ELECTRICAL AND CHEMICAL OSCILLATIONS IN COUPLED CELL SYSTEMS

我们使用数学模型来研究 离子振荡电活动的机制 细胞膜中的通道，并由细胞内化学物质调节 流程.我们感兴趣的是单细胞的行为， 细胞之间的交流和改变 行为我们的主要应用一直是生物物理基础， 胰腺β细胞中的胰岛素。我们已经研究了爆裂 膜电位的振荡和电的作用 胰岛细胞间的偶联长期目标 是为了了解细胞膜的动力学是如何与 细胞内事件来调节分泌，并推广到其他 分泌细胞和神经元。我们的主要工具是 解常微分方程和偏微分方程。我们使用 分析、几何、图形和数值技术， 动力系统的数学理论，以帮助建立和 解释模型。扰动技术用于得到 特殊情况下的分析结果。我们详细研究了 生物物理模型和简化模型， 进行分析。这种方法有助于隔离基本或 现象背后的最小机制，寻找一般 原则，以及其他概念和类比的应用 领域的我们认为，我们集团的作用是充当 数学和生物学科。这包括传播 数学工作的深刻见解， 语言和提醒数学家和其他理论家， 新的和具有挑战性的问题产生的生物问题。

We use mathematical models to study the mechanisms of oscillatory electrical activity arising from ion channels in cell membranes and modulated by intracellular chemical processes. We are interested in both the behavior of single cells and the ways in which cells communicate and modify each other's behavior. Our main application has been to the biophysical basis of insulin in pancreatic beta-cells. We have examined bursting oscillations in membrane potential and the role of electrical coupling between cells in the islet of Langerhans. Long term goals are to understand how the membrane dynamics interact with intracellular events to regulate sectretion and to generalize to other secretory cells and neurons. Our primary tool is the numerical solution of ordinary and partial differential equations. We use analytical, geometrical, graphical, and numerical techniques from the mathematical theory of dynamical systems to help construct and interpret the models. Perturbation techniques are used to get analytical results in special cases. We study both detailed biophysical models and simplified models which are more amenable to analysis. Such an approach aids the isolation of the essential or minimal mechanisms underlying phenomena, the search for general principles, and the application of concepts and analogies from other fields. We see a role for our group as intermediaries between the mathematical and biological disciplines. This includes disseminating the insights of mathematical work to biologists in accessible language and alerting mathematicians and other theoreticians to new and challenging problems arising from biological issues.