3:00 p.m., Friday (Jan. 10th)
Math Annex 1100
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).