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

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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.