Analysis of Peristaltic Waves & their Role in Migrating Physarum Plasmodia

The true slime mold \emph{Physarum polycephalum} exhibits a vast array of sophisticated manipulations of its intracellular cytoplasm. Growing microplasmodia of \emph{physarum} have been observed to adopt an elongated tadpole shape, then contract in a rhythmic, traveling wave pattern that resembles peristaltic pumping. This contraction drives a fast flow of non-gelated cytoplasm along the cell longitudinal axis. It has been hypothesized that this flow of cytoplasm is a driving factor in generating motility of the plasmodium. In this work, we use two different mathematical models to investigate how peristaltic pumping within \emph{physarum} may be used to drive cellular motility. We compare the relative phase of flow and deformation waves predicted by both models to similar phase data collected from \emph{in vivo} experiments using \emph{physarum} plasmodia. Both models suggest that a mechanical asymmetry in the cell is required to reproduce the experimental observations. Such a mechanical asymmetry is also shown to increase the potential for cellular migration, as measured by both stress generation and migration velocity.