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 ~2 μM 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 (Δδmax). 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 Δδmax from nonlinear least squares analyses requires initial protein concentrations that are ~0.5 × K D , and a maximum concentration for the ligand, or titrant, of ~10 × [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 Δδmax 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 Δδmax) is a straightforward approach to increasing the accuracy of measured dissociation constants for 1:1 protein–ligand interactions.