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的生物物理基础 胰腺β细胞分泌。我们研究了爆发振荡 以及细胞间电偶联的作用， 朗格汉斯岛长期目标是了解 膜动力学与细胞内事件相互作用以调节分泌 并推广到其他分泌细胞和神经元。 我们的主要工具是数值解的普通和部分 微分方程我们使用分析的，几何的，图形的， 从动力系统的数学理论到 帮助构建和解释模型。使用扰动技术 在特殊情况下得到分析结果。 我们研究了详细的生物物理模型和简化模型， 更容易分析。这种方法有助于隔离 基本或最低限度的机制的现象，寻找 一般原则，以及概念和类比的应用， 其他领域 我们认为我们的团队可以发挥数学和数学之间的中介作用 生物学科。这包括传播以下方面的见解： 数学工作的生物学家在可访问的语言和警报 数学家和其他理论家对新的和具有挑战性的问题 由生物学问题引起的。

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 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 Langerhans. 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 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.