A poroelastic model for mechanochemical waves and pattern formation in Physarum polycephalum

Many processes in living cells are controlled by biochemical substances regulating active stresses. The cytoplasm is an active material with both viscoelastic and liquid properties. First, we incorporate the active stress into a two-phase model of the cytoplasm which accounts for the spatiotemporal dynamics of the cytoskeleton and the cytosol. The cytoskeleton is described as a solid matrix that together with the cytosol as interstitial fluid constitutes a poroelastic material. We find different forms of mechanochemical waves including traveling, standing and rotating waves by employing linear stability analysis and numerical simulations in one and two spatial dimensions.

In a second step, we expand the chemo-mechanical model in order to model the manifold contraction patterns observed experimentally in protoplasmic droplets of Physarum polycephalum. To achieve this, we combine a biophysically realistic model of a calcium oscillator with the poroelastic model derived in the first part of the talk and assume that the active tension is regulated by calcium. With the help of two-dimensional simulations the model is shown to reproduce the contraction patterns observed in in protoplasmic droplets as well as a number of other traveling and standing wave patterns.

Co-authors: Markus Radszuweit (PTB Berlin), Sergio Alonso (PTB Berlin), Harald Engel (TU Berlin )