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.(内质网在形成钙振荡中的作用) 我们已经证明，加入一个仅具有线性摄取和释放机制的简单内质网足以解释胞内钙动力学的大部分特征，前提是内质网比胞内钙慢得多，但不是太慢。它必须能够在一个突发周期(几十秒到数百秒)内大量充盈和排空，以便将其缓慢的动力学传递给胞内的钙离子。 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包含还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)。见Bertram和Sherman(2004)。 然而，并不是所有的额外机制都有帮助。我们发现，包括活性钙诱导的钙释放(CICR)导致内质网不充盈和排空，以响应胞浆钙振荡，并无法解释当内质网摄取被阻断时胞质钙瞬变幅度的增加。一份报纸正在印刷中。 2.(胰岛中的电耦合和紧急振荡)我们扩展了我们的工作，即胰岛β细胞的异质性如何影响完整胰岛的集体行为。使用上面提到的幻象爆发模型(Bertram和Sherman，2004)，我们已经证明了快速和缓慢细胞的耦合可以产生通常在胰岛中看到的中期电振荡。这并不令人惊讶，但我们进一步发现，单细胞周期的双峰分布可以与通道电导的单峰分布一起产生。还可以构建仅由快速细胞或仅由慢细胞组成的胰岛，这些细胞在耦合时表现出中周期振荡。见Zimliki等人(2004年)。 3.(胰岛的联合电和代谢振荡)尽管胰岛的电振荡对于理解许多现象很重要，但它们的特性与体内观察到的脉动性胰岛素分泌不同。我们提出，这可以通过代谢(糖酵解)振荡对电振荡的调制来解释。特别是，这种组合可以解释观察到的膜电位、细胞内钙和代谢变量(如胰岛内氧、葡萄糖和线粒体膜电位)的复合振荡(爆发)。我们认为，糖酵解振荡维持协调胰岛素分泌和胰岛素作用的最佳时机，而电振荡控制每个脉搏中胰岛素的分泌量。见Bertram等人(2004年)。

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. (Role of the Endoplasmic Reticulum in Shaping Calcium Oscillations) We have shown that adding a simple ER with only linear uptake and release mechanisms is sufficient to account for most features of cytosolic Ca2+ kinetics, provided the ER is much slower than cytosolic Ca2+, but not too slow. It must be able to fill and empty substantially during a burst cycle (tens to hundreds of seconds) in order to impart its slow kinetics to cytosolic Ca2+. 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 in addition simulation of the triphasic transient response of islets to a step of glucose (latency, first phase spiking, and steady-state oscillation). See Bertram and Sherman (2004). Not all additional mechanisms are helpful, however. We have found that including active calcium-induced calcium release (CICR) results in an ER that does not fill and empty in response to cytosolic calcium oscillations and fails to account for the increase in the amplitude of cytosolic calcium transients when ER uptake is blocked. A paper is in press. 2. (Electrical Coupling and Emergent Oscillations in Pancreatic Islets) We have extended our work on how the heterogeneous properties of islet beta-cells contributes to the collective behavior of intact islets. Using the phantom bursting model mentioned above (Bertram and Sherman, 2004), we have shown that coupling fast and slow cells can produce the intermediate period electrical oscillations typically seen in islets. This is not very surprising, but we found further that a bimodal distribution of single-cell periods could be generated with a unimodal distribution of channel conductances. It is also possible to construct islets consisting of only fast cells or only slow cells that exhibit intermediate period oscillations when coupled. See Zimliki et al (2004). 3. (Combined Electrical and Metabolic Oscillations in Pancreatic Islets) Although electrical osscillations in pancreatic islets are important for understanding many phenomena, their properties are at variance with observations of pulsatile insulin secretion in vivo. We have proposed that this can be explained by the modulation of the electrical oscillations by metabolic (glycolytic) oscillations. In particular, this combination can account for the observations of compound oscillations (bursts of bursts) that have been observed in membrane potential, cytosolic calcium, and metabolic variables such as intra-islet oxygen and glucose and mitochondrial membrane potential. We suggest that the glycolytic oscillations maintain optimal timing to coordinate insulin secretion and insulin action while the electrical oscillations control the quantity of insulin secreted in each pulse. See Bertram et al (2004).