2 during shortening. If we assume that the amount of
crossbridges formed before shortening do not change the strain necessary for their
detachment, and the critical forces (P2) normalized by their isometric forces, as
well as their correspondent critical length (L2), should not change. Previous
studies that evaluated P1 during shortening (Roots et al, 2007) have suggested that
this early inflexion is born mostly by pre-powerstroke crossbridges (newly
attached crossbridges) performing the powerstroke. Assuming that increasing
Ca2+
concentration alters forces mostly by increasing the number of crossbridge
formation, without necessarily affecting the distribution of the population of
myosin attached to actin into pre and post-stroke states, it is expected that P1
would not change with different Ca2+
concentrations.
2.2.5.2 Modelling crossbridge kinetics
The developed model explains qualitatively L1, P1, L2, and P2 for different
ramp velocities. A parameter change representing the known kinetic effects of
blebbistatin also predicts the experimentally observed L1, P1, and L2. Furthermore,
on the level of actomyosin interaction, the model is mechanistic and based on
![Page 111: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/111.jpg)
111
experimental results. Together, these findings imply that important aspects of the
underlying molecular kinetics are captured in the model. It therefore seems
appropriate to extend our investigation of the crossbridge kinetics underlying the
ramp shortening force response using this model.
It has been hypothesized in earlier experimental and model studies that the
P1 critical point is associated with a transition from a purely elastic phase to a
repartitioning of the crossbridge populations in response to a decreased load on
the bound crossbridges. As can be seen in Figure 13, short after the ramp
shortening started, only a minimal change in the crossbridge populations was
visible. This corresponds to a phase in which only the passive elastic elements in
the muscle fibre are shortened, which decreases the measured force as well as the
load on the bound crossbridges. When P1 is reached, the load on bound
crossbridges is decreased so far as to appreciably increase the powerstroke
forward transition rate. As an effect, the pre-powerstroke crossbridges go through
the powerstroke fast, and an increasing percentage of crossbridges appears in the
post-powerstroke and the non-bound state. This shift in the crossbridge
populations first increases, and then decreases again till the crossbridge
populations reach a new steady state for the changed loading conditions. The
behaviour of the crossbridge populations visible in Figure 13 around the second
critical point at P2 suggests an association of P2 with the transition from an
increasing to a decreasing shifting behaviour in the crossbridge populations,
resulting in an asymptotic approach to a new, lowered steady state tension value.
![Page 112: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/112.jpg)
112
2.2.5.3 Mechanism of blebbistatin inhibition
When the fibres were treated with blebbistatin, a decrease in the maximum
isometric force P0 was observed. There was a significant decrease in P1, but no
significant changes in L1, P2 and L2 after blebbistatin treatment. Blebbistatin is a
myosin inhibitor that causes both, a reduction in the number of crossbridges
strongly attached to actin, and a redistribution of crossbridges towards a weakly
bound state, stabilizing the Myosin•ADP•Pi complex into a pre powerstroke state
(Allingham et al, 2005; Farman et al, 2008; Kovacs et al, 2004). Investigation of
our model indicated that a decrease in the binding energy of the myosin-actin tight
binding is a necessary molecular mechanism of blebbistatin inhibition of active
force development, in contrast to a reduction in the zeroth order rate constant of
the powerstroke transition it can explain the P0 reduction. This is in agreement
with the hypothesized disturbance of the tight binding protein-protein interface
(Allingham et al, 2005; Farman et al, 2008; Kovacs et al, 2004). Decrease of the
strength of tight binding as well as a reduction of the zeroth order rate constant of
the powerstroke transition were found to explain the observations for P1, L1, and
L2.
![Page 113: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/113.jpg)
113
Figure 13 - Simulated crossbridge dynamics during ramp shortening protocol with ramp
velocity 2L0/t0. A logarithmic time scale was used for all positive times; time 0 indicates start of
ramp shortening, negative times indicate isometric contraction phase before ramp shortening. A,
B) Force production, triangle and circle represent critical points P1 and P2, respectively. C, D)
Percentage of actively cycling crossbridges in the different kinetic states. Note logarithmic scaling
of vertical axis. E, F) Effective flux of crossbridges from pre- to post-powerstroke-state and from
post-powerstroke state to detached state. The effective flux is the rate at which crossbridges go
from a state xi to a state xj minus the rate at which crossbridges go from xj to xi. Note logarithmic
scaling of vertical axis. See also Discussion section and Supplementary Material. Simulation
parameters are included in the Supplementary Material.
Since we observed that blebbistatin affects some of the contractile
parameters during shortening and varying Ca2+
concentration had no effect, it is
important to discuss the difference between force inhibition by blebbistatin and by
the Ca2+
-troponin-tropomyosin complex. According to the most accepted model
of force regulation (Gordon et al, 2000), when Ca2+
binds to the troponin C (TnC),
it causes the displacement of tropomyosin, allowing crossbridge attachment to
actin and forming a weakly bound myosin–actin–ATP complex. ATP is then
hydrolysed and phosphate is released, forming a strongly bound myosin–actin–
ADP complex. The strongly bound complex causes conformational changes in
the thin filament, increasing the probability of new crossbridges to attach to actin.
![Page 114: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/114.jpg)
114
Therefore, the troponin-tropomyosin complex regulates force production mostly
by not allowing myosin-crossbridges to attach to actin, while blebbistatin
decreases the formation of the strong-bound step, after the formation of the
Myosin•ADP•Pi complex.
2.2.5.4 Indications for a load-dependent ADP-release step
Our model predicts surprisingly low occupancies of the post-powerstroke
state at maximal isometric contraction (see Fig. 4 and a more general derivation in
Supplementary Material). While maintenance of maximal isometric force by
mostly pre-powerstroke crossbridges is not necessarily wrong, the large presence
of pre-powerstroke crossbridges disagrees with X-ray diffraction studies showing
~40% of crossbridges in the (stereospecifically bound) post-powerstroke state
during isometric contraction at physiological temperatures (Koubassova et al,
2008). However, when we include the stress-sensitivity of ADP release
hypothesized for skeletal muscle (Nyitrai & Geeves, 2004), a non-vanishing
percentage of crossbridges in the post-powerstroke state for maximal isometric
force becomes possible (see Supplementary Material). Therefore, the strain-
sensitivity of the ADP release might play a greater role in ramp force responses
than appreciated so far. From the first comprehensive models of muscle molecular
mechanochemistry (Eisenberg et al, 1980) to more recent modeling studies
(Vilfan & Duke, 2003), a strain-sensitive ADP release has been assumed, thus it
should be an interesting future direction for more realistic models of skeletal
muscle crossbridge kinetics in ramp shortening and lengthening experiments.
![Page 115: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/115.jpg)
115
3 Force development during and after muscle length changes
3.1 Preface
It has been suggested that muscle stretch and shortening can induce long-
lasting changes in crossbridge kinetics: stretch could lead to an increase in the
number of attached crossbridges (Rassier & Herzog, 2005), whereas shortening
could lead to crossbridge deactivation (Marechal & Plaghki, 1979; Pun et al.,
2010). In both cases, the mechanisms by which these changes may occur and
how they relate to the long-lasting alterations in crossbridge kinetics and force
production are unclear.
Motivated by these questions, we decided to investigate force development
during and after length changes after altering the crossbridge population either by
changing Ca2+
concentration or inducing myosin-actin strong-bound via MgADP
activation. We hypothesized that, if the history dependence of force production
was linked to crossbridge kinetics, the effect would be observed in the residual
state of force production after length changes.
![Page 116: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/116.jpg)
116
3.2 The effects of Ca2+
and MgADP on force development during and after
muscle length changes
Fábio C. Minozzo
Dilson E. Rassier
Reprinted from : PloS One. 2013. 8(7) :e68866. doi:
10.1371/journal.pone.0068866
![Page 117: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/117.jpg)
117
3.2.1 Abstract
The goal of this study was to compare the effects of Ca2+
and MgADP
activation on force development in skeletal muscles during and after imposed
length changes. Single fibres dissected from the rabbit psoas were (i) activated in
pCa2+
4.5 and pCa2+
6.0, or (ii) activated in pCa2+
4.5 before and after
administration of 10mM MgADP. Fibres were activated in sarcomere lengths
(SL) of 2.65μm and 2.95μm, and subsequently stretched or shortened (5%SL at
1.0 SL.s−1
) to reach a final SL of 2.80 μm. The kinetics of force during stretch
were not altered by pCa2+
or MgADP, but the fast change in the slope of force
development (P1) observed during shortening and the corresponding SL extension
required to reach the change (L1) were higher in pCa2+
6.0 (P1= 0.22 + 0.02 Po;
L1= 5.26 + 0.24 nm.HS.1
) than in pCa2+
4.5 (P1= 0.15 + 0.01 Po; L1= 4.48 + 0.25
nm.HS.1
). L1 was also increased by MgADP activation during shortening. Force
enhancement after stretch was lower in pCa2+
4.5 (14.9 + 5.4%) than in pCa2+
6.0
(38.8+ 7.5%), while force depression after shortening was similar in both Ca2+
concentrations. The stiffness accompanied the force behavior after length
changes in all situations. MgADP did not affect force behavior after length
changes, although stiffness did not accompany the changes in force development
after stretch. Altogether, these results suggest that the mechanisms of force
generation during and after stretch are different from those obtained during and
after shortening.
![Page 118: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/118.jpg)
118
3.2.2 Introduction
Length changes imposed to activated muscles are commonly used to study
the molecular mechanisms of contraction (Colombini et al, 2009; Ford et al, 1977;
Lombardi & Piazzesi, 1990; Minozzo et al, 2012; Minozzo & Rassier, 2010;
Roots et al, 2007). When muscle fibres are activated and subsequently stretched
or shortened, force changes in four major steps: a fast rate of force change (phase
1) followed by a slower rate of force change (phase 2), after which the force
stabilizes slowly (phase 3) to asymptotically return to a new steady state (phase 4)
(Minozzo et al, 2012; Minozzo & Rassier, 2010; Roots et al, 2007). Although the
mechanisms by which myosin crossbridges contribute to force changes observed
during muscle stretch and shortening are still under investigation (Bickham et al,
2011; Brunello et al, 2007; Colomo et al, 1986; Fusi et al, 2010; Getz et al, 1998;
Ranatunga et al, 2010), phase 1 is commonly attributed to the elastic behavior of
the crossbridges, and phase 2 is commonly associated with changes in the
occupational fraction of crossbridges in the pre- and post-powerstroke states
during the actomyosin cycle (Minozzo et al, 2012; Roots et al, 2007).
After stretch or shortening, force stabilizes at a higher or a lower level
than that produced during isometric contractions at corresponding lengths,
respectively (phase 4); these phenomena have been referred to as residual force
enhancement and force depression (Abbott & Aubert, 1952; Julian & Morgan,
1979a; Pun et al, 2010). Attempts to correlate these last-longing changes in force
with changes that happen during length changes have proved inconclusive. It has
been suggested that stretch can induce changes in crossbridge kinetics leading to a
long-lasting increase in the number of crossbridges attached to actin (Rassier &
![Page 119: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/119.jpg)
119
Herzog, 2005), and that shortening can cause crossbridge deactivation due to
newly overlap zone formed between myosin and actin filaments (Marechal &
Plaghki, 1979; Pun et al, 2010). However, studies that measured stiffness – a
putative measurement of crossbridges attached to actin – are contradictory; some
show a direct relationship between stiffness and residual force changes (Herzog &
Leonard, 2000; Sugi & Tsuchiya, 1988) and others fail to find any correlation
between the two variables (Julian & Morgan, 1979a; Tsuchiya & Sugi, 1988).
The events dominating crossbridge kinetics during muscle stretch and
shortening, and their potential relation with the residual force enhancement and
depression need investigation. In this study, we approached this problem by
investigating force during and after length changes (shortening and stretching)
while altering either the population of attached crossbridges using different levels
of Ca2+
activation, or biasing crossbridges into a strong-binding with actin by
using MgADP activation (Shimizu et al, 1992). Based on previous studies
(Edman, 1996; Pinniger et al, 2006; Roots et al, 2007), we hypothesized that an
increase in the number of crossbridges would not affect the relative forces
produced during and after length changes, while changes in the crossbridges
binding state would affect force during and after length changes. Confirmation of
these hypotheses would link changes in crossbridge kinetics during length
changes to the long-lasting effects observed in skeletal muscles.
3.2.3 Methods
3.2.3.1 Fibre preparation
![Page 120: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/120.jpg)
120
Muscle bundles (2-3cm) from the rabbit psoas muscle were dissected, tied
to wooden sticks, and chemically permeabilized as previously described (Minozzo
et al, 2012; Minozzo & Rassier, 2010). Muscles were incubated in rigor solution
(pH = 7.0) for approximately 4 hours, then transferred to a rigor:glycerol (50:50)
solution for 15 hours, before storage in a fresh rigor:glycerol (50:50) solution
containing a cocktail of protease inhibitors (Roche Diagnostics, USA) in a freezer
(-20°C) for at least seven days. Prior to the experiment, one muscle sample was
transferred to a fresh rigor solution to be defrosted in the fridge (4oC) for one hour
before use. After cutting a small section (~ 4 mm in length) from the sample,
single fibres were dissected in relaxing solution (pH = 7.0) and fixed with two
aluminum foil clips. The fibres were placed inside a temperature-controlled
chamber and attached between a force transducer (Model 400A, Aurora Scientific,
Toronto, Canada) and a length controller (Model 312B, Aurora Scientific,
Toronto, Canada). The protocol was approved by the McGill University Animal
Care Committee (protocol # 5227) and complied with the guidelines of the
Canadian Council on Animal Care
3.2.3.2 Solutions.
The rigor solution (pH 7.0) was composed of (in mM): 50 Tris, 100 NaCl,
2 KCl, 2 MgCl2, and 10 EGTA. The relaxing solution used for muscle storage
and dissection (pH 7.0) was composed of (in mM): 100 KCl, 2 EGTA, 20
Imidazole, 4 ATP and 7 MgCl2. The experimental solutions with pCa2+
of 4.5,
6.0 and 9.0 (pH 7.0) contained (in mM): 20 imidazole, 14.5 creatine phosphate, 7
EGTA, 4 MgATP, 1 free Mg2+
, free Ca2+
in three concentration adjusted to obtain
pCa2+
of 9.0, 6.0 and 4.5. KCl was used to adjust the ionic strength to 180 mM in
![Page 121: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/121.jpg)
121
all solutions. The final concentrations of each metal-ligand complex were
calculated using a computer program based on Fabiato (1988). A pre-activating
solution (pH 7.0; pCa2+
9.0) with a reduced Ca2+
buffering capacity was used
immediately prior to activation to minimize a delay in diffusion (in mM): 68 KCl,
0.5 EGTA, 20 Imidazole, 14.5 PCr, 4.83 ATP, 0.0013.7 CaCl2, 5.41 MgCl2 and
6.5 HDTA. The MgADP solution was prepared by adding 0.214 g of MgADP to
50mL of activation solution (pCa2+
4.5), reaching a final MgADP concentration of
10mM (Pun et al, 2010).
3.2.3.3 Experimental protocol.
The average sarcomere length (SL) of the fibres in the experimental
chamber was calculated in relaxing solution using a high-speed video system
(HVSL, Aurora Scientific 901A, Toronto, Canada). Images from a selected
region of the fibres were collected at 1000-1500 frames/second, and the SL was
calculated using Fast Fourier Transform analysis based on the striation spacing
produced by dark and light bands of myosin and actin, respectively. The fibre
diameter and length were measured using a CCD camera (Go-3, QImaging, USA;
pixel size: 3.2µm X 3.2µm), and the cross-sectional area was estimated assuming
circular symmetry.
