Analysis of 31P NMR spectra of enzyme-bound reactants and products of adenylate kinase using density matrix theory of chemical exchange.

31P NMR spectra of equilibrium mixtures of enzyme-bound reactants and products of the adenylate kinase reaction (formula; see text) were analyzed by using computer simulations based on density matrix theory of chemical exchange. Since adenylate kinase has the unique feature that the reactants in the reverse direction are both ADP molecules, which are indistinguishable off the enzyme, the density matrix equations are formulated for the ABC + D in equilibrium A'B' + A"B" exchange appropriate for the reaction, in which the interchange of A'B' and A"B" is explicitly introduced. It is shown that the consideration of this interchange is essential to explain the experimentally observed line shapes. By comparison of the computer-simulated spectra with various values for the rates of the exchange with the experimental spectra for porcine adenylate kinase at pH 7.0 and T = 4 degrees C, the following characteristic rates were determined: interconversion rates, 375 +/- 30 s-1 (ATP formation) and 600 +/- 50 s-1 (ADP formation); interchange rates of donor and acceptor ADP's, 100 +/- 30 s-1 (in the presence of optimal Mg2+ concentration), 1500 +/- 100 s-1 (in the absence of Mg2+). It is shown that under the conditions of the experiments the interchange rate is the lower limit of the dissociation rate of ADP (or MgADP from the acceptor site if Mg2+ was present) from the enzyme complexes. The significance of these interchange rates and their values relative to the interconversion rates is discussed with special reference to the role of the Mg2+ ion in the differentiation of the two nucleotide binding sites on adenylate kinase.