The effect of cell geometry on polarization in budding yeast

The localization (or polarization) of proteins on the membrane during the mating of budding yeast (Saccharomyces cerevisiae) is an important model system for understanding simple pattern formation within cells. While there are many existing mathematical models of polarization, for both budding and mating, there are still many aspects of this process that are not well understood. In this paper we set out to elucidate the effect that the geometry of the cell can have on the dynamics of certain models of polarization. Specifically, we look at several spatial stochastic models of Cdc42 polarization that have been adapted from published models, on a variety of tip-shaped geometries, to replicate the shape change that occurs during the growth of the mating projection. We show here that there is a complex interplay between the dynamics of polarization and the shape of the cell. Our results show that while models of polarization can generate a stable polarization cap, its localization at the tip of mating projections is unstable, with the polarization cap drifting away from the tip of the projection in a geometry dependent manner. We also compare predictions from our computational results to experiments that observe cells with projections of varying lengths, and track the stability of the polarization cap. Lastly, we examine one model of actin polarization and show that it is unlikely, at least for the models studied here, that actin dynamics and vesicle traffic are able to overcome this effect of geometry.Author summary: The ability of cells to spontaneously break symmetry and form patterns via networks of protein reactions is a well-studied, yet not fully understood, phenomenon. One particularly useful model system is the mating of yeast cells, where a localization of proteins on the membrane leads to actin cable formation, vesicle traffic, changes in material properties of the cell wall and ultimately to the growth of a mating projection. There is no shortage of mathematical models describing the mechanisms of polarization, yet they are often formulated as differential equations on simple domains. The effect of geometry on the dynamics of polarization has not been systematically explored. There is an interaction between the length scales of polarization and the features of the geometry of the cell that has been under-appreciated and may lead to novel biological insights.