3:00 p.m., Friday (Jan. 10th)

Math Annex 1100

Eric Cytrynbaum

Mathematics, U C Davis

Aggregation and centering in fish melanophore cells - a quantitative exploration of cytoskeletal dynamics

I study a process of self-organization that occurs inside a cell called a fish melanophore in which pigment particles are seen to aggregate. The process is mediated by subcellular components called microtubules, which form part of the cytoskeleton. The same components are at work in the centering of chromosomes during cell division, and therefore provide a good "warmup" problem for that more complicated but fundamentally important biological process. When a fragment of the cell is excised to eliminate the centrosome (the regular cytoskeletal organizer) and therefore the cytoskeletal structure, stimulating the cell with adrenaline somehow reintroduces cytoskeletal organization, leading to the formation of a microtubule aster and the aggregation of the cell's pigment particles at the center of the fragment. It is this centering behaviour that is analogous to chromosome alignment during cell division.

We derive a system of seven non-linear PDEs (1D) that describes the biological system. Numerical simulations of the equations demonstrate certain observed features (aggregation) but not others (centering). The system can be reduced so as to facilitate analysis which allow for an understanding of the successes and failures of the original model. Finally, we generalize the reduced model to 2D, incorporating a stochatic element, and present numerical results.

In this talk, I will also briefly mention some of my previous work on the phenomenon of ventricular fibrillation in the heart, and the analysis of wave phenomena in the Fitzhugh Nagumo equations that formed the focus of my PhD work.

Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).

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