Mathematical Sciences: Dynamics in some Biological and Chemical Systems

研究者研究了生物和化学系统的几个数学模型。这些模型包括电兴奋细胞（如胰腺β细胞）的模型，以及等温催化剂表面上图案形成的模型。已经开发了许多模型来测试这些细胞中电活动背后的生物物理机制的不同假设。新的分析方法将被开发来预测和分类这些新模型的解的各种不同行为。系统模型耦合β细胞也被考虑。在实验中，在催化剂表面观察到非常复杂的行为，包括驻波、旋转螺旋和混沌动力学。研究了几个模型，以便了解负责这种丰富的模式形成结构的潜在数学机制。胰腺细胞负责胰岛素的分泌。这种分析将用于确定不同离子电流对β细胞电活动的相对贡献。这将有助于了解哪些电流负责细胞中的爆发活动，哪些电流控制每次爆发的持续时间。此外，该分析将用于确定葡萄糖感应机制，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认识。关于表面图案形成的话题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.