A thermodynamic muscle model and a chemical basis for A.V. Hill's muscle equation

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.