Nonlinear Phenomena in Complex Systems, 2006, Vol.9, No.2, pp.150-162

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2006, Vol.9, No.2, pp.150-162

Refractory-Activation Oscillator Model for the Cross-Bridge Formation in the Acto-Myosin System- Two Cooperative Phenomena in the Hill's Relation.
Y. Aizawa, T. Mitsui, and T. Kameda

The Refractory-Activation Oscillator model is proposed to explain the cross-bridge formation process in the acto-myosin system. First, the phase space structure of the refractory-activation oscillator is studied numerically and the bifurcation diagram of the attractor is analysed in detail. It is emphasized that the length of the refractory period influences the efficiency of the chemo-mechanical energy transformation very sensitively in the microscopic level. Next, the motion of the myosin filament is analysed by carrying out with the model composed of many refractory-activation oscillators, and it is shown that the Hill's relation can be reproduced by this model. The Hill's relation is explained in terms of the cooperative organization of many refractory-activation oscillators and a significant result is that two kinds of cooperative phenomena are embedded in the Hill's relation; one is the coherent cooperativity which generates high velocity and weak force in the sliding process, another is the turbulent cooperativity which generates strong force and low velocity in the sliding motion. The macroscopic efficiency of the chemo-mechanical energy transformation is discussed in relation to those cooperative aspects by use of the module-space diagram. Finally, the system size dependence of the force generation is analysed, and anomalous scaling laws are derived in each cooperative regime hidden behind the Hill's relation.
Key words: refractory-activation oscillator, cross-bridges, acto-myosin system, biphasic Hill's relation, coherent cooperativity, turbulent cooperativity

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