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

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 χ² 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 χ² 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, τ_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 τ_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 τ_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.