Abstract
Kinesin is a motor molecule that moves processively on microtubule tracks and is involved in active intracellular transport processes. For small loads, it is powered by the hydrolysis of one ATP molecule per step. Here we extent our previously introduced network theory in order to study the possibility of two different mechanical stepping transitions and the general behavior of the motor’s efficiency. Our theory shows explicitly how chemical and mechanical slip cycles emerge that weaken the coupling between ATP hydrolysis and mechanical stepping. Near chemomechanical equilibrium, the motor efficiency η may vary between η=1 for tight coupling and η=0 for loose coupling, depending on the relevance of the slip cycles. Far from chemomechanical equilibrium, on the other hand, the motor efficiency is found to decay as 1/Δμ with increasing Δμ irrespective of the presence of slip cycles, where Δμ represents the reaction free enthalpy or chemical potential difference per ATP hydrolysis.
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Smoluchowski, M.V.: Experimentell nachweisbare, der üblichen Thermodynamik widersprechende Molekularphänomene. Phys. Z. 13, 1069 (1912)
Huxley, A.F.: Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7, 255 (1957)
Peskin, C., Oster, G.: Coordinated hydrolysis explains the mechanical behavior of kinesin. Biophys. J. 68, S202 (1995)
Jülicher, F., Ajdari, A., Prost, J.: Modeling molecular motors. Rev. Mod. Phys. 69, 1269 (1997)
Reimann, P.: Brownian motors: noisy transport far from equilibrium. Phys. Rep. 361, 57 (2002)
Polanyi, M., Wigner, E.: Concerning the interference of natural oscillation as a reason for energy variations and chemical transformation. Z. Phys. Chem. 139, 439 (1928)
Eyring, H.: The activated complex in chemical reactions. J. Chem. Phys. 3, 98 (1935)
Kramers, H.A.: Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, 284 (1940)
Haldane, J.B.S.: Enzymes. MIT Press, Cambridge (1965)
Hill, T.L.: Interrelations between random walks on diagrams (graphs) with and without cycles. Proc. Natl. Acad. Sci. USA 85, 2879 (1988)
Liepelt, S., Lipowsky, R.: Steady-state balance conditions for molecular motor cycles and stochastic nonequilibrium processes. Europhys. Lett. 77, 50002 (2007)
Liepelt, S., Lipowsky, R.: Kinesin’s network of chemomechanical motor cycles. Phys. Rev. Lett. 98, 258102 (2007)
Lipowsky, R., Liepelt, S.: Chemomechanical coupling of molecular motors: thermodynamics, network representations, and balance conditions. J. Stat. Phys. 130, 39 (2008). Erratum, J. Stat. Phys. 135, 777 (2009)
Kolomeisky, A.B., Widom, B.: A simplified “ratchet” model of molecular motors. J. Stat. Phys. 93, 633 (1998)
Fisher, M.E., Kolomeisky, A.B.: Simple mechanochemistry described the dynamics of kinesin molecules. Proc. Natl. Acad. Sci. USA 98, 7748 (2001)
Fisher, M.E., Kim, Y.C.: Kinesin crouches to sprint but resists pushing. Proc. Natl. Acad. Sci. USA 102, 16209 (2005)
Carter, N.J., Cross, R.A.: Mechanics of the kinesin step. Nature 435, 308 (2005)
Hill, T.L.: Free Energy Transduction and Biochemical Cycle Kinetics. Springer, New York (1989)
Schnitzer, M.J., Block, S.M.: Kinesin hydrolyzes one ATP per 8-nm step. Nature 388, 386 (1997)
Hancock, W.O., Howard, J.: Processivity of the motor protein kinesin requires two heads. J. Cell Biol. 140, 1395 (1998)
Yildiz, A., Tomishige, M., Vale, R.D., Selvin, P.R.: Kinesin walks hand-over-hand. Science 303, 676 (2004)
Uemura, S., et al.: Kinesin-microtubule binding depends on both nucleotide state and loading direction. Proc. Natl. Acad. Sci. USA 99, 5977 (2002)
Guydosh, N.R., Block, S.M.: Backsteps induced by nucleotide analogs suggests the front head of kinesin is gated by strain. Proc. Natl. Acad. Sci. USA 103, 8054 (2006)
Mori, T., Vale, R.D., Tomishige, M.: How kinesin waits between steps. Nature 450, 750 (2007)
Alonso, M.C., Drummond, D.R., Kain, S., Hoeng, J., Amos, L., Cross, R.A.: An ATP gate controls tubulin binding by the tethered head of Kinesin-1. Science 316, 120 (2007)
Schief, W.R., Clark, R.H., Crevenna, A.H., Howard, J.: Inhibition of kinesin mobility by ADP and phosphate supports a hand-over-hand mechanism. Proc. Natl. Acad. Sci. USA 101, 1183 (2004)
Auerbach, S.D., Johnson, K.A.: Alternating site ATPase pathway of rat conventional kinesin. J. Biol. Chem. 280, 37048 (2005)
Taniguchi, Y., Nishiyama, M., Ishii, Y., Yanagida, T.: Entropy rectifies the Brownian steps of kinesin. Nat. Chem. Biol. 1, 342 (2005)
Liepelt, S., Lipowsky, R.: Operation modes of the molecular motor kinesin. Phys. Rev. E 79, 011917 (2009)
Nishiyama, M., Higuchi, H., Yanagida, T.: Chemomechanical coupling of the forward and backward steps of single kinesin molecules. Nat. Cell Biol. 4, 790 (2002)
Hyeon, C., Klumpp, S., Onuchic, J.N.: Kinesin’s backsteps under mechanical load. Phys. Chem. Chem. Phys. 11, 4899 (2009)
Lipowsky, R., Liepelt, S., Valleriani, A.: Energy conversion by molecular motors coupled to nucleotide hydrolysis. J. Stat. Phys. 135, 951 (2009)
Cantelo, R.C.: The 2nd law of thermodynamics in chemistry. J. Phys. Chem. 32, 982–988 (1928)
Lacoste, D., Lau, A.W.C., Mallick, K.: Fluctuation theorem and large deviation function for a solvable model of a molecular motor. Phys. Rev. E 78, 011915 (2008)
Hill, T.L.: Theoretical formalism for the sliding filament model of contraction of striated muscle, Part I. Prog. Biophys. Mol. Biol. 28, 267 (1974) (1974)
Parmeggiani, A., Jülicher, F., Ajdari, A., Prost, J.: Energy transduction of isothermal ratches: Generic aspects and specific examples close to and far away from equilibrium. Phys. Rev. E 60, 2127 (1999)
Klumpp, S., Lipowsky, R.: Cooperative cargo transport by several molecular motors. Proc. Natl. Acad. Sci. USA 102, 17284 (2005)
Cross, R.A.: The kinetic mechanism of kinesin. Trends Biochem. Sci. 29, 301 (2004)
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Liepelt, S., Lipowsky, R. Impact of Slip Cycles on the Operation Modes and Efficiency of Molecular Motors. J Stat Phys 141, 1–16 (2010). https://doi.org/10.1007/s10955-010-0050-5
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DOI: https://doi.org/10.1007/s10955-010-0050-5