# Phase Field Modeling of Dictyostelium Discoideum Chemotaxis

## TL;DR

This paper introduces a phase field model for Dictyostelium discoideum chemotaxis, integrating chemical signaling and cell movement to replicate pseudopodia patterns observed during chemotaxis.

## Contribution

It develops a novel coupled phase field and reaction-diffusion model that captures cell movement and chemical dynamics simultaneously.

## Key findings

- Successfully mimics pseudopodia patterns during chemotaxis
- Efficient spectral method for numerical solution
- Extends phase-field formulation for membrane-restricted components

## Abstract

A phase field approach is proposed to model the chemotaxis of Dictyostelium discoideum. In this framework, motion is controlled by active forces as determined by the Meinhardt model of chemical dynamics which is used to simulate directional sensing during chemotaxis. Then, the movement of the cell is achieved by the phase field dynamics, while the reaction-diffusion equations of the Meinhardt model are solved on an evolving cell boundary. This task requires the extension of the usual phase-field formulation to allow for components that are restricted to the membrane. The coupled system is numerically solved by an efficient spectral method under periodic boundary conditions. Numerical experiments show that our model system can successfully mimic the typically observed pseudopodia patterns during chemotaxis.