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NANOPHYSIQUE INTRODUCTION PHYSIQUE AUX NANOSCIENCES

NANOPHYSIQUE INTRODUCTION PHYSIQUE AUX NANOSCIENCES. 6. MOTEURS MOLECULAIRES. Pierre GASPARD. 2011-2012. BIOMOLECULES. ADN: Acide Désoxyribo-Nucléique (stockage d’information). -ACATGTAATTCATTTACACGC- -GTACATTAAGTAAATGTGCGT- A: adénine T: thymine C: cytosine G: guanine

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NANOPHYSIQUE INTRODUCTION PHYSIQUE AUX NANOSCIENCES

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  1. NANOPHYSIQUEINTRODUCTION PHYSIQUE AUX NANOSCIENCES 6. MOTEURS MOLECULAIRES Pierre GASPARD 2011-2012

  2. BIOMOLECULES ADN: Acide Désoxyribo-Nucléique (stockage d’information) -ACATGTAATTCATTTACACGC- -GTACATTAAGTAAATGTGCGT- A: adénine T: thymine C: cytosine G: guanine 1 paire de bases = 2 bits d’information ~ 64 atomes adénosine monophosphate adénosine triphosphate (stockage d’énergie) Watson & Crick, Franklin, Wilkins (1953)

  3. En plongée dans la cellule L’évolution biologique a transformé de simples vésicules en cellules munies de nombreuses organites. taille ~10-30 mm Chr. de Duve, Une visite guidée de la cellule vivante (De Boeck Université, Bruxelles, 1987).

  4. Dans une mitochondrie Centrale énergétique de la cellule: production de l’ATP (carburant cellulaire) membrane double, membrane interne avec: (1) pompes à protons (2) ATP synthases taille ~ 2-3 mm Chr. de Duve, Une visite guidée de la cellule vivante (De Boeck Université, Bruxelles, 1987).

  5. Moteur moléculaire FoF1-ATPase protéine: polymère d’acides aminés ATP synthase mitochondrie: centrale énergétique de la cellule F : turbine à protons F : génératrice d’ATP o 1 F : moteur à ATP F : pompe à protons 1 o

  6. Moteur moléculaire F1-ATPase combustible: adénosine triphosphate (ATP) actine -18 puissance = 10 Watt Moteur F 1 0,5 tour / sec 1,3 tour / sec 5 mm H. Noji, R. Yasuda, M. Yoshida, & K. Kinosita Jr., Nature 386 (1997) 299

  7. Moteur moléculaire F1-ATPase F : moteur à ATP H. Wang & G. Oster, Nature 396 (1998) 279 1 -18 puissance = 10 W (Watt) 0,5 tour / sec 1,3 tour / sec 5 mm H. Noji, R. Yasuda, M. Yoshida, & K. Kinosita Jr., Nature 386 (1997) 299

  8. 6 Locomotive à vapeur puissance = 5 10 W (Watt)

  9. Power plant of the cell: synthesis of ATP FoF1-ATPase INSIDE MITOCHONDRIA size ~ 2-3 mm Internal membrane with: Fo = proton turbine F1 = ATP synthase (23500 atoms) H. Wang & G. Oster, Nature 396 (1998) 279 Chr. de Duve, Une visite guidée de la cellule vivante (De Boeck Université, Bruxelles, 1987).

  10. ACTIN-MYOSIN MOLECULAR MOTOR myosin II: protein of about 6700 atoms cross-bridge mechanism

  11. Linear motors: • actin-myosin II (muscles) • kinesin-microtubule (anterograde transport cargo) • dynein-microtubule (retrograde transport cargo) Rotary motors: • F1-ATPase + actin filament or bead Powered by chemical energy: ATP hydrolysis ATP ADP + Pi difference of free energy: DG0 = -30.5 kJ/mole = -7.3 kcal/mole = -50 pN nm = -12.5kBT nonequilibrium thermodynamics kBT = 4 pN nm = 0.026 eV (300 K) importance of the chirality of the molecular structure for the directionality of motion under specific nonequilibrium conditions ATP ROTARY AND LINEAR MOLECULAR MOTORS

  12. F1-ATPase NANOMOTOR H. Noji, R. Yasuda, M. Yoshida, & K. Kinosita Jr., Nature 386 (1997) 299 R. Yasuda, H. Noji, M. Yoshida, K. Kinosita Jr. & H. Itoh, Nature 410 (2001) 898 F1 = (ab)3g chemical fuel of F1 : ATP cycle: power = 10-18 Watt chiral molecules

  13. DISCRETE-STATE STOCHASTIC PROCESSES FOR MOLECULAR MOTORS Markovian jump process between the discrete states s : master equation A. B. Kolomeisky & M. E. Fisher, Ann. Rev. Phys. Chem. 58 (2007) 675 R. Lipowsky & S. Liepelt, J. Stat. Phys. 130 (2008) 39 A. Garai, D. Chowdhury & M. P. Betterton, Phys. Rev. E 77 (2008) 061910 Fluctuation theorems: U. Seifert, EPL 70 (2005) 36 (rotary motor, 3 states) D. Andrieux & P. Gaspard, Phys. Rev. E 74 (2006) 011906 (rotary motor, F1-ATPase, 6 states) D. Lacoste, A. W. C. Lau & K. Mallick, Phys. Rev. E 78 (2008) 011915 (linear motor)

  14. F. Jülicher, A. Adjari & J. Prost, Rev. Mod. Phys. 69 (1997) 1269 CONTINUOUS STOCHASTIC PROCESSES coupled Fokker-Planck equations for the probability densities: Mechanical part: probability currents: diffusion coefficient: friction coefficient Chemical part: transition rates of the reactions Arrhenius’ law of chemical kinetics potentials for the wells: Ui(q) potentials for the transition states: Ui*(q) • P. Gaspard & E. Gerritsma, J. Theor. Biol. 247 (2007) 672