Two separate sets of experiments were performed during this study: (i)
fibres were activated in pCa2+
4.5 and pCa2+
6.0 (n = 13), or (ii) fibres were
activated in pCa2+
4.5 with or without MgADP (n = 7). Both sets of experiments
followed the same procedures. Fibres were first activated to produce isometric
contractions at nominal SLs of 2.65µm, 2.80µm and 2.95µm. Fibres were
subsequently activated at 2.65µm and 2.95µm, and a 5% SL change, at a speed of
![Page 122: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/122.jpg)
122
1.0 SL.s-1
(stretch or shortening, random order) was imposed after full force
development, obtaining a final SL of 2.80µm in both cases. In all trials, control
contractions at SL of 2.80μm were elicited at the end of the experiments, and if
isometric forces decreased by >15% in relation to the first isometric contraction,
or when the striation pattern corresponding to the SL became unclear, the
experiments were ended and the data was not used.
During all experiments, fibre stiffness (K) was assessed three times during
the contractions: after force was fully developed, but before length changes (30s
after activation started), immediately after the change in length and before the
force was stabilized (40.0075s after activation started), and after the force was
stabilized following the length changes (50s after activation started). Stiffness
was evaluated by applying a fast length step (dL = 0.3%Lo) to the fibres, and
dividing the change in force during this step by the length change (K = dF/dL)
(Colombini et al, 2005).
3.2.3.4 Data analysis.
The force and stiffness obtained after stretch, after shortening and during
the isometric reference contractions were compared between different conditions
from each set of experiment; (i) fibres activated in pCa2+
4.5 and 6.0, and (ii)
fibres activated in pCa2+
4.5 with or without MgADP. The changes in the slope of
force traces observed while fibres were stretched and shortened were detected
using a two-segment piecewise regression, as previously described (Minozzo et
al, 2012; Minozzo & Rassier, 2010). The regression results were accepted when
they presented a correlation coefficient (r2) >0.99. When this criterion was not
met (a few cases for detection of P1), we fitted a single linear regression in the
![Page 123: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/123.jpg)
123
data points spanning from the first 2-3ms in which force started to change, since
force is linear during this time (Minozzo et al, 2012; Roots et al, 2007). The
forces obtained at the first and second slope correspond to P1 and P2, and the SL
amplitudes necessary to achieve P1 and P2 were named L1 and L2, respectively
(Figure 1).
Figure 1 - Detection of force transients during stretch and shortening of activated muscle
fibres. Left-to-right: P2 and L2 detection during stretch and shortening, respectively. Force traces
are on the top and fibre length variation at the bottom (Po = isometric force; Lo = initial length).
The force rise during stretch and the force decay during shortening can be fitted by two linear
functions: y1= a1 + b1 × xi (restriction: xi ≤ xo) and y2 = a2 + b2 × xi (restriction: xi > xo), where
(xo, yo) represents coordinates of the critical transitions (coordinates for P2 in this
case), a1 and a2 are the intercepts of the two regression lines, and b1 and b2 are the slopes of the
two regression lines. The red traces in the graphs show the two-segmented piecewise regressions.
The residual sum of squares (RSS) is based on the sum of the squares of each regression line:
2
22
2
11
00
)()(
xx
ii
xx
ii
ii
xbayxbayRSS . RSS is used as a criterion to
determine the optimal values of a1, a2, b1, b2, and xo - those belonging to the minimal RSS are
considered optimal. The blue trace displayed on the inset correspond to a simple linear regression,
based on the best fit for the force coordinates (xo, yo) during the first 2-3ms, and P1 corresponds to
the first data point where the regression does not follow the force trace. In both cases the statistic
F-value and confidence intervals are calculated according to standard methods for regression
analyses. L1 and L2 are extrapolated by crossing a perpendicular line passing by P1 and P2,
respectively, until reaching the length traces.
3.2.3.5 Statistics
![Page 124: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/124.jpg)
124
A two-way analysis of variance (ANOVA) for repeated measures was
used to compare the forces and stiffness values in the different experiments (pCa2+
and MgADP conditions), before and after length changes. ANOVA for repeated
measures was also used to compare the values of P1, P2, L1, and L2 obtained
during shortening and stretch in the different sets of experiments. When
significant changes were observed, post-hoc analyses for multiple comparisons
were performed with Newman-Keuls tests. A level of significance of P ≤ 0.05
was set for all analyses. All values are presented as mean ± S.E.M.
3.2.4 Results
3.2.4.1 Transient forces during length changes
Experiments with different Ca2+
concentrations.
Figure 2 shows two isometric contractions produced during a typical
experiment in which a fibre was activated in pCa2+
4.5 and subsequently in pCa2+
6.0. The force produced in pCa2+
4.5 is in the range observed in previous studies
that used permeabilized fibres from mammalian muscles activated at low
temperatures (4-5ºC). These studies show forces ranging from 48 to 58 mN/mm2
when fibres contract at the plateau of the force-length relation (Bershitsky &
Tsaturyan, 2002; Radocaj et al, 2009; Ranatunga, 1996; Zhao & Kawai, 1994).
Since we activated fibres on average sarcomere lengths between 2.7µm and
2.9µm, the force should be 20–30% lower than that produced at the plateau of the
force-length relation, and thus our values are in close agreement with the
literature. The force decreased when fibres were activated in pCa2+
6.0 by 53.3 ±
![Page 125: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/125.jpg)
125
5.5%, similar to what has been reported in previous studies (Minozzo et al, 2012;
Minozzo & Rassier, 2010).
Figure 2 - Superimposed isometric contractions in different Ca2+
concentrations. Sample
records from typical isometric contractions produced in pCa2+
4.5 and pCa2+
6.0 (top), and
corresponding length traces (bottom). The average sarcomere lengths in each contraction were
2.82µm, and 2.83µm, respectively.
Figure 3 shows force and length traces recorded when a fibre was
stretched or shortened in two different Ca2+
concentrations. The force was
normalized by the maximum isometric force produced just before the stretch. The
values of P2 of 2.42 Po during stretch and 0.34 Po during shortening observed in
this fibre, when activated in pCa2+
4.5, are in agreement with previous studies
(Bagni et al, 2005; Lombardi & Piazzesi, 1990; Ranatunga et al, 2010; Roots et al,
2007). The value of L2 observed during stretch was comparable with previous
studies (Edman et al, 1978; Rack & Westbury, 1974), but higher than what we
observed before, where sarcomeres needed to be stretched by ~14nm.HS-1
before
a change in the force trace was observed (Minozzo & Rassier, 2010; Rassier,
2008). The difference may be related to the speed of stretch and SL, as in the
![Page 126: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/126.jpg)
126
previous study we used faster stretches at shorter SLs than used in the current
experiments.
During stretch, P2 and L2 were not different between contractions
performed in different pCa2+
(Figure 3A). We were unable to detect P1 during
stretch. However, during shortening, the P1 amplitude (absolute distance between
the P1 and Po, normalized by Po) and L1 were significantly higher in pCa2+
6.0
than in pCa2+
4.5 (Figure 3C). Note that the force does not reach a complete
steady state just after shortening. The reasons for such behavior may vary, but it
is likely associated with sarcomere length non-uniformities that develops with
loaded shortening during full fibre activation and/or thin filament deactivation
(Edman, 1975; Roots et al, 2007).
![Page 127: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/127.jpg)
127
Figure 3 - Force transients during length changes in different Ca2+
concentrations. (A)
Superimposed contractions showing the force increase during stretch while the fibre was activated
in pCa2+
4.5 (solid line) and pCa2+
6.0 (dashed line) (top), with corresponding changes in fibre
length (bottom). All forces were normalized by the isometric forces (Po) before the stretch. The
regression lines for the contractions produced in pCa2+
4.5 and pCa2+
6.0 are shown in blue and
red, respectively. (B) Superimposed contractions showing the force decrease during shortening
when a fibre was activated in pCa2+
4.5 (solid line) and pCa2+
6.0 (dashed line) (top), with the
corresponding length changes (bottom). (C) Closer view from the initial shortening phase,
showing that decreasing Ca2+
concentration induced an increase in L1 and P1 amplitudes. All
forces were normalized by the isometric forces (Po) before the shortening. The regression lines for
![Page 128: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/128.jpg)
128
the contractions produced in pCa2+
4.5 and pCa2+
6.0 are shown in blue and red, respectively.
Decreasing Ca2+
concentration increased L1 and P1 amplitude.
The stiffness decreased during shortening and increased during stretch
(Figure 4). The relative stiffness increased less than the force during stretch in
both pCa2+
4.5 and pCa2+
6.0, but decreased similarly during shortening in both
situations.
Figure 4 - Mean stiffness values during length changes. Mean stiffness values (+ S.E.M)
during isometric contractions (black bar), shortening (light grey bar) and stretch (dark grey bar)
from experiments performed in pCa2+
4.5 and pCa2+
6.0 (n = 13). Decreasing Ca2+
concentration
significantly decreased the stiffness in all conditions. In both pCa2+
, stiffness increased during
stretch and decreased during shortening. *
Significantly different from isometric, #
significantly
different from shortening, groups significantly different from each other.
Experiments with MgADP.
Figure 5 shows force and length traces recorded when a fibre was
stretched before and after MgADP treatment. The force was normalized by the
maximum isometric force produced before the stretch. P2 and L2 were not
![Page 129: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/129.jpg)
129
different between the two contractions (P1 and L1 were undetectable during
stretch) (Figure 5A). Figure 5B and 5C shows force and length traces recorded
during fibre shortening. L1 was longer with the presence of MgADP, while all the
other variables were not changed by MgADP (Figure 5C). The stiffness during
length changes decreased during shortening and increased during stretch (Figure
6).
Table 1 summarizes the force and length transient values obtained in the
two sets of experiments conducted in this study. Overall, during shortening P1
decreased and L1 increased at low Ca2+
concentration, whereas only L1 increased
when fibres where treated with MgADP.
Table 1. Force transients and respective half-sarcomere length extensions during
stretch and shortening
Direction Experiment P1 P2 L1 L2
Stretch i) Calcium pCa2+
4.5 - 2.51 + 0.19 - 29.83 ± 1.45
pCa2+
6.0 - 2.60 + 0.14 - 30.37 + 1.81
ii) MgADP Control - 2.48 + 0.14 - 27.33 + 0.70
MgADP - 2.47 + 0.21 25.28 + 1.71
Shortening i) Calcium pCa2+
4.5 0.85 + 0.02 0.28 + 0.04 4.48 + 0.25 29.51 + 1.67
pCa2+
6.0 0.78 + 0.02 * 0.19 + 0.07 5.26 + 0.17 * 30.17 + 1.49
ii) MgADP Control 0.80 + 0.03 0.09 + 0.14 4.34 + 0.19 26.77 + 0.94
MgADP 0.78 + 0.04 0.17 + 0.09 5.52 + 0.20 * 26.73 + 0.74
Legend: (i) Experiments performed with fibres activated in different Ca
2+ concentrations (n = 13).
(ii) Experiments performed with fibres treated with MgADP (n = 7). P1 and P2 correspond to the
force/isometric force (P/Po). L1 and L2 correspond to the half sarcomere extension obtained at P1
and P2, and are given in nm.HS-1
. * Significantly different from control.
![Page 130: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/130.jpg)
130
Figure 5 - Force transients during length changes in fibres treated with MgADP. (A)
Superimposed contractions showing the force increase during stretch (top) when the fibre was
activated in pCa2+
4.5 (solid line) and treated with MgADP (dashed line). The corresponding
length changes are show in the bottom panels. All forces were normalized by the isometric forces
(Po) before the stretch. The regression lines for the contractions produced in pCa2+
4.5 and in
presence of MgADP are shown in blue and red, respectively. (B) Superimposed contractions
showing the force decrease during shortening (top) when a fibre was activated at pCa2+
4.5 (solid
line) and treated with MgADP (dashed line). The corresponding changes in fibre length are shown
in the bottom. (C) Closer view from the initial shortening phase showing that MgADP activation
![Page 131: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/131.jpg)
131
induced an increase in L1. All forces were normalized by the isometric forces (Po) before the
shortening. The regression lines for the contractions produced in pCa2+
4.5 before and after
MgADP treatment are shown in blue and red, respectively. MgADP treatment increased L1
significantly, while it did not change the other variables.
Figure 6 - Mean stiffness values during length changes. Mean stiffness values (+ S.E.M)
during isometric contraction (black bar), shortening (light grey bar) and stretch (dark grey bar)
obtained in experiments performed in pCa2+
4.5 before and after MgADP treatment (n = 7).
MgADP did not affect stiffness, but in stiffness was always increased during stretch and decreased
during shortening. *
Significantly different from isometric contractions, #
significantly different
from shortening.
3.2.4.2 Residual force enhancement and depression
Experiments with different Ca2+
concentrations.
Figure 7 shows an experiment with three superimposed contractions
produced in pCa2+
4.5 in different SLs. The steady-state isometric forces after
stretch and shortening were higher and lower, respectively, than the force
produced during the isometric contraction at the corresponding length, as shown
before (Edman et al, 1993; Julian & Morgan, 1979a; Rassier et al, 2003c; Roots et
al, 2007; Sugi & Tsuchiya, 1988). Changing Ca2+
concentration changed the
![Page 132: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/132.jpg)
132
levels of force enhancement (Figure 8A), such that the increase in force was
higher when the fibre was activated and stretched in pCa2+
6.0 than in pCa2+
4.5.
This result was confirmed statistically; although the absolute force enhancement
(4.2 + 0.8 mN.mm-2
) was independent from pCa2+
, the relative enhancement was
higher in pCa2+
6.0 (38.8 + 7.4 %) when compared to pCa2+
4.5 (14.9 + 5.6%).
Changing Ca2+
concentration did not change the effects of shortening on the long-
lasting force; the residual force depression was similar in pCa2+
4.5 and pCa2+
6.0
(Figure 8B).
Figure 7 - Typical experiment for analysis of residual force enhancement and force
depression performed in pCa2+
4.5. Superimposed force traces (upper panel), SL traces (mid
panel), and length traces (lower panel) from a fibre activated in pCa2+
4.5 and kept isometric (in
black), stretched (in red), or shortened (in blue).
![Page 133: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/133.jpg)
133
Figure 8 - Residual force changes in different Ca2+
concentrations. (A) Sample records from a
typical experiment showing superimposed contractions produced by a fibre activated in pCa2+
4.5
and pCa2+
6.0. Black: isometric contraction at SL of 2.8μm. Red: isometric contraction at SL of
2.65μm followed by a 5% stretch. The corresponding length changes are shown in the lower
panels. (B) Mean (+ S.E.M.) relative forces from fibres activated in pCa2+
4.5 and pCa2+
6.0 (n =
13) in three conditions: isometric (black bar), shortened (light grey bar) and stretched (dark grey
bar). P = forces recorded 10s after length changes; Piso = force at the respective isometric
condition. *
significantly different from isometric, #
significantly different from shortening, significantly different from the same condition (shortened) in pCa
2+ 6.0.
![Page 134: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/134.jpg)
134
In order to test if the changes in the residual force as a result of pCa2+
could be attributed to variations in the number of crossbridges attached to actin,
we compared the stiffness after length changes and during isometric contractions.
Although the absolute stiffness was higher in pCa2+
4.5 (Figure 9), the stiffness
enhancement after stretch was significantly larger in pCa2+
6.0 (15.7 + 0.08%)
than in pCa2+
4.5 (6.4 + 0.03%). The level of stiffness depression after shortening
was similar (12.3 + 2.70%) in both Ca2+
concentrations.
Figure 9 - Mean stiffness after length changes. Mean stiffness values (+ S.E.M) measured
during isometric contractions (black bar), and when forces reach a new steady state after
shortening (light grey bar) and stretch (dark grey bar) in experiments performed in pCa2+
4.5 and
pCa2+
6.0. Decreasing Ca2+
concentration decreased the stiffness in all conditions. In both pCa2+
,
the stiffness during stretch and shortening was higher and lower, respectively, than during
isometric contractions. *
Significantly different from isometric, #
significantly different from
shortening, significantly different from each other.
