Enzyme kinetics of muscle glycogen phosphorylase b

Interest in the kinetics of glycogen phosphorylase has recently been renewed by the hypothesis of a glycogen shunt and by the potential of altering phosphorylase to treat type II diabetes. The wealth of data from studies of this enzyme in vitro and the need for a mathematical representation for use in the study of metabolic control systems make this enzyme an ideal subject for a mathematical model. We applied a two-part approach to the analysis of the kinetics of glycogen phosphorylase b (GPb). First, a continuous state model of enzyme-ligand interactions supported the view that two phosphates and four ATP or AMP molecules can bind to the enzyme, a result that agrees with spectroscopic and crystallographic studies. Second, using minimum error estimates from continuous state model fits to published data (that agreed well with reported error), we used a discrete state model of internal molecular events to show that GPb exists in three discrete states (two of which are inactive) and that state transitions are concerted. The results also show that under certain concentrations of substrate and effector, ATP can activate the enzyme, while under other conditions, it can competetively inhibit or noncompetitively inhibit the enzyme. This result is unexpected but is consistent with spectroscopic, crystallographic, and kinetic experiments and can explain several previously unexplained phenomena regarding GPb activity in vivo and in vitro.