Mishchenko A. Simulation study of sarcomere structure role in molecular mechanism of muscle contraction

Some aspects of relationship between sarcomere structure and muscle function are steel poorly understood. The aim of the work was to study the functional role of the myofilaments spatial structure in the process of sarcomere force generation and sliding in various contraction modes. Role of spatial structure has been studied in several aspects: its ability to modulate actomyosin interactions; its role in the cooperative effects formation in molecular motor assemblies; role of spatial effects in molecular mechanism of viscoelastic behavior of active muscle fibers. In order to reproduce constraints imposed on the interactions of cross bridges with actin binding sites in filament lattice the study used spatially distributed models. To understand the role of filaments lattice compliance and their local deformations in sarcomere mechanics a stochastic mechanochemical model of the pair compliant contractile filaments was considered. The presence of elasticity of contractile filaments influenced the sarcomere mechanics during isotonic contraction, isometric force development and force response to ramp lengthening. Local filaments deformations modulate actomyosin interactions by changing the mutual arrangement of cross-bridges and binding sites. They also affect the cooperative effects of cross-bridges by changing the regularity of the filament lattice structure. The presence of elasticity can also affect the mechanical operation of individual cross-bridges. The work that they do partially goes to the deformation of elastic filaments. It is shown that the discreteness of the filament lattice can be an important factor in the formation of collective effects between myosin motors. In particular, stepwise sliding of the half-sarcomere in isotonic mode was considered. The basis of such motion is the synchronization of individual cross-bridges mechanochemical transitions. Continuous histograms of step-size distribution that were retrieved in the model are similar to that obtained in the experiment. A mechanism and essential conditions for stepwise motion appearance in isotonic transient response, relations of their parameters with geometrical ones of filaments lattice were examined. Deterministic approximation of stochastic model that considers a pair of rigid contractile filaments interaction was introduced. 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. A comparison with Monte Carlo simulation demonstrates that approximation reproduces results for stochastic model with large number of cross-bridges. The proposed approach can also be applied to approximation of continuous Huxley-based models solutions. Advantage in this case over existing numerical methods is their greater numerical stability. A number of deterministic spatially distributed models that reproduce the viscoelastic mechanics of active rabbit psoas muscle fibers were created with using global optimization methods. The analysis of the spatiotemporal dynamics of the attached crossbridges distributions during the simulation of step and sinusoidal length perturbations, showed that the exponential processes (A), (B) and (C) are related with recovery of a disturbed edge areas of cross-bridges distributions. The importance of the spatial constrains in the implementation of the mechanism of the observed viscoelastic properties was shown.