![Page 135: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/135.jpg)
135
Figure - 10 Residual force changes after MgADP treatment. (A) Sample records recorded
during a typical experiment in a fibre activated in pCa2+
4.5 with 10mM MgADP. Black:
isometric contraction at SL of 2.8μm. Red: isometric contraction at SL of 2.65μm followed by a
5% length stretch. Blue: isometric contraction at SL 2.95μm followed by a 5% length shortening.
Lower panel: correspondent fibre length changes. (B) Mean (+ S.E.M.) forces produced by fibres
(n = 7) activated in pCa2+
4.5 and pCa2+
4.5 + 10mM MgADP during isometric contractions (black
bar), after shortening (light grey bar) and after stretch (dark grey bar). P = forces 10s after length
changes. Piso = force produced during the respective isometric condition. *
significantly different
from isometric, # significantly different from shortening.
Experiments with MgADP.
![Page 136: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/136.jpg)
136
Figure 10A shows a typical experiment with three superimposed
contractions produced in different SL by a fibre activated in pCa2+
4.5, in a
solution containing 10 mM MgADP. As in the case of the experiments using
different pCa2+
, the forces produced after stretch and shortening were higher and
lower, respectively, than the force produced during isometric contraction.
MgADP did not affect the residual force enhancement or the force depression
(Figure 10B). However stiffness after stretch did not increase in the presence of
MgADP (Figure 11). When all experiments (Ca2+
and MgADP) are pooled, the
relation between the history-dependence of force and stiffness is apparent (Figure
12), and shows that stiffness is affected by MgADP in the force enhanced state.
Figure - 11 Mean stiffness after length changes. Mean stiffness values (+ S.E.M) measured
during isometric contractions (black bar), and when forces reach a new steady state after
shortening (light grey bar) or stretch (dark grey bar) during experiments performed in pCa2+
4.5
with and without MgADP (n = 7). *
Significantly different from isometric, #
significantly different
from shortening.
![Page 137: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/137.jpg)
137
Figure 12: Relation between force and stiffness after length changes. Mean forces (P/Piso +
S.E.M.) plotted against the mean stiffness (S/Siso + S.E.M.). Relative stiffness in MgADP after
stretch does not follow the same trend as in Ca2+
solutions. P = force measured 10s after length
changes. Piso = force at the respective isometric condition; S = stiffness measured 10s after length
changes in every condition, Siso = stiffness at the respective isometric condition.
The stiffness measurements may be affected by compliance of the
sarcomeres, and most specifically the compliance of the filaments. Although
filament compliance may account for ∼50% of the sarcomere compliance (Huxley
et al, 1994), its actual contribution to the strain-force relationship in a half-
sarcomere is unknown. Isolated thick and thin filaments stretched from zero force
to maximal physiological force develop strains of 0.3% and 1.5%, respectively
(Liu & Pollack, 2002; Neumann et al, 1998), values that are too low for account
for the changes in stiffness that we observed in this study. Most importantly, even
![Page 138: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/138.jpg)
138
if the compliance affects slightly the stiffness values that we obtained, there is no
evidence that changes in Ca2+
concentration and MgADP affects the compliance
of the filaments, and therefore the comparisons made throughout our study remain
valid.
P2-to-peak/valley amplitude.
In order to analyze the relationship between the force increase and
decrease after stretch or shortening during phase 3 and the residual forces after
length changes, we measured the relative force difference (P/Po) between the
"peak" force during stretch and P2, and between the lowest force ("valley")
obtained during shortening and P2; these were named P2-to-peak or valley
amplitude, respectively. We noticed these amplitudes were significantly greater
in pCa2+
6.0 than in pCa2+
4.5, but they were not affected when MgADP was
added to the solution (Figure 13).
Figure – 13 Difference between P2 and forces at the end of length changes (peak for stretching
and valley for shortening). Left panel: experiments performed in different pCa2+
. Right panel:
experiments performed with MgADP. ST = P/Po during stretch (light gray bar), SH = P/Po during
shortening (black bar). *
Significant difference between two groups.
![Page 139: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/139.jpg)
139
3.2.5 Discussion
The main results of this study were that decreasing Ca2+
concentrations
decreased the relative force produced during shortening and increased the force
produced after stretch; these changes were accompanied by similar changes in
stiffness. MgADP affected stiffness during shortening and after stretch, without
concomitant changes in force. These results suggest that the mechanisms of force
changes during stretch and shortening are different from those observed after the
length changes, when forces have stabilized in a new steady-state.
3.2.5.1 Transient forces during length changes
We detected differences in P1 and L1 resulting from changing Ca2+
concentrations during shortening, as previously shown (Minozzo et al, 2012). P1
changes have been attributed mainly to crossbridges engaging in specific states of
the powerstroke during shortening (Minozzo et al, 2012; Ranatunga et al, 2010;
Roots et al, 2007). In a previous study (Minozzo et al, 2012), we developed a
model to better understand the effect of crossbridges biased into myosin.ADP.Pi
(pre-powerstroke) complex on P1. We observed that biasing crossbridges towards
a pre-powerstroke state caused a decrease in isometric force and a decrease in P1
during shortening. Although the experimental data in that study also showed a
trend to decrease P1 (figure 10 from Minozzo et al, 2012), the result was not
statistically significant. In the current study, we observed that relative P1
amplitude and L1 were increased in pCa2+
6.0. At lower Ca2+
concentrations, the
absolute population of non-attached crossbridges is expected to be high; this
population can affect the transition between non-force generating to force
![Page 140: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/140.jpg)
140
generating crossbridges via a cooperativity mechanism, which is more prominent
in low than in saturating Ca2+
concentrations (Fitzsimons et al, 2001). This
interpretation is consistent with the experiments that showed a direct relationship
between stiffness and P1 at different shortening velocities (Roots et al, 2007).
MgADP altered the relation between force development and stiffness
during shortening by increasing only L1, decreasing the stiffness/force ratio.
MgADP not only induces myosin strong-binding to actin (Fukuda et al, 1998),
which in turn would “turn-on” adjacent actin binding sites leading to myosin
cooperativity (Bremel & Weber, 1972), but also decreases the rigor stiffness
without concomitant changes in force (Dantzig et al, 1999).
P2 and L2 during shortening were not affected by lowering the Ca2+
concentration. Assuming that P2 and L2 represent the critical force and length,
respectively, at which crossbridges detach during shortening, our results are
consistent with the rationale that the number of crossbridges formed before
shortening does not change the relative strain necessary for their detachment
(Minozzo et al, 2012)
The values of P2 and L2 were not affected by Ca2+
concentration during
stretch. While one previous study showed an increase in P2 when Ca2+
was
elevated (Minozzo & Rassier, 2010), and associated the increase to an enhanced
stiffness/force ratio, another study (Stienen et al, 1992) showed an increase in the
stretch forces when Ca2+
was lowered from pCa2+
4.5 to pCa2+
6.3; these authors
linked their result to a greater reliance on the rate of crossbridge detachment in
low Ca2+
concentrations. Since the relative stiffness changes were not affected by
Ca2+
concentrations, the stiffness increase during stretch did not follow the force
![Page 141: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/141.jpg)
141
increase, suggesting the later does not occur due to an increase in the number of
crossbridges attached to actin. Instead, it suggests that the force increase during
stretch can be caused either by an increase in force produced per crossbridge, or
by pre-powerstroke crossbridges resisting to stretch (Getz et al, 1998; Minozzo &
Rassier, 2010). Therefore our results are in line with our working hypothesis,
which mainly attributes force changes during stretch to crossbridges in a pre-
powerstroke state. These crossbridges would not contribute to isometric force
generation, but would have the capacity to resist to stretch.
3.2.5.2 Residual force enhancement
Contrary to our hypothesis, the residual force enhancement was ~2.6-fold
larger in pCa2+
6.0 than in pCa2+
4.5. The effect of activation on the residual
force enhancement is unclear. Rassier et al (Rassier & Herzog, 2005) did not
observe changes in the force enhancement in intact fibres isolated form the frog
and activated with different frequencies of stimulation. However, Campbell and
Moss (Campbell & Moss, 2002) observed a greater relative force increase in a
second stretch when two consecutive stretches were applied at pCa2+
6.2 compared
to pCa2+
4.5. The authors suggested that the rate at which cycling crossbridges
reach a steady state is considerably longer at lower Ca2+
concentrations.
Considering that the residual force enhancement could be caused partially by an
increase in the number of attached crossbridges, fibres activated at lower Ca2+
concentration would have a greater population of crossbridges available to attach
after stretch, which in turn could be responsible for a higher force enhancement in
lower Ca2+
concentrations.
![Page 142: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/142.jpg)
142
If it is assumed that an increase in stiffness may be caused by an increase
in the number of crossbridges attached to actin, MgADP might have eliminated
this effect. Thus, a complementary mechanism to explain the increased residual
force enhancement in low Ca2+
concentration must exist, since the stiffness did
not increase as much as the force after stretch. Force enhancement has been also
associated with activation of passive structures during stretch (Bagni et al, 2004;
Cornachione & Rassier, 2012; Herzog & Leonard, 2002; Leonard & Herzog,
2010; Rassier, 2012). Titin stiffness may increase with increasing Ca2+
concentrations (Labeit et al, 2003), leading to an increased force produced during
stretch. While some studies showed an increased force when fibres lacking
myosin-actin interaction were activated with Ca2+
(Cornachione & Rassier, 2012;
Labeit et al, 2003) other studies (Stuyvers et al, 1998; Yamasaki et al, 2001)
showed that titin stiffness may decrease with increasing Ca2+
concentration.
Nevertheless, it is still temping to speculate that the increase in titin stiffness with
Ca2+
contributed to force enhancement.
Finally, we cannot exclude that the residual forces after length changes
may happen due to sarcomere/half-sarcomere length non-uniformity (Edman,
2012; Morgan, 1994; Rassier, 2012), a mechanism that would be also in line with
the differences found when fibres were activated in different pCa2+
. Accordingly,
activation would lead to a population of sarcomeres that would elongate more,
decreasing their amount of overlap until passive forces would emerge, while other
sarcomeres would elongate less. The “weak” sarcomeres that would continuously
elongate would reach a tension borne by passive elements that would equal the
tension of the “strong”, shorter sarcomeres. It has been shown that myofibrils
![Page 143: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/143.jpg)
143
stretched at low Ca2+
concentrations presented more sarcomeres “yielding”
(weakening) than at high Ca2+
concentration (Shimamoto et al, 2009). Assuming
the same happened in our experiments, activation in pCa2+
6.0 could have
generated more sarcomere non-uniformity, causing a greater force enhancement
than fibres activated in pCa2+
4.5.
3.2.5.3 Residual force depression
The changes in stiffness accompanied the changes in force after
shortening, suggesting a decrease in the number of attached crossbridges, as
previously observed (Sugi & Tsuchiya, 1988). Force depression has been
attributed to crossbridge inhibition caused by angular distortion of the actin
binding sites induced by shortening after activation (Marechal & Plaghki, 1979;
Pun et al, 2010). Changing Ca2+
concentrations did not change the residual force
depression. This confirms our hypothesis that the number of crossbridges attached
previously to shortening would not change the relative levels of force depression
since the crossbridge inhibition mechanism is mainly dependent on the amount of
new overlap zone formed between the two filaments after shortening.
The mechanisms proposing an inhibition of crossbridges attached in a
newly overlap zone was strengthened in a previous study that we performed with
isolated myofibrils (Pun et al. 2010). In that study the levels of force depression
were decreased by MgADP activation, suggesting that activation via
cooperativety counteracted part of the crossbridges inhibition caused by
shortening. Differently, in the present study the residual force depression was not
affected by MgADP activation. In the current study fibres were activated in
saturating Ca2+
levels together with higher levels of MgADP (~4 times higher
![Page 144: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/144.jpg)
144
than in the previous study). In this situation, the role of myosin cooperativity in
the force inhibition is likely decreased, as MgADP competes with MgATP for the
myosin binding site; the more ATP the lesser the influence of MgADP and
cooperativity on fibre activation (Fukuda et al, 1998). The reason MgADP was
added to Ca2+
solution in the present study was that we did not want only to work
with activation via cooperativity - in fact, we were interested in biasing a
relatively large proportion of crossbridges into strong-bound states, expecting an
opposite effect to what was previously observed with blebbistatin (Minozzo et al,
2012; Minozzo & Rassier, 2010).
3.2.5.4 Relation between the transient force and the residual forces
The relation between the force during and after length changes (phase 4)
remains unclear. Edman and Tsuchiya (Edman & Tsuchiya, 1996) found a strong
relationship between the level of force increase after P2 and the level of residual
force enhancement. They interpreted this first increase to a damping effect of
“weak sarcomeres” working in parallel to elastic elements - this increase would be
attenuated due to the release of elastic strain, but not cease after stretch. Assuming
that fibres activated in low Ca2+
would allow more sarcomere “weakening" during
and after stretch than at high Ca2+
concentration, one would expect that force
increase after P2 would also be increased when Ca2+
concentration is lowered.
Conversely, assuming that MgADP did not affect SL non-uniformity, it would not
alter the relation between these two phases of force increase. We found that the
levels of force enhancement after P2 were accompanied by similar levels of force
enhancement at different Ca2+
concentrations and when fibres were treated with
MgADP. Nevertheless, the relative force decline during shortening was more
![Page 145: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/145.jpg)
145
pronounced at pCa2+
6.0 than in pCa2+
4.5. Considering thin filament deactivation
the main mechanism for residual force depression (Marechal & Plaghki, 1979),
force decline after P2 could only be partially attributed to this mechanism (see
Roots et al. 2007). Apparently, distinct mechanisms are responsible also for force
behavior after P2 in stretch and shortening.
![Page 146: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/146.jpg)
146
4 Muscle residual force enhancement
4.1 Preface
It has been suggested that force enhancement after stretch is caused by
non-uniformities in sarcomere length (Morgan, 1990; Morgan, 1994). This
hypothesis has been tested in different laboratories with contradictory results and
interpretations (Edman, 2012; Herzog et al, 2006; Herzog & Leonard, 2006;
Morgan, 1994; Morgan & Proske, 2007; Rassier, 2012; Rassier & Herzog,
2004b). Recently, our laboratory challenged this theory by testing minimal
preparations that enabled tracking of individual sarcomeres from isolated
myofibrils (Pun et al, 2010; Rassier et al, 2003a), or that used mechanically
isolated single sarcomeres (Pavlov et al, 2009a; Rassier & Pavlov, 2012). We
observed force enhancement in individual sarcomeres. However, these studies
suggest that force enhancement may be partially attributed to half-sarcomere
length non-uniformities, and partially to sarcomeric properties (e.g. changes in
crossbridge kinetics). However, to directly evaluate this hypothesis we needed to
perform measurements in half-sarcomeres, a preparation never developed prior to
this study. Hence, the goal of our study was to (i) develop a technique to isolate
and perform mechanical measurements in half-sarcomeres, and (ii) to evaluate if
force enhancement after stretch was present in half-sarcomeres, , which would
show that force enhancement can be linked to sarcomeric proteins.
![Page 147: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/147.jpg)
147
4.2 Force produced after stretch in sarcomeres and half-sarcomeres isolated
from skeletal muscles
Fábio C. Minozzo
Bruno M. Baroni
José A. Correa
Marco A. Vaz
Dilson E. Rassier
Reprint from: Scientific Reports. 2013. (3):2320. doi:10.1038/srep02320
![Page 148: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/148.jpg)
148
4.2.1 Abstract
The goal of this study was to evaluate if isolated sarcomeres and half-
sarcomeres produce a long-lasting increase in force after a stretch is imposed
during activation. Single and half-sarcomeres were isolated from myofibrils using
micro-needles, which were also used for force measurements. After full force
development, both preparations were stretched by different magnitudes. The
sarcomere length (SL) or half-sarcomere length variations (HSL) were extracted
by measuring the initial and final distances from the Z-line to the adjacent Z-line
or to a region externally adjacent to the M-line of the sarcomere, respectively.
