ELECTRICAL AND CHEMICAL OSCILLATIONS IN COUPLED CELL SYSTEMS

我们使用数学模型来研究振荡电活动的机制所产生的离子通道在细胞膜和细胞内的化学过程调制。 我们感兴趣的是单细胞的行为和细胞之间的通信方式，并修改彼此的行为。我们的主要应用是胰腺β细胞胰岛素分泌的生物物理基础。 我们已经研究了膜电位的爆发振荡和胰岛细胞之间的电耦合的作用。长期目标是了解膜动力学如何与细胞内事件相互作用以调节分泌。 我们也比较，对比，并概括到其他分泌细胞和神经元，包括GnRH分泌下丘脑神经元，垂体生长激素细胞，和快速神经递质分泌的神经末梢。我们的主要工具是常微分方程和偏微分方程的数值解。 我们使用动力系统数学理论中的分析、几何、图形和数值技术来帮助构建和解释模型。在特殊情况下，利用摄动技术得到了解析结果。我们研究了详细的生物物理模型和简化的模型，更适合分析。 这种方法有助于分离现象背后的基本或最低限度的机制，寻找一般原则，并应用其他领域的概念和类比。我们看到了我们小组作为数学和生物学科之间的中介的作用。 这包括传播的见解数学工作的生物学家在可访问的语言和提醒数学家和其他理论家的新的和具有挑战性的问题所产生的生物问题。

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 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. We also compare, contrast, and generalize to other secretory cells and neurons, including GnRH-secreting hypothalamic neurons, pituitary somatotrophs, and fast neurotransmitter secretion at nerve terminals. 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.