The hyperbolic effect of density and strength of inter beta-cell coupling on islet bursting: a theoretical investigation

BACKGROUND: Insulin, the principal regulating hormone of blood glucose, is released through the bursting of the pancreatic islets. Increasing evidence indicates the importance of islet morphostructure in its function, and the need of a quantitative investigation. Recently we have studied this problem from the perspective of islet bursting of insulin, utilizing a new 3D hexagonal closest packing (HCP) model of islet structure that we have developed. Quantitative non-linear dependence of islet function on its structure was found. In this study, we further investigate two key structural measures: the number of neighboring cells that each β-cell is coupled to, n(c), and the coupling strength, g(c). RESULTS: β-cell clusters of different sizes with number of β-cells n(β )ranging from 1–343, n(c )from 0–12, and g(c )from 0–1000 pS, were simulated. Three functional measures of islet bursting characteristics – fraction of bursting β-cells f(b), synchronization index λ, and bursting period T(b), were quantified. The results revealed a hyperbolic dependence on the combined effect of n(c )and g(c). From this we propose to define a dimensionless cluster coupling index or CCI, as a composite measure for islet morphostructural integrity. We show that the robustness of islet oscillatory bursting depends on CCI, with all three functional measures f(b), λ and T(b )increasing monotonically with CCI when it is small, and plateau around CCI = 1. CONCLUSION: CCI is a good islet function predictor. It has the potential of linking islet structure and function, and providing insight to identify therapeutic targets for the preservation and restoration of islet β-cell mass and function.