The Mathematical Biology Seminar series presents Gregory Moses on “Clustering and stability in a positive-feedback system” on Wednesday, Feb. 18, from 5:15-6:10 in Morton 326.
Moses is a graduate student in Ohio University’s mathematics program.
Abstract: Over the past few years, we have studied a model of the cell division cycle (CDC) of yeast, where the presence of cells in one area of the CDC impact the growth rate of cells in another area. This is intended to model the clustering in the CDC observed in bioreactors, and we have primarily considered inhibitory feedback as being appropriate for this purpose. Recent work by Buckalew et al in the Drosophila embryo division cycles, however, has utilized an excitatory feedback mechanism, motivating a more careful study of the stability of solutions in that case.
We present an (almost) complete characterization of stability of cyclic solutions under positive feedback in this model; comment on the interesting facets of the open question that renders our results only almost complete; and observe and explain number-theoretic patterns towards the edge of parameter space, for both positive and negative feedback.
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