Particle-based simulations of polarity establishment reveal stochastic promotion of Turing pattern formation

Abstract

Polarity establishment, the spontaneous generation of asymmetric molecular distributions, is a crucial component of many cellular functions. Saccharomyces cerevisiae (yeast) undergoes directed growth during budding and mating, and is an ideal model organism for studying polarization. In yeast and many other cell types, the Rho GTPase Cdc42 is the key molecular player in polarity establishment. During yeast polarization, multiple patches of Cdc42 initially form, then resolve into a single front. Because polarization relies on strong positive feedback, it is likely that the amplification of molecular-level fluctuations underlies the generation of multiple nascent patches. In the absence of spatial cues, these fluctuations may be key to driving polarization. Here we used particle-based simulations to investigate the role of stochastic effects in a Turing-type model of yeast polarity establishment. In the model, reactions take place either between two molecules on the membrane, or between a cytosolic and a membrane-bound molecule. Thus, we developed a computational platform that explicitly simulates molecules at and near the cell membrane, and implicitly handles molecules away from the membrane. To evaluate stochastic effects, we compared particle simulations to deterministic reaction-diffusion equation simulations. Defining macroscopic rate constants that are consistent with the microscopic parameters for this system is challenging, because diffusion occurs in two dimensions and particles exchange between the membrane and cytoplasm. We address this problem by empirically estimating macroscopic rate constants from appropriately designed particle-based simulations. Ultimately, we find that stochastic fluctuations speed polarity establishment and permit polarization in parameter regions predicted to be Turing stable. These effects can operate at Cdc42 abundances expected of yeast cells, and promote polarization on timescales consistent with experimental results. To our knowledge, our work represents the first particle-based simulations of a model for yeast polarization that is based on a Turing mechanism.

Author summary

Many cells need to generate and maintain biochemical signals in specific subcellular regions. This phenomenon is broadly called polarity establishment, and is important in fundamental processes such as cell migration and differentiation. A key polarity factor found in diverse organisms, including yeast and humans, is the protein Cdc42. In yeast, Cdc42-dependent polarization occurs through a self-reinforcing biochemical signaling loop. Directional cues can guide polarity establishment, but interestingly, yeast can polarize in the absence of such a cue. The mechanism thought to underlie this symmetry breaking involves the amplification of inhomogeneities in molecular distributions that arise from molecular-level fluctuations. We investigated the effects of random fluctuations on polarization by performing particle-based simulations of the Cdc42 signaling network. We found that fluctuations can facilitate polarization, allowing faster polarization, and polarization over a broader range of concentrations. Our observations may help understand how polarity works in other systems.