Accuracy of optimized chemical-exchange parameters derived by fitting CPMG R2 dispersion profiles when R2(0a) not = R2(0b)

Abstract

The transverse relaxation rate, R2, measured as a function of the effective field (R2 dispersion) using a Carr-Purcell-Meiboom-Gill (CPMG) pulse train, is well suited to detect conformational exchange in proteins. The dispersion data are commonly fitted by a two-site (sites a and b) exchange model with four parameters: the relative population, pa, the difference in chemical shifts of the two sites, deltaomega, the correlation time for exchange, tau(ex), and the intrinsic relaxation rate (i.e., transverse relaxation rate in the absence of chemical exchange), R2(0). Although the intrinsic relaxation rates of the two sites, R2(0a) and R2(0b), can differ, they are normally assumed to be the same (i.e., R2(0a) = R2(0b) = R2(0)) when fitting dispersion data. The purpose of this investigation is to determine the magnitudes of the errors in the optimized exchange parameters that are introduced by the assumption that R2(0a) = R2(0b). In order to accomplish this goal, we first generated synthetic constant-time CPMG R2 dispersion data assuming two-site exchange with R2(0a) not equal R2(0b), and then fitted the synthetic data assuming two-site exchange with R2(0) = R2(0a) = R2(0b). Although all the synthetic data generated assuming R2(0a) not equal R2(0b) were well fitted (assuming R2(0a) = R2(0b)), the optimized values of pa and tau(ex) differed from their true values, whereas the optimized values of deltaomega values did not. A theoretical analysis using the Carver-Richards equation explains these results, and yields simple, general equations for estimating the magnitudes of the errors in the optimized parameters, as a function of (R2(0a) - R2(0b)).