Increased precision for analysis of protein-ligand dissociation constants determined from chemical shift titrations

NMR is ideally suited for the analysis of protein-protein and protein ligand interactions with dissociation constants ranging from similar to 2 mu M to similar to 1 mM, and with kinetics in the fast exchange regime on the NMR timescale. For the determination of dissociation constants (K (D) ) of 1:1 protein-protein or protein-ligand interactions using NMR, the protein and ligand concentrations must necessarily be similar in magnitude to the K (D) , and nonlinear least squares analysis of chemical shift changes as a function of ligand concentration is employed to determine estimates for the parameters K (D) and the maximum chemical shift change (Delta delta(max)). During a typical NMR titration, the initial protein concentration, [P (0)], is held nearly constant. For this condition, to determine the most accurate parameters for K (D) and Delta delta(max) from nonlinear least squares analyses requires initial protein concentrations that are similar to 0.5 x K (D) , and a maximum concentration for the ligand, or titrant, of similar to 10 x [P (0)]. From a practical standpoint, these requirements are often difficult to achieve. Using Monte Carlo simulations, we demonstrate that co-variation of the ligand and protein concentrations during a titration leads to an increase in the precision of the fitted K (D) and Delta delta(max) values when [P (0)] > K (D) . Importantly, judicious choice of protein and ligand concentrations for a given NMR titration, combined with nonlinear least squares analyses using two independent variables (ligand and protein concentrations) and two parameters (K (D) and Delta delta(max)) is a straightforward approach to increasing the accuracy of measured dissociation constants for 1:1 protein-ligand interactions.