Relaxation Rate Measurements

2 Relaxation Rate Measurements. - Measurement and analysis of traditional laboratory frame heteronuclear relaxation parameters R, R2 and NOE were summarised by Palmer in a review. The publication concentrates on the dynamic processes on ps-ns time scale in proteins. The theoretical part has a general character, while the experimental section and examples deal mainly with N relaxation. A source of systematic error in the commonly used T2 CPMG measurements was highlighted by Korzhnev et al The authors observed offset-dependent difference between T2 and Tip values. This difference was attributed to the off-resonance effects of N 180° pulses. When uncorrected, the error can be misinterpreted as a contribution from a slow conformational exchange. The authors suggested a numerical correction procedure. 

The interpretation of relaxation data is most often performed either with reduced spectral density or the Lipari-Szabo approach. The first is easy to implement as the values of spectral density at discrete frequencies are derived from a linear combinations of relaxation rates, but it does not provide any insight into a physical model of the motion. The second approach provides parameters that are related to the model of the internal motion, but the data analysis requires non-linear optimisation and a selection of a suitable model. A graphical way to relate the two approaches is described by Andrec et al Comparison of calculated parametric curves correlating 7h and Jn values for different Lipari-Szabo models of the internal motion with the experimental values provides a range of parameter values compatible with the data and allows to select a suitable model. The method is particularly useful at the initial stage of the data analysis. 

A graphical approach was also used by Millet and Pons to analyse anisotropy of rotational diffusion in proteins. The values of Z)j and DJD compatible with R IRi ratios are presented as a contour plot. The intersection of the contour plots for different residues provides the values of anisotropy parameters compatible with experimental data. The obtained parameters can be used as starting values for further optimisation. The method is apphcable to axially symmetric rotation. A combination of approximate and exact methods was used by Ghose et al. to reduce the computational time of the determination of rotational diffusion tensor from NMR relaxation data. The initial values of the tensor components and its orientation are evaluated from the approximate solution, which substantially reduces the search space during the exact calculations. The method was applied for the estimation of relative domain orientation of a dual domain protein. 

Canet et al found that the standard Lipari-Szabo approach was inadequate for the analysis of multifield N relaxation parameters of a 86 residue protein even when the extended model or anisotropy of the overall motion were introduced. To remedy the situation they used the correlation function in 

Successful use of the ID super-WEFT method for the determination of paramagnetic broadening was reported by Ma et al The method allows selective observation of broad resonances in the spectra that can be subsequently curve fitted to deduce paramagnetic broadening. 

The longitudinal relaxation rates of both donor and acceptor N in Watson-Crick base pairs can be measured simultaneously in the experiment presented by Bytchenkoff and Bodenhausen. The proton magnetisation is initially converted into the antiphase coherence of the donor which then evolves with the J(N°,N ) coupling between the donor and acceptor nitrogens and refocused to generate longitudinal magnetisation on the acceptor At the same time the 

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In addition to the standard constraints introduced previously, structural constraints obtainable from the effects of the paramagnetic center(s) on the NMR properties of the nuclei of the protein can be used (24, 103). In iron-sulfur proteins, both nuclear relaxation rates and hyperfine shifts can be employed for this purpose. The paramagnetic enhancement of nuclear relaxation rates [Eqs. (1) and (2)] depends on the sixth power of the nucleus-metal distance (note that this is analogous to the case of NOEs, where there is a dependence on the sixth power of the nucleus-nucleus distance). It is thus possible to estimate such distances from nuclear relaxation rate measurements, which can be converted into upper (and lower) distance limits. When there is more than one metal ion, the individual contributions of all metal ions must be summed up (101, 104-108). If all the metal ions are equivalent (as in reduced HiPIPs), the global paramagnetic contribution to the 7th nuclear relaxation rate is given by... 

According to these equations, the effect of selectively perturbing the spin states of spins i and j is to isolate the cross-relaxation paths common to these two spins. Combining Eqs. 15 and 19, the individual cross-relaxation terms are readily determined from single-selective and double-selective relaxation-rate measurements, that is. 

