Abstract
Pancreatic beta-cells coupled by gap junctions in sufficiently large clusters exhibit regular electrical bursting activity, which is described by the Chay-Keizer model and its variants. According to most reports, however, isolated cells exhibit disorganized spiking. We have previously (Sherman, A. J. Rinzel, and J. Keizer, 1988. Biophys. J. 54:411-425) modeled these behaviors by hypothesizing that stochastic channel fluctuations disrupt the bursts. We showed that when cells are coupled by infinite conductance gap junctions, so that the cluster is isopotential and may be viewed as a single "supercell," the fluctuations are shared over a larger membrane area and hence dampened. Bursting emerges when there are more than approximately 50 cells in the cluster. In the model the temporal organization of spikes into bursts increases the amplitude of intracellular calcium oscillations, which may be relevant for insulin secretion. We now extend the previous work by considering the case of a true "multicell" model with finite gap junctional conductance. Whereas the previous study assumed that the cells were synchronized, we can now study the process of synchronization itself. We show that, for sufficiently large clusters, the cells both synchronize and begin to burst with moderate, physiologically reasonable gap junctional conductance. An unexpected finding is that the burst period is longer, and calcium amplitude greater, than when coupling is infinitely strong, with an optimum in the range of 150-250 pS. Our model is in good agreement with recent experimental data of Perez-Armendariz, M., D. C. Spray, and M. V. L. Bennett. (1991. Biophys. J. 59:76-92) showing extensive gap junctions in beta-cell pairs with mean interfacial conductance of 213 +/- 113 pS. The optimality property of our model is noteworthy because simple slow-wave models without spikes do not show the same behavior.