The hepatic adenylate cyclase system. III. A mathematical model for the steady state kinetics of catalysis and nucleotide regulation.

This paper presents a steady state kinetic model for hepatic adenylate cyclase. The activity of the enzyme has been assayed in the presence of a range of concentrations of magnesium, adenylylimidodiphosphate (App(NH)p), 5'-guanylylimidodiphosphate (Gpp(NH)p), and in the presence and absence of saturating concentrations of glucagon. The data were tested against proposed models using an iterative least squares curve fitting program (SAAM25) and confidence estimates for the model parameters were obtained. Hepatic adenylate cyclase is viewed as an enzyme having three characteristic states of catalytic function (E, E', E''). Each state has its own intrinsic activity in carrying out the catalysis of MgApp(NH)p-3 minus to form cyclic adenosine 3':5'-monophosphate. It is shown, in agreement with a proposal by de Haën, that unchelated substrate can inhibit adenylate cyclase activity. It is further concluded that this inhibition is principally due to App(NH)pH-3 minus. The three catalytic states differ markedly in their susceptibility to inhibition as well as in their Vmax, but the Km for MgApp(NH)p-2 minus is essentially the same for all states. The state transitions induced by Gpp(NH)p and by hormone are considered. Gpp(NH)p binding to state E causes transformation to state E'. State E' undergoes spontaneous transformation to state E''. Glucagon augments the transition from E' to E''. We conclude that the activating species of Gpp(NH)p is an unchelated form, most probably Gpp(NH)p-4 minus. Our results indicate that state E' is significantly more susceptible to inhibition by App(NH)pH-3 minus than the other two states. Certain phenomena occurring in fat cell adenylate cyclase are discussed in light of our findings in hepatic adenylate cyclase.