Half-sarcomeres generated approximately the same amount of isometric force
(29.0 ± SD 15.5 nN.μm-2
) as single sarcomeres (32.1 ± SD 15.3 nN.μm-2
) when
activated. In both cases, the steady-state forces after stretch were higher than the
forces during isometric contractions at similar conditions. The results suggest that
stretch-induced force enhancement is partly caused by proteins within the half-
sarcomere.
![Page 149: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/149.jpg)
149
4.2.2 Introduction
When an activated muscle is stretched during activation, the force that is
being produced increases significantly. After the stretch, the force declines but
remains higher than that produced during isometric contractions at corresponding
lengths (Abbott & Aubert, 1952). The mechanism behind this long-last increase in
force is unknown. Sarcomere length non-uniformities (Morgan, 1990; Morgan,
1994) that develop during activation and after stretch (Julian & Morgan, 1979a)
have been commonly used to explain the residual force enhancement, but this
hypothesis has been challenged by studies performed with isolated myofibrils,
which allow tracking of individual sarcomeres (Pun et al, 2010; Rassier et al,
2003a), and more tellingly by studies performed with individual sarcomeres
(Pavlov et al, 2009a; Rassier & Pavlov, 2012). The latter are particularly
important; it was observed that single sarcomeres produce force enhancement
when stretched during activation (Rassier & Pavlov, 2012).
In one of these studies (Rassier & Pavlov, 2012), significant A-band
displacements toward one of the sides of the sarcomeres during activation and
stretch were observed, corroborating previous findings showing non-uniform
behavior of half-sarcomeres in myofibrils during contractions (Telley et al, 2006a)
and after stretch (Telley et al, 2006b). The amount of A-band displacement was
significantly correlated to the levels of force enhancement (Rassier & Pavlov,
2012), suggesting that half-sarcomere length could play a role in force
enhancement. Accordingly, one of the half-sides of the sarcomere would be
stronger after stretch due to an increase in filament overlap, while titin from the
other half would be strained, ultimately contributing to the overall extra gain in
![Page 150: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/150.jpg)
150
force. In fact, a recent model that simulated force behaviour after stretch
considering non-uniform half-sarcomeres was able to predict force enhancement
at levels that were similar to those observed experimentally – between 2% and
~13% (Campbell et al, 2011).
The next logical step in the evaluation of the mechanisms behind the
stretch-induced force enhancement is evaluating the effects of stretch on half-
sarcomeres, which has been impossible so far due to technical limitations. We
developed a technique that allows, for the first time, experiments to be performed
with mechanically isolated half-sarcomeres. Our first goal was to test if half-
sarcomeres would reliably contract when activated, generating levels of force in
line with those previously reported in larger preparations. Our second goal was to
test if half-sarcomeres would produce an increase in force during stretch, and if
the force would remain elevated after the end of the stretch. The latter would
indicate that the residual force enhancement commonly seen in larger preparations
is a phenomenon associated with the half sarcomere, a preparation where A-band
movements during activation and stretch are prevented.
4.2.3 Results
Isolated half-sarcomeres generated approximately the same amount of
force (29.0 ± 15.5 -2
, n=17) as single sarcomeres (32.1 ± 15.3 -2
,
n=18) during isometric contractions. These levels of force are slightly lower than
previously reported (Pavlov et al, 2009a; Rassier & Pavlov, 2012); the difference
may be due to temperature, as the current study used 10°C, lower than previous
![Page 151: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/151.jpg)
151
studies that used 15°C (Pavlov et al, 2009a) or 20°C (Pavlov et al, 2009a; Pavlov
et al, 2009b).
![Page 152: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/152.jpg)
152
Figure 1 – Typical experiment overview. A - Superimposed force traces (upper panel) and
length traces (lower panel), from a single sarcomere activated in pCa2+
4.5 and kept isometric (in
black) or stretched during activation (in red). B - Superimposed force traces (upper panel) and
length traces (lower panel), from a half-sarcomere activated in pCa2+
4.5 and kept isometric (in
black) or stretched (in red). In both cases, force enhancement (FE) was calculated as the difference
between the isometric (in black) and steady state force (in red) achieved after stretch. Note that for
the actual FE calculation, the passive component was also taken into account.
Figure 1 shows superimposed force traces obtained during an experiment
with a single sarcomere (A), and a half-sarcomere (B). In both cases, the steady-
state forces after stretch were higher than the force produced during the isometric
contraction at the corresponding SL and HSL. Passive forces were taken into
account when calculating the amount of force enhancement; the passive-tension-
curve was derived from another set of sarcomeres that were passively stretched
from ~2.5 to 4.0 μm. Figure 2 shows the pooled data from both groups plotted
over a predicted force-length curve based on the filament lengths of rabbit psoas
(Sosa et al, 1994).
An ANCOVA model showed that, after adjusting for the amount of stretch
applied to the sarcomeres and half sarcomeres, there was a significant difference
in the average force produced after stretch when compared to the isometric
contractions (p = 0.0004). However, we did not observe differences between the
two groups (sarcomeres and half-sarcomeres) (p = 0.3). There was no interaction
between the group (sarcomere, half-sarcomere) and the condition (isometric, after
stretch), implying that the difference in mean force after stretch is independent of
the preparation. The statistical results are shown in details in Tables 1 and 2. Note
that this table summarizes only the experiments that were used in the ANCOVA
analysis; outliers and experiments which were not completed are not presented in
here.
![Page 153: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/153.jpg)
153
Table 1. Force (in nN.μm-2
) produced by half-sarcomeres and single sarcomeres
during isometric contractions, and contractions in which a stretch was imposed
during full activation. The adjusted means are the results of adjusting the force
values for the amount of stretch using the ANCOVA analysis.
Force produced
during isometric
contraction
Force produced
after stretch
Mean (±SD) Adjusted
mean (±SEM)
Mean (±SD) Adjusted mean
(±SEM)
Half-sarcomere
(n = 10)
24.7 ± 9.5 24.6 ± 3.6 37.7 ± 7.3 37.6 ± 2.1
Single
sarcomere
(n = 14)
30.8 ± 11.9 30.9 ± 3.0 37.4 ± 5.5 37.5 ± 1.8
Table 2. Results of the ANCOVA analysis when comparing the conditions (after
stretch and during the isometric contraction) and the group (single sarcomeres and
half-sarcomeres), adjusted for the amount of stretch. SE: Standard error of the
mean difference. CI: Confidence interval of the mean difference.
Force (nN.μm-2
) Mean Difference SE Adjusted 95% CI
Force produced
after stretch vs.
during isometric
contraction
9.8 2.4 (4.9, 14.7)
Force produced by
half-sarcomeres vs.
single sarcomeres
3.1 3.1 (3.3, 9.5)
![Page 154: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/154.jpg)
154
Figure 2 – Mean force values (±SD) produced by single and half-sarcomeres. Predictive force-
length relationship, constructed based on the filament lengths of rabbit psoas (Sosa et al, 1994)
Mean isometric forces (±SD) produced by single (black closed symbols) and half-sarcomeres
(black open symbols). The dashed line corresponds to exemplary passive force curves derived
from two sets of experiments with relaxed sarcomeres (small crosses), the dash-dotted line
corresponds to the descending limb of the force-length relationship, the continuous line
corresponds to the sum of the predictive force-length relationship to the passive curve. The mean
forces after a stretch are shown in red for single sarcomeres (closed-triangle) and half sarcomeres
(opened-triangle). The circles represent mean force values (±SD) from isometric contractions
performed close to the plateau of the force-length relation, while the squares represent mean (±SD)
values from isometric contractions performed at longer SL and HSL.
4.2.4 Discussion
This is the first study that shows the feasibility of mechanically
isolating and testing half-sarcomeres from striated muscles. The preparation may
open opportunities for future studies on the mechanics of striated muscles with
far-reaching implications; the half-sarcomere is the smallest functional unit of
![Page 155: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/155.jpg)
155
muscle that contains all molecules in a three-dimensional intact lattice. The forces
produced by the half-sarcomeres are within the range of those observed in larger
preparations, including sarcomeres (Pavlov et al, 2009a; Pavlov et al, 2009b;
Rassier & Pavlov, 2012), myofibrils (Bartoo et al, 1993; de Tombe et al, 2007;
Pun et al, 2010; Rassier, 2008) , and cells (Minozzo et al, 2012; Minozzo &
Rassier, 2010; Stienen et al, 1992). Most importantly, in the context of the current
study, our results show that the force produced by the half-sarcomeres is
significantly increased during stretch, and it remains enhanced after stretch.
Although it is difficult to directly compare the forces after stretch with the force
produced at precisely similar lengths with this preparation, our results indicate
clearly that half-sarcomeres can produce a long-lasting force enhancement. When
we compared the forces after stretch with forces produced at isometric
contractions at relatively similar lengths, and most directly when we compare the
same forces with the predicted force-length relation curve for isometric
contractions based on the degree of filament overlap (Gordon et al, 1966) using
the filament length from the rabbit psoas muscles (Sosa et al, 1994), they are
clearly elevated. This result suggests a mechanism other than HSL non-uniformity
in force enhancement.
Previously, we showed that single sarcomeres were able to produce
residual force enhancement (Rassier & Pavlov, 2012). We attributed the
phenomenon partially to A-band displacements that happen during activation and
stretch. We suggested that force enhancement was caused partly by half-
sarcomere length non-uniformities, and partly by passive components present
within the half-sarcomeres, although we have not measured the mechanics of half-
![Page 156: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/156.jpg)
156
sarcomeres. In the current study we confirmed that elements within the half-
sarcomere can produce a stretch-induced force enhancement, as the average
steady state force produced when half-sarcomeres were stretched after activation
was ~20% higher than their corresponding average isometric reference. The most
likely mechanisms that can explain force enhancement in isolated half-sarcomeres
are an increase in the number of attached crossbridges after stretch, and/or an
increase in the stiffness of titin upon muscle activation (Cornachione & Rassier,
2012; Labeit et al, 2003). Recent studies suggest that the increase in stiffness after
stretch is in fact caused by an increase in the stiffness of titin (Colombini et al,
2010; Cornachione & Rassier, 2012), which could also explain our results with
half-sarcomeres. Titin molecule becomes stiffer upon Ca2+
binding (Labeit et al,
2003), which can lead to an increased force after stretch (Cornachione & Rassier,
2012).
Based on expected forces to be produced during isometric contractions,
confirmed by the isometric forces that we measured in this study that falls into the
well-defined force-length relation (Gordon et al, 1966), the levels of a stretch-
induced increase in force is in the same order of magnitude as reported in
previous studies (Pavlov et al, 2009a). However, our results are in stunning
contradiction with a previous study using myofibrils, which found extremely
larger levels of force enhancement (>250%) after stretch (Leonard & Herzog,
2010). In that study, myofibrils were stretched by approximately 40% SL along
the descending limb of the force-length relation. We could not repeat such
experiments; stretches of similar magnitude invariably cause irreversible damage
to the preparations.
![Page 157: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/157.jpg)
157
Although single sarcomere and half-sarcomere preparations offer
innumerous advantages with a large potential for the study of molecular
mechanics of striated muscles, they also have a few limitations when compared to
larger preparations (i.e. single fibres and muscle bundles). First, the number of
contractions that can be elicited with these preparations before a decrease in force
is observed (likely due to damage) is reduced to three to four activations, which
makes its use limited according to the goals of the study. Second, it is very
difficult to control the amount of half-sarcomere shortening during activation and
contractions. This limitation also makes difficult to control the actual magnitude
of stretch that is imposed to the preparation during experiments. Lastly, inserting
a micro-needle inside the preparations is invasive, and could interfere with its
contractile properties. It could change the myosin-to-myosin filaments spacing
altering the probability of myosin-actin interactions in certain regions of the half-
sarcomere. Although we were not able to overcome these limitations, our results
show force traces that not only resemble the behaviour of larger preparations
(activation and relaxation), but are also within the range of values of force
produced by larger preparations, including sarcomeres (Pavlov et al, 2009a;
Pavlov et al, 2009b; Rassier & Pavlov, 2012) myofibrils (Bartoo et al, 1993; de
Tombe et al, 2007; Pun et al, 2010; Rassier 2008) and cells (Minozzo & Rassier,
2010; Minozzo et al, 2012; Stienen et al, 1992). Thus, we are confident that our
results are reliable and represent the true contractile activity of the sarcomeres and
half-sarcomeres.
In conclusion, we presented an experimental preparation that can be used
to test the mechanics of the most basic contractile unit of striated muscles: the
![Page 158: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/158.jpg)
158
half-sarcomere. The forces produced by half-sarcomeres are similar to those
produced by larger preparations, providing confidence that they are not damaged
and can be used for solving a variety of issues in the field of muscle biophysics.
The half sarcomeres produce a long-lasting increase in force after stretch,
suggesting that sarcomeric components are involved in residual force
enhancement. We suggest that titin is such component – future work should test
directly this hypothesis.
4.2.5 Methods
4.2.5.1 Preparation of the single and half-sarcomeres
Single and half sarcomeres were isolated from rabbit psoas muscle using a
modified procedure explained previously by our group (Pavlov et al, 2009a).
Briefly, small bundles of the muscles were tied to wooden sticks, and chemically
permeabilized using a standard protocol (Rassier & Pavlov, 2012) The muscles
were incubated in rigor solution (pH = 7.0) for approximately 4 hours, after which
they were transferred to a rigor:glycerol (50:50) solution for 20 hours. The
samples were placed in a new rigor:glycerol (50:50) solution with the addition of
a mixture of protease inhibitors (Roche Diagnostics, USA) and stored in a freezer
(−20°C) for at least seven days. The protocol was approved by the McGill
University Animal Care Committee and complied with the guidelines of the
Canadian Council on Animal Care.
On the day of the experiment, a muscle sample was transferred to a fresh
rigor solution and stored in the fridge for one hour before use. A small section of
the sample was extracted (~1 mm3) and homogenized in a rigor solution (pH =
![Page 159: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/159.jpg)
159
7.0) using the following sequence: twice for 5 s at 7,500 rpm, and once for 3 s at
18,000 rpm. The homogenizing protocol produces a supernatant containing single
myofibrils. This homogenate was transferred into an experimental chamber with
the bottom made of a vacuum grease-sealed glass coverslip (thickness: 0.15 mm),
placed on the stage of an inverted microscope (NIKON Eclipse TE 2000U). The
chamber was filled with rigor solution, and the temperature was controlled at
~10°C with a circulating cooling solution running through a channel surrounding
the chamber. The sample was rinsed several times, and after a rest period of 5
min, the rigor solution was slowly exchanged by a relaxing solution. A myofibril
was chosen based on its striation appearance, and either a single sarcomere or a
half sarcomere was selected for mechanical experimentation.
4.2.5.2 Micro-needle production and calibration
The micro-needles were produced with a vertical pipette puller (KOPF
720, David Kopf Instruments) and calibrated by a cross-bending method (Pavlov
et al, 2009a), using a pair of micro-fabricated cantilevers of known stiffness (489
and 592 nN/μm). The final stiffness of the micro-needles used during these
experiments varied between 35 and 400 nN/μm.
4.2.5.3 Mechanical isolation, visualization, and force measurement of single and
half-sarcomeres
Using micromanipulators (Narishige NT-88-V3, Tokyo, Japan), single
sarcomeres or half-sarcomeres were captured by two pre-calibrated micro-needles
(Figures 3 and 4). The dimensions of the micro-needles were similar to those used
in our previous study using single sarcomeres; the needles present a conical-
shaped tip, and only a small length (~1.5 µm, Figure 3 in red) is inserted into the
![Page 160: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/160.jpg)
160
myofibril. The diameters of the circular cross-sectional area of the portion of the
cone inside the myofibril are normally bellow ~0.5-0.7 µm, while its tip is under
0.2 µm.
