Effects of diffusion of calcium and metabolites in pancreatic islets: Killing oscillations with a pitchfork

¹ National Institutes of Health
² National Insitutes of Health
³ Florida State University

^* To whom correspondence should be addressed. E-mail: asherman{at}nih.gov.

Submitted on November 23, 2005
Revised on January 5, 2006
Accepted on 1 February 2006

	Abstract

Cell coupling is important for the normal function of the beta-cells of the pancreatic islet of Langerhans, which secrete insulin in response to elevated plasma glucose. In the islets, electrical and metabolic communication 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. In order 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 (Bertram et al, Biophys. J. 87:3074--3087 2004). 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.

Key Words: calcium oscillations, coupled oscillators, diffusion, gap junctions, mathematical modeling, synchronization