Numerical simulation of the dynamics of molecular markers involved in cell polarisation

TL;DR

This paper presents numerical simulations of nonlinear convection-diffusion models to understand cell polarization, demonstrating their ability to describe the formation of a polarisome through intracellular protein dynamics.

Contribution

The study introduces mathematical models based on nonlinear equations and provides numerical simulations showing their effectiveness in capturing cell polarization phenomena.

Findings

Models can simulate spontaneous and signal-triggered polarization.

Simulations illustrate formation of a polarisome.

Nonlinear convection-diffusion equations effectively describe protein dynamics.

Abstract

A cell is polarised when it has developed a main axis of organisation through the reorganisation of its cytosqueleton and its intracellular organelles. Polarisation can occur spontaneously or be triggered by external signals, like gradients of signaling molecules ... In this work, we study mathematical models for cell polarisation. These models are based on nonlinear convection-diffusion equations. 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.