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.
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