Analysis and Extension of a Model for Oscillatory Islet Activity

II型糖尿病占全世界所有糖尿病病例的约90%，2013年有3.68亿人被诊断患有II型糖尿病。虽然它是一种复杂的疾病，有许多相互作用的因素，有一个共识，一个主要组成部分是功能障碍的胰腺β细胞释放激素胰岛素。在正常个体中，这些细胞以脉冲方式释放胰岛素，脉冲幅度反映葡萄糖水平。现在有确凿的证据表明，脉冲胰岛素比恒定胰岛素更有效地刺激肝脏的降糖作用。此外，已经表明II型糖尿病患者及其近亲显示出紊乱的胰岛素水平，而不是非糖尿病患者的更有规律的胰岛素脉冲。该项目旨在更好地了解导致β细胞脉冲式胰岛素分泌的细胞内途径。它还试图了解同样表现出脉冲式胰岛素分泌的小鼠如何以维持节律性细胞活动和胰岛素分泌的方式补偿关键蛋白质的基因敲除。总的来说，该项目将深入了解脉冲式胰岛素分泌的复杂生物学，并将推动数学分析技术，这些技术在复杂的细胞内信号传导系统（如胰腺β细胞）中非常有用。参与该研究项目的研究生将接受广泛的跨学科培训，以回答由实验数据驱动的数学问题。还将制作可供公众使用的软件。自2004年首次发表以来，Bertram及其同事一直在不断发展双振子模型。该模型描述了代谢、细胞内钙动力学和电活动这三种信号通路如何结合联合收割机以产生受细胞外葡萄糖水平调节的脉动胰岛素分泌。模型的复杂性使得很难理解系统的动态特性，但应用快/慢分析技术可以利用模型变量的时间尺度分离，并将系统正式分解为以不同速率变化的子系统。这种强大的多尺度分析技术将被应用于改善我们对葡萄糖和其他底物诱导的模型β细胞活性振荡的理解，以及存在于小鼠细胞中的振荡，其中不同的关键蛋白质被基因敲除。因为有几个缓慢变化的变量，所以有许多不同的方法可以使用快/慢分析技术。这些不同的方法进行了探讨，并将产生互补的见解。虽然该项目的重点是β细胞活性的振荡，但所使用的分析方法适用于广泛的动态模型，因此该项目中的数学发展可以适用于其他复杂的生物系统。

Type II diabetes makes up about 90% of all cases of diabetes world wide, and 368 million people were diagnosed with type II diabetes in 2013. Although it is a complex disease with many interacting factors, there is agreement that a major component is dysfunction of the pancreatic beta cells that release the hormone insulin. In normal individuals, these cells release insulin in pulses, with the pulse amplitude reflecting the glucose level. There is now conclusive evidence that pulsatile insulin is more effective than constant insulin at stimulating glucose-lowering actions of the liver. In addition, it has been shown that type II diabetics, and their nearest relatives, show disorganized insulin levels, rather than the more regular insulin pulses of non-diabetics. This project seeks to better understand the intracellular pathways that result in pulsatile insulin secretion from beta cells. It also seeks to understand how mice, which also exhibit pulsatile insulin secretion, compensate for genetic knockouts of key proteins in such a way that rhythmic cellular activity and insulin secretion is maintained. Overall, the project will yield insights into the complex biology of pulsatile insulin secretion, and will push forward mathematical analysis techniques that are useful in complex intracellular signaling systems such as those in pancreatic beta cells. Graduate students involved in this research project will receive broad interdisciplinary training in answering mathematical questions driven by experimental data. Publicly available software will also be produced. The Dual Oscillator Model has been under continuous development by Bertram and associates since it was first published in 2004. This model describes how three signaling pathways, metabolism, intracellular calcium dynamics, and electrical activity combine to produce pulsatile insulin secretion that is modulated by the extracellular glucose level. The complexity of the model makes it difficult to understand the dynamics of the system, but application of the fast/slow analysis technique allows one to take advantage of the separation of time scales of the model variables and formally decompose the system into subsystems that vary at different rates. This powerful multi-scale analysis technique will be applied to improve our understanding of oscillations in activity of the model beta cell that are induced by glucose and other substrates, as well as oscillations that are present in cells from mice in which different key proteins are genetically knocked out. Because there are several slowly changing variables, there are a number of different ways in which the fast/slow analysis technique can be used. These different approaches are explored, and will yield complementary insights. While the focus of the project is on oscillations in beta cell activity, the analysis approach used is applicable to a wide range of dynamic models, so the mathematical developments made in this project can be adapted to other complex biological systems.