Electrical And Chemical Oscillations In Coupled Cells

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。我们小组的另一个角色是在数学和生物学科之间进行调解。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。 该项目的最新工作包括： 1.(胰岛钙和电压振荡)我们应用我们最近开发的钙子空间模型来解释单个β细胞和胰岛之间的差异。特别是，我们表明，如果在模型中包括信道噪声，则可以解释孤立小区的详细属性。然后，我们观察到的三类单细胞行为(尖峰细胞、快速爆发细胞和平台细胞)在模型中通过改变钙通道电导来获得。这个单一参数的变化解释了当一个人通过这三个类别的过程中，尖峰幅度的减少，频率的减少，以及平台分数的增加。 在一项补充研究中，我们(与L.Satin的实验实验室)对比了缝隙连接偶联作用的两个假说。一种可能性是，单个β细胞能够产生类似胰岛的振荡，而这种耦合只需要同步振荡。或者，可能需要耦合才能发生振荡。我们已经通过使用缝隙连接蛋白Cx43(Cx43)的反义mRNA来降低偶联强度来测试这一点。我们发现，偶联程度降低的胰岛表现与我们之前研究中的单细胞相似：它们表现出快速的尖峰或破裂，但不像完整的胰岛那样缓慢破裂。 与R.Bertram一起，我们分析了当前一类模型的动力学，包括内质网钙动力学和ATP/ADP的振荡比值。我们追溯了从最早的β细胞模型开始的此类模型的发展，显示了每种包含的机制的贡献。内质网动力学的包含足以解释在胰岛素分泌增强剂乙酰胆碱存在的情况下突发频率的增加。核苷酸比率动力学的纳入首次允许模拟胰岛对一步葡萄糖的三相瞬时反应(潜伏期、第一相尖峰和稳态振荡)。 我们还探索了一个模型，在这个模型中，负反馈不是由体内的钙提供的，而是由分泌的胰岛素的自分泌和旁分泌效应提供的。 2.(钙离子扩散和缓冲的计算机模拟)我们应用我们的Calc(“Calculator”；http://mrb.niddk.nih.gov/matveev)软件包)模拟突触前终末缓冲的钙离子扩散，探索E.Neher提出的缓冲饱和假说。这一假说试图解释短期突触易化是由于内源性缓冲液饱和导致连续钙尖峰幅度增加的结果。这与我们之前发表的一个模型形成了对比，在该模型中，尖峰之后剩余钙的增加负责促进。这两种模式不是相互排斥的，而是可以共存的。也有可能不同的机制在不同类型的神经末梢中占主导地位。我们对这两个机制运行的条件进行了系统分析。 3.(代谢胰岛素信号)我们以前开发的代谢胰岛素信号的详细模型现在已经出现。这些计算机文件以XPP格式发布在http://mrb.niddk.nih.gov/sherman/insulin.html网站上，并已包含在CellML库中：http://www.cellml.org/examples/repository/sedaghat_model_2002_doc.html.

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. Another role for our group is to mediate 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. (Islet calcium and voltage oscillations) We have applied our recently developed calcium subspace model to illuminate the differences between single beta cells and islets. In particular, we showed that the detailed properties of isolated cells can be accounted for if channel noise is included in the model. The three classes of single-cell behavior we observe (spikers, fast bursters, and plateau cells) are then obtained in the model by varying calcium channel conductance. This single parameter change explains the decrease in spike amplitude, decrease in frequency, and increase in plateau fraction as one progresses through the three classes. In a complementary study, we have (with the experimental laboratory of L. Satin) contrasted two hypotheses for the role of gap junctional coupling. One possibility is that individual beta-cells are capable of islet-like oscillations, and the coupling is needed only to synchronize the oscillations. Alternatively, it may be that coupling is needed for oscillations to occur at all. We have tested this by using anti-sense mRNA for the gap junction protein connexin 43 (Cx43) to reduce coupling strength. We find that islets with reduced coupling behave like the single cells in our previous study: they show fast spiking or bursting, but not the slow bursting seen in intact islets. With R. Bertram, we have analyzed the dynamics of the current class of models, which include ER calcium dynamics and oscillatory ATP/ADP ratio. We trace the development of such models from the earliest beta-cell model, showing the contribution of each included mechanism. Inclusion of ER dynamics is sufficient to account for the increase of burst frequency in the presence of the insulin-secretion potentiator acetylcholine. Inclusion of nucleotide ratio dynamics permits for the first time simulation of the triphasic transient response of islets to a step of glucose (latency, first phase spiking, and steady-state oscillation). We have also explored a model in which negative feedback is provided not by internal calcium, but by autocrine and paracrine effects of secreted insulin. 2.(Computer modeling of calcium diffusion and buffering) We have applied our CalC ("Calcium Calculator"; http://mrb.niddk.nih.gov/matveev) software package for simulation of buffered Ca2+ diffusion in a presynaptic terminal, to explore the buffer saturation hypothesis proposed by E. Neher. This hypothesis attempts to explain short-term synaptic facilitation as a consequence of an increase in the amplitude of successive calcium spikes due to saturation of endogenous buffers. This contrasts with a model we have previously published in which a rise of the residual calcium remaining after the spikes is responsible for facilitation. The two models are not mutually exclusive, but can coexist. It is also possible that different mechanisms predominate in different types of nerve terminals. We have carried out a systematic analysis of the conditions for the two mechanisms to operate. 3. (Metabolic insulin signaling) The detailed model of metabolic insulin signaling, which we previously developed, has now appeared. The computer files are posted at http://mrb.niddk.nih.gov/sherman/insulin.html in xpp format and have also been included in a CellML repository: http://www.cellml.org/examples/repository/sedaghat_model_2002_doc.html.