ELECTRICAL AND CHEMICAL OSCILLATIONS IN COUPLED CELL SYSTEMS

我们使用数学模型来研究振荡的机制， 细胞膜中离子通道产生的电活动， 由细胞内化学过程调节。我们对两者都感兴趣 单细胞的行为以及细胞之间的交流方式， 改变彼此的行为。 我们的主要应用是胰岛素分泌的生物物理基础 在胰腺β细胞中。我们已经研究了爆发振荡， 膜电位和细胞间电耦合的作用 朗格汉斯岛长期目标是了解细胞膜 动力学与细胞内相互作用;调节分泌和 也适用于其他分泌细胞和神经元。 我们的主要工具是常微分方程的数值解 方程我们使用分析，几何，图形和数值 动力系统的数学理论的技术，以帮助 构建和解释模型。扰动技术用于得到 特殊情况下的分析结果。 我们使用详细的生物物理模型和简化的模型， 更易于分析。通过选择和组合特征， 提取现象的本质，得出一般原理， 便于与相关领域的工作人员沟通。

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 secretion in pancreatic beta-cells. We have examined bursting oscillations in membrane potential and the role of electrical coupling between cells in the islet of Longerhans. Long term goals are to understand how the membrane dynamics interact with intracellular; events to regulate secretion and to generalize to other secretory cells and neurons. Our primary tool is the numerical solution of ordinary 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 work with both detailed biophysical models and simplified models which are more amenable to analysis. By selecting and combining features we can distill the essence of the phenomena, derive general principles, and facilitate communication with workers in related fields.