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.
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We thank M. Altschuler, A. Artyukhin, T. Kurtz, C. Neuhauser, M. Rosen, R. Ranganathan, B. Shraiman, G. Süel and O. Weiner for their positive feedback. We additionally thank P. Crews for latrunculin A and R. Li for the yeast strain. This research was supported by an NIH grant (RO1 GM071794), an NSF grant (DMS 0405084), the Endowed Scholars program at UT Southwestern Medical Center, and the Welch Foundation (I-1619, I-1644).
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Altschuler, S., Angenent, S., Wang, Y. et al. On the spontaneous emergence of cell polarity. Nature 454, 886–889 (2008). https://doi.org/10.1038/nature07119
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