  15. FREE-ENTHALPY POTENTIALS Potential wells obtained by inverting the experimental probability distributions: R. Yasuda, H. Noji, M. Yoshida, K. Kinosita Jr. & H. Itoh, Nature 410 (2001) 898 potentials for the transition states Ui*(q) potentials for the wells Ui(q) • three-fold rotation symmetry: group C3 • absence of parity symmetry (chirality) • P. Gaspard & E. Gerritsma, J. Theor. Biol. 247 (2007) 672

  16. RANDOM TRAJECTORIESOF THEF1 -ATPase MOTOR Random trajectories simulated by a model: P. Gaspard & E. Gerritsma, J. Theor. Biol. 247 (2007) 672 Random trajectories observed in experiments R. Yasuda, H. Noji, M. Yoshida, K. Kinosita Jr. & H. Itoh, Nature 410 (2001) 898 Michaelis-Menten kinetics

  17. Crossover from reaction-limited regime to friction-limited regime F1-ATPase ROTATION RATE VERSUS FRICTION P. Gaspard & E. Gerritsma, J. Theor. Biol. 247 (2007) 672

  18. F1-ATPase UNDER AN EXTERNAL TORQUE (e.g. from Fo) stall torque ATP synthesis ATP consumption H. Itoh , A. Takahashi, K. Adachi, H. Noji, R. Yasuda, M. Yoshida, K. Kinosita Jr., Mechanically driven ATP synthesis by F1-ATPase, Nature 427 (2004) 465

  19. EFFICIENCIES OF F1-ATPase F1-ATPase under an external torque (e.g. from Fo) number of ATP synthesized or consumed per revolution: tight chemomechanical coupling for |t| < 27 pN nm chemical efficiency in ATP synthesis: mechanical efficiency in energy transduction: F. Jülicher, A. Adjari & J. Prost, Rev. Mod. Phys. 69 (1997) 1269

  20. TIGHT/LOOSE CHEMOMECHANICAL COUPLING tight coupling condition: entropy production: chemomechanical affinity: shift of effective equilibrium by the external torque E. Gerritsma & P. Gaspard, unpublished

  21. DISCRETE-STATE MODEL FOR THE F1-ATPase MOTOR 1 The angle jump at each reactive event: the tight coupling condition is always fulfilled. Markovian jump process between the discrete states s : transition rates: dependence on friction z and torque t : fitted to the continuous model E. Gerritsma & P. Gaspard, unpublished

  22. DISCRETE-STATE MODEL FOR THE F1-ATPase MOTOR 2 master equation : stationary solution: mean rotation rate (rev/sec): D. Andrieux & P. Gaspard, Phys. Rev. E 74 (2006) 011906 E. Gerritsma & P. Gaspard, unpublished

  23. F1-ATPase ROTATION RATE VERSUS AFFINITY dimensionless affinity or thermodynamic force: mean rotation rate: highly nonlinear dependence on A linear regime around equilibrium: nonlinear regime far from equilibrium: equilibrium: A = 1: 3.1 days/rev ! The F1 molecular motor typically works in a highly nonlinear regime far from equilibrium. E. Gerritsma & P. Gaspard, unpublished

  24. FULL COUNTING STATISTICS & FLUCTUATION THEOREM discrete-state model: generating function of the statistical cumulants of the number Nt of reactive events during the time t : 1st cumulant: mean rate A. B. Kolomeisky & M. E. Fisher, Ann. Rev. Phys. Chem. 58 (2007) 675 2nd cumulant: diffusivity fluctuation theorem: chemomechanical affinity: D. Andrieux & P. Gaspard, Phys. Rev. E 74 (2006) 011906 E. Gerritsma & P. Gaspard, unpublished

  25. FLUCTUATION THEOREM FOR THE F1-ATPase MOTOR:NO EXTERNAL TORQUE affinity or thermodynamic force: Fluctuation theorem for the number St of substeps: P(St = -s) exp(sA/2) very long time interval: t = 104 s D. Andrieux & P. Gaspard, Phys. Rev. E 74 (2006) 011906

  26. FLUCTUATION THEOREM FOR THE F1-ATPase MOTOR:WITH EXTERNAL TORQUE chemomechanical affinity: Fluctuation theorem for the number St of substeps: shorter time interval: xP(St = -s) exp(sA/2) oP(St = s) E. Gerritsma & P. Gaspard, unpublished

  27. FLUCTUATION THEOREM & TIGHT CHEMOMECHANICAL COUPLING Loose coupling: independent mechanical & chemical fluctuating currents D. Andrieux & P. Gaspard, J. Chem. Phys. 121 (2004) 6167 D. Andrieux & P. Gaspard, Phys. Rev. E 74 (2006) 011906 D. Lacoste et al., Phys. Rev. E 80 (2009) 021923 E. Gerritsma & P. Gaspard, unpublished Tight coupling: chemomechanical affinity: U. Seifert, EPL 70 (2005) 36 (rotary motor, 3 states) D. Andrieux & P. Gaspard, Phys. Rev. E 74 (2006) 011906 (rotary motor, F1-ATPase, 6 states) D. Lacoste, A. W. C. Lau & K. Mallick, Phys. Rev. E 78 (2008) 011915 (linear motors)

  28. OUT-OF-EQUILIBRIUM DIRECTIONALITYIN THE F1-ATPase NANOMOTOR 3 2 1 at equilibrium: detailed balance between …212132131223132… forward and backward rotations, (random) zero currents out of equilibrium: directionality of motion: …123123123123123… non-zero currents, (more regular) dynamical order

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