Stimulus secretion coupling in pancreatic beta-cells

我们在过去几年的主要活动之一是开发了一个全面的膜电位和钙振荡模型，其时间尺度从几秒到几分钟不等。这些都会导致相应的胰岛素分泌振荡。该模型的基本假设是，较快的(几十秒)振荡源于钙对离子通道的反馈，可能是钙激活的钾(K(Ca))通道和ATP依赖的钾(K(ATP)通道)，而较慢的(5分钟)振荡来自代谢的振荡。代谢振荡通过K(ATP)通道转化为电振荡。值得注意的是，后者是胰岛素刺激药物的一线靶点，例如用于治疗2型糖尿病的磺脲类药物(甲苯丁胺、格列本脲)。因此，该模型由一个电子振荡器(EO)和一个代谢(糖酵解)振荡器(G)组成)，称为双振荡器模型(DOM)。我们目前正在通过几种方式测试这一模型。去年我们报道，通过NAD(P)H测量分析的代谢振荡通常持续在稳定的钙中，表明代谢振荡不是代谢振荡所必需的。然而，这两者通常是相继发现的，钙振荡以及平均钙水平确实影响代谢振荡。我们现在已经用K(ATP)通道电导的测量证实了这些发现，并正在准备一篇关于这个主题的论文。 我们已经写了一篇评论(参考文献#1)关于生理学中的动力系统方法，以增强生理学社区的益处，最近其他人的两篇论文提出了一个新的、更全面的(快速)β细胞电活动模型。虽然我们已经使我们的模型尽可能地简单，但新的模型包括更广泛的机制集。这就提出了如何评估不同机制的相对重要性以及细胞如何使用冗余的问题。新模型和其他类似模型的复杂性也给理解该模型的工作原理以及它的能力和局限性带来了挑战。这篇评论用最少的数学知识描述了如何仍然有效地应用分叉图。这样的图是参数区域的一级映射，在其中可以发现模型的各种行为，包括稳态、尖峰和爆裂。它们还提供了一种方法，通过利用不同的过程(在这里，尖峰和突发)在不同的时间尺度(&lt；1秒与10-60秒)上运行并且可以被认为是半独立的这一事实来剖析动力学。这将集体行为减少为更简单的子系统的行为，并极大地增加了分析的能力。进化也可以利用这种时间尺度的分离，因为它有助于使细胞功能模块化--单个子系统可以改变，对其他子系统的影响有限。该审查可作为本报告所述工作的说教指南而有益地阅读。评论中的一位人物被选为该杂志7月刊的封面艺术。 在β细胞爆裂模型中，时间尺度分离的一个特别有趣的应用是重置现象。从最早的β细胞模型(Chay-Keizer，1983)中得到的一个见解是，发生尖峰的平台是由双稳定建立的。也就是说，如果慢变钙是固定的，电池可以处于低电压(-60 mV)稳定状态或高电压(-20 mV)尖峰状态。因此，短暂的电刺激应该能够将细胞从一种状态切换到另一种状态。此外，模型预测，在传递扰动的低电压(静默)阶段越晚，诱导高电压(活动)阶段越短。实验已经证实，沉默-活跃的相变可以像预期的那样被诱导，但诱导相变的持续时间似乎并不依赖于何时施加扰动。在参考文献中。#2我们与Bertram小组合作表明，最近的β细胞模型，用两个控制活跃和静止期持续时间的慢变量，可以解释迄今为止令人困惑的实验观察。 裁判员#4解决了β细胞和密切相关但不同的垂体细胞的爆裂模型中的双稳态、可重置性和时标分离的问题。在我们关于神经元和内分泌细胞的数学建模的报告中对此进行了详细的讨论。 在与Max Pietropaolo(密歇根大学)的合作下，我和博士后Anmar Khadra开始了实验室治疗1型糖尿病(T1D)的新工作，其特征是对β细胞的自身免疫破坏。长期以来，Pietropaolo一直对使用胰岛自身抗体作为进展为T1D的风险的生物标志物感兴趣。虽然进展速度的差异与不同自身抗体的出现或自身抗体类型的数量有关，但我们试图通过建立β细胞、T细胞和B细胞之间相互作用的数学模型来确定其潜在机制。我们确定了两个控制进展到T1D的时间的关键参数，即T细胞对β细胞的亲和力和它们的杀伤效率。该模型还能够解释亲和力成熟的现象，在这种现象中，T细胞的亲和力随着时间的推移而增加，从而加速了疾病的进程。参见参考文献#3.

