Abstract
Molecular motors convert chemical energy into mechanical work while operating in an environment dominated by Brownian motion. The aim of this paper is to explore the flow of energy between the molecular motors and its surroundings, in particular, its efficiency. Based on the Fokker-Planck equation with either N or infinite chemical states, we find that the energy efficiency of molecular motors, whether the Stokes efficiency or the usual thermodynamic efficiency, is strictly less than one, because of the dissipation of the energy in both the overdamped surroundings and in the process of the chemical reaction.
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Alonso, M.C., Drummond, D.R., Kain, S., Hoeng, J., Amos, L., Cross, R.A.: An ATP gate controls tibulin binding by the tethered head of kinesin-1. Science 316, 120–123 (2007)
Asbury, C.L., Fehr, A.N., Block, S.M.: Kinesin moves by an asymmetric hand-over-hand mechanism. Science 302, 2130–2134 (2003)
Astumian, R.D.: Biasing the random walk of a molecular motor. J. Phys. Condens. Matter 17, S3753–S3766 (2005)
Block, S.M., Goldstein, L.S.B., Schnapp, B.J.: Bead movement by single kinesin molecules studied with optical tweezers. Nature 348, 348–352 (1990)
Carter, N.J., Cross, R.A.: Mechanics of the kinesin step. Nature 435, 308–312 (2005)
Christof, J., Gebhardt, M., Clemen, A.E.-M., Jaud, J., Rief, M.: Myosin-v is a mechanical ratchet. Proc. Natl. Acad. Sci. USA 103, 8680–8685 (2006)
De Groot, S.R., Mazur, P.: Non-equilibrium Thermodynamics. North-Holland, Amsterdam (1962)
Hackney, D.D.: Processive motor movement. Science 316, 58–59 (2007)
Hooft, A.M., Maki, E.J., Cox, K.K., Baker, J.E.: An accelerated state of myosin-based actin motility. Biochemistry 46, 3513–3520 (2007)
Howard, J.: Mechanics of Motor Proteins and the Cytoskeleton. Sinauer Associates, Sunderland (2001)
Keller, D., Bustamante, C.: The mechanochemistry of molecular motors. Biophys. J. 78, 541–556 (2000)
Kudo, S., Magariyama, Y., Aizawa, S.: Abrupt changes in flagella rotation observed by laser dark-filed microscopy. Nature 346, 677–680 (1990)
Kull, F.J., Sablin, E.P., Fletterick, R.J., Vale, R.D.: Crystal structure of the kinesin motor domain reveals a structural similarity to myosin. Nature 380, 550–555 (1996)
Liepelt, S., Lipowsky, R.: Kinesin’s network of chemomechanical motor cycles. Phys. Rev. Lett. 98, 258102 (2007)
Lindén, M., Wallin, M.: Dwell time symmetry in random walks and molecular motors. Biophys. J. 92, 3804–3816 (2007)
Nishiyama, M., Higuchi, H., Yanagida, T.: Chemomechanical coupling of the forward and backward steps of single kinesin molecules. Nat. Cell Biol. 4, 790–797 (2002)
Noji, H., Yasuda, R., Yoshida, M., Kinosita, K., Jr.: Direct observation of the rotation of F1-ATPase. Nature 386, 299–302 (1997)
Parmeggiani, A., Julicher, F., Ajdari, A., Prost, J.: Energy transduction of isothermal ratchets: Generic aspects and specific examples close to and far from equilibrium. Phys. Rev. E 60, 2127 (1999)
Parrondo, J.M.R., De Cisneros, B.J.: Energetics of Brownian motors: a review. Appl. Phys. A 75, 179–191 (2002)
Qian, H.: The mathematical theory of molecular motor movement and chemomechanical energy transduction. J. Math. Chem. 27, 219–234 (2000)
Qian, H.: Motor protein with nonequilibrium potential: Its thermodynamics and efficiency. Phys. Rev. E 69, 012901 (2004)
Reimann, P.: Brownian motors: noisy transport far from equilibrium. Phys. Rep. 361, 57 (2002)
Sands, M., Feynman, R.P., Leighton, R.B.: The Feynman Lectures on Physics. Addison-Wesley, Reading (1963)
Sakakibara, H., Kojima, H., Sakai, Y., Katayama, E., Oiwa, K.: Inner-arm dynein c of chlamydomonas flagella is a single-headed processive motor. Nature 400, 596–589 (1999)
Shiroguchi, K., Kinosita, K., Jr.: Myosin v walks by lever Brownian motion. Science 316, 1208–1212 (2007)
Svoboda, K., Block, S.M.: Force and velocity measured for single kinesin molecules. Cell 77, 773–784 (1994)
Taniguchi, Y., Nishiyama, M., Ishhi, Y., Yanagida, T.: Entropy rectifies the Brownian step of kinesin. Nat. Chem. Biol. 1, 342–347 (2005)
Vale, R.D.: The way things move: Looking under the hood of molecular motor proteins. Science 288, 88 (2000)
Vale, R.D.: The molecular motor toolbox for intracellular transport. Cell 112, 467–480 (2003)
Vale, R.D., Funatsu, T., Pierce, D.W., Romberg, L., Harada, Y., Yanagida, T.: Direct observation of single kinesin molecules moving along microtubules. Nature 380, 451–453 (1996)
Wang, H., Oster, G.: The stokes efficiency for molecular motors and its applications. Europhys. Lett. 57, 134–140 (2002)
Yildiz, A., Tomishige, M., Vale, R.D., Selvin, P.R.: Kinesin walks hand-over-hand. Science 303, 676 (2004)
Zhang, Y.: Three phase model of the processive motor protein kinesin. Biophys. Chem. 136, 19–22 (2008)
Zheng, W., Fan, D., Wang, Z., Feng, M.: Kinesin is an evolutionarily fine-tuned molecular ratchet-and-pawl device of decisively locked direction. Biophys. J. 93, 3363–3372 (2007)
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Zhang, Y. The Efficiency of Molecular Motors. J Stat Phys 134, 669–679 (2009). https://doi.org/10.1007/s10955-009-9695-3
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DOI: https://doi.org/10.1007/s10955-009-9695-3