On the Electrical Activity and Glucose Response of Insulin-Secreting Cells

John Rinzel
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John Rinzel: NIDDK National Institutes of Health, Mathematical Research Branch

A chapter in Biomathematics and Related Computational Problems, 1988, pp 685-696 from Springer

Abstract: Abstract The β-cells of the mammalian pancreas exhibit electrical bursting activity in response to glucose (Fig. 1). A nonlinear differential equation model, developed by Chay and Keizer [8], describes several aspects of this bursting behavior for a representative cell (in a coupled, synchronized population). In this theory, the time scale of a burst is determined by the slow dynamics of intracellular free calcium, Ca, and the fast, spike generating, dynamics incorporates a calcium-activated K+ (K-Ca) channel as the site for slow feedback from Ca. We review how the structure of such models can be understood by using a singular perturbation dissection of the fast and slow subsystems of the model. We then outline how, under two different hypotheses for glucose action, an extended model leads to two different predictions for the time course of Ca. Finally we describe a further (stochastic) modification of the model to explore the question of why a single isolated β-cell does not burst, but electrically coupled cells in clusters do show bursting.

Keywords: Silent Phase; Random Opening; Intracellular Free Calcium; Fast Subsystem; Burst Pattern (search for similar items in EconPapers)
Date: 1988
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DOI: 10.1007/978-94-009-2975-3_62

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