Role of mechanics in the appearance of oscillatory instability and standing waves of the mechanochemical activity in the Physarum polycephalum plasmodium

The modes of continuously distributed mechanochemical self-sustained oscillations (autowaves) exhibited by the Physarum plasmodium under different experimental conditions are reviewed. The role of the stretch-induced activation of contractile oscillations in the spatiotemporal self-organization of the plasmodium is elucidated. Different mathematical models describing contractile autowaves in ectoplasm and the streaming of the endoplasm are considered. Our mathematical models, which are based on the hypothesis of local positive feedback between the deformation and contraction of the contractile apparatus, are also presented. The feedback is mediated through a chemical regulatory system, whose kinetics involves the coupling to the mechanical strain. The mathematical analysis and computer simulations have demonstrated that the solutions of the models agree quantitatively with the experimental data. In particular, the only hydrodynamic interactions between the different parts of the plasmodium via the streaming endoplasm can lead to globally coordinated ectoplasmic contractions and vigorous shuttle endoplasmic streaming. These models, with empirically determined values of the viscoelastic parameters, well simulate the form and duration of the transient contractile processes observed after the isolation of the strands as well as the subsequent excitation of auto-oscillations and their stretch-induced activation under isotonic and isometric conditions.