Figure 3 – Needle dimensions. Tip of a glass micro-needle piercing a myofibril (on the left)
externally adjacent to the Z-line from one if its sarcomeres. The figure shows representative
measurements (on the top-left, yellow arrows) of five arbitrary cross-sectional areas of the conical-
shaped tip of the needle. The red arrow represents how much of this tip was inserted in the
myofibril; this value was never higher than 1.5μm. Magnification = 150X.
The needles were pierced externally adjacent to Z-lines in the case of sarcomeres
(Figure 4D), or between the Z-line and internally adjacent to the M-line (Figure
4B, 4C). The samples were raised from the glass coverslip by ~0.5-1.0μm. Under
high magnification provided by an oil immersion phase-contrast lens (Nikon plan-
fluor, x100, numerical aperture 1.30), the images of the single and half-
sarcomeres were further magnified 1.5x by an internal microscope function. The
contrast between the micro-needles produces a pattern of light intensity peaks that
![Page 161: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/161.jpg)
161
allow for tracking of their centroids using a particle tracker algorithm (Sbalzarini
& Koumoutsakos, 2005). The half-sarcomere length was obtained by interpolating
the displacement of the micro-needles from the initial to the final distances
measured from the Z-line to the center of the sarcomere. The force produced
during activation of the single and half-sarcomeres was obtained by measuring the
displacement of the micro-needles, as described elsewhere (Pavlov et al, 2009a).
4.2.5.3 Solutions
The rigor solution (pH 7.0) was composed of (in mM): 50 Tris, 100 NaCl,
2 KCl, 2 MgCl2, and 10 EGTA. The activating (pCa2+
of 4.5) and relaxing (pCa2+
of 9.0) - pH 7.0- solutions contained (in mM): 20 imidazole, 14.5 creatine
phosphate, 7 EGTA, 4 MgATP, 1 free Mg2+
, free Ca2+
in two concentrations
adjusted to obtain pCa2+
of 4.5 (32µM) and 9.0 (1nM); KCl was used to adjust the
ionic strength to 180 mM in all solutions.
4.2.5.4 Protocol
Single sarcomeres (n=18) and half-sarcomeres (n=17) were immersed in
relaxing solution for 1-2 s. The solution was rapidly replaced by an activating
solution using a computer-controlled, multichannel perfusion system (VC-6M,
Harvard Apparatus) and a double-barreled pipette (Pavlov et al, 2009a). When
surrounded by the activating solution, the preparations contracted and produced
force. Each experiment counted with 2-3 isometric contractions produced at
different lengths, and a contraction in which a stretch was imposed to the
preparation. For the isometric contractions, the sarcomeres and half sarcomeres
were passively adjusted to a desired length before activation; the nominal lengths
were chosen to be 2.7 µm and 3.0 µm for the two contractions. However,
![Page 162: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/162.jpg)
162
differently from experiments performed with larger preparations, activation of
sarcomeres and half-sarcomeres produced varying degrees of shortening, which
made it difficult to have the experiments at exactly the same lengths.
For the stretch contraction, after full force development was obtained,
single sarcomeres and half-sarcomeres were stretched by different magnitudes,
ranging from 15 - 36% of half-sarcomere length (HSL), at speeds ranging from
1.35 to 3.15 μm.s−1.HSL−1. After the end of the stretch, the myofibrils were held
isometric for at least 5 s before relaxation. Nominal length changes induced to the
preparation resulted in varying levels of actual sarcomere/half-sarcomere
stretching, which made a precise pre-determination of the final lengths difficult.
For each preparation we performed a series of passive stretches, starting at ~2.4
µm and ending at ~ 3.8 µm, with intervals of at least 10 s between stretches.
![Page 163: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/163.jpg)
163
Figure 4 – Half and single sarcomere isolation. A - Glass micro-needles approaching a single
myofibril on the microscope coverslip (magnification = 90X). B - Half-sarcomere being caught
between the micro-needles. The myofibril is still on the coverslip (magnification = 90X). C - Half-
sarcomere isolated and lifted (~2μm) from the coverslip (magnification = 150X). D - Single
sarcomere caught by the two micro-needles (magnification = 150X).
4.2.5.3 Data analysis
The results of this study are reported as means ± standard deviations (SD),
since all the data analyzed were normally distributed. To compare the mean
isometric forces between sarcomeres and half-sarcomeres, we used T-tests for
independent samples. A two-way, mixed model, analysis of covariance
![Page 164: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/164.jpg)
164
(ANCOVA) was used to compare averages of forces produced after stretch and
during isometric contractions at similar conditions, as well as the two groups
investigated in this study (sarcomeres and half-sarcomeres), after adjusting for the
amount of stretch. The mixed model ANCOVA takes into account the possible
correlation between repeated measures within each experiment because they were
subjected to both conditions (isometric and after stretch), and enabled the amount
of stretch, which may influence the levels of force enhancement, to be used as a
covariate in the model, to more accurately assess the potential differences in
forces. The assumption of homogeneity of slopes for the ANCOVA model was
checked by introducing and testing interaction effect terms between both the
groups (sarcomere and half-sarcomere) and the conditions (isometric, after
stretch), and the covariate (amount of stretch). The assumptions of linearity,
normality and equal variances of errors, as well as the presence of possible
outliers, were explored with analysis of residuals. The statistical analyses were
carried out with SAS software (version 9.2). All hypothesis tests were two-sided
and performed at the 0.05 significance level.
![Page 165: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/165.jpg)
165
5 Final considerations
5.1 Summary and conclusion
The results from the first study presented in this thesis showed that the
force produced during stretch of muscle fibres was considerably increased when
treated with the myosin inhibitor blebbistatin, whereas it was moderately
increased with Ca2+
concentration. The critical force (Pc), a measurement of the
force produced at the crossbridge rupture point, was largely influenced by the
number of crossbridges in the pre-powerstroke state prior to stretch, which was
accompanied by an increase in the critical length (Lc) associated with the
maximum crossbridge extension for detachment from actin. These results suggest
that pre-powerstroke crossbridges are largely responsible for the force increase
during stretch. These crossbridges are less strained than crossbridges in the
strong-bound state, which explains why Lc increases in the presence of
blebbistatin. Increasing Ca2+
concentration also increased the Pc, by mechanisms
likely associated with the attachment of additional crossbridges during stretch.
Our second study showed that blebbistatin decreased forces during muscle
shortening. However, blebbistatin only affected P1, assumedly related to the point
where crossbridges start the powerstroke. We developed a model to better
understand the effects of blebbistatin, and observed that blebbistatin biased
crossbridges into a pre-powerstroke state by hindering crossbridge attachment to
actin. We did not find any significant effects of Ca2+
on force produced during
shortening. Critical force (P2) was not affected by blebbistatin or by changing
Ca2+
levels. These results led us to conclude that force development during
![Page 166: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/166.jpg)
166
shortening is dominated by a strain dependency that is different from the force
produced during stretch, as length changes happen in the same direction of the
powerstroke; biasing crossbridges into pre-powerstroke states does not affect the
point where they detach during shortening.
In the third study we investigated force development during and after
stretch and shortening, with their relation with the residual force changes. By
changing Ca2+
concentrations during the experiments, we concluded that critical
forces (P2) are not affected by the number of attached crossbridges. The stretch
forces were not significantly altered by Ca2+
, whereas P1 amplitude and L1 during
shortening were increased with decreasing Ca2+
concentrations. We speculate that
the slight increase in P1 amplitude and L1 during shortening occurred due to a
delay on the crossbridges' onset of powerstroke, likely caused by the slow
engagement of “non-bound” to pre-stroke crossbridges (v. Campbell & Moss,
2002). We also observed an increase in L1 induced by MgADP during shortening,
which may be linked to a decrease in the stiffness-to-force ratio caused by
MgADP. Changing Ca2+
concentration did not affect the residual force
depression. However, contrary to our hypothesis, decreasing Ca2+
concentration
increased the levels of force enhancement after stretch. This might have occurred
due to an increase i) in the number of available crossbridges to bind to actin, or ii)
in SL non-uniformity. Finally, adding MgADP did not alter force depression or
enhancement, but MgADP inhibited an increase in stiffness, suggesting that an
increase in the number of crossbridges attached to actin cannot fully account for
force enhancement.
![Page 167: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/167.jpg)
167
The main goal of the forth study was to check if residual force
enhancement could be only attributed to non-uniformities in half-sarcomeres or if
it also resides within the half-sarcomere, as partially suggested by our third study.
The results showed that force enhancement was present in half-sarcomeres,
suggesting either an increase in the amount of crossbridges induced by stretch or
titin stiffening upon Ca2+
activation.
In conclusion, the studies presented in this thesis suggest that force
development during stretch is largely caused by crossbridges in pre-powerstroke
state, while force development during shortening is only slightly affected by
crossbridges in pre-powerstroke state; more specifically only during the fastest
phase of force changes. The residual force enhancement is caused by
complementary mechanisms; we speculate: i) an increase in the number of
attached crossbridges to actin, and ii) half-sarcomere non-uniformities, and iii)
titin stiffening upon Ca2+
activation. Finally, the residual force depression is
largely caused by crossbridge deactivation upon muscle shortening.
5.2 Future directions
The four studies in this thesis demonstrate that changes in crossbridge
kinetics mostly govern the mechanisms of force development during length
changes, while they are only partially involved in the force behaviour after length
changes.
During the development of these studies, several questions were raised.
Among these questions, it is worth noting the following: 1: Based on the
indications that the number of myosin crossbridges increases during stretch and
![Page 168: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/168.jpg)
168
decreases during shortening after P2, what are the underlying mechanisms and
how do they possibly relate and/or explain the residual force changes? 2: What is
the mechanism causing force enhancement in half-sarcomeres?
Changes in crossbridge kinetics during stretch or shortening could be
elicited via conformational alterations on the actin filament that would lead to
changes in the number of available myosin binding sites. One way to test this
hypothesis would be first checking if the force produced after pulling or pushing
two sets of isolated thick and thin filaments would be enhanced or depressed in
relation to when force is produced by the two sets sliding past each other, when
reaching a similar amount of overlap. If there is no force enhancement or
depression in bare actin filaments, residual force behaviour could be related to
crossbridge kinetics through Ca2+
regulation of the thin filament. In order to
further test this mechanism, the next step would be performing the same
experiment but using actin filaments containing the regulatory proteins (i.e.
troponin and tropomyosin) where interaction between myosin and actin is
regulated via Ca2+
binding to troponin, that induces displacement of tropomyosin,
revealing the myosin binding sites. If regulated actin filaments present force
enhancement or depression, the increase/decrease in the number of myosin
binding sites could be the mechanism responsible for the changes in number of
crossbridges induced by stretch or shortening during muscle activation.
Finally, we suggested that titin could become stiffer in the presence of
Ca2+
and be responsible for force enhancement after stretch. However, if titin
causes a stretch-induced force enhancement, its gain in stiffness would likely be
related to its molecular conformation before Ca2+
binding and stretch. To test this
![Page 169: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/169.jpg)
169
hypothesis, we could use atomic force microscopy (AFM), where a titin molecule
adhered to a surface is attached to an atomic force cantilever. When the cantilever
is moved away from the surface, the force can be measured by tracking the tip
displacement of the cantilever. Titin molecule would be stretched from its initial
conformation to approximately its maximal contour length and released several
times; every time Ca2+
solution would be flushed at a different titin length, while a
relaxing solution wash would precede every cycle.
![Page 170: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/170.jpg)
170
Reference list
Abbott BC, Aubert X (1952) The force exerted by active striated muscle during
and after change of length. JPhysiol 117: 77-86
Abbott BC, Aubert XM, Hill AV (1951) The absorption of work by a muscle
stretched during a single twitch or a short tetanus. ProcRSocLond B BiolSci 139:
86-104
Allingham JS, Klenchin VA, Rayment I (2006) Actin-targeting natural products:
structures, properties and mechanisms of action. Cell MolLife Sci 63: 2119-2134
Allingham JS, Smith R, Rayment I (2005) The structural basis of blebbistatin
inhibition and specificity for myosin II. NatStructMolBiol 12: 378-379
Bagni MA, Cecchi G, Colombini B (2005) Crossbridge properties investigated by
fast ramp stretching of activated frog muscle fibres. JPhysiol 565: 261-268
Bagni MA, Cecchi G, Colombini B, Colomo F (2002) A non-cross-bridge
stiffness in activated frog muscle fibres. BiophysJ 82: 3118-3127
![Page 171: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/171.jpg)
171
Bagni MA, Colombini B, Geiger P, Berlinguer PR, Cecchi G (2004) Non-cross-
bridge calcium-dependent stiffness in frog muscle fibres. AmJPhysiol Cell Physiol
286: C1353-C1357
Barany M (1967) ATPase activity of myosin correlated with speed of muscle
shortening. JGenPhysiol 50: Suppl-218
Bartoo ML, Popov VI, Fearn LA, Pollack GH (1993) Active tension generation in
isolated skeletal myofibrils. JMuscle ResCell Motil 14: 498-510
Bershitsky SY, Tsaturyan AK (2002) The elementary force generation process
probed by temperature and length perturbations in muscle fibres from the rabbit.
The Journal of physiology 540: 971-988
Bickham DC, West TG, Webb MR, Woledge RC, Curtin NA, Ferenczi MA
(2011) Millisecond-scale biochemical response to change in strain. Biophys J 101:
2445-2454
Bremel RD, Weber A (1972) Cooperation within actin filament in vertebrate
skeletal muscle. NatNew Biol 238: 97-101
Bressler BH (1985) Tension responses of frog skeletal muscle to ramp and step
length changes. CanJPhysiol Pharmacol 63: 1617-1620
![Page 172: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/172.jpg)
172
Brown IE, Loeb GE (2000) Measured and modeled properties of mammalian
skeletal muscle: III. the effects of stimulus frequency on stretch-induced force
enhancement and shortening-induced force depression. Journal of muscle
research and cell motility 21: 21-31
Brunello E, Reconditi M, Elangovan R, Linari M, Sun YB, Narayanan T, Panine
P, Piazzesi G, Irving M, Lombardi V (2007) Skeletal muscle resists stretch by
rapid binding of the second motor domain of myosin to actin.
ProcNatlAcadSciUSA 104: 20114-20119
Bullimore SR, Leonard TR, Rassier DE, Herzog W (2007) History-dependence of
isometric muscle force: effect of prior stretch or shortening amplitude. JBiomech
40: 1518-1524
Campbell KS (2006) Filament compliance effects can explain tension overshoots
during force development. Biophys J 91: 4102-4109
Campbell KS, Moss RL (2002) History-dependent mechanical properties of
permeabilized rat soleus muscle fibres. BiophysJ 82: 929-943
Campbell SG, Hatfield PC, Campbell KS (2011) A mathematical model of muscle
containing heterogeneous half-sarcomeres exhibits residual force enhancement.
PLoS computational biology 7: e1002156
![Page 173: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/173.jpg)
173
Cheung A, Dantzig JA, Hollingworth S, Baylor SM, Goldman YE, Mitchison TJ,
Straight AF (2002) A small-molecule inhibitor of skeletal muscle myosin II.
Nature cell biology 4: 83-88
Chinn M, Getz EB, Cooke R, Lehman SL (2003) Force enhancement by PEG
during ramp stretches of skeletal muscle. JMuscle ResCell Motil 24: 571-578
Colombini B, Bagni MA, Cecchi G, Griffiths PJ (2007a) Effects of solution
tonicity on crossbridge properties and myosin lever arm disposition in intact frog
muscle fibres. JPhysiol 578: 337-346
Colombini B, Bagni MA, Palmini RB, Cecchi G (2005) Crossbridge formation
detected by stiffness measurements in single muscle fibres. AdvExpMedBiol 565:
127-140
Colombini B, Nocella M, Bagni MA, Griffiths PJ, Cecchi G (2010) Is the cross-
bridge stiffness proportional to tension during muscle fibre activation? Biophys J
98: 2582-2590
Colombini B, Nocella M, Benelli G, Cecchi G, Bagni MA (2007b) Crossbridge
properties during force enhancement by slow stretching in single intact frog
muscle fibres. JPhysiol 585: 607-615
![Page 174: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/174.jpg)
174
Colombini B, Nocella M, Benelli G, Cecchi G, Bagni MA (2008) Effect of
temperature on cross-bridge properties in intact frog muscle fibres. AmJPhysiol
Cell Physiol 294: C1113-C1117
Colombini B, Nocella M, Benelli G, Cecchi G, Griffiths PJ, Bagni MA (2009)
Reversal of the myosin power stroke induced by fast stretching of intact skeletal
muscle fibres. BiophysJ 97: 2922-2929
Colomo F, Lombardi V, Piazzesi G (1986) A velocity-dependent shortening
depression in the development of the force-velocity relation in frog muscle fibres.
