The investigator develops deterministic and stochastic two-dimensional computational models of the lamellipodia of fish keratocyte, fibroblast and nematode sperm cells. He derives and analyzes model equations for (i) protrusion of the leading edge, (ii) contraction of the lamellipodial cytoskeleton, and (iii) turnover and regulation of the lamellipodial cytoskeleton. The equations are integrated into the realistic two-dimensional model of the lamellipod. Simulations of the model equations on a free boundary domain produce maps of movements, forces and shapes that are compared with available experimental data to validate the models. The investigator uses a novel combination of mathematical analysis and computer simulations to develop explanatory and predictive models of migrating cells. Cell migration is fundamentally important in morphogenesis, wound healing, and cancer. It is based on a complex self-organized mechanochemical machine. Some relevant velocities, forces, rates and concentrations have been measured, but minute details of integration of forces, movements and chemical reactions into the cell migration are unclear. The investigator's goal is to understand quantitatively the molecular basis of cell movements. The models allow testing plausible scenarios of cell movements. They provide a new interdisciplinary level of understanding cell movements and new methods of predicting cell behavior in important medical and technological situations such as cell division, chemotaxis, phagocytosis, and wound healing. Students and postdoctoral researchers are involved in the project, enhancing the development of a trained workforce at the critical intersection of mathematics and biology.
