Mathematical Sciences: Dynamics in some Biological and Chemical Systems

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The investigator studies several mathematical models for biological and chemical systems. These include models for electrically excitable cells such as pancreatic beta-cells, and models for pattern formation on isothermal catalyst surfaces. Numerous models have been developed to test different hypothesis for the biophysical mechanisms that underlie the electrical activity in these cells. New analytic methods will be developed to predict and classify the variety of different behaviors of solutions to these recent models. Systems that model coupled beta-cells are also considered. Very complex behaviors including standing waves, rotating spirals, and chaotic dynamics have been observed experimentally on catalyst surfaces. Several models are studied in order to understand the underlying mathematical mechanisms responsible for this rich structure of pattern formation. Pancreatic beta-cells are responsible for the secretion of insulin. This analysis will be used to determine the relative contributions of different ion currents to the beta-cell electrical activity. It will help in understanding which of these currents are responsible for bursting activity in the cells, and which currents govern the duration of each burst. Moreover, this analysis will be used to identify glucose-sensing mechanisms and determine the role of the electrical activity in stimulating insulin release. This work contributes to fundamental understanding of pancreatic functions. Topics on the formation of surface patterns arise in connection with studies of the behavior of catalysts.