JPhysiol 380: 227-238
Cornachione AS, Rassier DE (2012) A non-cross-bridge, static tension is present
in permeabilized skeletal muscle fibres after active force inhibition or actin
extraction. American journal of physiology Cell physiology 302: C566-574
Coupland ME, Puchert E, Ranatunga KW (2001) Temperature dependence of
active tension in mammalian (rabbit psoas) muscle fibres: effect of inorganic
phosphate. JPhysiol 536: 879-891
Daniel TL, Trimble AC, Chase PB (1998) Compliant realignment of binding sites
in muscle: transient behavior and mechanical tuning. BiophysJ 74: 1611-1621
![Page 175: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/175.jpg)
175
Dantzig JA, Barsotti RJ, Manz S, Sweeney HL, Goldman YE (1999) The ADP
release step of the smooth muscle cross-bridge cycle is not directly associated
with force generation. BiophysJ 77: 386-397
De Ruiter CJ, De Haan A, Jones DA, Sargeant AJ (1998) Shortening-induced
force depression in human adductor pollicis muscle. The Journal of physiology
507 ( Pt 2): 583-591
de Tombe PP, Belus A, Piroddi N, Scellini B, Walker JS, Martin AF, Tesi C,
Poggesi C (2007) Myofilament calcium sensitivity does not affect cross-bridge
activation-relaxation kinetics. AmJPhysiol RegulIntegrComp Physiol 292: R1129-
R1136
Edman KA (1975) Mechanical deactivation induced by active shortening in
isolated muscle fibres of the frog. JPhysiol 246: 255-275
Edman KA (1996) Fatigue vs. shortening-induced deactivation in striated muscle.
Acta Physiol Scand 156: 183-192
Edman KA (1999) The force bearing capacity of frog muscle fibres during
stretch: its relation to sarcomere length and fibre width. JPhysiol 519 Pt 2: 515-
526
![Page 176: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/176.jpg)
176
Edman KA (2012) Residual force enhancement after stretch in striated muscle. A
consequence of increased myofilament overlap? The Journal of physiology 590:
1339-1345
Edman KA, Caputo C, Lou F (1993) Depression of tetanic force induced by
loaded shortening of frog muscle fibres. JPhysiol 466: 535-552
Edman KA, Elzinga G, Noble MI (1978) Enhancement of mechanical
performance by stretch during tetanic contractions of vertebrate skeletal muscle
fibres. JPhysiol 281: 139-155
Edman KA, Elzinga G, Noble MI (1981) Critical sarcomere extension required to
recruit a decaying component of extra force during stretch in tetanic contractions
of frog skeletal muscle fibres. JGenPhysiol 78: 365-382
Edman KA, Elzinga G, Noble MI (1982) Residual force enhancement after stretch
of contracting frog single muscle fibres. JGenPhysiol 80: 769-784
Edman KA, Tsuchiya T (1996) Strain of passive elements during force
enhancement by stretch in frog muscle fibres. JPhysiol 490 ( Pt 1): 191-205
Eisenberg E, Hill TL (1985) Muscle contraction and free energy transduction in
biological systems. Science 227: 999-1006
![Page 177: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/177.jpg)
177
Eisenberg E, Hill TL, Chen Y (1980) Cross-bridge model of muscle contraction.
Quantitative analysis. BiophysJ 29: 195-227
Ettema GJ, Huijing PA, de Haan A (1992) The potentiating effect of prestretch on
the contractile performance of rat gastrocnemius medialis muscle during
subsequent shortening and isometric contractions. The Journal of experimental
biology 165: 121-136
Fabiato A (1988) Computer programs for calculating total from specified free or
free from specified total ionic concentrations in aqueous solutions containing
multiple metals and ligands. Methods Enzymol 157: 378-417
Farman GP, Tachampa K, Mateja R, Cazorla O, Lacampagne A, de Tombe PP
(2008) Blebbistatin: use as inhibitor of muscle contraction. Pflugers Arch 455:
995-1005
Fitzsimons DP, Patel JR, Campbell KS, Moss RL (2001) Cooperative
mechanisms in the activation dependence of the rate of force development in
rabbit skinned skeletal muscle fibres. JGenPhysiol 117: 133-148
Flitney FW, Hirst DG (1978) Cross-bridge detachment and sarcomere 'give'
during stretch of active frog's muscle. The Journal of physiology 276: 449-465
![Page 178: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/178.jpg)
178
Ford LE, Huxley AF, Simmons RM (1977) Tension responses to sudden length
change in stimulated frog muscle fibres near slack length. JPhysiol 269: 441-515
Fukuda N, Fujita H, Fujita T, Ishiwata S (1998) Regulatory roles of MgADP and
calcium in tension development of skinned cardiac muscle. JMuscle ResCell Motil
19: 909-921
Fusi L, Reconditi M, Linari M, Brunello E, Elangovan R, Lombardi V, Piazzesi G
(2010) The mechanism of the resistance to stretch of isometrically contracting
single muscle fibres. The Journal of physiology 588: 495-510
Getz EB, Cooke R, Lehman SL (1998) Phase transition in force during ramp
stretches of skeletal muscle. BiophysJ 75: 2971-2983
Gordon AM, Homsher E, Regnier M (2000) Regulation of contraction in striated
muscle. Physiol Rev 80: 853-924
Gordon AM, Huxley AF, Julian FJ (1966) The variation in isometric tension with
sarcomere length in vertebrate muscle fibres. JPhysiol 184: 170-192
Granzier HL, Burns DH, Pollack GH (1989) Sarcomere length dependence of the
force-velocity relation in single frog muscle fibres. BiophysJ 55: 499-507
![Page 179: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/179.jpg)
179
Granzier HL, Pollack GH (1989) Effect of active pre-shortening on isometric and
isotonic performance of single frog muscle fibres. JPhysiol 415: 299-327
Harry JD, Ward AW, Heglund NC, Morgan DL, McMahon TA (1990) Cross-
bridge cycling theories cannot explain high-speed lengthening behavior in frog
muscle. BiophysJ 57: 201-208
Herzog W, Lee EJ, Rassier DE (2006) Residual force enhancement in skeletal
muscle. JPhysiol 574: 635-642
Herzog W, Leonard TR (1997) Depression of cat soleus-forces following
isokinetic shortening. JBiomech 30: 865-872
Herzog W, Leonard TR (2000) The history dependence of force production in
mammalian skeletal muscle following stretch-shortening and shortening-stretch
cycles. JBiomech 33: 531-542
Herzog W, Leonard TR (2002) Force enhancement following stretching of
skeletal muscle: a new mechanism. JExpBiol 205: 1275-1283
Herzog W, Leonard TR (2006) Response to the (Morgan and Proske) Letter to the
Editor by Walter Herzog (on behalf of the authors) and Tim Leonard. JPhysiol
![Page 180: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/180.jpg)
180
Herzog W, Leonard TR, Wu JZ (1998) Force depression following skeletal
muscle shortening is long lasting. JBiomech 31: 1163-1168
Herzog W, Leonard TR, Wu JZ (2000) The relationship between force depression
following shortening and mechanical work in skeletal muscle. JBiomech 33: 659-
668
Herzog W, Schachar R, Leonard TR (2003) Characterization of the passive
component of force enhancement following active stretching of skeletal muscle.
JExpBiol 206: 3635-3643
Hill AV (1938) The heat of shortening and the dynamic constants of muscle.
Proceedings of the Royal Society B-Biological Sciences 126: 136-195
Hill TL. (2004) Free Energy Transduction and Biochemical Cycle Kinetics.
Hill TL, Eisenberg E, Chen YD, Podolsky RJ (1975) Some self-consistent two-
state sliding filament models of muscle contraction. Biophys J 15: 335-372
Holmes KC (1997) The swinging lever-arm hypothesis of muscle contraction.
Current biology : CB 7: R112-118
![Page 181: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/181.jpg)
181
Houdusse A, Szent-Gyorgyi AG, Cohen C (2000) Three conformational states of
scallop myosin S1. Proceedings of the National Academy of Sciences of the
United States of America 97: 11238-11243
Huxley AF (1957) Muscle structure and theories of contraction.
ProgBiophysBiophysChem 7: 255-318
Huxley AF, Niedergerke R (1954) Structural changes in muscle during
contraction; interference microscopy of living muscle fibres. Nature 173: 971-973
Huxley AF, Simmons RM (1971) Proposed mechanism of force generation in
striated muscle. Nature 233: 533-538
Huxley H, Hanson J (1954) Changes in the cross-striations of muscle during
contraction and stretch and their structural interpretation. Nature 173: 973-976
Huxley HE, Stewart A, Sosa H, Irving T (1994) X-ray diffraction measurements
of the extensibility of actin and myosin filaments in contracting muscle. BiophysJ
67: 2411-2421
Josephson RK, Stokes DR (1999) Work-dependent deactivation of a crustacean
muscle. The Journal of experimental biology 202: 2551-2565
![Page 182: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/182.jpg)
182
Joumaa V, Herzog W (2010) Force depression in single myofibrils. J Appl
Physiol 108: 356-362
Joumaa V, Leonard TR, Herzog W (2008) Residual force enhancement in
myofibrils and sarcomeres. ProcBiolSci 275: 1411-1419
Julian FJ, Morgan DL (1979a) The effect on tension of non-uniform distribution
of length changes applied to frog muscle fibres. JPhysiol 293: 379-392
Julian FJ, Morgan DL (1979b) Intersarcomere dynamics during fixed-end tetanic
contractions of frog muscle fibres. JPhysiol 293: 365-378
Julian FJ, Sollins KR, Sollins MR (1974) A model for the transient and steady-
state mechanical behavior of contracting muscle. BiophysJ 14: 546-562
Julian FJ, Sollins MR, Moss RL (1978) Sarcomere length non-uniformity in
relation to tetanic responses of stretched skeletal muscle fibres. ProcRSocLond B
BiolSci 200: 109-116
Kolega J (2004) Phototoxicity and photoinactivation of blebbistatin in UV and
visible light. BiochemBiophysResCommun 320: 1020-1025
![Page 183: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/183.jpg)
183
Koubassova NA, Bershitsky SY, Ferenczi MA, Tsaturyan AK (2008) Direct
modeling of X-ray diffraction pattern from contracting skeletal muscle. BiophysJ
95: 2880-2894
Kovacs M, Toth J, Hetenyi C, Malnasi-Csizmadia A, Sellers JR (2004)
Mechanism of blebbistatin inhibition of myosin II. JBiolChem 279: 35557-35563
Labeit D, Watanabe K, Witt C, Fujita H, Wu Y, Lahmers S, Funck T, Labeit S,
Granzier H (2003) Calcium-dependent molecular spring elements in the giant
protein titin. ProcNatlAcadSciUSA 100: 13716-13721
Lee EJ, Herzog W (2009) Shortening-induced force depression is primarily
caused by cross-bridges in strongly bound states. JBiomech
Lee HD, Herzog W (2002) Force enhancement following muscle stretch of
electrically stimulated and voluntarily activated human adductor pollicis. JPhysiol
545: 321-330
Lee HD, Herzog W (2003) Force depression following muscle shortening of
voluntarily activated and electrically stimulated human adductor pollicis. JPhysiol
551: 993-1003
![Page 184: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/184.jpg)
184
Leonard TR, Herzog W (2010) Regulation of muscle force in the absence of
actin-myosin-based cross-bridge interaction. American journal of physiology Cell
physiology 299: C14-20
Limouze J, Straight AF, Mitchison T, Sellers JR (2004) Specificity of
blebbistatin, an inhibitor of myosin II. JMuscle ResCell Motil 25: 337-341
Linari M, Caremani M, Piperio C, Brandt P, Lombardi V (2007) Stiffness and
fraction of Myosin motors responsible for active force in permeabilized muscle
fibres from rabbit psoas. BiophysJ 92: 2476-2490
Linari M, Lucii L, Reconditi M, Casoni ME, Amenitsch H, Bernstorff S, Piazzesi
G, Lombardi V (2000a) A combined mechanical and X-ray diffraction study of
stretch potentiation in single frog muscle fibres. JPhysiol 526 Pt 3: 589-596
Linari M, Piazzesi G, Dobbie I, Koubassova N, Reconditi M, Narayanan T, Diat
O, Irving M, Lombardi V (2000b) Interference fine structure and sarcomere
length dependence of the axial x-ray pattern from active single muscle fibres.
ProcNatlAcadSciUSA 97: 7226-7231
Linari M, Woledge RC, Curtin NA (2003) Energy storage during stretch of active
single fibres from frog skeletal muscle. The Journal of physiology 548: 461-474
![Page 185: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/185.jpg)
185
Liu X, Pollack GH (2002) Mechanics of F-actin characterized with
microfabricated cantilevers. BiophysJ 83: 2705-2715
Lombardi V, Piazzesi G (1990) The contractile response during steady
lengthening of stimulated frog muscle fibres. JPhysiol 431: 141-171
Marechal G, Plaghki L (1979) The deficit of the isometric tetanic tension
redeveloped after a release of frog muscle at a constant velocity. JGenPhysiol 73:
453-467
Minozzo FC, Hilbert L, Rassier DE (2012) Pre-Power-Stroke Cross-Bridges
Contribute to Force Transients during Imposed Shortening in Isolated Muscle
Fibres. PloS one 7: e29356
Minozzo FC, Rassier DE (2010) Effects of blebbistatin and Ca2+ concentration
on force produced during stretch of skeletal muscle fibres. American journal of
physiology Cell physiology 299: C1127-1135
Moreno-Gonzalez A, Fredlund J, Regnier M (2005) Cardiac troponin C (TnC) and
a site I skeletal TnC mutant alter Ca2+ versus crossbridge contribution to force in
rabbit skeletal fibres. JPhysiol 562: 873-884
Morgan DL (1990) New insights into the behavior of muscle during active
lengthening. BiophysJ 57: 209-221
![Page 186: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/186.jpg)
186
Morgan DL (1994) An explanation for residual increased tension in striated
muscle after stretch during contraction. ExpPhysiol 79: 831-838
Morgan DL, Proske U (2007) Can all residual force enhancement be explained by
sarcomere non-uniformities? JPhysiol 578: 613-615
Morgan DL, Whitehead NP, Wise AK, Gregory JE, Proske U (2000) Tension
changes in the cat soleus muscle following slow stretch or shortening of the
contracting muscle. JPhysiol 522 Pt 3: 503-513
Neumann T, Fauver M, Pollack GH (1998) Elastic properties of isolated thick
filaments measured by nanofabricated cantilevers. BiophysJ 75: 938-947
Nyitrai M, Geeves MA (2004) Adenosine diphosphate and strain sensitivity in
myosin motors. PhilosTransRSocLond B BiolSci 359: 1867-1877
Pavlov I, Novinger R, Rassier DE (2009a) The mechanical behavior of individual
sarcomeres of myofibrils isolated from rabbit psoas muscle. AmJPhysiol Cell
Physiol
Pavlov I, Novinger R, Rassier DE (2009b) Sarcomere dynamics in skeletal muscle
myofibrils during isometric contractions. JBiomech
![Page 187: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/187.jpg)
187
Peterson DR, Rassier DE, Herzog W (2004) Force enhancement in single skeletal
muscle fibres on the ascending limb of the force-length relationship. JExpBiol
207: 2787-2791
Piazzesi G, Linari M, Reconditi M, Vanzi F, Lombardi V (1997) Cross-bridge
detachment and attachment following a step stretch imposed on active single frog
muscle fibres. JPhysiol 498 ( Pt 1): 3-15
Piazzesi G, Reconditi M, Koubassova N, Decostre V, Linari M, Lucii L,
Lombardi V (2003) Temperature dependence of the force-generating process in
single fibres from frog skeletal muscle. JPhysiol 549: 93-106
Piazzesi G, Reconditi M, Linari M, Lucii L, Sun YB, Narayanan T, Boesecke P,
Lombardi V, Irving M (2002) Mechanism of force generation by myosin heads in
skeletal muscle. Nature 415: 659-662
Pinniger GJ, Bruton JD, Westerblad H, Ranatunga KW (2005) Effects of a
myosin-II inhibitor (N-benzyl-p-toluene sulphonamide, BTS) on contractile
characteristics of intact fast-twitch mammalian muscle fibres. JMuscle ResCell
Motil 26: 135-141
Pinniger GJ, Cresswell AG (2007) Residual force enhancement after lengthening
is present during submaximal plantar flexion and dorsiflexion actions in humans.
