A Monte Carlo study of stochastic phenomena in biological systems—: I. Mathematical treatment of the geometrical structure of muscle

Abstract

The geometrical structure of the molecular constitution of muscle is studied mathematically with regard to the elementary processes of chemomechanical energy conversion caused by the interaction between cross-bridges and actin sites. Based on a simplified model for the half-sarcomere, the structural unit of muscle, examinations are made by computer simulation of the effect of geometrical structure on muscle contraction and of its influence on the stochastic behavior of the elementary process. It is shown that muscle contraction sharply depends on the geometrical structure even if the property of individual elementary process is the same, and that a cyclic change, called a “reverberation,” appears among elementary processes only when the geometrical structure satisfies some mathematical conditions, as the natural structure in fact does. It is also shown that the noise in the elementary process is much reduced when the elementary processes are connected by a reverberation cycle, which leads to smooth and efficient contraction of muscle.