Slow molecular tumbling

For a long time, magic-angle spinning (MAS A has helped biomolecular NMR applications in cases where slow molecular tumbling or susceptibility effects prohibit high-resolution spectroscopy under static conditions. For example, the benehcial effect of MAS has been observed for structural studies on biopolymers, model membranes,... 

For a rigidly held, three-spin system, or when existing internal motion is very slow compared to the overall molecular tumbling, all relaxation methods appear to be adequate for structure determination, provided that the following assumptions are valid (a) relaxation occurs mainly through intramolecular, dipolar interactions between protons (b) the motion is isotropic and (c) differences in the relaxation rates between lines of a multiplet are negligibly small, that is, spins are weakly coupled. This simple case is demonstrated in Table V, which gives the calculated interproton distances for the bicycloheptanol derivative (52) of which H-1, -2, and -3 represent a typical example of a weakly coupled, isolated three-spin... 

If the molecular tumbling rate is slow enough that larger electron-electron dipolar couplings are not motionally averaged, Fourier deconvolution can be used to analyze dipolar interactions in fluid solution.18 Distances in doubly spin-labelled rhodopsin were measured by Fourier deconvolution of CW line-shape changes in room temperature solution.78 The broadening function was modelled as the sum of Pake patterns from a distribution of distances. As a reference point for the distance measurements one label was attached at the cytoplasmic termination of transmembrane helix 1. The second label was attached near the cytoplasmic termination of transmembrane helix 7 or in the short helix 8. The distances and conformational flexibility in the dark state are... 

Spin-spin relaxation of nuclei is accelerated when the nuclei participate in a dipolar bond (O — H, N — H, 13C—1H). Spin-spin relaxation involving dipole-dipole interaction is very effective in solids and viscous liquids with slow molecular motion, since the magnetic fields caused by slowly tumbling dipoles change very slowly. 

By comparison, a saturated methine carbon (C-H) has a CSA of only 25 ppm because the mobility of electrons around the carbon nucleus is much less in an sp3-hybridized carbon and depends much less on the orientation of the C-H bond with respect to B0. In solution-state NMR we only see the isotropic chemical shift, < iso, and the fixed-position chemical shifts and the CSA value are obtained from solid-state NMR measurements. Although CSA does not affect chemical shifts in solution, it does contribute to NMR relaxation and can be exploited to sharpen peaks of large molecules such as proteins in solution. For large molecules, such as proteins, nucleic acids, and polymers, or in viscous solutions, molecular tumbling is slow and CSA broadens NMR lines due to incomplete averaging of the three principle chemical shift values on the NMR timescale. Like isotropic chemical shifts, CSA in parts per million is independent of magnetic field strength B0 but is proportional to B0 when expressed in hertz. Because linewidths are measured in... 

Based on random fields, relaxation theory R2 decreases as molecular tumbling gets faster and more effectively averages the residual dipolar broadening. Both in the fast and slow motion limits, R2 is proportional to tc. ... 

The motion of the R1 nitroxide in a protein has contributions from the overall tumbling of the protein, the internal motions of the side chain, and fluctuations in the backbone structure. For membrane proteins such as rhodopsin, the correlation time for molecular tumbling is slow on the EPR time scale defined above and can be ignored. The internal motion of the R1 side chain is due to torsional oscillations about the bonds that connect the nitroxide to the backbone, and the correlation times for these motions lie in the nanosecond regime where the EPR spectra are highly sensitive to changes in rate. 

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