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Calcium and Glycolysis Mediate Multiple Bursting Modes in Pancreatic Islets

Richard Bertram ^*, Leslie Satin , Min Zhang , Paul Smolen  and Arthur Sherman 

^* Department of Mathematics and Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida; Department of Pharmacology and Toxicology, Virginia Commonwealth University Medical Center, Richmond, Virginia; Department of Neurobiology and Anatomy, W. M. Keck Center for the Neurobiology of Learning and Memory, The University of Texas-Houston Medical School, Houston, Texas; and Laboratory of Biological Modeling, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland

Correspondence: Address reprint requests to Richard Bertram, Tel.: 850-644-7195; E-mail: bertram{at}math.fsu.edu.

Pancreatic islets of Langerhans produce bursts of electrical activity when exposed to stimulatory glucose levels. These bursts often have a regular repeating pattern, with a period of 10–60 s. In some cases, however, the bursts are episodic, clustered into bursts of bursts, which we call compound bursting. Consistent with this are recordings of free Ca²⁺ concentration, oxygen consumption, mitochondrial membrane potential, and intraislet glucose levels that exhibit very slow oscillations, with faster oscillations superimposed. We describe a new mathematical model of the pancreatic ß-cell that can account for these multimodal patterns. The model includes the feedback of cytosolic Ca²⁺ onto ion channels that can account for bursting, and a metabolic subsystem that is capable of producing slow oscillations driven by oscillations in glycolysis. This slow rhythm is responsible for the slow mode of compound bursting in the model. We also show that it is possible for glycolytic oscillations alone to drive a very slow form of bursting, which we call "glycolytic bursting." Finally, the model predicts that there is bistability between stationary and oscillatory glycolysis for a range of parameter values. We provide experimental support for this model prediction. Overall, the model can account for a diversity of islet behaviors described in the literature over the past 20 years.

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