On the spontaneous emergence of cell polarity

Abstract

Many cell types can spontaneously switch from spatial homogeneity to a polarized state — even without external cues. A mathematical model now strips this phenomenon down to its bare bones. Favouring chance recruitment of a given signalling molecule to sites at the cell's membrane where it is already bound — a positive feedback — is sufficient to allow the spontaneous emergence of polarity, provided that the total pool of this molecule is small. When the number of molecules becomes too high, other biological mechanisms such as cytoskeleton-based transport are needed. The model is reminiscent of some population genetics studies and is confirmed experimentally in Cdc42-dependent polarization of yeast cells. A mathematical model shows that favouring chance recruitment of a given signalling molecule to sites at the cell's membrane where it is already bound-a positive feedback-is sufficient to allow the spontaneous emergence of polarity, provided that the total pool of this molecule is small. Diverse cell polarity networks require positive feedback for locally amplifying distributions of signalling molecules at the plasma membrane1. Additional mechanisms, such as directed transport2 or coupled inhibitors3,4, have been proposed to be required for reinforcing a unique axis of polarity. Here we analyse a simple model of positive feedback, with strong analogy to the ‘stepping stone’ model of population genetics5, in which a single species of diffusible, membrane-bound signalling molecules can self-recruit from a cytoplasmic pool. We identify an intrinsic stochastic mechanism through which positive feedback alone is sufficient to account for the spontaneous establishment of a single site of polarity. We find that the polarization frequency has an inverse dependence on the number of signalling molecules: the frequency of polarization decreases as the number of molecules becomes large. Experimental observation of polarizing Cdc42 in budding yeast is consistent with this prediction. Our work suggests that positive feedback can work alone or with additional mechanisms to create robust cell polarity.