Institute of Continuous Media Mechanics UB RAS, Perm, Russia

Abstract. The research is devoted to the study of the process of eukaryotic cell loading at a constant rate based on a statistical-thermodynamic model considering the orientational properties of the cytoskeleton. The presented results demonstrate the sufficiency of the considered model representation, as well as its potential for detailed study of the evolution of the filament network. It is assumed that the actin cytoskeleton contributes mainly to the mechanical response of the cell. In accordance with this hypothesis, an order parameter of filament segments characterizing their current orientation is introduced. Using self-consistent field methods, the free energy dependent on this parameter is obtained. This characteristic allows us to assess scenarios of the evolution of the actin cytoskeleton structure. Following the theory of linear thermodynamics, an evolutionary equation describing the mechanical behavior of a representative volume of eukaryotic cells that satisfy the basic thermodynamic laws is obtained. Analytical dependencies obtained using a parallel combination of Scott-Blair fractional elements are considered as test data against which the check of the examined model is performed to verify its suitability. This mechanical analog approximates quite accurately the results of atomic force microscopy measurements for a wide class of cells, but does not allow studying the process of microstructure evolution. The problem of optimization of parameters of the statistical-thermodynamic model of a cell in comparison with a fractional model has been formulated and solved. The results of solutions of the statistical-thermodynamic model with the selected parameters are in good qualitative and quantitative agreement with the test dependencies. Variation of the value of the relative calculation error from the value of the step of integration of the evolutionary differential equation of the representative volume of the cell is presented in order to confirm the reliability of the obtained results of modeling the process of loading with constant rate.

Key words: cell mechanics, actin cytoskeleton, viscoelasticity, statistical thermodynamics, rheological models with fractional operators, atomic force microscopy.