A biophysical mechanism for muscle contraction and spontaneous oscillation

Based on a simplified model of mechanochemical actin-activated myosin ATPase cycle the muscle state equation and muscle kinetic equation are deduced from the biochemical thermodynamic principles. A set of chemical kinetic equations describing the cycle is established. From the non-equilibrium steady state solution of the set of equations, the experimental data on the fraction of myosin heads in any biochemical state independent of the concentration of inorganic phosphate, [Pi], and the data on the active, isometric muscle force varying logarithmically with [Pi] are explained. Therefore, how force as a state variable coupled to chemical reaction in muscle system is clarified and the muscle state equation is set up. Based on the muscle state equation, by use of the worm-like chain fits on the force versus extension characteristic of elastic elements in muscle and taking the viscous frictional force into account, a kinetic equation for sarcomeres is given and through the solution of the equation, both contraction and spontaneous oscillation of sarcomeres are explained in a natural way. The computational results agree well with experimental data. In the last section of the paper the implications relating to the possibly existed power stroke in the actin-myosin system are explored briefly in terms of the proposed simplified model on actomyosin ATPase cycle.