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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 Fratzl Matthew Harrington Dieter Fischer. Potsdam, Germany. 108th STATISTICAL MECHANICS CONFERENCE December 2012. mussel byssus. whelk egg capsule. i mportant yield.

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

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

  2. mussel byssus whelk egg capsule importantyield importantyield slow immediate recovery 1) Stiffness 400 MPa 100 MPa 2) Extensibility Relatively high initialstiffness 3) Recovery

  3. Mussel byssal threads Self-healing fibres

  4. yield elastic relaxation „healing“ ~ 24h 1h Mechanical function of Zn – Histidine bonds M. Harrington et al, 2008

  5. Egg capsules of marine whelk Busycotypuscanaliculatus Harrington et al.2012 J Roy Soc Interface

  6. α-helix Raman α β* extendedβ*

  7. X-ray (small-angle) diffraction

  8. Phase coexistence yield Raman intensity XRD intensity α β* stress strain

  9. Co-existenceoftwophasesduringyield Elasticbehaviour W(s) = (k/2) (s – s0)2

  10. Worm-likechain (Kratky/Porod 1949) Moleculewithkinks (Misof et al. 1998) extended phase β* Force f actual length s kink number ν length atrest s0 persistence length lp extended (contour) length L (s > s0)

  11. Relation betweenforce and potential energy: High strain Low strain WLC kink model αphase (elastic) β* phase (entropic)

  12. fa All molecularsegments in thefiberseethe same force mechanicalequilibrium: Completeanalogytothermodynamicequilibrium:

  13. WLC and kinkmodelnearly identical on thisscale Total energy internal energy work of appliedforce αstablestabilitylimitα + β* sclow

  14. Relation toexperiment Whatcanbemeasured (by in-situ synchrotron x-raydiffraction): Force as a function of meanelongation The criticalforceatyield (α-β* coexistence) The yieldpoint (start of α-β* coexistence) Reconstruct W(s) Number of molecules per cross-sectionalarea

  15. Phase transformationkinetics in analogytopseudoelasticity in NiTi thermodynamicdrivingforce kineticequation fraction of β* segments in thefiber Hypothesis: loadatcontant stress rate, (loading) and (unloading) Based on: R. Abeyaratne, J.K. Knowles, Evolution of Phase Transitions – A Continuum Theory (Cambridge University Press, Cambridge, 2006)

  16. Slow or fast stretching Blue: Red: Green: WLC Equilibrium line

  17. mussel byssus whelk egg capsule Cooperativity of manyweakbonds phasetransition

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