Molecular correlation time effect

In addition to the dipole-dipole relaxation processes, which depend on the strength and frequency of the fluctuating magnetic fields around the nuclei, there are other factors that affect nOe (a) the intrinsic nature of the nuclei I and S, (b) the internuclear distance (r,s) between them, and (c) the rate of tumbling of the relevant segment of the molecule in which the nuclei 1 and S are present (i.e., the effective molecular correlation time, Tf). 

LIG. 22 A schematic illustration of the dependence of NMR relaxation times T and T2 on the molecular correlation time, xc, characterizing molecular mobility in a singlecomponent system. Both slow and fast motions are effective for T2 relaxation, but only fast motions near w0 are effective in Tx relaxation. 

Indeed, 13C spin-lattice relaxation times can also reflect conformational changes of a protein, i.e. helix to random coil transitions. This was demonstrated with models of polyamino acids [178-180], in which definite conformations can be generated, e.g. by addition of chemicals or by changes in temperature. Thus effective molecular correlation times tc determined from spin-lattice relaxation times and the NOE factors were 24-32 ns/rad for the a carbons of poly-(/f-benzyl L-glutamate) in the more rigid helical form and about 0.8 ms/rad for the more flexible random coil form [180],... 

This simple relaxation theory becomes invalid, however, if motional anisotropy, or internal motions, or both, are involved. Then, the rotational correlation-time in Eq. 30 is an effective correlation-time, containing contributions from reorientation about the principal axes of the rotational-diffusion tensor. In order to separate these contributions, a physical model to describe the manner by which a molecule tumbles is required. Complete expressions for intramolecular, dipolar relaxation-rates for the three classes of spherical, axially symmetric, and asymmetric top molecules have been evaluated by Werbelow and Grant, in order to incorporate into the relaxation theory the appropriate rotational-diffusion model developed by Woess-ner. Methyl internal motion has been treated in a few instances, by using the equations of Woessner and coworkers to describe internal rotation superimposed on the overall, molecular tumbling. Nevertheless, if motional anisotropy is present, it is wiser not to attempt a quantitative determination of interproton distances from measured, proton relaxation-rates, although semiquantitative conclusions are probably justified by neglecting motional anisotropy, as will be seen in the following Section. 

Up to this point only overall motion of the molecule has been considered, but often there is internal motion, in addition to overall molecular tumbling, which needs to be considered to obtain a correct expression for the spectral density function. Here we apply the model-free approach to treat internal motion where the unique information is specified by a generalized order parameter S, which is a measure of the spatial restriction of internal motion, and the effective correlation time re, which is a measure of the rate of internal motion [7, 8], The model-free approach only holds if internal motion is an order of magnitude (<0.3 ns) faster than overall reorientation and can therefore be separated from overall molecular tumbling. The spectral density has the following simple expression in the model-free formalism ... 

The dependence of (20 MHz and 25° C) on is graphically represented in Pig. 3 for monoaqua Gd(III) complexes with different values of the rotational correlation times. The limiting effect of the residence lifetime is small for low molecular weight complexes (xf> = 50 100 ps) and detectable only when On the other hand, for slowly tumbling... 

The molecular reorientational correlation time tends to dominate the overall correlation time of low molecular weight Gd(III) chelates, particularly in the high field region, and therefore represents a key parameter in governing their relaxivity. The effect of the increase in x on the shape and amplitude of the NMRD profiles was understood in detail early on and, as a consequence, the attempts at optimizing the relaxivity were primarily focused on slowing down the rotation by increasing the size of the... 

We analyzed the temperature dependence of 1/Ti using the semi-classical BPP model for the effect of molecular motion on 1/Ti [32]. In this model, 1/Ti can be related to the values of correlation time, Tc, which is the characteristic time between significant fluctuations in the local magnetic field experienced by a spin due to moleciflar motions or reorientations of a molecule. As usual, it is assumed that Tc follows Arrhenius-hke behavior ... 

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