Cytomechanics of oscillatory contractions. Modeling the longitudinal dynamics of Physarum polycephalum protoplasmic strands

Abstract

A mathematical model of the longitudinal dynamics of an isolated strand of the Physarum polycephalum plasmodium has been constructed. Its contractile system is considered as a continual viscoelastic medium with passive and active components. The mathematical description of the longitudinal dynamics of the plasmodial strand is reduced to a system of three first-order differential equations, whose variables are its active stress, deformation, and the intracellular concentration of calcium ions. The model is based on the hypothesis that there exists a feedback loop, which appears because of the influence of strand stretching on the rate of the release of calcium ions, which in turn controls the active contraction and deformation of the strand. Nonlinear interactions between the variables evoke a loss of the stationary state stability and a self-excitation of mechanochemical autooscillations when the external load exceeds some critical value. The results of numerical solutions of the model with the empirically determined viscoelastic parameters are in good agreement with the available experimental data and testify to the adequacy of the description of strand dynamics by the mathematical model in which the contractile apparatus is a part of the cellular control system. In particular, this model well simulates the form and duration of transient mechanochemical processes observed under isotonic and isometric conditions immediately after strand isolation, as well as the subsequent excitation of autooscillations of the contractile activity and their activation by strand stretching.