Modeling the phase transformation which controls the mechanical behavior of a protein filament

18
Modeling the phase transformation which controls the mechanical behavior of a protein filament Peter Fratzl Matthew Harrington Dieter Fischer Potsdam, Germany 108th STATISTICAL MECHANICS CONFERENCE December 2012

description

Modeling the phase transformation which controls the mechanical behavior of a protein filament. Peter Fratzl Matthew Harrington Dieter Fischer. Potsdam, Germany. 108th STATISTICAL MECHANICS CONFERENCE December 2012. mussel byssus. whelk egg capsule. i mportant yield. - PowerPoint PPT Presentation

Transcript of Modeling the phase transformation which controls the mechanical behavior of a protein filament

Page 1: Modeling the phase transformation which controls the mechanical behavior of a protein filament

Modeling the phase transformation which controls the mechanical behavior of a protein filament

Peter FratzlMatthew

HarringtonDieter Fischer

Potsdam, Germany

108th STATISTICAL MECHANICS CONFERENCEDecember 2012

Page 2: Modeling the phase transformation which controls the mechanical behavior of a protein filament

musselbyssus

whelk eggcapsule

Relatively high initial stiffness

400 MPa 100 MPa 1) Stiffness

important yieldimportant yield

2) Extensibility

slow

immediate recovery

3) Recovery

Page 3: Modeling the phase transformation which controls the mechanical behavior of a protein filament
Page 4: Modeling the phase transformation which controls the mechanical behavior of a protein filament

Mussel byssal threads

Self-healing fibres

Page 5: Modeling the phase transformation which controls the mechanical behavior of a protein filament

yield

relaxation

„healing“ ~ 24h

Mechanical function of Zn – Histidine bonds

M. Harrington et al, 2008

elastic

1h

Page 6: Modeling the phase transformation which controls the mechanical behavior of a protein filament

Egg capsules of marine whelk

Busycotypus canaliculatus

Harrington et al. 2012J Roy Soc Interface

Page 7: Modeling the phase transformation which controls the mechanical behavior of a protein filament

α-helix

extended β*

αβ*

Raman

Page 8: Modeling the phase transformation which controls the mechanical behavior of a protein filament

X-ray (small-angle) diffraction

Page 9: Modeling the phase transformation which controls the mechanical behavior of a protein filament

Ramanintensity

XRD intensity

stress strain

αβ*

Phase coexistenceyield

Page 10: Modeling the phase transformation which controls the mechanical behavior of a protein filament

Co-existence of two phases during yield

Elastic behaviour

W(s) = (k/2) (s – s0)2

Page 11: Modeling the phase transformation which controls the mechanical behavior of a protein filament

Force f

actuallength

s

extended(contour)

lengthL

21 1

14 4

p

kT s sf

l L L

persistencelengthlp

kinknumber

ν

lengthat rest

s0

Worm-like chain(Kratky/Porod 1949)

Molecule with kinks(Misof et al. 1998)

(s > s0)

extendedphase

β*

0 0

0

s s skT

fL L s L s

Page 12: Modeling the phase transformation which controls the mechanical behavior of a protein filament

21

( ) 24

B

p

k T s s LW s W

l L L L s

0 0

0

( ) 1 log 1

B s sk T s s

W s WL L s L L L

21 1

14 4

B

p

k T s sf

l L L

0 0

0

B s s sk T

fL L s L s

f k s s

21( )

2 W s W k s s

Relation between force and potential energy:

W

fs

β* phase (entropic)α phase (elastic)

Low strainHigh strain

WLC

kinkmodel

Page 13: Modeling the phase transformation which controls the mechanical behavior of a protein filament

All molecular segments in the fiber see the same force

fa

mechanical equilibrium: *

a

WWf

s s

Complete analogy to thermodynamic equilibrium:

*

a

WW

c c

Page 14: Modeling the phase transformation which controls the mechanical behavior of a protein filament

( ) aW s f s s

D-period(nm)

100 120 140 160

ela

stic ene

rgy density (M

Jm-3

)

0

1

2

3

4

Total energy

D-period(nm)

100 120 140 160-1

0

1

2

3

100 120

W(x) -

(x - s)

-1

0

1

2

3

100 120-1

0

1

2

3

WLC and kink model nearlyidentical on this scale

internalenergy

work ofapplied force

α stable stability limit α + β*

sclow

Page 15: Modeling the phase transformation which controls the mechanical behavior of a protein filament

𝜎= ρ 𝑓

Relation to experiment

What can be measured(by in-situ synchrotron

x-ray diffraction):

Force as a function of mean elongation

The critical force at yield (α-β* coexistence)

The yield point (start of α-β* coexistence)

( )af s

Yaf

clows

Number of moleculesper cross-sectional area

Reconstruct W(s)

Page 16: Modeling the phase transformation which controls the mechanical behavior of a protein filament

* * aW W f s s

Based on: R. Abeyaratne, J.K. Knowles, Evolution of Phase Transitions – A Continuum Theory (Cambridge University Press, Cambridge, 2006)

Phase transformation kineticsin analogy to pseudoelasticity in NiTi

thermodynamic driving force

d

dt

kinetic equation

fraction of β* segments in the fiber

Hypothesis: load at contant stress rate, (loading) and (unloading)af

af

Page 17: Modeling the phase transformation which controls the mechanical behavior of a protein filament

Slow or fast stretching

Blue: Red:

Green:

WLC

Equilibriumline

Page 18: Modeling the phase transformation which controls the mechanical behavior of a protein filament

musselbyssus

whelk eggcapsule

Cooperativity of many weak bonds phase transition