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

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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

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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

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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

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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,

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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.

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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.

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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

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(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

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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

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.

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

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

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

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

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

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.

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.

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.

20

PART I – LITERATURE REVIEW

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).

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

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)

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

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

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

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

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).

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

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

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

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

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;

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

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).

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

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,

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) .

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).

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-

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

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

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

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),

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).

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

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

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:

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:

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.

51

PART II – EXPERIMENTAL STUDIES

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,

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.

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.

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.

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

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.

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

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

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.

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

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

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.

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

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

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).

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

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

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.

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

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

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

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.

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

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

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

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

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

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

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.

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.

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.

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.

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

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

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

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

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

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).

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

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

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

/

/

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.

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

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

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.

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.

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

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

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

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).

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

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).

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

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

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

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

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

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

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

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.

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.

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.

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.

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.

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

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.

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 &

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

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

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

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

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

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 ±

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

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).

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

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

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.

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

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

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).

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.

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.

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.

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.

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

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.

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

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

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.

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

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

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

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.

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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.

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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

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.

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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

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

151

studies that used 15°C (Pavlov et al, 2009a) or 20°C (Pavlov et al, 2009a; Pavlov

et al, 2009b).

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.

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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)

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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

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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-

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.

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

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 =

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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

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

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,

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.

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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

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.

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

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.

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

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

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.

170

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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

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

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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:

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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

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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.

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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

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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.

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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

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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

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).

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.

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.

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:

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.

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.

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

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:

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 :

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.

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).

216

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