On thermodynamics and relaxation properties of eukaryotic cells

Mechanical properties of eukaryotic cells play an important role in the development of pathological processes. Currently, there are no complete models reflecting the full phenomenology of the mechanical behavior of the cell. Statistical thermodynamics methods have the potential to provide a framework for understanding the influence of structural properties on the stress-strain state of cells under external loading. In this paper, we develop a statistically based thermodynamic description of the eukaryotic cell to simulate the processes of cell contraction or extension as well as stress relaxation. In addition, it is proposed to use an order parameter to describe the orientation properties of the cell cytoskeleton and obtained a form of free energy, depending on this parameter, temperature and external stress. An orientation-viscoelastic body as a model of a representative cell volume has been proposed in this paper. Following the linear thermodynamics, the evolution equations describing the mechanical behavior of the representative cell volume have been derived. It was shown that the power law for the relaxation times conventionally introduced by the usage of the fractional derivatives in generalized Maxwell-Kelvin viscoelasticity of the cell cytoskeleton mechanical behavior follows from the orientation kinetics of the ensemble of actin filaments revealing the orientation ordering with the signs of the first kind criticality. The introduction of a relaxation spectrum is discussed, allowing one to improve the consistency of simulation results with atomic force microscopy data of living cells.