Stochastic model for cell polarity

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.Comment: Published in at http://dx.doi.org/10.1214/11-AAP788 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org