Mathematics Colloquia and Seminars

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Chemotaxis is the directed movement of cells in response to extracellular chemical signals. It is crucial in many processes such as bioremediation, wound healing and cancer metastasis. Chemotaxis of cell populations has been widely described using phenomenological PDE models such as Keller-Segel equations. Fundamental questions of these models include the applicability of them and connections of them with cellular processes such as cell signalling and movement. In this talk, I will address these questions for chemotaxis of swimming bacteria. Our results show that these models can quantitatively describe bacterial chemotaxis if cells are subject to small signal variations, but are only qualitative if the signal gradient becomes large. For the small gradient case, we derive explicit formulas to relate macroscopic parameters in these models to the detailed biochemistry of intracellular signalling. For the large gradient case, we suggest new models to be used to describe the population dynamics. Time permitting, I will briefly talk about our recent work on modelling segregation of the axonal cytoskeleton in diseases.