Motional anisotropy

Small molecules in low viscosity solutions have, typically, rotational correlation times of a few tens of picoseconds, which means that the extreme narrowing conditions usually prevail. As a consequence, the interpretation of certain relaxation parameters, such as carbon-13 and NOE for proton-bearing carbons, is very simple. Basically, tlie DCC for a directly bonded CH pair can be assumed to be known and the experiments yield a value of the correlation time, t. One interesting application of the measurement of is to follow its variation with the site in the molecule (motional anisotropy), with temperature (the correlation... 

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. 

The excellent resolution of the 0-tensor components at W band has been used to measure the relaxation properties of QA in the Zn-substituted bRC of R. sphaeroides.m The experiment showed, in contrast to the respective ubiquinone radical in organic solution, an anisotropic relaxation behavior in the pulse high field ESE experiments. From the analysis of the T2 experiments a motional anisotropy of Q% in the protein pocket was deduced with a preferred libration about the C-O symmetry axis. Recently, similar experiments were also performed on Qb- in ZnbRCs. Compared to QA different echo decay time constants were found. A model was proposed in which the relaxation is related to reorientational fluctuations around the quinones specific H-bonds to the protein.142... 

A more quantitative interpretation of methyl relaxation requires a knowledge of the motional anisotropy of the entire molecule. Thus the activation energy of methyl rotation can be estimated from 7] data if the rotational diffusion tensor of the molecule, mentioned in Section 3.3.3.3, is known [164]. 

Vasudev, R., Zare, R.N., and Dixon, R.N. (1983). Dynamics of photodissociation of HONO at 369 nm Motional anisotropy and internal state distribution of the OH fragment, Chem. Phys. Lett. 96, 399-402. 

VqS is the magnitude of the residual tensor. The averaging factor S is the orientational order parameter, i.e., the degree of motional anisotropy, of a given C-2H bond (with respect to its average direction of orientation) ... 

Recent improvements in the details of the CLP crystallization procedure and crystal treatment have led to even better diffracting crystals. At 1.4 A resolution, refinement, including anisotropic B factors, illustrates, the thermal motion anisotropy of the retinal and key neighbors (Fig. 4, see color insert manuscript in preparation). 

In membranes, the motional anisotropies in the lateral plane of the membrane are sufficiently different from diffusion in the transverse plane that the two are separately measured and reported [4b, 20d,e]. Membrane ffip-ffop and transmembrane diffusion of molecules and ions across the bilayer were considered in a previous section. The lateral motion of surfactants and additives inserted into the lipid bilayer can be characterized by the two-dimensional diffusion coefficient (/)/). Lateral diffusion of molecules in the bilayer membrane is often an obligatory step in membrane electron-transfer reactions, e.g., when both reactants are adsorbed at the interface, that can be rate-limiting [41]. Values of D/ have been determined for surfactant monomers and probe molecules dissolved in the membrane bilayer typical values are given in Table 2. In general, lateral diffusion coefficients of molecules in vesicle... 

Recent C T, measurements performed on various bulk polymers with low Tg, such as polyisoprene, polyisobutylene, polyvinylmethylether and polypropyleneoxide, have shown that the experimental value of T at the minimum is always much higher than the prediction from Hall-Helfand expression. Thus, this discrepancy cannot be assigned to a specific motional anisotropy of the cis 1,4 sequences of the polybutadiene chain. It seems more likely to assign it to a fast anisotropic motion of the CH bonds inside a cone. In the case of polybutadiene, the corresponding half angle of the cones should be 26° and 36° for CH and CH2... 

Precision measurements of the temperature dependence of QS are not common in tin Mdssbauer spectroscopy, primarily because the splittings vary little with temperature, and most chemical structural interpretations can be based on the QS value at a single temperature, typically 77 K. The theory needed for the interpretation of the QS parameter in tin compounds has not been developed to such a point as to make precision measurements worthwhile.21-23 However, the thermal variation of the QS is commonly studied for two main reasons for monitoring structural phase transitions and for the study of the motional anisotropy... 

Equation 3 neglects effects of anisotropic motion on both longitudinal and transverse relaxation rates 2). Recent experiments using deuterium NMR on samples similar to those studied here show significant nuclear electric quadrupole splittings that imply an anisotropic component in the water molecule motion ( ). Such motional anisotropy will depress and elevate T]. 

J. P. Cohen-Addad and R. Vogin, "Molecular motion anisotropy as reflected by a pseudo solid nuclear spin echo Observation of chain constraints in molten cis-1,4-polybutadiene," Phys. Rev. Letters 33, 940-943 (1974). 

Steady-state fluorescence anisotropy of 8.5 pM of calcofluor in the presence of 5.5 pM tti -acid glycoprotein 445 nm and 300 nm) was performed at different temperatures. The Perrin plot representation (Fig. 8.21b) yields a rotational con-elation time equal to 19 ns at 20 °C, revealing the absence of a segmental motion. Anisotropy results are in good agreement with those obtained by red-edge excitation spectra experiments, i.e., Calcofluor is boimd tightly to the carbohydrate residues of the protein. 

The sensitivity of typical NMR experiments to the type and time scale of various motions is illustrated in Fig. 7. For simplicity, we have chosen equal correlation times for all motions, namely = 1 x 10 s, = 1 x 10 s and Xg = 5 x 10 s. The powder spectra refer to quadrupole echo sequences [57], and characterize two-site jumps (a, b), three-site jumps (c), planar rotational diffusion (d), tetrahedral jumps (e) and isotropic spherical diffusion (f), respectively. The significant differences of the lineshapes arise from the different motional anisotropies. Evidently, quadrupole echo spectra [57] contain valuable information on the type of motion [10,48,49, 58]. 

Carbon relaxation with proton spin-spin coupling was investigated for several n-alkanes, e.g. in selectively deuteriated nonane C4D9CH2C4D9 with one isolated CH2 group. For this isolated AX2 spin system, dipolar relaxation was analysed in terms of spectral densities Jch hch> chh hh- The results indicate that motion at each segment of the chain has local prolate symmetric-top character, and correlation times point to greater motional anisotropy at the middle of the chain rather than at the ends. ... 

Investigation of nitrogen relaxation may also be of interest, in deriving information about anisotropic molecular motion. In fact the determination of a single value cannot be considered as a proof of isotropic motion, if independent internuclear vectors have not been examined. In this respect, results derived from N H dipolar interactions may provide determining complementary information about eventual motional anisotropy. 

Order parameter (Scd) The deuterium order parameter is a measure of the motional anisotropy of the particular C—D bond investigated and yields its time-averaged orientation. If denotes the instantaneous angle between the C—D bond and the direction of the bilayer normal then Scd is defined as... 

Magnetic resonance techniques, in particular phosphorus ( P) and deuterium ( H) magnetic resonance, in combination with selectively deuterated lipids, have yielded quantitative information on the ordering, motional anisotropy, and dynamics of membrane components. This information is essential for understanding the function of biological membranes. 

Cross-polarization is more effective for rigid systems than for mobile structures. When extensive motion occurs, the C-H dipolar interactions are reduced, and this reduction causes a lower cross-polarization rate. In some systems, mobile components can exhibit sufficient motional anisotropy to permit cross-polarization because the anisotropy can impart a residual static component to the overall motion [69]. This appears to be the case for elastomeric systems. 

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