Quantitative determination of NOE rates in perdeuterated and protonated proteins: practical and theoretical aspects

Precision and accuracy are the limiting factors in extracting structural and dynamic information from experimental NOEs. In this study, error sources at all stages of such an analysis are identified and errors are estimated. The data set of H(N)-H(N) cross-relaxation rates obtained from triple-labeled ubiquitin presented in [B. Vögeli, T.F. Segawa, D. Leitz, A. Sobol, A. Choutko, D. Trzesniak, W. van Gunsteren, R. Riek, J. Am. Chem. Soc. 131 (47) (2009) 17215-17225] is extended to rates obtained from a double-labeled sample. Analog data sets are presented for GB3. It is shown that quantitative NOE rates can be determined with high accuracy from both triple-labeled as well as double-labeled samples. The quality of experimental cross-relaxation rates obtained from 3D HXQC-NOESY and NOESY-HXQC experiments is discussed. It is shown that NOESY-HXQC experiments provide rates of the same quality as HXQC-NOESY if both diagonal and cross peaks for a spin pair can be resolved. Expressions for cross-relaxation rates for anisotropically tumbling molecules exhibiting fast and slow motion are derived. The impact of anisotropy on the prediction of cross-relaxation rates and on the conversion of experimental rates into effective distances is discussed. For molecules with anisotropy D(II)/D( perpendicular) up to five the distance error is smaller than 2%. Finally, "averaged order parameters" are calculated for specific secondary-structural elements showing similar trends for ubiquitin and GB3.