Understanding the Causes and Cures of Type 2 Diabetes with a Mathematical Model

Arthur Sherman
National Institutes of Health

(March 3, 2014 3:00 PM - 3:50 PM)

Understanding the Causes and Cures of Type 2 Diabetes with a Mathematical Model

Abstract

We present a mathematical model for regulation of beta-cell mass and function based on the pioneering work of Topp et al, J. Theor. Biol. 206:605 2000.  Their model added a layer of slow negative feedback to the classic insulin-glucose loop in the form of a glucose-dependent growth-death law for beta-cell mass.  We add to that model regulation of beta-cell function on intermediate time scales.  The model quantifies the relative contributions of insulin action and insulin secretion defects to type 2 diabetes (T2D) and explains why prevention is easier than cure.  The latter is a consequence of bistability, which also underlies the success of bariatric surgery and acute caloric restriction in reversing T2D.   With a further enhancement to include the dynamics of exocytosis, the model describes the mechanistic bases of the canonical pathways to T2D, elevated fasting glucose vs. elevated post-prandial glucose, and clarifies their relationship to the early transient and late sustained phases of insulin secretion.  The model gives new insight into the significance of the fact that insulin secretion is higher for pre-diabetics and early diabetics than for normal individuals ("Starling's law of the pancreas"), which has led some to question whether impaired insulin secretion is necessary for diabetes or even to propose that excessive insulin secretion triggers the disease.  The presentation will serve as an example of how theorists can use relatively elementary mathematics to engage constructively in important debates in the experimental community.