Error estimation and global fitting in transverse-relaxation dispersion experiments to determine chemical-exchange...

Off-resonance effects can introduce significant systematic errors in R2 measurements in constant-time Carr-Purcell-Meiboom-Gill (CPMG) transverse relaxation dispersion experiments. For an off-resonance chemical shift of 500 Hz, 15N relaxation dispersion profiles obtained from experiment and computer simulation indicated a systematic error of ca. 3%. This error is three- to five-fold larger than the random error in R2 caused by noise. Good estimates of total R2 uncertainty are critical in order to obtain accurate estimates in optimized chemical exchange parameters and their uncertainties derived from chi2 minimization of a target function. Here, we present a simple empirical approach that provides a good estimate of the total error (systematic + random) in 15N R2 values measured for the HIV protease. The advantage of this empirical error estimate is that it is applicable even when some of the factors that contribute to the off-resonance error are not known. These errors are incorporated into a chi2 minimization protocol, in which the Carver-Richards equation is used fit the observed R2 dispersion profiles, that yields optimized chemical exchange parameters and their confidence limits. Optimized parameters are also derived, using the same protein sample and data-fitting protocol, from 1H R2 measurements in which systematic errors are negligible. Although 1H and 15N relaxation profiles of individual residues were well fit, the optimized exchange parameters had large uncertainties (confidence limits). In contrast, when a single pair of exchange parameters (the exchange lifetime, tau(ex), and the fractional population, p(a)), were constrained to globally fit all R2 profiles for residues in the dimer interface of the protein, confidence limits were less than 8% for all optimized exchange parameters. In addition, F-tests showed that quality of the fits obtained using tau(ex), p(a) as global parameters were not improved when these parameters were free to fit the R2 profiles of individual residues. Finally, nearly the same optimized global tau(ex), p(a) values were obtained, when the 1H and 15N data sets for residues in the dimer interface, were fit independently; the difference in optimized global parameters, ca. 10%, was of marginal significance according to the F-test.