ELECTRICAL AND CHEMICAL OSCILLATIONS IN COUPLED CELL SYSTEMS

我们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和 受细胞内化学过程的调节。我们感兴趣的是 无论是单个细胞的行为，还是细胞 相互交流和修改对方的行为。 我们的主要应用是胰岛素的生物物理基础。 胰岛β细胞。我们已经研究了爆发性振荡 膜电位与细胞间电耦合的作用 在朗格汉斯岛上。长期目标是理解 膜动力学与细胞内事件相互作用以调节 并推广到其他分泌细胞和神经元。 我们的主要工具是常解和偏解的数值解 微分方程式。我们使用解析的、几何的、图形的、 以及来自动力学数学理论的数值技巧 帮助构建和解释模型的系统。摄动 在特殊情况下，使用技术来获得分析结果。 我们研究了详细的生物物理模型和简化的模型 更易于分析。这种方法有助于隔离 现象背后的基本或最小的机制，即研究 通则，以及概念和类比的应用 从其他领域。 我们认为，我们的团队将扮演一个中介角色，在 和生物学科。这包括传播洞察力 以通俗易懂的语言向生物学家介绍数学工作，并提醒 数学家和其他理论家对新的和具有挑战性的问题的研究 由生物问题引起的。

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.