Proton relaxivity

The second reason is related to the misconception that proton dipolar relaxation-rates for the average molecule are far too complicated for practical use in stereochemical problems. This belief has been encouraged, perhaps, by the formidable, density-matrix calculations " commonly used by physicists and physical chemists for a rigorous interpretation of relaxation phenomena in multispin systems. However, proton-relaxation experiments reported by Freeman, Hill, Hall, and their coworkers " have demonstrated that pessimism regarding the interpretation of proton relaxation-rates may be unjustified. Valuable information of considerable importance for the carbohydrate chemist may be derived for the average molecule of interest from a simple treatment of relaxation rates. 

In proton-relaxation experiments, R, values are used extensively, whereas 7, values are more frequently reported for C relaxation measurements. Although there is no special merit in this preference for C 7, values, the pairwise additivity of relaxation contributions in proton-relaxation experiments is more clearly apparent for the relaxation rates. 

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. 

Fig. 4.—The Three Distinct Proton-Proton Relaxation Pathways in a Six-membered Ring in the C, Conformation. [Vicinal-Gauche (vg),vicinal-tranr (vt), and 1,3-diaxial (aa). Geminal relaxation-pathways are not shown.]...

We used modifications of the standard solid-state CP-MAS (cross-polarisation, magic-angle spinning) experiment to allow the proton relaxation characteristics to be measured for each peak in the C spectrum. It is known that highly mobile, hydrated polymers can not be seen using either usual CP-MAS C spectrum or solution NMR (6). We found, however, that by a combination of a long-contact experiment and a delayed-contact experiment we could reconstruct a C spectrum of the cell-wall components that are normally too mobile to be visible. With these techniques we were able to determine the mobility of pectins and their approximate spatial location in comparison to cellulose. 

By measuring the proton relaxation times, and T,p, it is possible to estimate the mobility of polymer chains within the cell wall (11). Proton spin relaxation editing (PSRE) is a method of expressing these results. It separates the components seen in a conventional CP-MAS C spectra into low-mobility and intermediate-mobility components. If PSRE is applied to a experiment (12) the mobility of the... 

The observed proton relaxation rate, l/rlobs, is the sum of a diamagnetic contribution, 1/Tld, and the paramagnetic relaxation rate enhancement, 1/Tlp, this latter being linearly proportional to the concentration of the paramagnetic species, [Gd], In Equation (1), the concentration is usually given in mmol L 1, thus the unity of proton relaxivity, rh is mM 1 s 1. 

It is clear from the above equations that numerous parameters (proton exchange rate, kcx = l/rm rotational correlation time, tr electronic relaxation times, 1 /rlj2e Gd proton distance, rGdH hydration number, q) all influence the inner-sphere proton relaxivity. Simulated proton relaxivity curves, like that in Figure 3, are often used to visualize better the effect of the... 

Figure 3 Effect of the water exchange rate, kex, and the rotational correlation time, rR, on inner-sphere proton relaxivity. The plot was simulated for a particular value of the longitudinal electron spin relaxation rate, 1/Tie — 5.28xlOss 1. The marketed contrast agents all have relaxivities around 4—5mM 1s 1 in contrast to the theoretically attainable values over lOOrnM-1 s 1, and this is mainly due to their fast rotation...

For low molecular weight Gd111 chelates, it is mainly fast rotation that limits proton relaxivity (Figure 3). In order to circumvent this problem, Gd111 poly(aminocarboxylates) have been linked via either covalent or noncovalent interactions to different macromolecules. 

Electronic relaxation is a crucial and difficult issue in the analysis of proton relaxivity data. The difficulty resides, on the one hand, in the lack of a theory valid in all real conditions, and on the other hand in the technical problems of independent and direct determination of electronic relaxation parameters. Proton relaxivity is essentially influenced by the longitudinal electron spin relaxation time, Tle, of Gd111. This decay is too fast to be assessed by commonly available techniques, though very recently Tlc values have been directly measured.74 Nevertheless,... 

Table 3 Comparison of rotational correlation times and proton relaxivities for low molecular weight and...

Figure 6 Effect of the increased rotational correlation time on the proton relaxivity of MP2269, a Gd111 chelate capable of noncovalent protein binding (Scheme 2). The lower NMRD curve was measured in water, whereas the upper curve was obtained in a 10%w/v bovine serum albumin solution in which the chelate is completely bound to the protein. The rotational correlation times calculated are rR=105ps in the nonbound state, and rR= 1,000 ps in the protein-bound state (t=35°C). For this chelate, the water exchange...

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