| Many facets of mathematics, science and engineering rely on numerical methods to study complex systems, for which analytical methods fail. For example, in particle-based models the positions of individual particles under the influence of various forces are monitored over time. These models are used to study phenomena ranging from the structure and dynamics of galaxies (where particles represent stars) to proteins (where particles represent atoms). In this document, we present two applications of particle-based modeling to study microscopic dynamics in cell biology, which would otherwise be invisible by current experimental methods. In both models, the particles represent protein molecules, and we calculate the stochastic biochemical reactions and diffusion of tens of thousands of proteins over time. We utilize Generally Programmable Graphics Processing Units (GPGPUs) to achieve the high performance computing necessary to simulate these large scale models.;Chapter 1 begins with the observation that the mobility of Rac1 molecules, which are important regulators of the cell cytoskeleton, is spatially regulated in migrating cells. Specifically, Rac1 molecules near the leading edge have less mobility than those in the trailing edge. We create a particle-based stochastic reaction-diffusion model to test the hypothesis that patches of actin, called 'actin islands', are responsible for this observation. We find that these islands are capable of producing the spatially-dependent mobility measured by in vivo experiments.;Chapters 2 and 3 discuss a more complex model built to study cellular gradient sensing, which is the ability of singular cells to detect external chemical gradients. This fundamental biological process allows cells to move or grow towards favorable environments and away from toxic environments. We study this process in the context of yeast mating; wherein, a haploid yeast cell senses the pheromone emitted by a mating partner. These cells are capable of sensing shallow gradients, in which molecular-level noise from reactions and diffusion is relatively large. Chapter 2 describes the particle-based stochastic reaction-diffusion model we built to quantify noise-reduction mechanisms proposed elsewhere. Chapter 3 shows neither time-averaging nor receptor endocytosis sufficiently reduces noise; however, the pheromone protease Bar1 may improve gradient sensing in certain cases. |
