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Diffusion of Calcium and Metabolites in Pancreatic Islets: Killing Oscillations with a Pitchfork

Krasimira Tsaneva-Atanasova ^*, Charles L. Zimliki , Richard Bertram  and Arthur Sherman ^*

^* Laboratory of Biological Modeling, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland; Center for Devices and Radiological Health, Federal Department of Agriculture, Rockville, Maryland; and Department of Mathematics and Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida

Correspondence: Address reprint requests to Arthur Sherman, Laboratory of Biological Modeling, NIDDK, National Institutes of Health, 12 South Dr., Rm. 4007, Bethesda, MD 20892. Tel.: 301-496-4325; Fax: 301-402-0535; E-mail: asherman{at}nih.gov.

Cell coupling is important for the normal function of the ß-cells of the pancreatic islet of Langerhans, which secrete insulin in response to elevated plasma glucose. In the islets, electrical and metabolic communications are mediated by gap junctions. Although electrical coupling is believed to account for synchronization of the islets, the role and significance of diffusion of calcium and metabolites are not clear. To address these questions we analyze two different mathematical models of islet calcium and electrical dynamics. To study diffusion of calcium, we use a modified Morris-Lecar model. Based on our analysis, we conclude that intercellular diffusion of calcium is not necessary for islet synchronization, at most supplementing electrical coupling. Metabolic coupling is investigated with a recent mathematical model incorporating glycolytic oscillations. Bifurcation analysis of the coupled system reveals several modes of behavior, depending on the relative strength of electrical and metabolic coupling. We find that whereas electrical coupling always produces synchrony, metabolic coupling can abolish both oscillations and synchrony, explaining some puzzling experimental observations. We suggest that these modes are generic features of square-wave bursters and relaxation oscillators coupled through either the activation or recovery variable.

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