A stochastic version of the Pedersen-Sherman insulin secretion model

Pedersen and Sherman have recently developed a multi-pool model of insulin vesicle secretion from pancreatic beta-cells [12]. In the PedersenSherman model, pool sizes are reported as concentrations; however, concentrations of the different pools vary by as much as seven orders of magnitude. Very low concentrations indicate there could be discrete numbers of vesicles in some of the pools, leading naturally to the questions regarding stochasticity in the signalling pathway. We therefore simulate a discrete counterpart of the deterministic model with a (hybrid) Gillespie-style stochastic simulation algorithm. The stochastic simulations are calibrated to the deterministic model in the mean. We estimate the variances in pool sizes numerically and show it closely tracks the mean, indicating a Poisson-like result. Our numerical results demonstrate that the mean behavior indicated in the Pedersen-Sherman model is evident with just one islet.