Mechanistic mathematical model of polarity in yeast.

The establishment of cell polarity involves positive-feedback mechanisms that concentrate polarity regulators, including the conserved GTPase Cdc42p, at the "front" of the polarized cell. Previous studies in yeast suggested the presence of two parallel positive-feedback loops, one operating as a diffusion-based system, and the other involving actin-directed trafficking of Cdc42p on vesicles. F-actin (and hence directed vesicle traffic) speeds fluorescence recovery of Cdc42p after photobleaching, suggesting that vesicle traffic of Cdc42p contributes to polarization. We present a mathematical modeling framework that combines previously developed mechanistic reaction-diffusion and vesicle-trafficking models. Surprisingly, the combined model recapitulated the observed effect of vesicle traffic on Cdc42p dynamics even when the vesicles did not carry significant amounts of Cdc42p. Vesicle traffic reduced the concentration of Cdc42p at the front, so that fluorescence recovery mediated by Cdc42p flux from the cytoplasm took less time to replenish the bleached pool. Simulations in which Cdc42p was concentrated into vesicles or depleted from vesicles yielded almost identical predictions, because Cdc42p flux from the cytoplasm was dominant. These findings indicate that vesicle-mediated delivery of Cdc42p is not required to explain the observed Cdc42p dynamics, and raise the question of whether such Cdc42p traffic actually contributes to polarity establishment.