A mathematically modelled cytogel cortex exhibits periodic Ca++-modulated contraction cycles seen in Physarum shuttle...

If each of many cells of an embryo (or different zones in a single cell) possess identical active cytogel machinery, having the 'right' mechanochemical response properties, then the collective interaction among those identical participants leads automatically to the globally coherent tissue deformations seen in embryogenesis, and to shuttle streaming in the plasmodial slime mould Physarum polycephalum. Biologically plausible, and experimentally verifiable hypotheses are proposed concerning how the tension generated by a strand of cytogel is determined by the deformation it suffers and by the concentration of a contraction trigger chemical, Ca2+, whose kinetics involve coupling to mechanical strain. The consequences of these hypotheses, deduced by solving the appropriate differential equation systems numerically, and displayed in computer-animated films, closely imitate diverse tissue deformation events seen in developing embryos. The same hypotheses on cytogel behaviour are used to model a thick-walled Physarum vein segment, and two such segments are set up to be able to pump endoplasm back and forth between them. Under certain conditions, this model exhibits spontaneous rhythmic mechanochemical oscillations, many features of which correlate well with shuttle streaming in Physarum. Small gradual variations of parameters, presumably under genetic control, are shown to cause abrupt and biologically interesting bifurcations of the qualitative behaviour of the model.