Slow Variable Dominance in Pancreatic β-Cell Models

Like nerve and many other endocrine cells, pancreatic beta-cells are electrically excitable and produce electrical impulses in response to elevations in glucose. These electrical impulses typically come in the form of bursting. One type of bursting model with two or more slow variables has been called 'phantom bursting' since the burst period is a blend of the time constants of the slow variables. In this dissertation, the relative contributions that slow variables make to the bursting produced by two different phantom bursting models are quantified using a measure called the 'dominance factor'. Using this quantification, it is demonstrated that the control of different phases of the burst can be shifted from one slow variable to another by changing a model parameter. It is also demonstrated that the contributions that the slow processes make to bursting can be non-obvious. One application of the dominance factor is in making predictions about the resetting properties of the model cells. This application is demonstrated using a general phantom bursting model.