1 … protein conformations … protein-protein bonds … biomembranesfrom mechano-biology to soft -material science … strength and stability are all about time under stress ! Evan Evans Professor Emeritus Physics and Pathology, the University of British Columbia Biomedical Engineering, Boston University Fundamentum Natura: strength and stability of biological structures are ultimately limited by thermal nucleation of a catastrophic nanoscale defect. Criticial to the survival of a biological tissue and its machinery of life, strategic sites for stress-driven failure are protein conformations, protein-protein bonds, and membrane interfaces. Although potentially self-healing, refolding a mechanically denatured protein, or reconnecting a broken protein-protein bond, or closing an open hole in a membrane requires nearly immediate suppression of stress to avoid catastrophe! Emphasizing the importance of stress history, and stress rate in particular, I will illustrate the physics that governs the statistical frequency for failure using examples from single molecule and single membrane mechanical experiments. [ contact: E.A. Evans, D.A. Calderwood, Science 316 (2007) E. Evans, K. Halvorsen, K. Kinoshita, W.P. Wong, in Handbook of Single-Molecule Biophysics, P. Hinterdorfer, A. van Oijen (eds.), 20, © Springer Science+Business Media, LLC (2009) K. Kinoshita, A. Leung, S. Simon, E. Evans, Biophys. J. 98 (2010) E. Evans, K. Kinoshita,, S. Simon, A. Leung, Biophys. J. 98 (2010) E.A. Evans, B.A. Smith, New Journal of Physics 13 (2010) (pp 29)

2 nanoscale impact of force … kinetic transitions far from equilibrium … … atomic scale .. nm pulling force amplifies off rate and suppresses on rate E(Qn) koff ~ ko exp(f x /kBT) | x | < nm critical defect !!    nm ko ~ (109 /s) exp[- Eo /kBT]  { Evans & Calderwood, Science 316, }

3 conformational calamity … mechanical unfolding and thermal denaturation 37o o RBC | nm | RBC poly spectrin  10 m  | nm |

4 mechanical unfolding … pulling force exponentiates unfolding rate~ 5 nm V f 2 m   { Paci & Karplus 2000 } ~ 35 nm 4 x spectrin-Ig survival of folded structure  kunf(fk)  - (Nk /Nk) /tk { Evans, Halvorsen, Kinoshita, Wong, in Handbook of Single-Molecule Biophysics, Springer Science+Business Media, 2009}

5 “-energy of bond” << “work of structural deformation”nanostructural complexity … mechanical dissociation of cell adhesion bonds … f leukocyte ligand receptor 2 m   “-energy of bond” << “work of structural deformation” Edeform ~1500 kBT f* x ~ 5-10 kBT { Kinoshita, Leung, Simon, Evans, BJ 98, } { note: kBT  4 zepto-Joule }

6 large “energy dissipation”nanostructural complexity … cohesive failure alters adhesive dynamics … f leukocyte ligand receptor 2 m    … kBT !! reduces force … extends lifetime ! E*deform … kBT !! * cyto-unbinding extends lifetime ! large “energy dissipation” { Kinoshita, Leung, Simon, Evans, BJ 98, }

7  mechanical strength and survival of a “single” bond under increasing force f { = rf t } V glass bead f 2 m   continuum (Markov) limit ICAM L 2  500 kBT ! statistics of survival  koff(fk)  - (Nk /Nk) /tk “failure can occur at any level of force” … while failure frequency increases with force … so how can we compare mechanical strengths between different bonds ? The simplest statistical measure of strength is the “most probable” failure force f . For exponential dependence of koff on force { ~ ko exp(f /f ) } as above, mechanical strength rises logarithmically with force-loading rate rf . Driven far from equilibrium, “bond” strength, f  = f ln[rf /kof], emerges above a loading rate rf*  kof set by frequency of spontaneous dissociation ko and the force scale for reducing the activation barrier by one thermal-energy unit i.e. f = kBT/ x . { Evans and Ritchie, BJ 72, }

8 Footnote: Poisson reality … each “single” bond failure is a rare-random eventglass bead f 2 m   discrete (Bernouli) statisitics ICAM L 2  statistics of failure  koff(fi)  ln(1+1/Ni+1) /ti  “the instantaneous frequency of failure ranges from zero to infinity” … note … average frequency closely follows the Markov continuum limit (dashed line)  ln(1+Nk/Ni+k) /tk x  kT  ln( ) / f … emphasizing the kinetic basis for critical-defect size

9  … critical-defect areas a  kT { ln() /  } ~ 1 nm2mechanical poration and lysis of biomembranes under increasing tension  { = r t } continuum (Markov) limit discrete (Bernouli) statisitics - P(t) 10 m   SOPC:Ch 3 m   RBC  … critical-defect areas a  kT { ln() /  } ~ 1 nm2 { Evans & Smith, NJP 13, }

10 stability of soft-condensed matter in biology… protein conformations … protein-protein bonds … biomembranes fundamentum natura … “strength and stability of soft matter structures are ultimately limited by thermal nucleation of critical-size defects within a macromolecular complex” i.e. survival depends on mesoscopic connections between force – time – chemistry !!

11 University of British Columbia Acknowledged here are two decades of the creative theoretical and experimental developments performed at the University of British Columbia and Boston University by exceptional doctoral students and post docs (now elsewhere). University of British Columbia Anthony Yeung (University of Alberta CA) Ken P. Ritchie (Purdue University USA) Andreas Zilker (Bavaria DE) Florian Ludwig (Utrecht NL) Pierre Nassoy (Bordeaux FR) Rudolph Merkel (Jülich DE) Hans-Gunther Doebereiner (University of Bremen DE) Koji Kinoshita (SDU Odense DK) Ben A. Smith (Biogen USA) Boston University Wesley P. Wong (Harvard University USA) Ken Halvorsen (SUNY Albany USA) Koji Kinoshita (SDU Odense DK) Special thanks to EE Munich hosts … Dr. Erich Sackmann, Professor Emeritus, Physics Department E22, TUM (Garching) ; and the Alexander von Humboldt Foundation