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Chemotaxis is a directed cell movement in response to external chemicalstimuli. In this paper, we propose a simple model for the origin of chemotaxis- namely how a directed movement in response to an external chemical signal mayoccur based on purely reaction-diffusion equations reflecting inner working ofthe cells. The model is inspired by the well-studied role of the rho-GTPaseCdc42 regulator of cell polarity, in particular in yeast cells. We analyzeseveral versions of the model in order to better understand its analyticproperties, and prove global regularity in one and two dimensions. Usingcomputer simulations, we demonstrate that in the framework of this model, atleast in certain parameter regimes, the speed of the directed movement appearsto be proportional to the size of the gradient of signalling chemical. Thiscoincides with the form of the chemical drift in the most studied mean fieldmodel of chemotaxis, the Keller-Segel equation.

A simple reaction-diffusion system as a possible model for the origin of chemotaxis