A Mathematical Study of the Biochemical and Electrical Dynamics of Pancreatic Islets

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。该研究项目的长期目标是了解胰腺β细胞的许多子系统如何相互作用以在小鼠中产生胰岛素振荡（大鼠和人类也表现出振荡）。这些振荡对血糖水平的正常调节至关重要，而振荡的丧失与II型糖尿病有关。朗格汉斯胰岛有节奏的胰岛素分泌是由于β细胞有节奏的爆发性电活动，以及随之而来的细胞内钙浓度的节律。细胞内钙和三磷酸腺苷（ATP）都反馈到细胞的电子系统，打开或关闭离子通道，从而影响细胞的电活动。该项目侧重于产生ATP的代谢子系统，以及对先前开发的代谢驱动爆发和从胰岛分离的单个β细胞中发生的快速电爆发模型的数学分析。核心假设是，胰岛经常表现出的慢电爆发振荡和偶发性爆发，与体内观察到的胰岛素振荡周期相同，是由代谢振荡驱动的。这些振荡的一种机制是糖酵解，糖代谢的第一阶段。然而，在新陈代谢的另外两个阶段——柠檬酸循环和氧化磷酸化——中固有的振荡可能是一个缓慢的过程，它驱动缓慢的爆发活动，并将更快的爆发聚集在一起，形成周期性的发作。这种可能性将通过数学建模和分析进行研究，以及对柠檬酸循环中间体的周期性测量表明振荡的机制。回到代谢的糖酵解成分，建模研究将与合作实验室的实验研究并行进行，以确定磷酸果糖激酶-2 （PFK-2）酶如何调节糖酵解振荡。哺乳动物（包括老鼠、人类、狗和人类）的胰岛素分泌是脉动的，周期约为5分钟。这些可以在血液中测量的胰岛素振荡对正常的葡萄糖稳态很重要，因为振荡的破坏与II型糖尿病有关。胰岛素是由胰腺中被称为朗格汉斯岛的微型器官分泌的，该器官主要由分泌胰岛素的β细胞组成。十多年来，首席研究员一直在研究胰岛素分泌振荡的生物物理机制。这项研究包括数学建模和分析，以及在合作实验室进行的并行实验研究。因此，这是一个真正的多学科项目。目前的项目使用当前胰腺β细胞的数学模型来了解β细胞葡萄糖代谢的振荡如何导致β细胞的电活动和胰岛素分泌的振荡。此外，分岔分析和混合模式振荡领域的最新数学方法将用于理解从胰岛分离出来的β细胞的振荡电活动。目的是通过数学分析来确定，在一个完整的胰岛中，单细胞的行为是如何转化为完全不同的β细胞的行为的。这项研究的长期目标是更好地了解胰岛的正常功能，这将最终为II型糖尿病中发生的胰岛功能障碍提供见解。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The long-term goal of this research project is to understand how the many subsystems of the pancreatic beta-cell interact to produce insulin oscillations in mice (rats and humans also exhibit oscillations). These oscillations are crucial for the normal regulation of blood glucose levels, and loss of oscillations is linked to type II diabetes. Rhythmic insulin secretion from pancreatic islets of Langerhans is due to rhythmic bursting electrical activity in the beta-cells, and a consequent rhythm in the intracellular calcium concentration. Both the intracellular calcium and adenosine triphosphate (ATP) feed back onto the cell's electrical subsystem, opening or closing ion channels and thus affecting the cell's electrical activity. This project focuses on the metabolic subsystem that produces ATP, and on a mathematical analysis of previously-developed models of metabolismdriven bursting and the fast electrical bursting that occurs in single beta-cells that are isolated from the islet. The central hypothesis is that the slow electrical bursting oscillations and episodic bursting that are often exhibited by pancreatic islets, and that have the same period as insulin oscillations observed in vivo, are driven by oscillations in metabolism. One mechanism for these oscillations is in glycolysis, the first stage of glucose metabolism. However, it is possible that oscillations inherent in one of the other two stages of metabolism, the citric acid cycle and oxidative phosphorylation, could be the slow process that drives slow bursting activity and that clusters faster bursts together into periodic episodes. This possibility will be investigated using mathematical modeling and analysis, as will what measurements of periodicity in citric acid cycle intermediates indicate about the mechanism of the oscillations. Returning to the glycolytic component of metabolism, modeling studies will be conducted in parallel with experimental studies in a collaborating laboratory to determine how the enzyme phosphosphofructokinase-2 (PFK-2) may modulate glycolytic oscillations.Insulin secretion in mammals, including rats, humans, dogs, and humans, is pulsatile, with a period of about five minutes. These insulin oscillations, which can be measured in the blood, are important for normal glucose homeostasis, since disruption of the oscillations is linked to type II diabetes. Insulin is secreted from micro-organs in the pancreas called Islets of Langerhans, composed largely of insulin-secreting beta-cells. For more than a decade now, the principal investigator has been investigating the biophysical mechanism for the oscillations in insulin secretion. This research involves mathematical modeling and analysis, and parallel experimental studies in a collaborating laboratory. It is thus a truly multidisciplinary project. The current project uses a current mathematical model of pancreatic beta-cells to understand how oscillations in the metabolism of glucose by the beta-cells can lead to oscillations in the electrical activity and insulin secretion from the beta-cells. In addition, bifurcation analysis and recent mathematical methods in the area of Mixed Mode Oscillations will be used to understand the oscillatory electrical activity of beta-cells that have been isolated from an islet. The intention is to determine, using this mathematical analysis, how single-cell behavior is converted to the very different behavior of beta-cells in an intact islet. The long-term goal of this research is to better understand the normal functioning of islets, which will ultimately provide insights into the dysfunction of islets that occurs in type II diabetes.