William R. Holmes, Vanderbilt University, Department of Physics and Astronomy

Modeling and analysis of spatially organizing systems regulating cell polarity and organization

Cellular organization is regulated by a complex network of interactions among cytoskeletal regulators. In this talk, I will use mathematical modeling to show how these complex interactions can give rise to a range of morphological cellular behaviors. From a mathematical perspective, this can be viewed as a problem of understanding the source of and links between a number of distinct types of spatio-temporal pattern formation. I will thus first introduce new non-linear perturbation tools that I have helped develop and have used extensively to study these problems. These tools substantially simplify the non-linear analysis of systems involving more than two or three interacting variables while providing more information than common linear tools (e.g. Turing analysis). I’ll then discuss a number of applications including 1) understanding how protein dynamics (e.g., Rho GTPases) give rise to a diverse array of cellular morphologies observed experimentally, 2) how interactions between these regulators give rise to a novel type of wave dynamics, and 3) how feedbacks between these proteins and mechanical membrane tension provide a means for cells to adapt to high concentration signaling environments.