Mathematical Sciences: Dynamics in some Biological and Chemical Systems

研究人员研究了生物和化学系统的几个数学模型。这些模型包括胰腺β细胞等电可兴奋细胞的模型，以及等温催化剂表面图案形成的模型。已经开发了许多模型来检验这些细胞中电活动背后的生物物理机制的不同假说。将开发新的分析方法来预测和分类这些最新模型的解的不同行为的种类。对耦合的β细胞建模的系统也被考虑在内。实验上观察到了催化剂表面非常复杂的行为，包括驻波、旋转螺旋和混沌动力学。研究了几个模型，以了解导致这种丰富的图案形成结构的潜在数学机制。胰岛β细胞负责胰岛素的分泌。这一分析将被用来确定不同离子电流对β细胞电活动的相对贡献。这将有助于理解这些电流中的哪一种负责细胞中的猝发活动，以及哪些电流支配着每次猝发的持续时间。此外，这一分析将被用来识别葡萄糖敏感机制，并确定电活动在刺激胰岛素释放中的作用。这项工作有助于对胰腺功能的基本了解。表面花纹的形成与催化剂行为的研究有关。

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.