Modeling Fission-Yeast Growth Partitioning and Oscillating Cortical Cdc42 Populations

Abstract

Polarity proteins mark two distinct, opposite regions of the fission-yeast cell membrane. These regions provide sites for growth, and maintaining them allows the cell to keep its elongated shape over generations. We present evidence that these regions compete for Cdc42, a growth precursor. A nonlinear-dynamics model divides the Cdc42 population into three subpopulations--one at each tip, one in the cytoplasm--and describes Cdc42 distributions by stable steady states of the dynamical system. This model describes this competition with differential equations that include autocatalytic accumulation and saturation of Cdc42 at the cell tips. According to this model, short cells must be monopolar and long cells must be bipolar, but cells of intermediate length could be either_stable monopolar and bipolar steady states coexist for intermediate lengths. However these divisions depend on parameters, as illustrated by a phase diagram. In addition to its polarization, we found that Cdc42 oscillates between tips. We present a delayed-differential-equation model that adds delayed amplification of dissociation at the tips, and show that the complete model survives at least three experimental challenges. First, we decrease the amount of Cdc42 by removing its effector, Gef1; this leads to later bipolarity. Second, we probe the coexistence region with actin-depolymerizing drug Latrunculin A; this shows that longer monopolar cells can become bipolar following a disturbance. Third, we calculate lower cross-correlations between tips in longer mutant cells; this suggests a decrease in competition's importance as cells grow further. We demonstrate possible effects of noise on this model and speculate on the competitive advantage gained despite the cost of maintaining active oscillations.