A continuum model of contraction waves and protoplasm streaming in strands of Physarum plasmodium.

We present a mathematical model for continuously distributed mechanochemical autooscillations (autowaves) in a protoplasmic strand of Physarum polycephalum. The model is based on a hypothesis of local positive feedback between deformation and contraction of the contractile apparatus. This feedback is mediated through a cell regulatory system whose kinetics involves coupling to mechanical strain. Mathematical analysis and computer simulations have demonstrated that the solutions of the model agree quantitatively with the available experimental data. In particular, hydrodynamic interaction alone, between different sections of the strand via the streaming endoplasm, is capable of inducing the characteristic contractile behavior.