A comparison of mathematical models for a recycling cascade in glycogenolysis

Mathematical models are derived which describe a cyclic-AMP initiated recycling enzyme cascade for the activation of glycogen phosphorylase. The components of the cascade are protein kinase, phosphorylase kinase, phosphorylase kinase phosphatase, phosphorylase, and phosphorylase phosphatase. Two classes of models are formulated and compared. The models differ only in the molecular hypothesis for activation of protein kinase by cyclic-AMP; in one case the assumption leads to second order kinetics, in the other third order kinetics are indicated. Amplification and a fast response time are the prime features of both classes of models for the activation of phosphorylase. The role of free calcium in optimizing the activation and deactivation of the cascade is discussed.