31P NMR studies of the arginine kinase reaction. Equilibrium constants and exchange rates at stoichiometric enzyme concentration.

The arginine kinase reaction, the reversible transfer of the terminal phosphoryl group of ATP to L-arginine, has been investigated by the technique of 31P NMR at catalytic and stoichiometric concentrations of the enzyme. Three of the four substrates, ATP, ADP, and P-arginine produce easily distinguishable resonances in the 31P NMR spectrum, thus permitting a determination of equilibrium constants from the integrated areas of the resonances. From the linewidths, the exchange rates between reactants and products may be evaluated. At pH 7.25 and a temperature of 12 degrees, the equilibrium constant at catalytic enzyme concentration: Keq = [MgADP] [P-arginine]/[MgATP] [L-arginine], is found to be 0.10 +/- 0.02 and that at stoichiometric enzyme concentration: K'eq = [E-MgADP] [E-P-arginine]/[E-MgATP] [E-arginine] to be 1.56 +/- 0.5. Thus, as the enzyme concentration increased, the production of P-arginine is increasingly favored. From the NMR line shapes in the presence of excess enzyme, the rate of the single step, the transfer of the phosphoryl group on the surface of the enzyme is found to be 192 +/- 15 s-1 in the forward direction, i.e. from E-MgATP, and 154 +/- 15 s-1 in the reverse direction from E-P-argine. At 12 degrees and pH 7.25, the rate of the overall reaction in the forward direction was determined from kinetic measurements to be 19 s-1, an order of magnitude slower than the rate measured by NMR. It can, therefore, be concluded that the interconversion of substrates on the surface of the enzyme is not the rate-determining step in the overal reaction. From the equilibrium constants and other known data the dissociation constant of P-arginine from its enzyme complex can be determined and is found to be 100 muM.