Advanced Mathematical Modelling of Pancreatic β-Cells

Abstract

Insulin-secreting pancreatic $\beta$-cells are responsible for maintaining the whole body glucose homeostasis. Dysfunction or loss of $\beta$-cell mass results in impaired insulin secretion and, in some cases, diabetes. Many of the factors that influence $\beta$-cell function or insulin exocytosis, however, are not fully understood. To support the investigation, mathematical models have been developed and used to design experiments. In this dissertation, we present the Integrated Oscillator Model (IOM) that is one of the mathematical models used for the investigation of the mechanism behind the bursting activity that underlies intracellular Ca$^{2+}$ oscillations and pulsatile insulin secretion. The IOM describes the interaction of the cellular electrical activity and intracellular Ca$^{2+}$ with glucose metabolism via numerous feedforward and feedback pathways. These interactions, in turn, produce metabolic oscillations with a sawtooth or pulsatile time course, reflecting different oscillation mechanisms. We determine conditions favorable to each type of oscillations, and show that the model accounts for key experimental findings of $\beta$-cell activity. We propose several extensions of the model to include all the main elements involved in the insulin secretion. The latest and most sophisticated model describes the complex metabolism in the mitochondria and the several biological processes in the insulin exocytosis cascade. The model, also, captures the changes in the $\beta$-cell activity and the resulting amount of secreted insulin in response to different concentrations of glucose in the blood. The model predictions, in agreement with findings reported in the experimental literature, show an increase of insulin secretion when the glucose level is high and a basal-low insulin concentration when the glucose level decreases. Finally, we use the new model to simulate the interaction among $\beta$-cells (through gap junction) within the same islet. The simulations show that the electrical coupling is sufficient to synchronize the $\beta$-cells within an islet. We also show that the amplitude of the oscillations in the insulin secretion rate is bigger when the $\beta$-cells synchronize. This suggests a more efficient secretion of insulin in the bloodstream when the cells burst in unison, as it has been observed experimentally