Cell polarity is a classic example of symmetry-breaking in biology. In response to an internal or external cue, the cell asymmetrically localizes components that were previously uniformly distributed. Although cell polarity is an essential feature of living cells, it is far from being well-understood. Previous mathematical modeling has produced insights into generic mechanisms that can explain the formation and maintenance of polarization. The bulk of this work has relied on deterministic modeling. Using a combination of computational modeling and biological experiments, we closely examine an important prototype of cell polarity: the pheromone-induced formation of the Saccharomyces cerevisiae polarisome. Our spatial stochastic model of polarisome formation is composed of a reaction network based on evidence from the literature, and we estimated parameters using our experimental data.

We find that noise in the system results in a behavior we term spatial stochastic amplification , a phenomenon where increased noise results in tighter polarization. This model includes a putative role for a scaffold protein, Spa2, in stabilizing actin cables. We quantify, via experiments and modeling, both the dynamics and spatial distribution of the polarisome in various Spa2 partial deletions and find evidence supporting the existence of this novel function for Spa2. Simulating our polarisome model highlighted the need for efficient methods for spatial stochastic simulation. To that end, we have developed the diffusive finite state projection (DFSP) method. This method relies on taking interleaving steps of reaction and diffusion, and then solving diffusion efficiently with a finite state projection. As with many other approximate methods for spatial stochastic simulation, the DFSP method relies on splitting the reaction-diffusion master equation (RDME) operator.

However, because there has been no published method for estimating (and thus controlling) the error generated from splitting the RDME operator, we developed a local estimator for this error. This estimator allows practical adaptive implementation of many existing algorithms and opens the door to parallelization of spatial stochastic simulation.