Deterministic approximation of stochastic spatially explicit model of actin-myosin interaction in discrete filament lattice

One of commonly used approaches of biophysical modeling of muscle contractile apparatus is spatially explicit discrete lattice models in Monte Carlo simulation. Such models allow to reproduce structural features and actin-myosin interaction in the muscle contractile system more accurately. Limitation of such models is their low computational efficiency and stochasticity under certain circumstances. This work introduces deterministic approximation of stochastic model that considers a pair of rigid contractile filaments interaction. Approximation background is discreetness of spacing between cross-bridges and binding sites. Due to this property cross-bridges can be divided into discrete groups with the same strain, and considered statistically using the set of ordinary differential equations. Deterministic model is more computationally efficient, operates with average values. Within the given approach isotonic contraction was simulated. A comparison with Monte Carlo simulation demonstrates that approximation reproduces results for stochastic model with large number of cross-bridges. Also within the deterministic model a mechanism and essential conditions for oscillations appearance in isotonic transient response, relations of their parameters with geometrical ones of filaments lattice were examined, theoretical and experimental results were compared. The proposed approach can also be applied to approximation of continuous Huxley-based models solutions. Advantage over existing numerical methods is their greater numerical stability.