Direct measurements of a relationship between force and actin-myosin biochemistry in muscle suggest that molecular forces in active muscle rapidly equilibrate among, not within, individual myosin crossbridges [Baker et al. (1999) Biophys J 77: 2657-2664]. This observation suggests a thermodynamic model of muscle contraction in which muscle, not an individual myosin crossbridge, is treated as a near-equilibrium system. The general approach can be applied to any ensemble of molecular motors that undergo a physicochemical step against a constant external potential. In this paper we apply the model to a simple two-state crossbridge scheme like that proposed by A.F. Huxley (1957) [Prog Biophys 7: 255-317], and we immediately obtain A.V. Hill's muscle equation. We show that this equation accurately describes steady-state muscle mechanics, biochemistry and energetics. This thermodynamic model provides a novel description of force-dependent actin-myosin kinetics in muscle and provides precise chemical expressions for myosin cooperativity, myosin duty ratios, the number of working strokes per ATP hydrolyzed, muscle efficiency, and energy transfer.
Bibliographical noteFunding Information:
We thank R.D. Astumian, R. Cooke, E. de la Cruz, M.E. Fisher, Y. Goldman, J. Grinband, T.L. Hill, A.F. Huxley, A.B. Kolomeisky, L.E.W. LaConte, D.W. Maughan, J.R. Moore, K.A. Palmiter, E. Pate, J. Patlak, and E.W. Taylor for helpful discussions and comments, with special thanks to D.M. Warshaw for his contributions and support. This work was supported by the National Institutes of Health (AR32961) and the Minnesota Supercomputer Institute.