Incorporating covalent and allosteric effects into rate equations: the case of muscle glycogen synthase

Several enzymes have been described that undergo both allosteric and covalent regulation, but, to date, there exists no succinct kinetic description that is able to account for both of these mechanisms of regulation. Muscle glycogen synthase, an enzyme implicated in the pathogenesis of several metabolic diseases, is activated by glucose 6-phosphate and inhibited by ATP and phosphorylation at multiple sites. A kinetic description of glycogen synthase could provide insight into the relative importance of these modifiers. In the present study we show, using non-linear parameter optimization with robust weight estimation, that a Monod-Wyman-Changeux model in which phosphorylation favours the inactive T conformation provides a satisfactory description of muscle glycogen synthase kinetics. The best-fit model suggests that glucose 6-phosphate and ATP compete for the same allosteric site, but that ATP also competes with the substrate UDP-glucose for the active site. The novelty of our approach lies in treating covalent modification as equivalent to allosteric modification. Using the obtained rate equation, the relationship between enzyme activity and phosphorylation state is explored and shown to agree with experimental results. The methodology we propose could also be applied to other enzymes that undergo both allosteric and covalent modification.