Stochastic model for cell polarity

TL;DR

This paper analyzes a stochastic model of cell polarity, demonstrating how feedback mechanisms lead to spatial asymmetry in molecules on the cell membrane, with results connecting the model to Fleming--Viot processes.

Contribution

The paper extends previous models by representing cell polarity as an evolving population process and establishing its connection to Fleming--Viot processes under certain conditions.

Findings

Cell polarity emerges in the stochastic model due to feedback.

The model converges to a Fleming--Viot process in the infinite population limit.

Cell polarity depends on specific biological parameters.

Abstract

Cell polarity refers to the spatial asymmetry of molecules on the cell membrane. Altschuler, Angenent, Wang and Wu have proposed a stochastic model for studying the emergence of polarity in the presence of feedback between molecules. We analyze their model further by representing it as a model of an evolving population with interacting individuals. Under a suitable scaling of parameters, we show that in the infinite population limit we get a Fleming--Viot process. Using well-known results for such processes, we establish that cell polarity is exhibited by the model and also study its dependence on the biological parameters of the model.