Modeling a simplified regulatory system of blood glucose at molecular levels

In this paper, we propose a new mathematical control system for a simplified regulatory system of blood glucose by taking into account the dynamics of glucose and glycogen in liver and the dynamics of insulin and glucagon receptors at the molecular level. Numerical simulations show that the proposed feedback control system agrees approximately with published experimental data. Sensitivity analysis predicts that feedback control gains of insulin receptors and glucagon receptors are robust. Using the model, we develop a new formula to compute the insulin sensitivity. The formula shows that the insulin sensitivity depends on various parameters that determine the insulin influence on insulin-dependent glucose utilization and reflect the efficiency of binding of insulin to its receptors. Using Lyapunov indirect method, we prove that the new control system is input-output stable. The stability result provides theoretical evidence for the phenomenon that the blood glucose fluctuates within a narrow range in response to the exogenous glucose input from food. We also show that the regulatory system is controllable and observable. These structural system properties could explain why the glucose level can be regulated.