The effect of noise and coupling on beta cell excitation dynamics

Bursting electrical behavior is commonly observed in a variety of nerve and endocrine cells, including that in electrically coupled β-cells located in intact pancreatic islets. However, individual β-cells usually display either spiking or very fast bursting behavior, and the difference between isolated and coupled cells has been suggested to be due to stochastic fluctuations of the plasma membrane ion channels, which are supposed to have a stronger effect on single cells than on cells situated in clusters (the channel sharing hypothesis). This effect of noise has previously been studied using numerical simulations. We show here how the application of two recent methods allows an analytic treatment of the stochastic effects on the location of the saddle-node and homoclinic bifurcations, which determine the burst period. Thus, the stochastic system can be analyzed similarly to the deterministic system, but with a quantitative description of the effect of noise. This approach supports previous investigations of the channel sharing hypothesis. For beta cells coupled via gap junctions we briefly discuss the effects of the ATP driven potassium ion gate on reaction diffusion type waves. It is shown how these effects lead to wave block phenomena in glucose gradients across an islet of Langerhans.