Abstract:
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.
