Mathematical Investigation of Hydrodynamic Contributions to Amoeboid Cell Motility in Physarum polycephalum

In this work, we investigate the role of intracellular fluid flow in the migration of Physarum polycephalum. We develop two distinct models. Initially, we model the intracellular space of a physarum plasmodium as a peristaltic chamber. We derive a PDE relating the deformation of the chamber boundary and the flux of fluid along the chamber center line. We then solve this PDE for two distinct boundary deformations and evaluate the characteristic stress associated with the peristaltic flow. We compare the derived stress, as well as the relative phase of the deformation and flow waves, with values seen in experiments. Second, we develop a poro-elastic model of the interior of physarum that accounts for cytoskeletal structure, as well as adhesive interactions with the substrate. We develop this model within a framework similar to the Immersed Boundary method, which readily allows for computer simulation. We then use this model to simulate cell crawling across a range of parameters that characterize the coordination of adhesion to the substrate. We identify a spatio-temporal form of adhesion coordination that is consistent with experiments. We also show that this form is both efficient and robust, when compared to similar forms of adhesion coordination.