| Summary: | Cells that move in response to an external signal are crucial for diverse physiological processes such as embryogenesis, neurogenesis, wound healing and immune surveillance. Motile cells are also implicated in disease processes such as rheumatoid arthritis and metastatic cancer. Polymerization of the protein actin, one of the three proteins in a cell’s cytoskeleton, generates the force required to propel a cell in response to a stimulus. The goal of this thesis is to use mathematical modelling to gain a better understanding of how spatial asymmetries in signalling molecules are established and how these signalling molecules direct actin polymerization to produce characteristic actin densities and persistent directed motion. As a first step in understanding the complicated signalling cascades activated by an external signal, I identify modules important for regulation of actin polymerization in motile cells. Based on experimental evidence, I focus on phosphoinositides (PIs), membrane-bound lipids that mediate sensing of external gradients, and Rho proteins, potent regulators of the actin cytoskeleton. I consider models of actin dynamics, Rho proteins and PIs in isolation based on known or observed biochemical events. I then formulate a combined model that simulates actin polymerization dynamics under the regulation of both PIs and Rho proteins. I base all the models proposed here on experimental observations that indicate how PIs and Rho proteins interact with each other and how they affect actin dynamics. The models presented here generate behaviours consistent with experimental observations of both normal and mutant cells and suggest possible mechanisms for recent experimental observations. I show that a model based on biological evidence using reasonable parameter values gives rise to spatial profiles of signalling molecules and actin filaments that are consistent with experimental observations. I find that crosstalk between Rho proteins is required for maintenance of directed motion. I suggest how actin polymerization could be involved in the maintenance of the spatial gradients of PIs and propose experiments to test my hypothesis. These testable hypotheses can be used to guide experiments that could then be used to further refine the models and shed light on the regulatory processes involved in cell motility. === Science, Faculty of === Mathematics, Department of === Graduate
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