J Appl Physiol 102: 18-25
![Page 188: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/188.jpg)
188
Pinniger GJ, Ranatunga KW, Offer GW (2006) Crossbridge and non-crossbridge
contributions to tension in lengthening rat muscle: force-induced reversal of the
power stroke. JPhysiol 573: 627-643
Power GA, Rice CL, Vandervoort AA (2012a) Increased residual force
enhancement in older adults is associated with a maintenance of eccentric
strength. PloS one 7: e48044
Power GA, Rice CL, Vandervoort AA (2012b) Residual force enhancement
following eccentric induced muscle damage. J Biomech 45: 1835-1841
Pun C, Syed A, Rassier DE (2010) History-dependent properties of skeletal
muscle myofibrils contracting along the ascending limb of the force-length
relationship. ProcBiolSci 277: 475-484
Rack PM, Westbury DR (1974) The short range stiffness of active mammalian
muscle and its effect on mechanical properties. The Journal of physiology 240:
331-350
Radocaj A, Weiss T, Helsby WI, Brenner B, Kraft T (2009) Force-generating
cross-bridges during ramp-shaped releases: evidence for a new structural state.
Biophys J 96: 1430-1446
![Page 189: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/189.jpg)
189
Ramamurthy B, Yengo CM, Straight AF, Mitchison TJ, Sweeney HL (2004)
Kinetic mechanism of blebbistatin inhibition of nonmuscle myosin IIb.
Biochemistry 43: 14832-14839
Ranatunga KW (1996) Endothermic force generation in fast and slow mammalian
(rabbit) muscle fibres. BiophysJ 71: 1905-1913
Ranatunga KW, Coupland ME, Pinniger GJ, Roots H, Offer GW (2007) Force
generation examined by laser temperature-jumps in shortening and lengthening
mammalian (rabbit psoas) muscle fibres. JPhysiol 585: 263-277
Ranatunga KW, Roots H, Pinniger GJ, Offer GW (2010) Crossbridge and non-
crossbridge contributions to force in shortening and lengthening muscle.
AdvExpMedBiol 682: 207-221
Rassier DE (2008) Pre-power stroke cross bridges contribute to force during
stretch of skeletal muscle myofibrils. ProcBiolSci 275: 2577-2586
Rassier DE (2012) The mechanisms of the residual force enhancement after
stretch of skeletal muscle: non-uniformity in half-sarcomeres and stiffness of titin.
Proceedings Biological sciences / The Royal Society
Rassier DE, Herzog W (2004a) Active force inhibition and stretch-induced force
enhancement in frog muscle treated with BDM. JApplPhysiol 97: 1395-1400
![Page 190: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/190.jpg)
190
Rassier DE, Herzog W (2004b) Considerations on the history dependence of
muscle contraction. JApplPhysiol 96: 419-427
Rassier DE, Herzog W (2004c) Effects of shortening on stretch-induced force
enhancement in single skeletal muscle fibres. JBiomech 37: 1305-1312
Rassier DE, Herzog W (2005) Relationship between force and stiffness in muscle
fibres after stretch. JApplPhysiol 99: 1769-1775
Rassier DE, Herzog W, Pollack GH (2003a) Dynamics of individual sarcomeres
during and after stretch in activated single myofibrils. ProcBiolSci 270: 1735-
1740
Rassier DE, Herzog W, Pollack GH (2003b) Stretch-induced force enhancement
and stability of skeletal muscle myofibrils. AdvExpMedBiol 538: 501-515
Rassier DE, Herzog W, Wakeling J, Syme DA (2003c) Stretch-induced, steady-
state force enhancement in single skeletal muscle fibres exceeds the isometric
force at optimum fibre length. JBiomech 36: 1309-1316
Rassier DE, Pavlov I (2012) Force produced by isolated sarcomeres and half-
sarcomeres after an imposed stretch. American journal of physiology Cell
physiology 302: C240-248
![Page 191: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/191.jpg)
191
Rayment I, Holden HM, Whittaker M, Yohn CB, Lorenz M, Holmes KC,
Milligan RA (1993) Structure of the actin-myosin complex and its implications
for muscle contraction. Science 261: 58-65
Roots H, Offer GW, Ranatunga KW (2007) Comparison of the tension responses
to ramp shortening and lengthening in intact mammalian muscle fibres:
crossbridge and non-crossbridge contributions. JMuscle ResCell Motil 28: 123-
139
Roots H, Ranatunga KW (2008) An analysis of the temperature dependence of
force, during steady shortening at different velocities, in (mammalian) fast muscle
fibres. JMuscle ResCell Motil 29: 9-24
Sbalzarini IF, Koumoutsakos P (2005) Feature point tracking and trajectory
analysis for video imaging in cell biology. Journal of structural biology 151: 182-
195
Shaw MA, Ostap EM, Goldman YE (2003) Mechanism of inhibition of skeletal
muscle actomyosin by N-benzyl-p-toluenesulfonamide. Biochemistry 42: 6128-
6135
![Page 192: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/192.jpg)
192
Shimamoto Y, Suzuki M, Mikhailenko SV, Yasuda K, Ishiwata S (2009) Inter-
sarcomere coordination in muscle revealed through individual sarcomere response
to quick stretch. ProcNatlAcadSciUSA 106: 11954-11959
Shimizu H, Fujita T, Ishiwata S (1992) Regulation of tension development by
MgADP and Pi without Ca2+. Role in spontaneous tension oscillation of skeletal
muscle. BiophysJ 61: 1087-1098
Sosa H, Popp D, Ouyang G, Huxley HE (1994) Ultrastructure of skeletal muscle
fibres studied by a plunge quick freezing method: myofilament lengths. BiophysJ
67: 283-292
Stewart M, Franks-Skiba K, Cooke R (2009) Myosin regulatory light chain
phosphorylation inhibits shortening velocities of skeletal muscle fibres in the
presence of the myosin inhibitor blebbistatin. JMuscle ResCell Motil
Stienen GJ, Blange T, Schnerr MC (1978) Tension responses of frog sartorius
muscle to quick ramp-shaped shortenings and some effects of metabolic
inhibition. Pflugers Archiv : European journal of physiology 376: 97-104
Stienen GJ, Versteeg PG, Papp Z, Elzinga G (1992) Mechanical properties of
skinned rabbit psoas and soleus muscle fibres during lengthening: effects of
phosphate and Ca2+. JPhysiol 451: 503-523
![Page 193: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/193.jpg)
193
Straight AF, Cheung A, Limouze J, Chen I, Westwood NJ, Sellers JR, Mitchison
TJ (2003) Dissecting temporal and spatial control of cytokinesis with a myosin II
Inhibitor. Science 299: 1743-1747
Stuyvers BD, Miura M, Jin JP, ter Keurs HE (1998) Ca(2+)-dependence of
diastolic properties of cardiac sarcomeres: involvement of titin. Progress in
biophysics and molecular biology 69: 425-443
Sugi H, Tsuchiya T (1988) Stiffness changes during enhancement and deficit of
isometric force by slow length changes in frog skeletal muscle fibres. JPhysiol
407: 215-229
Telley IA, Denoth J, Stussi E, Pfitzer G, Stehle R (2006a) Half-sarcomere
dynamics in myofibrils during activation and relaxation studied by tracking
fluorescent markers. BiophysJ 90: 514-530
Telley IA, Stehle R, Ranatunga KW, Pfitzer G, Stussi E, Denoth J (2006b)
Dynamic behaviour of half-sarcomeres during and after stretch in activated rabbit
psoas myofibrils: sarcomere asymmetry but no 'sarcomere popping'. JPhysiol 573:
173-185
Tsuchiya T, Sugi H (1988) Muscle stiffness changes during enhancement and
deficit of isometric force in response to slow length changes. AdvExpMedBiol
226: 503-511
![Page 194: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/194.jpg)
194
Van Noten P, Van Leemputte M (2013) Force depression and relaxation kinetics
after active shortening and deactivation in mouse soleus muscle. J Biomech 46:
1021-1026
Veigel C, Molloy JE, Schmitz S, Kendrick-Jones J (2003) Load-dependent
kinetics of force production by smooth muscle myosin measured with optical
tweezers. NatCell Biol 5: 980-986
Vieth E (1989) Fitting piecewise linear regression functions to biological
responses. J Appl Physiol 67: 390-396
Vilfan A, Duke T (2003) Instabilities in the transient response of muscle.
BiophysJ 85: 818-827
Wakabayashi K, Sugimoto Y, Tanaka H, Ueno Y, Takezawa Y, Amemiya Y
(1994) X-ray diffraction evidence for the extensibility of actin and myosin
filaments during muscle contraction. Biophys J 67: 2422-2435
Wang Y, Fuchs F (2001) Interfilament spacing, Ca2+ sensitivity, and Ca2+
binding in skinned bovine cardiac muscle. JMuscle ResCell Motil 22: 251-257
![Page 195: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/195.jpg)
195
Woledge RC, Curtin NA, Linari M (2003) Energy storage during stretch of active
single fibres. Advances in experimental medicine and biology 538: 627-633;
discussion 634
Yamasaki R, Berri M, Wu Y, Trombitas K, McNabb M, Kellermayer MS, Witt C,
Labeit D, Labeit S, Greaser M, Granzier H (2001) Titin-actin interaction in mouse
myocardium: passive tension modulation and its regulation by calcium/S100A1.
BiophysJ 81: 2297-2313
Zhao Y, Kawai M (1994) Kinetic and thermodynamic studies of the cross-bridge
cycle in rabbit psoas muscle fibres. Biophys J 67: 1655-1668
![Page 196: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/196.jpg)
196
APPENDICES
Crossbridge Model Development and Analysis
1 General approach and structure of appendix
This model serves as a simple approach to understanding the contributions
of actin-myosin crossbridges (simply called crossbridges hereafter) in different
kinetic states to the force transients observed in single fibre ramp stretch and
shortening experiments. Other more comprehensive models for such studies exist,
taking into account contributions of sarcomere non-uniformities and the behavior
of other proteins than actin and myosin under the influence of ramp length
alterations. Our focus, however, is only on the very early response to ramp stretch
and shortening. The specific P1 and P2 features of force transients have been
ascribed to mostly crosbridge dynamics before (Pinniger, Ranatunga and Offer
2006, Roots, Offer and Ranatunga 2007). We can therefore explore in how far
crossbridge dynamics alone can explain the observed force transients.
To construct a simple, though realistic dynamical system to model the
stretch and shortening response, we consider two features: (1) An active
contractile element drivenby the crossbridge interaction between actin and myosin
under dynamically changing loads, (2) A passive elastic element with linear force
response to stretch, see Figure 1 in the main text.
First, we will introduce our general model. Second, we will evaluate our
model numerically, including the examination of two possible ways to account for
blebbistatin inhibition. This general model can be applied to simulate force
response curves for ramp shortening and lengthening with different ramp
![Page 197: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/197.jpg)
197
velocities. Finally, using a simplified generic model, we will investigate the
distribution into pre- and post-power-stroke crossbridges at maximal isometric
force and rule out one potential blebbistatin inhibition mechanism as a necessary
one.
2 Model development
2.1 Active contractile element
Effectively cycling crossbridges: Even at full activation of a muscle, not
all crossbridges are actively participating in the propulsion of thin filaments. At
lower activation, even less crossbridges take part in this action. We consider in
our model only those crossbridges which are effectively available for this
interaction, often referred to as actively cycling crossbridges. As an example,
when inside our model we speak of almost 100% crossbridges in states bound to
thin filament, this really means that almost 100% of those crossbridges that are
actively cycling are also bound to a thin filament. This does not mean that all
myosins present in thick filaments are bound to actin, as by our definition actually
a great number of them could effectively not be cycling. In the following we will
refer to the number of effectively cycling crossbridges as N.
Kinetic states: We imagine a population of N effectively cycling
crossbridges, and assume that changes in their total number due to overlap and
activation changes can be neglected. These crossbridges can be in three states: (1)
weak-bound, pre-powerstroke state with ADP and P bound (2) tight-bound, post-
powerstroke state with ADP bound, and (3) non-bound, i.e. without myosin
attached but ATP or ADP.P bound to the myosin catalytic pocket. We assume a
![Page 198: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/198.jpg)
198
high number of cross-bridges, so instead of treating single cross-bridges, we
follow the fraction of crossbridges in each of the kinetic states. We name these
fractions x1 , x2 and x3 for pre-powerstroke, post-powerstroke and non-bound,
respectively. When these state occupancies are multiplied by the total crossbridge
number N, the number of crossbridges in a specific state can be calculated.
As any crossbridge has to be in one of these three states, they sum up to 1:
which allows us to express x3 in terms of x1 and x2
so we have effectively reduced our system to two kinetic states.
Transitions between states: Regular crossbridge cycling can, in principle,
proceed forward and backward, and the utilization of free energy from ATP
hydrolysis biases this cycle into the forward direction (Hill 2004). As we assumed
three kinetic states which are ordered into a single kinetic cycle, we have six
transition rates between the kinetic states, see Figure S1. These define the
dynamic behavior of the crossbridge population with respect to their occupancy of
kinetic states:
![Page 199: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/199.jpg)
199
The transition rates are determined by their specific zeroth order rate
constants, substrate concentrations and force applied to the crossbridge:
In k12 and k21 the stress dependent term has been divided by 2 for an
equal partitioning of stress dependence to the forward and backward power-stroke
transition. This was chosen as the model results agree well with our data. In k13 a
“ripping” term has been introduced which bypasses the regular kinetic cycle.
When the muscle fibre is stretched, crossbridges are stressed against their regular
direction of cycling, and are therefore prone to forceful “ripping” off the actin
filament without completion of the regular crossbridge cycle. The crossbridge
“ripping” under stretch is expressed in the last term in k13. These effective
![Page 200: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/200.jpg)
200
transition k0 rates between the x states include the total number of crossbridges:
where the are zeroth order transition rate constants for single
crossbridges.
Figure S1 - Crossbridge kinetic scheme used in the general model. Three kinetic states are
assumed: (1) a pre-powerstroke state, (2) a post-powerstroke state, and (3) a non-bound state, in
which myosin is not attached to actin. The transition ratefunctions kij displayed with the arrows
between the kinetic states characterize the dynamic behavior of the cross-bridge population. Solid
arrows indicate transitions, which are part of the regular cross-bridge cycle. The dashed line is a
transition stemming from reverse stretch of pre-powerstroke myosin, which detaches from actin
without completing the regular crossbridge cycle. The transition associated with rate k13 contains
contributions from the regular crossbridge cycle as well as “ripping”, i.e. forced detachment of
myosin cross-bridges from stretch on the fibre. In the main paper, we use a reduction of this
model, where all parameters related to this forced cross-bridge “ripping” are set equal 0.
