Mathematical Sciences: Dynamics in some Biological and Chemical Systems

数学科学：某些生物和化学系统中的动力学

• 批准号: 9203299
• 负责人: David Terman
• 金额: $ 12.33万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-15 至 1996-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203299&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamics; some; Biological

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.

研究人员研究了几个数学模型， 生物和化学系统。 这些模型包括 电可兴奋细胞，如胰腺β细胞，和 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不同的假设 对于生物物理机制， 这些细胞中的活性。 将开发新的分析方法 预测和分类的各种不同的行为， 这些新模型的解决方案。 耦合建模的系统 还考虑了β细胞。 非常复杂的行为，包括 驻波、旋转螺旋和混沌动力学 在催化剂表面上实验观察到的。 有几种型号 为了理解基本的数学原理 负责这种丰富的模式结构的机制 阵 胰腺β细胞负责分泌 胰岛素 该分析将用于确定相对 不同离子流对β细胞的贡献 电活动。 这将有助于理解 这些电流负责大脑中的爆发活动， 细胞，以及哪些电流控制每个突发的持续时间。 此外，该分析将用于识别葡萄糖传感 机制，并确定电活动的作用， 刺激胰岛素释放。 这项工作有助于 对胰腺功能的基本了解。 话题 表面图案的形成与以下研究有关： 催化剂的行为。