Analysis of peristaltic waves and their role in migratingPhysarumplasmodia

Abstract

The true slime mold Physarum polycephalum exhibits a vast array of sophisticated manipulations of its intracellular cytoplasm. Growing microplasmodia of 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 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 in vivo experiments using Physarum plasmodia. The first is a PDE model based on a dimensional reduction of peristaltic pumping within a finite length chamber. The second is a more sophisticated computational model which accounts for more general shape changes, more complex cellular mechanics, and dynamically modulated adhesion to the underlying substrate. This models allows us to directly compute cell crawling speed. 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.

A lumped parameter model of endoplasm flow in Physarum polycephalum explains migration and polarization-induced asymmetry during the onset of locomotion

“…These contractions drive the observed cytoplasm flow along the longitudinal axis of the amoeba. The entire locomotion process is far from completely understood, but an asymmetry of the cell in terms of a softness gradient [9] seems to play a big role, as well as substrate adhesion [4, 40] and the transition from endo- to ectoplasm and vice versa.…”

“…It is known that the front of a migrating plasmodium is softer than the back. Local softening of the actin cortex plays a big role in the amoeboid movement of P. polycephalum [3, 9]. The ultrastructural analysis of a migrating mesoplasmodium also shows a denser, more organized actin cortex in the back and a weaker cortex in the front [8].…”

“…As we have described earlier [8], blebbing at the front, an asymmetrical actin distribution throughout the cell, and the presence of actin asters in the uroid, but their absence in the frontal area, provide a strong argument for a softer front. Furthermore, as Lewis and coworkers have shown [9], a softer front is a prerequisite for cell migration. In order to move forward, the cell needs to polarize and then establish a softness gradient.…”

Oscillatory motion of a droplet in an active poroelastic two-phase model

“…In [21,50], the front-to-back symmetry was broken by introducing externally imposed traveling waves of friction strength and contractile stress. Another approach to break the spatial symmetry in the time averaged distribution of the regulator variable c is to include reaction kinetics for the regulator as done in models for resting Physarum droplets earlier [31,33].…”

Emergence of dynamic contractile patterns in slime mold confined in a ring geometry

“…We will discuss this point hereafter. Note that in a plasmodium free to move, travelling waves are involved in the mechanism of peristaltic locomotion [5,[18][19][20].…”