A Novel Mathematical Model of Muscle Contraction

In a spatially explicit stochastic simulation of myosin S1 heads attaching to a single actin filament, a force overshoot during initial force develop-ment was observed. Employing the same model of the actomyosin cycle with the same transition rates in a mass-action approach did not show the same results. An analysis of the head populations revealed a qualitatively different behaviour during the transient phases. Subtle differences in the model assumptions were identified as cause of these differences. In mass-action models the detached myosin S1 heads were modelled locally, while spatially explicit stochastic simulations provided a global supply of myosin. Differences in model responses were particularly elevated in transitions that started from a model state where a high percentage of myosin heads was bound. In the stochastic simulations the myosin heads first had to detach before they could bind to the actin filament again, while the local myosin S1 supply in the mass-action models led to a faster response due to read-ily available myosin heads for attachment. Similarly, the myosin limitation in the stochastic simulation explained the initial force overshoots. A novel mathematical model of muscle contraction was developed on the basis of these observations. Computational results were used to demonstrate that the predictions of the new model exactly matched those of the spatially explicit stochastic simulations, which required significantly more computa-tional effort