A Mathematical Model of Beta-cell Population Size Under the Influence of Regulatory Factors

Diabetes is a disease characterized by the inability of the body to properly regulate insulin levels in the bloodstream. Beta-cells are responsible for the production of insulin and a substantial shrinkage in the size of the beta-cell population can lead to diabetes. We present a model of functional beta-cell population growth by examining data sets reporting beta-cell population size in mice. We will first determine the primary regulatory factor of beta-cell population growth using a non-parametric statistical test. Using this factor as the independent variable, we will then use non-linear fitting approaches to identify the growth laws followed by beta-cells during mouse development. Once these growth laws have been determined, we will modify the models to include potential sources of beta-cell death. The two sources of beta-cell death that will be considered in this study are auto-immune infiltration and endoplasmic reticulum (ER) stress induced apoptosis. The physiology of auto-immune infiltration and ER-stress will be used to create functions to represent them. These functions will then be compiled with the natural growth laws previously established to yield a complete model of beta-cell population growth under the influence of regulatory factors. Finally, we will determine the steady states of this model and their stability in order to analyze the changes in the nonlinear dynamics of this system upon introduction of these regulatory factors.