Abstract
The GTPase Cdc42 is the master regulator of cell polarisation. During this process the active form of Cdc42 is accumulated at a particular site on the cell membrane called the pole. It is believed that the accumulation of the active Cdc42 resulting in a pole is driven by a combination of activation-inactivation reactions and diffusion. It has been proposed using mathematical modelling that this is the result of diffusion-driven instability, originally proposed by Alan Turing. In this study we develop a 3D bulk-surface model of the dynamics of Cdc42. We show that the model can undergo both classic and non-classic Turing instability. We thoroughly investigate the parameter space for which this occurs. Using simulations we show that the model can be used to simulate polarisation and to predict a number of relevant quantitative measures, including pole size and time to polarisation.
