ELECTRICAL AND CHEMICAL OSCILLATIONS IN COUPLED CELL SYSTEMS

我们使用数学模型来研究由细胞膜离子通道引起并由细胞内化学过程调节的振荡电活动的机制。我们既对单细胞的行为感兴趣，也对细胞之间交流和改变彼此行为的方式感兴趣。我们的主要应用是研究胰腺β细胞分泌胰岛素的生物物理基础。我们研究了膜电位的破裂振荡和朗格汉斯岛细胞间电耦合的作用。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。我们还对其他分泌细胞和神经元进行了比较、对比和归纳，包括分泌gnrh的下丘脑神经元、垂体生长因子和神经末梢快速分泌神经递质。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解析、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，采用微扰技术得到分析结果。我们研究了详细的生物物理模型和更易于分析的简化模型。这种方法有助于分离现象背后的基本或最小机制，寻找一般原则，以及应用其他领域的概念和类比。我们认为我们的团队是数学和生物学科之间的中介。这包括以通俗易懂的语言向生物学家传播数学工作的见解，并提醒数学家和其他理论家注意生物学问题中出现的新的和具有挑战性的问题。-数学建模，离子通道，钙，糖尿病，突触

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 others 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 inthe 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. - mathematical modeling, ion channels, calcium, diabetes, synapses