Abstract
We describe the energetics of motor proteins by taking F\(_1\)-ATPase as an example. To clarify the meaning of the mechanical works which are experimentally measured, we first identify the heat, which satisfies the second law of thermodynamics, and next formulate the work through the first law of thermodynamics. The theoretical expressions of the mechanical works reveal that the experimentally measured works have a theoretical basis. Contrary to the mechanical work, the measurement of the heat is still developing. We introduce an attempt to measure a part of the heat, which is related to the experimentally accessible quantities through a nonequilibrium equality.
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References
Abrahams JP, Andrew GW, Leslie AG, Lutter R, Walker JE (1994) Structure at 2.8 Å resolution of F\(_1\)-ATPase from bovine heart mitochondria. Nature 370(6491):621–628
Crooks GE (1999) Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. Phys Rev E 60(3):2721–2726
Elston T, Wang H, Oster G (1998) Energy transduction in ATP synthase. Nature 391(6666):510–513
Gaspard P, Gerritsma E (2007) The stochastic chemomechanics of the F\(_1\)-ATPase molecular motor. J Theor Biology 247(4):672–686
Harada T, Sasa SI (2005) Equality connecting energy dissipation with a violation of the fluctuation-response relation. Phys Rev Lett 95(13)
Harada T, Sasa SI, (2006) Energy dissipation and violation of the fluctuation-response relation in nonequilibrium Langevin systems. Phys Rev E 73(2)
Harada Y, Sakurada K, Aoki T, Thomas DD, Yanagida T (1990) Mechanochemical coupling in actomyosin energy transduction studied by in vitro movement assay. J Mol Biol 216(1):49–68
Itoh H, Takahashi A, Adachi K, Noji H, Yasuda R, Yoshida M, Kinosita K (2004) Mechanically driven ATP synthesis by F\(_1\)-ATPase. Nature 427(6973):465–468
Jarzynski C (1997) Nonequilibrium equality for free energy differences. Phys Rev Lett 78(14):2690–2693
Kramers HA (1940) Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7(4):284–304
Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22(1):79–86
Kurchan J (1998) Fluctuation theorem for stochastic dynamics. J Phys A: Math Gen 31(16):3719–3729
Liu MS, Todd BD, Sadus RJ (2003) Kinetics and chemomechanical properties of the F\(_1\)-ATPase molecular motor. J Chem Phys 118(21):9890–9898
Noji H, Yasuda R, Yoshida M, Kinosita K (1997) Direct observation of the rotation of F\(_1\)-ATPase. Nature 386(6622):299–302
Noji H, Bald D, Yasuda R, Itoh H, Yoshida M, Kinosita K (2001) Purine but Not Pyrimidine Nucleotides Support Rotation of F\(_1\)-ATPase. J Biol Chem 276(27):25480–25486
Oster G, Wang H (2000)Reverse engineering a protein: the mechanochemistry of ATP synthase. Biochimica et Biophysica Acta (BBA)—Bioenergetics 1458(2):482–510
Rosing J, Slater EC (1972) The value of \(\Delta G^\circ \) for the hydrolysis of ATP. Biochimica et Biophysica Acta (BBA)—Bioenergetics 267(2):275–290
Saita E, Suzuki T, Kinosita K, Yoshida M (2015) Simple mechanism whereby the F\(_1\)-ATPase motor rotates with near-perfect chemomechanical energy conversion. Proc Natl Acad Sci 112(31):9626–9631
Sekimoto K (2010) Stochastic energetics. In: Lecture notes in physics, vol 799. Springer, Berlin. ISBN 978-3-642-05410-5
Toyabe S, Muneyuki E (2015) Single molecule thermodynamics of ATP synthesis by F\(_1\)-ATPase. New J Phys 17(1):015008
Toyabe S, Okamoto T, Watanabe-Nakayama T, Taketani H, Kudo S, Muneyuki E (2010) Nonequilibrium energetics of a single F\(_1\)-ATPase molecule. Phys Rev Lett 104(19)
Toyabe S, Watanabe-Nakayama T, Okamoto T, Kudo S, Muneyuki E (2011) Thermodynamic efficiency and mechanochemical coupling of F\(_1\)-ATPase. Proc Natl Acad Sci 108(44):17951–17956
Toyabe S, Ueno H, Muneyuki E (2012) Recovery of state-specific potential of molecular motor from single-molecule trajectory. EPL (Europhysics Letters) 97(4):40004
van Kampen NG (1992) Stochastic Processes in Physics and Chemistry. North-Holland personal library. North-Holland, Amsterdam Tokyo. ISBN 0-444-89349-0
Watanabe R, Okuno D, Sakakihara S, Shimabukuro K, Iino R, Yoshida M, Noji H (2012) Mechanical modulation of catalytic power on F\(_1\)-ATPase. Nat Chem Biol 8(1):86–92
Watanabe-Nakayama T, Toyabe S, Kudo S, Sugiyama S, Yoshida M, Muneyuki E (2008) Effect of external torque on the ATP-driven rotation of F\(_1\)-ATPase. Biochem Biophys Res Commun 366(4):951–957
Yasuda R, Noji H, Kinosita K, Yoshida M (1998) F\(_1\)-ATPase Is a Highly Efficient Molecular Motor that Rotates with Discrete \(120^\circ \) Steps. Cell 93(7):1117–1124
Yasuda R, Noji H, Yoshida M, Kinosita K, Itoh H (2001) Resolution of distinct rotational substeps by submillisecond kinetic analysis of F\(_1\)-ATPase. Nature 410(6831):898–904
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Nakayama, Y., Muneyuki, E. (2018). Ratchet Model of Motor Proteins and Its Energetics. In: Suzuki, M. (eds) The Role of Water in ATP Hydrolysis Energy Transduction by Protein Machinery. Springer, Singapore. https://doi.org/10.1007/978-981-10-8459-1_14
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DOI: https://doi.org/10.1007/978-981-10-8459-1_14
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