Numerical simulation on a cell polarisation model: the polar case

TL;DR

This paper performs numerical simulations on cell polarization models based on nonlinear convection-diffusion equations, demonstrating their ability to describe polarization phenomena such as polarisome formation.

Contribution

It provides a numerical analysis of existing cell polarization models, highlighting their capacity to simulate polarization and polarisome emergence.

Findings

Models can simulate spontaneous polarization.

Numerical results illustrate polarisome formation.

Models capture positive feedback in protein localization.

Abstract

When it is polarised, a cell develops an asymmetric distribution of specific molecular markers, cytoskeleton and cell membrane shape. Polarisation can occur spontaneously or be triggered by external signals, like gradients of signalling molecules... In this work, we use the published models of cell polarisation and we set a numerical analysis for these models. They are based on nonlinear convection-diffusion equations and the nonlinearity in the transport term expresses the positive loop between the level of protein concentration localised in a small area of the cell membrane and the number of new proteins that will be convected to the same area. We perform numerical simulations and we illustrate that these models are rich enough to describe the apparition of a polarisome.