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.
Highlights
Cell polarity refers to the localization of signaling molecules to specific regions of the plasma membrane, and is required for fundamental cellular processes such as migration, directed growth, and differentiation
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
Summary
Cell polarity refers to the localization of signaling molecules to specific regions of the plasma membrane, and is required for fundamental cellular processes such as migration, directed growth, and differentiation. Mathematical models have been used to explain spontaneous pattern formation by biochemical systems since the 1950s [2,3] These models use diffusion-driven instabilities to generate symmetry breaking without relying on mechanisms such as diffusional barriers, directed transport, and molecular cross-linking. Instead, these systems require: (1) positive feedback to amplify local fluctuations; (2) chemical species that diffuse at different rates; and (3) a mechanism for limiting the growth of the polarity site. Goryachev and Polkhilko were the earliest to use a Turing-type model to study yeast polarization [4]. Non-Turing type models of polarity require perturbations of finite strength to induce pattern formation [5]
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