Oscillating contractions and cytoplasmic flows in Physarum polycephalum

Flows over remarkably long distances are crucial to the functioning of many organisms, across all kingdoms of life. They are fundamental to power deformations required for migration or development, or to spread resources and signals. The slime mould Physarum polycephalum exemplifies both the important role of cytoplasmic flows and their remarkable organisation.

Several networks of *Physarum polycephalum*. The big darker blobs are oat flakes. Picture by Felix Bäuerle.

This organism consists of a network tubes filled with fluid. Actomyosin is organised circumferentially around the tubes. This contractile cortex generates radial oscillations of the tubes and flow of their fluid content. Those oscillations are strikingly organised, with single waves of contractions encompassing the entire organism up to a size of almost 2 centimetres. Positive stimuli, like food, increase the amplitude of the contractions and were recently shown to propagate by advection in the cytoplasm.

Following these observations, I developed a chemomechanical model of acto-myosin cortex mechanics coupled to a contraction-triggering, soluble chemical. The chemical itself is advected with the flows generated by the cortex driven deformations of a tube. The theoretical model predicts a dynamic instability giving rise to stable patterns of cortex contraction waves and oscillatory flows. Surprisingly, multiple patterns can be randomly generated. Notably, their size does not always match with the analytical prediction. By simulating a growing system, patterns several times larger than the prediction can be robustly simulated, consistent with the sizes observed experimentally.

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