Geometrical resonance in the refractory-activation oscillator model for the crossbridge formation in the actomyosin system

In a previous study, the refractory-activation oscillator system (RAO system) was proposed to explain the crossbridge formation process in the actomyosin system. In this paper, the RAO system is analyzed to make clear how the geometrical structure of the actomyosin system affects its sliding dynamics and cooperative phenomena in the muscle contraction process. The geometrical structure is characterized by the spatial period ratio between myosin and actin filaments. First, the sliding velocity of the RAO model is shown to depend very sensitively on the period ratio, which we call velocity resonance. Next, the origin and the detailed aspects of the resonance are discussed based on the notion of maximum spacing between the relative equilibrium positions of myosin molecules. An important result is that the condition for the resonance depends not only on the period ratio but also on the number of myosin molecules (the system size N) because the width of each resonance zone changes by a law of O(N^-1). This means that an appropriate value of the period ratio must be realized in order to accomplish a coherent sliding motion in the actomyosin system under the condition of a finite N.