How to detect internal motion by homonuclear NMR

NOESY and ROESY cross-peak intensities depend on internuclear distances and internal motion. Internal motion is usually ignored, and NOESY cross-peak intensities are interpreted in terms of internuclear distances only. Off-resonance ROESY experiments measure a weighted average of NOE and ROE. The weight can be described and experimentally set by an angle theta;. For large enough molecules, NOE and ROE have opposite signs. Therefore, each cross-peak intensity becomes zero for an angle theta;(0). For any sample, the maximum angle theta;(0) is determined by the overall motion of the molecule. Smaller theta;(0) values reflect the angular component of internal motions. Because individual cross-peaks are analyzed, the method evaluates internal motions of individual H,H vectors. The reduction of theta;(0) is largest for internal motions on a time scale of 100-300 ps. The sensitivity of theta;(0) for internal motions decreases with increasing molecular weight. We estimate that detecting internal motions will be practicable for molecules up to about 15 kDa. We describe a protocol to measure theta;(0) from a series of off-resonance ROESY spectra. For such a series, we describe the choice of experimental parameters, a procedure to extract theta;(0) from the raw data, and the interpretation of theta;(0) in terms of internal motions. In the small protein BPTI, we analyzed 75 cross-peaks. The precision of theta;(0) was 0.25 degrees, as compared to typical reductions of theta;(0) of 3 degrees. We found a well-defined maximum theta;(0) for cross-peaks in rigid parts of the molecule, which reflects the overall motion of the molecule. For BPTI, also many structurally important long-range cross-peaks appear rigid. The lower theta;(0) values of long-range contacts involving methyl groups are consistent with methyl rotation on the 25-ps time scale. The lower theta;(0) values of the flexible C-terminus and of flexible side chains translate into upper limits for the angular order parameter of 0.4 and 0.5-0.8, respectively. Off-resonance ROESY can monitor internal motions of H,H contacts that are used in a structure calculation. Because no isotope labeling is needed, off-resonance ROESY can be used to detect internal motions in a wide range of natural products.