Analysis of Equilibrium Data from Proton Magnetic Relaxation Rates of Water for Manganese-Nucleotide-Kinase Ternary Complexes

Abstract

Abstract The reliability of equilibrium constants and enhancement factors, et, for ternary metal-substrate-enzyme complexes determined by proton relaxation rate titration methods has been examined. Approximations inherent in graphical procedures for analyzing the experimental data have been avoided by obtaining exact numerical solutions for the system of complex equilibria and subjecting the titration data to nonlinear least squares error analysis by computer techniques. Computer analysis of titration data for the adenylate kinase-Mn(II)-ATP system gave values for et significantly different from et values obtained by graphical analysis of the same data; at 42° the computer value for et was 22, to be contrasted with the graphical value of 170. The respective fits of theoretical curves drawn with the graphical and computer constants strongly support the et from the computer analysis as well as the fact that the value of et derived graphically exceeds the theoretical limit. For the Mn(II)-ADP creatine kinase system only a limited region of the saturation curve with respect to ternary complex formation is available for measurement under attainable experimental conditions. Hence, the experimental data obtained at 24° under optimal conditions, previously determined in exploratory experiments, can still be fitted to a relatively large range of equilibrium constants, K2, for the ternary complex (40 µm to 100 µm). However, despite the rather large uncertainty in K2, the variation in et is only 10% (21 ± 2) over the whole range of K2 values. This degree of accuracy in et should be quite satisfactory for evaluating molecular parameters of the ternary complex from the magnitude of et.