Tumbling rates

In order for relaxation to occur through Wj, the magnetic field fluctuations need to correspond to the Larmor precession frequency of the nuclei, while relaxation via requires field fluctuations at double the Larmor frequency. To produce such field fluctuations, the tumbling rate should be the reciprocal of the molecular correlation time, i.e., f), so most efficient relaxation occurs only when voT, approaches 1. In very small, rapidly tumbling molecules, such as methanol, the concentration of the fluctuating magnetic fields spectral density) at the Larmor frequency is very low, so the relaxation processes Wj and do not occur efficiently and the nuclei of such molecules can accordingly relax very slowly. Such molecules have... 

When the zero-quantum 1% transition is greater than double-quantum Wi, the nOe enhancements will be negative. Similarly, when is greater than 1%, the resultant nOe will have a positive sign. The predominance of Wi and over one another depends on the molecular motion. It is known that the Wo transition is maximal when the molecule tumbles at a rate of about 1 KHz, while the Wi transition is fastest at a tumbling rate of about 800 MHz. On this basis, a rough idea of the sign of nOe can be obtained. For example, small molecules in nonviscous... 

One potential problem that can occur with slightly larger molecules (typically of m.w. > 600) is that the NOE response in both NOE and 2-D (NOESY) experiments is related to the tumbling rate of molecules in solution. The larger the molecule, the slower it will tumble and at a certain point, all expected enhancements will be nullified. This null point depends not only on the tumbling rate (and therefore the size, or more accurately, the shape of the molecule) but also on the field strength of the... 

In order to combat this, the rotating frame Overhauser effect spectroscopy (ROESY) techniques can be employed. An in-depth discussion of how this technique works is outside the remit of this book but suffice to say, in the ROESY methods (1- and 2-D), NOE data is acquired as if in a weak r.f. field rather than in a large, static magnetic field and this assures that all NOEs are present and positive, irrespective of tumbling rate and magnet size. It is possible that some TOCSY correlations can break through in ROESY spectra but these will have opposite phase to the genuine ROESY correlations and so should therefore not be a problem - unless they should overlap accidentally with them. A 2-D ROESY spectrum of the naphthalene compound is shown below (Spectrum 8.6). 

In metalloproteins, the paramagnet is an inseparable part of the native biomacromolecule, and so anisotropy in the metal EPR is not averaged away in aqueous solution at ambient temperatures. This opens the way to study metalloprotein EPR under conditions that would seem to approach those of the physiology of the cell more closely than when using frozen aqueous solutions. Still the number of papers describing metalloprotein bioEPR studies in the frozen state by far outnumbers studies in the liquid state. Several additional theoretical and practical problems are related to the latter (1) increased spin-lattice relaxation rate, (2) (bio)chemical reactivity, (3) unfavorable Boltzmann distributions, (4) limited tumbling rates, and (5) undefined g-strain. 

Finally, the last step of the procedure for optimizing experimental conditions is to identify the denaturation temperature of the protein. This step is important because the rotational tumbling rate of a protein increases with temperature, and faster tumbling results in sharper resonance lines. Therefore, the temperature during the NMR experiments should be as high as possible without denaturating the protein. The denaturation temperature can best be determined by either CD-spectroscopy or one-dimensional NMR. 

The anisotropy of the overall tumbling will result in the dependence of spin-relaxation properties of a given 15N nucleus on the orientation of the NH-bond in the molecule. This orientational dependence is caused by differences in the apparent tumbling rates sensed by various internuclear vectors in an anisotropically tumbling molecule. Assume we have a molecule with the principal components of the overall rotational diffusion tensor Dx, Dy, and l)z (x, y, and z denote the principal axes of the diffusion tensor), and let Dx< Dy< Dz. 

This section intends to provide the reader with some examples of how the high relaxivity challenge has been tackled for Gd(III) complexes so far. For the sake of clarity, this section has been divided in three sub-sections in relation to the specific relaxation parameter considered for relaxivity enhancement, namely the hydration state of the metal centre, the tumbling rate of the CA, and the exchange rate of the mobile protons coordinated to the paramagnetic center. 

Lee et al. evolved a comprehensive analytical-theoretical treatment, based on the solution of the reorientational isotropic diffusion equation, for an ensemble of high-spin systems under motion. These authors developed an analytical expression for the slow-tumbling motional region that relates the orientational-motion correlation time t (in s), or the corresponding tumbling rate t, with the step separation bB, of the ESR fine structure of a quartet by Eq. 8,... 

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... 

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