Electrical And Chemical Oscillations In Coupled Cell Sys

我们使用数学模型来研究细胞膜上离子通道产生并受细胞内化学过程调制的振荡电活动的机制。我们既对单个细胞的行为感兴趣，也对细胞之间的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岛β细胞分泌胰岛素的生物物理基础。我们研究了朗格汉斯胰岛细胞膜电位的爆发性振荡和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来调节分泌。我们还比较、对比和推广到其他分泌细胞和神经元，包括分泌GnRH的下丘脑神经元、垂体生长激素和神经末梢的快速神经递质分泌。我们的主要工具是常微分方程组和偏微分方程组的数值解。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，采用摄动法得到分析结果。我们既研究详细的生物物理模型，也研究更易于分析的简化模型。这种方法有助于隔离现象背后的基本或最小机制，寻找一般原理，并应用其他领域的概念和类比。我们认为我们的团队将扮演数学和生物学科之间的中间人的角色。这包括用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产生的新的和具有挑战性的问题。最近在这个项目上的工作包括：1.我们开发了一个模型来解释在胰腺β细胞和胰岛中观察到的膜电位和钙的大范围振荡周期(从几秒到几分钟)。假设振荡由两个缓慢的负反馈过程控制，一个时间常数为1-5秒，另一个时间常数为2分钟。不存在具有中间时间常数的过程--在该范围内的振荡是由两个较快和较慢的过程之间的相互作用引起的。在与Satin实验室的合作中，我们确认了该模型的一个关键预测，即适当的注入电流可以从快速细胞中引发中等规模的振荡。这首次表明从胰岛分离的细胞确实可以表现出中等程度的振荡(参考文献)。#1)。2.我们研究了胰岛β细胞的电耦合如何对观察到的中尺度(10-60秒)钙离子和膜电位的爆发性振荡起作用。我们专注于Satin实验室鉴定的分离细胞亚群(30%-50%)，这些细胞表现出快速而持续的尖峰，而不是阵发性尖峰。我们之前已经证明，这种细胞，当电耦合时，可以转化为爆发物。然而，这种现象并不强健，只存在于小范围的耦合强度。我们现在已经从数学上证明并分析了随机离子通道波动的非线性效应(参考文献2)。#2)和参数的异质性(参考文献#3)可以增强这种突发的形式。这项研究为我们之前的演示提供了一个有趣的对比和补充，即噪音和异质性在加入细胞时阻碍了爆炸，而细胞是内在的爆发，当去耦合时。3.我们将以前对胰岛β细胞内钙离子通道(SOC)的研究扩展到下丘脑中分泌GnRH的神经内分泌细胞。在与Stojilkovic实验室的合作中，我们证明了SOC可以解释GnRH刺激细胞时动作电位频率和胞浆钙水平的增加(细胞有自己的分泌产物的自身受体)。参见参考文献。我们对钙离子在开放的钙离子通道附近的稳态空间分布进行了详细的数学分析，以及钙离子缓冲剂是如何改变它的。这导致了对以前由其他人使用启发式论证获得的几个近似公式的系统和统一的处理。这样的处理还表明各种近似在哪些参数范围内是有效的，并导致更精确的改进近似，前提是它们在适当的参数范围内使用。参见参考文献#5.

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. Recent work on this project includes: 1. We developed a model to account for the wide range of oscillation periods for membrane potential and calcium observed in pancreatic beta-cells and islets (from seconds to minutes). The hypothesis was that oscillations are governed by two slow, negative feedback processes, one with a time constant of 1-5 seconds, and one with a time constant of 2 minutes. There is no process with an intermediate time constant - oscillations in that range result from the interaction between the two faster and slower processes. In collaboration with the Satin lab we confirmed a key prediction of the model that appropriate injected currents could elicit medium-scale oscillations from fast cells. This showed for the first time that isolated cells from pancreatic islets could indeed exhibit medium oscillations (Ref. #1). 2. We have studied how electrical coupling of pancreatic beta-cells contributes to medium-scale (10-60 sec) bursting oscillations in calcium and membrane potential observed in pancreatic islets. We focused on the sub-group (30 - 50%) of isolated cells identified by the Satin lab that show rapid and continuous spiking rather than bursts of spikes. We had previously shown that such cells, when electrically coupled, could be transformed into bursters. However, the phenomenon was not robust, existing only for a small range of coupling strengths. We have now shown and analyzed mathematically that nonlinear effects of stochastic ion channel fluctuations (Ref. # 2) and heterogeneity of parameters (Ref. # 3) can enhance this form of emergent bursting. This study provides an interesting contrast and complement to our previous demonstrations that noise and heterogeneity hinder bursting when added to cells that are intrinsic bursters when uncoupled. 3. We have extended our previous studies of store-operated calcium channels (SOC) in pancreatic beta-cells to neuro-endocrine cells of the hypothalamus that secrete GnRH. In collaboration with the Stojilkovic lab, we showed that SOC could account for the increased action potential frequency and increased cytosolic calcium levels seen when the cells are stimulated with GnRH (the cells have autoreceptors for their own secretion product). See Refs. # 4 and 6. 4. We have carried out a detailed mathematical analysis of the steady-state spatial profile of calcium near an open calcium channel and how it is modified by calcium buffers. This resulted in a systematic and unified treatment of several approximate formulas previously obtained by others using heuristic arguments. Such a treatment also indicates in which parameter regimes the various approximations are valid and leads to refined approximations that are more accurate, provided they are used in the appropriate parameter regimes. See Ref. #5.