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

Abstract

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 (Δδ(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 Δδ(max) 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 Δδ(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 Δδ(max)) is a straightforward approach to increasing the accuracy of measured dissociation constants for 1:1 protein-ligand interactions.