One of our main activities over the last few years has been the development of a comprehensive model for oscillations of membrane potential and calcium on time scales ranging from seconds to minutes. These lead to corresponding oscillations of insulin secretion. The basic hypothesis of the model is that the faster (tens of seconds) oscillations stem from feedback of calcium onto ion channels, likely calcium-activated potassium (K(Ca)) channels and ATP-dependent potassium (K(ATP)) channels, whereas the slower (five minutes) oscillations stem from oscillations in metabolism. The metabolic oscillations are transduced into electrical oscillations via the K(ATP) channels. The latter, notably, are a first-line target of insulin-stimulating drugs, such as the sulfonylureas (tolbutamide, glyburide) used in the treatment of Type 2 Diabetes. The model thus consists of an electrical oscillator (EO) and a metabolic (glycolytic) oscillator (G)) and is referred to as the Dual Oscillator Model (DOM). We are currently testing this model in several ways. Last year we reported that metabolic oscillations, assayed by NAD(P)H measurements, often persist in steady calcium, indicating that calcium oscillations are not required for metabolic oscillations. The two, however, are generally found in tandem, and the calcium oscillations, as well as mean calcium level, do influence the metabolic oscillations. We have now confirmed these findings with measurements of K(ATP) channel conductance and are preparing a paper on the subject. We have written a commentary (Ref. # 1)about dynamical systems methods in physiology in order to enhance the benefit for the physiology community of two recent papers by others presenting a new, more comprehensive model for (fast) beta-cell electrical activity. Whereas we have made our models as simple as possible for the phenemona addressed, the new model includes a much wider set of mechanisms. This raises issues of how to assess the relative importance of the different mechanisms and of how cells use redundancy. The complexity of the new model and others like it also poses a challenge for understanding how the model works and what its capabilities and limitations are. The commentary describes with a minimum of mathematics how bifurcation diagrams can still be applied effectively. Such diagrams are at one level maps of the parameter regimes in which the various behaviors of the model, including steady states, spiking and bursting, are found. They also provide a way to dissect the dynamics by exploiting the fact that different processes (here, spiking and bursting) operate on different time scales (< 1 sec vs. 10 - 60 sec) and can be considered as semi-independent. This reduces the collective behavior into the behavior of simpler sub-systems and greatly increases the power of analysis. Evolution may exploit such timescale separation as well, as it serves to make cell function modular - the individual subsystems can be altered with limited effect on the others. The review can be profitably read as a didactic guide to the work described in this report. A figure from the commentary was selected as the cover art for the journal's July issue. A particularly interesting application of the separation of timescales in models for bursting in beta cells is the phenomenon of resetting. An insight from the earliest beta-cell model (Chay-Keizer, 1983) is that the plateau from which spiking occurs is established by bi-stability. That is, if the slow variable calcium is fixed, the cell can sit at either a low-voltage (-60 mV) steady state or a high-voltage (-20 mV) spiking state. Consequently, brief electrical stimuli should be able to switch the cell from one state to the other. Moreover, the models predicted that the later in the low-voltage (silent) phase in which the perturbation is delivered, the shorter would be the induced high-voltage (active) phase. Experiments have confirmed that silent-active phase transitions can be induced as expected, but the duration of the induced phase does not seem to depend on when the perturbation is applied. In Ref. # 2 we show in collaboration with the Bertram group that more recent beta-cell models, with two slow variables controlling the active and silent phase durations can account for this heretofore puzzling experimental observation. Ref. # 4 addresses the issues of bistability, resettability and separation of timescales in models of bursting for both beta cells and closely related but different pituitary cells. It is discussed in detail in our report on Mathematical Modeling of Neurons and Endocrine Cells. In collaboration with Max Pietropaolo (U. Michigan) post-doctoral fellow Anmar Khadra and I began a new line of work for the lab on Type 1 Diabetes (T1D), characterized by auto-immune destruction of beta cells. Pietropaolo has a long-standing interest in use of islet autoantibodies as biomarkers of risk for progression to T1D. While differences in rate of progression have been correlated with the appearance of different autoantibodies or the number of autoantibody types, we sought to determine the underlying mechanism by developing a mathematical model for the interactions among beta cells, T cells and B cells. We identified two key parameters controlling the time to progression to T1D, the avidity of the T cells for beta cells and their killing efficiency. The model was also able to illuminate the phenomenon of avidity maturation, in which T-cell avidity increases over time, accelerating the disease process. See Ref. # 3.