ELECTRICAL AND CHEMICAL OSCILLATIONS IN COUPLED CELL SYSTEMS

我们用数学模型来研究振荡电的机理。 由细胞膜上的离子通道引起的活性并受 细胞内的化学过程。我们对这两种行为都很感兴趣 单个细胞以及细胞之间相互交流和修改的方式 行为。 我们的主要应用是胰岛素分泌的生物物理基础。 在胰岛β细胞中。我们研究了膜中的爆发性振荡 胰岛细胞间的电耦合作用及电位 朗格汉斯。长期目标是了解膜动力学是如何 与细胞内事件相互作用以调节分泌并概括 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。我们使用分析、几何、图形和 数值技术从动力系统的数学理论到 帮助构建和解释模型。使用了微扰技术 在特殊情况下获得分析结果。 我们研究了详细的生物物理模型和简化的模型，它们是 更易于分析。这样的方法有助于隔离 现象背后的基本或最低限度的机制，寻找属 原理，以及其他领域的概念和类比的应用 我们认为我们的团队将扮演数学和数学之间的中介角色 生物学科。这包括传播对 以通俗易懂的语言和警报向生物学家提供数学工作 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 electrica activity arising from ion channels in cell membranes and modulated by intracellular chemical processes. We are interested in both the behavior o single cells and the ways in which cells communicate and modify each other' behavior. Our main application has been to the biophysical basis of insulin secretion in pancreatic beta-cells. We have examined bursting oscillations in membra 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 secretion and to generalize 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 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 genera 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.