Relaxation residual dipolar coupling

Molecular modeling is an indispensable tool in the determination of macromolecular structures from NMR data and in the interpretation of the data. Thus, state-of-the-art molecular dynamics simulations can reproduce relaxation data well [9,96] and supply a model of the motion in atomic detail. Qualitative aspects of correlated backbone motions can be understood from NMR structure ensembles [63]. Additional data, in particular residual dipolar couplings, improve the precision and accuracy of NMR structures qualitatively [12]. 

Since the discovery of the nuclear Overhauser effect (NOE, see previous section) [4, 5] and scalar coupling constants [36, 37] decades ago, NMR-derived structure calculations of biomolecules largely depended on the measurement of these two parameters [38]. Recently it became possible to use cross-correlated relaxation (CCR) to directly measure angles between bond vectors [39] (see also Chapt 7). In addition, residual dipolar couplings of weakly aligned molecules were discovered to measure the orientation of bond vectors relative to the alignment tensor (see Sect 16.5). Measurement of cross-correlated relaxation was described experimentally earlier for homonuclear cases [40, 41] and is widely used in solid-state NMR [42 14]. 

Sample deformations modify the number of accessible conformations of intercross-link chains (cf. Figure 7.7), so that they can be detected by analysis of relaxation and residual dipolar couplings. This is illustrated for strained rubber bands with a cut in Figures 7.6 and 7.11. 

In elastomer samples with macroscopic segmental orientation, the residual dipolar couplings are oriented as well, so that also the transverse relaxation decay depends on orientation. Therefore, the relaxation rate 1/T2 of a strained rubber band exhibits an orientation dependence, which is characteristic of the orientational distribution function of the residual dipolar interactions in the network. For perfect order the orientation dependence is determined by the square of the second Legendre polynomial [14]. Nearly perfect molecular order has been observed in porcine tendon by the orientation dependence of 1/T2 [77]. It can be concluded, that the NMR-MOUSE appears suitable to discriminate effects of macroscopic molecular order from effects of temperature and cross-link density by the orientation dependence of T2. 

Since its first description in 1971 [35], gel-phase NMR was applied to peptide chemistry by Manatt and coworkers [36, 37], These authors used 13C NMR to determine the extent of chloromethylation of crosslinked polymers and 19F NMR to monitor protection-deprotection reactions. These two nuclei are the most commonly used in these types of studies, mainly because of their significant chemical shift dispersion, which can alleviate in part the resolution loss due to the non ideal linewidth obtained in the gel state. Apart from restricted molecular motion, that shortens T2 because of an efficient transverse relaxation, other sources of line-broadening derive from magnetic susceptibility variations within the sample (due to the physical heterogeneity of the system) and residual dipolar couplings. 

NEW TECHNIQUES FOR PROTEIN NMR RESIDUAL DIPOLAR COUPLINGS AND TRANSVERSE RELAXATION OPTIMIZED SPECTROSCOPY (TROSY)... 

A number of recently developed methods offer the potential for improving the quality of NMR structures and for increasing the size of proteins that will be examined. In particular, the use of residual dipolar couplings and of anisotropic contributions to relaxation provide new kinds of restraints that promise to lead to more accurate NMR structures.78 80 The recently developed TROSY (transverse relaxation optimized spectroscopy) method81 exploits relaxation phenomena to produce spectra with narrow lines, and promises to significantly expand the size of protein targets that can be examined by NMR from the current limit of 35 kDa to perhaps 150 kDa. 

Static H Multiple Quantum (MQ) NMR spectroscopy, on the other hand, has shown the ability to more reliably quantitatively characterize elastomer network structure and heterogeneities (14-19). H MQ NMR methods allow for the measurement of absolute residual dipolar couplings (cooperative dynamics without interference from magnetic susceptibility and field gradients which complicate relaxation measurements (13, 14, 20,21). It has previously been shown that the residual dipolar couplings are directly related to the dynamic order parameter, Sb, and the crosslink density (1/N)(P) ... 

Almond et investigated how aqueous dynamical simulations of flexible molecules can be compared against NMR data. The methodology compares state-of-the-art NMR residual dipolar coupling, NOESY and relaxation, to molecular dynamics simulations in water over several nanoseconds. In contrast to many previous applications of residual dipolar couplings in structure investigation of biomolecules, the approach described here uses MD simulations to provide a dynamic representation of the molecules. 

Meiler et al applied the model-free approach to the dynamic interpretation of residual dipolar couplings in globular proteins. Ishima et aO compared the methyl rotation axis order parameters derived from the model-free analyses of the and longitudinal and transverse relaxation rates measured in the same protein sample. Best et al reported the results of molecular dynamics simulations compared with NMR relaxation experiments for maltose and isomaltose. Using the model-free formalism they could estimate reliable order parameters. Baber et used an extended model-... 

Fio. 9.3.4 Excitation with a surface coil of 9 mm diameter in a Bo gradient of the order of lOT/m by the NMR-MOUSE (a) Series train of CPMG echoes from a carbon-black filled SBR section of an intact car tyre with a steel belt. A fit of the echo envelope with an exponential decay function yields a transverse relaxation time Ti [Eidl]. (b) Variation of the pulse duration in an a — te/l — Ta — ts/ i- pulse sequence for different rf frequencies. For each frequency maxima and minima are observed which define the nominal 90° and 180° pulse widths. With decreasing rf frequency the distance of the sensitive volume from the rf coil increases. A frequency of 17.5 MHz correspond to depths of 0-0.5 mm, 16MHz to 0.5-1.0mm, and 16.5 MHz to 1.0-1.5 mm into the sample [Gut3], (c) Hahn- and solid-echo envelopes for a sample of carbon-black filled cross-linked SBR. The Hahn-echo decay is faster because of residual dipolar couplings which are partially refocused by the solid-echo [Gut3]. (d) Multi-echo excitation. 

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