![Page 201: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/201.jpg)
201
Load dependence: The load dependence of life times (which are inverse
proportional to transition rates) of kinetic states on external load has been shown
for several slow myosin types (Veigel et al. 2003, Nyitrai and Geeves 2004,
Laakso et al. 2008). The functional form of the stress dependence found therein
corresponds with Hill’s exponential load-dependence (Hill 2004) for the power-
stroke transition, which we employed in our model.
Normalized nucleotide and P concentrations: In the transition rate expressions
we use normalized concentrations
where no subscript denotes the actual concentrations in μM and the
subscript 0 denotes the equilibrium concentration in μM. The equilibrium
concentrations are related to the free energy of hydrolysis at standard conditions
[ATP] = [ADP] = [Pi] = 1mM in the following way
where < 0 is the free energy of ATP hydrolysis of one ATP molecule
in units of kBT . According to [3] the free energy of ATP hydrolysis under
physiological conditions is = − 12. 34 in units of kBT at laboratory standard
![Page 202: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/202.jpg)
202
temperature T = 298. 15K = 25o C. The nucleotide concentrations atp and adp
only occur as a ratio in our reaction rates, sowe only need one equilibrium
concentration to normalize them. Thus we set [ATP0] = 1 without loss of
generality. We get
For equation (13) to be valid, the following relation must hold
This shows that only the equilibrium concentration [Pi,0 ] can be freely
chosen in the framework of our model. Note that by this normalization all rate
constants except those for forceful detachment are thermodynamically well-
defined with respect to heat dissipation per crossbridge cycle and the free
energy of ATP hydrolysis which takes into consideration the present
calculation o nucleotides and phosphate:
where W = F . is the mechanical work done per forward crossbridge
cycle completion.
![Page 203: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/203.jpg)
203
For a forward cycle completion, a powerstroke against an effectively
sensed force F has to be overcome along an effective step size .
2.2 Passive element with linear elasticity
In the experiment, the force P of the muscle fibre is measured. We assume,
that this force distributes equally over all attached cross-bridges, so that the same
load F is experienced by all attached crossbridges:
The force arises from stretching the muscle fibre to a length , which is
longer than the length . is the length which the molecular contractile
apparatus would attain in its current configuration without external stretch. t
denotes the time after start of the lengthening or shortening ramp. The force is
connected to the difference between actual length and molecular configuration
length by an elastic modulus , which is assumed to be constant over all
lengths of the fibre:
When we combine the equations (17) and (18) we get
![Page 204: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/204.jpg)
204
with the effective elastic modulus /N experienced by a single
crossbridge. In a ramp experiment, is typically controlled externally by the
operator, and is therefore given as an external condition. Differently,
changes dependent on the dynamic behavior of the crossbridge population. The
following differential equation
exp
describes how the rate of change of depends on the crossbridge cycle
transition rates.This expression incorporates the effective myosin step size and
the relaxation distance from a single reverse stretched pre-powerstroke
crossbridge being "ripped" off.
3 Numerical evaluation
3.1 Simulation of force curves
To implement our experiments in silico, we mimick the ramp shortening
and stretching. First, we initialize the simulation at a start time Twait < 0, whose
absolute value determines how long the fibre is held isometrically at L = 0 before
the ramp starts. This waiting time allows the fibre to contract close to the
isometric force maximum, accordingly we used the value at t = 0 as the maximal
![Page 205: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/205.jpg)
205
isometric force P0 = P(t = 0). At time t = 0 we start a ramp length change
which changes the fibre length by a maximal length change Lmax at
a constant ramp velocity vramp . vramp is in units of , which we have to choose
as a model parameter. Note that does not refer to the actual length of the
fibre, but to the length change from the isometric length. We evaluated our model
with the MatLab ode15s adaptive time step size integrator for stiff ODEs, see
Figures 2 and S2. Regular ODE integrators proved inefficient due to the rapid
changes in force right after beginning of the ramp shortening.
3.2 Detection of critical points
P1 was detected as a dominant peak in the curvature Curv of the force trace, P2
was detected as a characteristic transition in log10(Curv) from a curved decay to a
linear decay, see Figure S3. The transition of a curved decay to a linear decay was
detected as the first high peak in the second derivative of log10(Curv) with a
negative value of the first derivative of log10(Curv).
![Page 206: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/206.jpg)
206
Model
parameter
Meaning General
Model
Shortening
model
Unit
s Forward/backward partitioning of
force dependence 0.5 0.5 -
dP Effective step size for power-stroke 50 100 -
C Effective elastic modulus 100 20 -
L0 Ramp length per unit time 0.8 7 -
Power-stroke zeroth order rate
constant 1 1 1/t0
Detachment zeroth order rate
constant 0.0025 0.0025 1/t0
Attachment zeroth order rate
constant 0.025 0.025 1/t0
[P0] Equilibrium concentration of
phosphate 50 50 M
Katt Affinity of myosin head for binding
site 8 8 -
rip “Ripping” stretch dependence
parameter 0.25 0 -
ds Step size for one ripped off myosin 80 0 -
“Ripping” zeroth order rate constant 0.0025 0 1/t0
Concentration Meaning General
Model
Shortening
model Unit
[ATP] ATP concentration 500 500 M
[ADP] ADP concentration 5 5 M
[Pi] Pi concentration 5 5 M
Table 1 - Free model parameters and conditions Parameters and conditions as determined by
adjustment to experimental data. Nucleotide concentrations have been assigned assumed values.
General model parameters include forced crossbridge ripping and are used in the model appendix
for shortening and lengthening response simulation. The shortening model parameters do not
incorporate crossbridge ripping, and are used for all other simulations and apply for all model
results referenced in the main text.
![Page 207: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/207.jpg)
207
Figure S2 - Ramp shortening and lengthening model traces. The characteristic P1 and P2
transitions for ramp shortening (traces with force decrease during ramp) and lengthening (traces
with force increase during ramp) become visible from simulation of the general model. For
features observed in experiment see Pinniger et al (2006) and Roots et al (2007) . (A) Force vs.
time for the complete experimental protocol including isometric contraction at negative times and
a ramp stretch beginning with time t = 0 and ending when maximal ramp length is reached. (B)
Zoom into (A) to make visible features of the overall force response including the P2 features of
lengthening and shortening and the P1 characteristic indentation of the lengthening force response.
(C) Zoom of A) to make visible the early force response including the P1 characteristic force drop
right after beginning of a ramp shortening. Ramp velocities Vramp = −2L0M
, −1L0M
, 1L0M
, 2L0M
;
simulation parameters given in table 1, general model.
![Page 208: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/208.jpg)
208
Figure S3 Detection of critical points from simulated force responses to ramp shortening. In
all graphs heavy lines represent a simulation for Vramp = 2.0L0, the regular lines are for Vramp = 1,
0.5, 0.25, 0.125, in respective order away from the heavy line. (A) L(t) (solid black)
and Lmol(t) (dashed red) in units of L0 vs. time in units of t0. After starting the ramp L decreases,
and in effect Lmol becomes more similar to L, which effects a force decrease. (B) Force response to
ramp shortening. Circles indicate the P1 transition, triangles the P2 transition. (C) Percentage of
crossbridges in pre-powerstroke (solid black), postpower-stroke (dotted blue) and Non-bound
(dashed red) State. (D) log10 of the curvature Curv of the force response. Circles indicate the
detection points of P1 at the first curvature maximum. (E) First derivative with respect to time
of log10(Curv). (F) Second derivative with respect to time of log10(Curv). Triangles indicate the
detection points of P2 at the first maximum with a negative value in the first time derivative.
3.3 Blebbistatin inhibition
To predict the effects of blebbistatin inhibition, we need to incorporate the
effects of a reduced binding energy for the closing of the myosin binding cleft on
actin. We set the binding energy reduction to be = 0. 35. As a result of the
reduced binding energy, the free energy level of the tight bound state x2 is
increased. Rate constants into that state get lowered, rate constants from that state
increase:
![Page 209: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/209.jpg)
209
where the prime marks the rate constants for reduced binding energy. For
details see main text and Figure 12, for predicted changes to the critical points see
Figure 11. Another possible mechanism of blebbistatin inhibition is a lowering of
the power-stroke zeroth order rate constant . This change predicts the
blebbistatin effect on the critical points accurately, see Figure S4, but a reduction
of isometric maximal force P0 is only predicted for changes in , not changes in
kP, see equation (36).
4 General conclusions from a simple model
4.1 Simplified generic model
To understand how the mechanism of blebbistatin inhibition can be
properly included in our model, we will simplify it to the necessary elements:
where we omitted the differential equation for x3 = 1 − x2 − x1 . k0 is the
zeroth order power-stroke transition rate, all other zeroth order rates have been set
equal to 1. = − − W is the free energy dissipation to heat during the
forward powerstroke transition, < 0 is the chemical free energy released in
this transition and W is the mechanical work exerted during the power-stroke.
is the free energy dissipated to heat during the detachment of myosin from actin.
![Page 210: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/210.jpg)
210
In skeletal muscle myosin it can be equated with the free energy released in this
step by ATP binding and ADP release = const. s is a partitioning
parameter that describes the detailed load-dependence of the forward and the
backward power-stroke transition.
4.2 Partitioning of bound crossbridges at maximal isometric contraction
In a steady state must hold. Thus, we set (23) and (24) equal
to 0, and subtract these expressions. Considering further that at maximal isometric
contraction
we get
which describes the ratio of cross-bridges in the pre-powerstroke state
over cross-bridges in the post-powerstroke state. In skeletal muscle myosin, the
detachment of crossbridges after the powerstroke is very rapid (Nyitrai and
Geeves 2004), which is indicative of a high free energy release during this step:
0. Applying this condition to (26) shows x1/x2 1 x1 x2. Thus, at
maximal isometric contraction we would expect most bound crossbridges to be in
the pre-power-stroke state, as is observed in simulations of the full model, too.
![Page 211: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/211.jpg)
211
Differentiation of (26) with respect to k0 yields
so the zeroth order transition rate of the powerstroke does not affect the
pre-post partitioning of bound crossbridges at maximal isometric contraction.
Effect of strain-sensitive ADP release: As discussed in a review by
Nyitrai and Geeves (2004), strain sensitivity of ADP release in skeletal muscle
myosin has not been proven directly yet, but should likely be the case. Our model
does not yet include strain sensitivity of ADP release. Let us, in our simplified
generic model, estimate the expected effect of stress-sensitive ADP release on the
crossbridge partitioning at maximal isometric force. Let us again take (26) and for
simplicity assume s = 1 and k0 = 0.5 without assuming = const.:
At the maximal isometric force must hold in our model. In
the case of not load-sensitive ADP release = const. and we get = − ,
and therefore also x1/x2 = . Assuming 0 (see Nyitrai & Geeves,
2004) we recover the case x1 x2 discussed above.
Now we want to introduce a load-sensitive ADP release step instead, as
hypothesized by Nyitrai and Geeves (2004). To get an estimate of the effect we
![Page 212: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/212.jpg)
212
assume that the ADP release-associated heat release is not constant, but
= instead. Then, for = 0 to be fulfilled, 0 must
be. With this, from (28) we get
This ad-hoc investigation indicates that stress-sensitive ADP release could
actually alter the x1 x2 ratio we found for no stress-sensitivity of ADP release
more towards x1 and x2 to be of the same order of magnitude.
4.3 Maximal isometric force
Now, we want to understand how the reduction of isometric maximal
force P0 by blebbistatin inhibition can be explained in our simplified model.
Blebbistatin interferes with the tight binding of myosin to actin by placing itself at
the interface between myosin’s actin binding cleft and the actin binding site
(Ramamurthy et al. 2004). It seems reasonable that this would lead to a reduction
of the binding energy associated with the tight bound state, see Figure 12 in main
text. We include this reduction of binding energy into our simplified model in
the following manner:
![Page 213: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/213.jpg)
213
see also figure 12 in the main text. At maximal isometric contraction, the
free energy released during one crossbridge cycle − and the mechanical work
exerted during one crossbridge cycle W are equal. In consequence, a detailed
equilibrium is established in the three state kinetic cycle (Hill 2004). We can use
the detailed equilibrium condition to express the bound crossbridges populations
in x1 and x2 in terms of the non-bound crossbridge population x3:
We substitute into and get
We can now determined the fraction of pbound of crossbridges that are
bound:
When we assume a number N of effectively cycling crossbridges, we can
calculate the maximum isometric force P0 which the bound crossbridges Nbound =
pboundN can sustain using W = /Nbound :
![Page 214: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/214.jpg)
214
where is an effective myosin step size. The expression − is
constant, so we can state the following proportionality:
Thus, for increasing the maximal isometric force decreases
monotonously. This is in accordance with the experimentally observed reduction
in maximal isometric force P0 with increasing blebbistatin concentrations. Also, it
is clear that P0 is not affected by changes in k0, the zeroth order rate constant of
the powerstroke transition, see (27). In consequence, a reduction in the binding
energy of the tight binding of the myosin S1 actin binding cleft to actin is in our
model is in accordance with the observed blebbistatin inhibition in our
experiments, while a reduction in k0 is not. This means a is a necessary
effect of blebbistatin inhibition, while a reduction of k0 can additionally take
place. When only the effect of a ko reduction on the critical points along is
viewed, the blebbistatin inhibition effect seems to be well predicted, see Figure
S4. However, we showed in (27) that the P0 reduction for increasing blebbistatin
concentration is not explicable by a reduction of k0.
![Page 215: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/215.jpg)
215
Figure S4 - Blebbistatin effect on ramp shortening critical points in experiment and model
simulation assuming reduction of the powerstroke zeroth order rate constant. (A)
Experimentally measured P1 for different ramp velocities. Solid line: pCa4.5 with blebbistatin,
dotted and dashed line: pCa4.5 and pCa6 without blebbistatin, respectively. (B) P1 detected in
simulation for different ramp velocities. Solid line: blebbistation inhibition modeled by reduction
of the zeroth order powerstroke-rate constant k0' = k0/1.75. Dashed line: no blebbistation
inhibition. (C, D, E) Experimentally determined L1, P2, L2, respectively; same conditions as in (A).
(F, G, H) L1, P2, L2 detected in simulated ramp shortening, respectively; same conditions as in
(B).
![Page 216: FORCE DEVELOPMENT DURING AND AFTER …digitool.library.mcgill.ca/thesisfile119614.pdf3 Force development during and after muscle ... 3.2 The effects of Ca2+ and MgADP on force development](https://reader031.fdocuments.net/reader031/viewer/2022020412/5ae964b07f8b9a8b2b912c37/html5/thumbnails/216.jpg)
216
References
Hill, T. L. 2004. Free Energy Transduction and Biochemical Cycle Kinetics.
Laakso, J. M., J. H. Lewis, H. Shuman & E. M. Ostap (2008) Myosin I can act as
a molecular force sensor. Science, 321, 133-6.
Nyitrai, M. & M. A. Geeves (2004) Adenosine diphosphate and strain sensitivity
in myosin motors. Philos.Trans.R.Soc.Lond B Biol.Sci., 359, 1867-1877.
Pinniger, G. J., K. W. Ranatunga & G. W. Offer (2006) Crossbridge and non-
crossbridge contributions to tension in lengthening rat muscle: force-
induced reversal of the power stroke. J.Physiol, 573, 627-643.
Ramamurthy, B., C. M. Yengo, A. F. Straight, T. J. Mitchison & H. L. Sweeney
(2004) Kinetic mechanism of blebbistatin inhibition of nonmuscle myosin
IIb. Biochemistry, 43, 14832-14839.
Roots, H., G. W. Offer & K. W. Ranatunga (2007) Comparison of the tension
responses to ramp shortening and lengthening in intact mammalian muscle
fibres: crossbridge and non-crossbridge contributions. J.Muscle Res.Cell
Motil., 28, 123-139.
Veigel, C., J. E. Molloy, S. Schmitz & J. Kendrick-Jones (2003) Load-dependent
kinetics of force production by smooth muscle myosin measured with
optical tweezers. Nat.Cell Biol., 5, 980-986.