Flow-induced channel formation in the cytoplasm of motile cells

Abstract

A model is presented to explain the development of flow channels within the cytoplasm of the plasmodium of the giant amoeba Physarum polycephalum. The formation of channels is related to the development of a self-organizing tubular network in large cells. Experiments indicate that the flow of cytoplasm is involved in the development and organization of these networks, and the mathematical model proposed here is motivated by recent experiments involving the observation of development of flow channel in small cells. A model of pressure-driven flow through a polymer network is presented in which the rate of flow increases the rate of depolymerization. Numerical solutions and asymptotic analysis of the model in one spatial dimension show that under very general assumptions this model predicts the formation of channels in response to flow.

Experimental models for Murray’s law

“…This provides a driving force for protoplasmic streaming, although initially it is undirected and uniform across the plasmodium. However, Guy et al proposed for a migrating plasmodium that an initially homogeneous flow of protoplasmic sol can de-stabilise the actin skeleton as it moves through the porous protoplasmic gel [35]. This in turn initiates channel formation if the flow is sufficiently rapid, through flow-dependent actin disruption and gel-sol interconversion.…”

Intracellular Fluid Mechanics: Coupling Cytoplasmic Flow with Active Cytoskeletal Gel

“…Numerical simulations revealed that a phase shift between the contractile wave and periodic changes in adhesion strength is the key to directional locomotion. Another notable application of the poroelastic model to Physarum is the study by Guy et al (2011), who used the Brinkman equation instead of Darcy's law, because in some regions of the cell, the volume fraction of polymer is very low and the macroscale viscous stresses are relevant. The important result of this study is that upon introduction to the model of the very plausible assumption that the frictional force from the fluid increases the depolymerization rate of the polymer network, a flow channel along the central axis of the cell evolves, as observed experimentally.…”

Oscillations and uniaxial mechanochemical waves in a model of an active poroelastic medium: Application to deformation patterns in protoplasmic droplets of Physarum polycephalum

“…The morphology of such networks is analyzed from the point of view of the physiology [14,16,17,18] as well as in the frame of graph theory [19,20,21,22,23]. On the other hand, the scientific focus also lies on small cellular structures of about 50 -800 µm length, where the amoeboid motility of migrating microplasmodia [24,25,26,27,28,29,30] is currently intensively investigated.…”