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

## TL;DR

This paper models amoeboid movement in Physarum polycephalum using an active poroelastic two-phase framework, capturing oscillatory behaviors and flow patterns but not net motion, aligning with experimental observations.

## Contribution

It extends a poroelastic two-phase model to include free boundaries and substrate friction, revealing oscillatory motion and flow patterns consistent with experiments.

## Key findings

- Reproduces experimentally observed oscillation periods and amplitudes.
- Predicts alternating flow directions at boundaries and in the center.
- Shows no net motion occurs in the model due to spatially uniform substrate friction.

## Abstract

We investigate flow-driven amoeboid motility as exhibited by microplasmodia of Physarum polycephalum. A poroelastic two-phase model with rigid boundaries is extended to the case of free boundaries and substrate friction. The cytoskeleton is modeled as an active viscoelastic solid permeated by a fluid phase describing the cytosol. A feedback loop between a chemical regulator, active mechanical deformations, and induced flows gives rise to oscillatory and irregular motion accompanied by spatio-temporal contraction patterns. We cover extended parameter regimes of active tension and substrate friction by numerical simulations in one spatial dimension and reproduce experimentally observed oscillation periods and amplitudes. In line with experiments, the model predicts alternating forward and backward ectoplasmatic flow at the boundaries with reversed flow in the center. However, for all cases of periodic and irregular motion, we observe practically no net motion. A simple theoretical argument shows that directed motion is not possible with a spatially independent substrate friction.