Information on the thesis

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 cross-
bridges 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.
Key words: sarcomere, cross-bridges, spatially explicit model, viscoelastic
properties, collective effects, contractile filaments compliance