Effect of Dipolar Cross Correlation on Model-Free Motional Parameters Obtained from 13C Relaxation in AX 2 Systems

Abstract

The importance of dipolar cross correlation in 13C relaxation studies of molecular motion in AX 2 spin systems (A = 13C, X = 1H) was examined. Several different models for the internal motion, including two restricted-diffusion, and two-site jump models, the Kinosita model [K. Kinosita, Jr., S. Kawato, and A. Ikegami, Biophys. J. 20, 289 (1977)], and an axially symmetric model, were applied through the Lipari and Szabo [ J. Am. Chem. Soc. 104, 4546 (1982)] formalism to calculate errors in 13C T 1, obtained from inversion-recovery measurements under proton saturation, and NOE when dipolar cross correlation is neglected. Motional parameters in the Lipari and Szabo formalism, τ m, S 2, and τ e, were then determined from T 1 and NOE (including the errors) and compared with parameters initially used to simulate the relaxation data. The resulting differences in the motional parameters, while model dependent, were generally small for plausible motions. At larger S 2 values (≥ 0.6), the errors in both τ m and S 2 were <5%. Errors in τ e increased with S 2 but were usually less than 10%. Larger errors in the parameters were found for an axially symmetric model, but with τ m fixed even those were >5% only for the τ m = 1 ns, τ e = 10 ps case. Furthermore, it was observed that deviations in a given motional parameter were mostly of the same sign, which allows bounds to be set on experimentally derived parameters. Relaxation data for the peptide melittin synthesized with gly enriched with 13C at the backbone cu position and with lys enriched with 13C in the side chain were examined in light of the results of the simulations. All in all, it appears that neglect of dipolar cross correlation in 13C T 1 (With proton saturation) and NOE measurements in AX 2 systems does not lead to major problems in interpretation of the results in terms of molecular motion.