Glucose-induced period-doubling cascade in the electrical activity of pancreatic β-cells

In the presence of stimulatory concentrations of glucose, the membrane potential of pancreatic beta-cells may experience a transition from periods of rapid spike-like oscillations alternating with a pseudo-steady state to spike-only oscillations. Insulin secretion from beta-cells closely correlates the periods of spike-like oscillations. The purpose of this paper is to study the mathematical structure which underlines this transitional stage in a pancreatic beta-cell model. It is demonstrated that the transition can be chaotic but becomes more and more regular with increase in glucose. In particular, the system undergoes a reversed period-doubling cascade leading to the spike-only oscillations as the glucose concentration crosses a threshold. The transition interval in glucose concentration is estimated to be extremely small in terms of the rate of change for the calcium dynamics in the beta-cells. The methods are based on the theory of unimodal maps and the geometric and asymptotic theories of singular perturbations.