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 thetadegrees. For any sample, the maximum angle thetadegrees is determined by the overall motion of the molecule. Smaller thetadegrees 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 thetadegrees is largest for internal motions on a time scale of 100-300 ps. The sensitivity of thetadegrees 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 thetadegrees from a series of off-resonance ROESY spectra. For such a series, we describe the choice of experimental parameters, a procedure to extract thetadegrees from the raw data, and the interpretation of thetadegrees in terms of internal motions, In the small protein BPTI, we analyzed 75 cross-peaks. The precision of thetadegrees was 0.25degrees, as compared to typical reductions of thetadegrees of 3degrees. We found a well-defined maximum thetadegrees 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 thetadegrees values of long-range contacts involving methyl groups are consistent with methyl rotation on the 25-ps time scale. The lower thetadegrees 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.