Mathematics Colloquia and Seminars

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Abstract: Crawling cells, for example the white blood cells that crawl in your body in search of infections, display many distinct dynamical patterns, driven by both biochemistry (diffusion and reactions between chemical species) and mechanics (physical forces between the components inside cells). Our understanding of these spatiotemporal patterns has been aided by mathematical modeling using techniques including partial differential equations (PDEs). Recently, traveling waves have been observed in the protein actin, which powers certain cells’ ability to crawl. Following experimental observation of one type of crawling cell, the fish epithelial keratocyte, we hypothesized that traveling waves are excitable waves arising from interactions of three components: actin, the adhesions that attach the cell to its environment, and VASP, a protein that regulates actin. We developed a mathematical model formulated as a system of PDEs with a nonlocal integral term and noise. Numerical solutions lead to a number of predictions, including that VASP also exhibits a traveling wave out of phase with the actin wave, confirmed in further experiments. Our model also reveals a role for tension in the membrane that surrounds the cell, which otherwise would be difficult to observe directly by experiment.

Pizza and soda will be provided.