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Mathematics Colloquium: Morphology and Migration: Cellular Adaptations from Learning to Wound Healing
4:10 p.m. Neill 5W
Abstract: Living organisms possess multiple ways to adapt to changes in their environment, many at the cellular level. In this talk, we look at two examples of cellular adaptation: The interdependence of form and function in the extension and contraction of Hippocampal neurons, and the extension-adhesion-contraction model for crawling in simple cells. We will compare mathematical models for these adaptations and look at tools for analyzing the models and their simulations Dedritic spines protrude from the surface of a neuron, often within its dentritic arbor. They are the loci for 95 percent of excitable neuronal connections in the central nervous system. In recent experiments, caffeine-induced calcium released from internal stores caused dendritic spine extension, while glutamate-induced increases in calcium caused them to contract. We develop a continuum model for calcium-mediated dynamic dendritic morphology and explore the implications these adaptations may have upon neuronal signaling. Analysis confirms the existence of limit cycles and equilibrium points for activity and morphology in distinct parts of the dendritic tree. Migration of animal cells underlies wound healing and cancer cell metastasis. These cells accomplish motion using a complex network of actin and myosin, with localized protrusion and contraction. However, these proteins are involved in many aspects of cell behavior and require a host of accessory proteins, adding to the complexity of experimental interpretation and the modeling process. We, therefore, will look at simpler cells which crawl in a similar manner and attempt to fully understand their dynamics before adding complexity.