31P NMR lineshapes of beta-P (ATP) in the presence of Mg2+ and Ca2+: estimate of exchange rates.

The 31P NMR chemical shift of beta-P of adenosine triphosphate (ATP) undergoes a substantial change (approximately 2-3 ppm) upon chelation of divalent ions such as Mg2+ or Ca2+. In the presence of nonsaturating amounts of Mg2+ or Ca2+, the lineshape of this resonance depends on the characteristic association and dissociation rates of these metal-ATP complexes. A procedure for computer simulation of this lineshape is outlined. A comparison of computer-simulated lineshapes with the experimental lineshapes obtained at 121 MHz was used to determine the following dissociation rate of Mg2+ and Ca2+ from their ATP complexes at 20 degrees C and pH 8.0: Ca2+, greater than 3 X 10(5) s-1 (Hepes buffer); Mg2+, 1200 s-1 (no buffer), 1000 s-1 (Tris buffer) and 2100 s-1 (Hepes buffer). The limits of error are +/- 10% in these values. For the Mg2+ complexes, the rates were determined as a function of temperature to obtain activation energies (with a maximum deviation of 10% in the least-squares fit): 8.1 Kcal/mole (no buffer and Hepes buffer) and 6.8 kcal/mole (Tris buffer). Lineshapes of the beta-P resonance simulated as a function of Mg2+ concentration, using 2100 s-1 for the dissociation rate, are also presented. The computer simulation of lineshapes offers a reliable and straightforward method for the determination of exchange rates of diamagnetic cations from their ATP complexes, under a variety of sample conditions.

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.