A chemical kinetic theory on muscle contraction and spontaneous oscillation

From a set of chemical kinetic equations describing the actin-activated myosin ATPase cycle, we show that, in active muscle, the fraction of myosin heads in any given biochemical state is independent of both [ADP] and [Pi]. Combining muscle mechanics data of Pate and Cooke, we deduce the muscle state equation in which muscle force is a state variable of the muscle system. The theoretical results are consistent with Bakerʹs experimental data but somewhat different from conventional muscle theory. Based on the muscle state equation with the knowledge of special structure of muscle, we present a physical mechanism which can lead to both contraction and oscillation of sarcomeres. It explains the muscle spontaneous oscillatory contraction in a natural way and agrees well with experimental data. The model will be helpful in studying the oscillatory behavior of cilia and flagella.