Analysis and Extension of a Model for Oscillatory Islet Activity

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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.