A novel stochastic simulation approach enables exploration of mechanisms for regulating polarity site movement

Abstract

Cells polarize their movement or growth toward external directional cues in many different contexts. For example, budding yeast cells grow toward potential mating partners in response to pheromone gradients. Directed growth is controlled by polarity factors that assemble into clusters at the cell membrane. The clusters assemble, disassemble, and move between different regions of the membrane before eventually forming a stable polarity site directed toward the pheromone source. Pathways that regulate clustering have been identified but the molecular mechanisms that regulate cluster mobility are not well understood. To gain insight into the contribution of chemical noise to cluster behavior we simulated clustering within the reaction-diffusion master equation (RDME) framework to account for molecular-level fluctuations. RDME simulations are a computationally efficient approximation, but their results can diverge from the underlying microscopic dynamics. We implemented novel concentration-dependent rate constants that improved the accuracy of RDME-based simulations of cluster behavior, allowing us to efficiently investigate how cluster dynamics might be regulated. Molecular noise was effective in relocating clusters when the clusters contained low numbers of limiting polarity factors, and when Cdc42, the central polarity regulator, exhibited short dwell times at the polarity site. Cluster stabilization occurred when abundances or binding rates were altered to either lengthen dwell times or increase the number of polarity molecules in the cluster. We validated key results using full 3D particle-based simulations. Understanding the mechanisms cells use to regulate the dynamics of polarity clusters should provide insights into how cells dynamically track external directional cues.

Particle-based simulations reveal two positive feedback loops allow relocation and stabilization of the polarity site during yeast mating

“…To systematically investigate whether the core yeast polarity circuit can yield indecisive Cdc42 clustering like that seen in mating cells, we used a previously validated model developed to describe Cdc42 behavior in vegetative yeast cells [12,17,32,33] 1). The model species are inactive Cdc42 (which can exchange between membrane and cytosolic compartments), active Cdc42 (which is restricted to the membrane compartment), and a complex between an effector and an activator of Cdc42 (here called Bem1-GEF).…”

“…Diffusion coefficient in cytoplasm Dc 15 µm 2 s -1 15 µm 2 s -1 [17] Diffusion coefficient on membrane Dm 0.0025 µm 2 s -1 0.0025 µm Total Cdc42 Cdc42 1800-3500 molecules 1800-3500 molecules [17] Total Bem1-GEF Bem1-GEF 20-600 molecules 20-600 molecules [17,32] Reactive radius r 0.05 µm 0.05 µm [17] Time step Dt 0.1 ms 0.1 ms [17] References are for the 2D model parameters. Probability rates l are presented for second-order reactions.…”

“…A value of K close to zero signifies a uniform distribution, and the larger the value of K the more polarized the distribution. We designated a threshold value of 1.5 to distinguish unpolarized (K < 1.5) from polarized (K ≥ 1.5) states for all 2D simulations (S1A earlier work [32]. Thus, it would require very precise control for cells to exploit this parameter regime to develop transitory polarity.…”

“…However, experimental findings suggest that yeast polarization is robust to increased molecular abundances [16,62,63], indicative of more robust nonlinear positive feedback. Particle-based models with non-linear positive feedback could also display noise-driven relocation of polarity clusters, but (as with the linear feedback model) such behavior required fine-tuning and only occurred in a small region of parameter space [32]. Thus, it remained unclear whether simply incorporating molecular noise into a polarity circuit would suffice to explain the indecisive polarity behavior seen in mating yeast.…”

“…Reaction rates for the 3D model are listed in Tables 1-3. Initial choices for the rate constants in the 3D simulations were obtained by converting rate constants from the 2D simulations using the method of Ramirez et al [32].…”