The second separation method involves n.O.e. experiments in combination with non-selective relaxation-rate measurements. One example concerns the orientation of the anomeric hydroxyl group of molecule 2 in Me2SO solution. By measuring nonselective spin-lattice relaxation-rat s and n.0.e. values for OH-1, H-1, H-2, H-3, and H-4, and solving the system of Eq. 13, the various py values were calculated. Using these and the correlation time, t, obtained by C relaxation measurements, the various interproton distances were calculated. The distances between the ring protons of 2, as well as the computer-simulated values for the H-l,OH and H-2,OH distances was commensurate with a dihedral angle of 60 30° for the H-l-C-l-OH array, as had also been deduced by the deuterium-substitution method mentioned earlier. 

By now, water exchange has been studied on more than one hundred Gdm complexes with the help of 170 NMR, and the large body of data available has been reviewed recently (48). Variable temperature 170 transverse relaxation rate measurements provide the rate of the water exchange, whereas the mechanism can be assessed by determining the activation volume, AVt, from variable pressure 170 T2 measurements (49,50). The technique of 170 NMR has been described in detail (51). 

In general, an FFC relaxation rate measurement requires a series of elementary experiments in which the duration x of just one of the fixed-field intervals varies, while each of the switching intervals has always the same duration. Only in this way can one guarantee that the measured relaxation rate is correct and that it corresponds to the relaxation field present during the variable-duration interval (to be discussed later). 

A further application of relaxation rate measurements is that similar 1/71 ratios in a series of lanthanide complexes may be taken to indicate an isostructural series. However, this approach has the limitation that if only part of the complex is studied, perhaps an organic ligand, its 71 ratios would be independent of changes, for example changes in the extent of hydration in the remainder of the complex, provided that the conformation of the ligand relative to the lanthanide ion were preserved. An excellent example of the use of 71 data in a quite different way is its use to determine hydration numbers of lanthanide dipicolinate complexes.562... 

ESR spectra of type 2 Cu suggest the presence of three to four nitrogen ligands, while bound water has also been implicated by proton relaxation rate measurements. A number of anionic inhibitors bind to type 2 Cu. These results suggest that substrates may bind to the type 2 copper centres in oxidases. 

The ligation of Ln3+ by DTPA, DTPA-BPA, DTPA-BGLUCA, and DTPA-BEN-GALAA has been derived from Nd3+-C distances as evaluated from Nd3+-induced 13C relaxation rate enhancements [5-8]. The distances obtained are in agreement with those observed in crystal structures of this class of compounds. H NMR studies on various paramagnetic [Ln(DTPA)]2 complexes [9,10] and 13C relaxation rate measurements on the diamagnetic [La(DTPA)] 2 confirm this mode of coordination [11]. A detailed X-ray absorption spectroscopy study of [Gd(DTPA)2-] also showed that the local structure around the Gd3+ ion in aqueous solution is similar to that in crystals [12]. 

The water exchange rate on a Gd(III) complex can be directly determined by variable temperature transverse 170 relaxation rate measurements. The para-... 

Carbon-13 rotating-frame relaxation rate measurements are used to elucidate the mechanism of gas transport in glassy polymers. The nmr relaxation measurements show that antiplasticization-plasticization of a glassy polymer by a low molecular weight additive effects the cooperative main-chain motions of the polymer. The correlation of the diffusion coefficients of gases with the main-chain motions in the polymer-additive blends shows that the diffusion of gases in polymers is controlled by the cooperative motions, thus providing experimental verification of the molecular theory of diffusion. Carbon-13 nmr relaxation... 

Stuart et al. employed relaxation rate measurements of 15N in the backbone of a uniformly 15N-labeled peptide representing the N-terminal 49 residues of the Nun protein from lambdoid phage HK002 to determine the dynamics of the peptide when bound to a 17-residue RNA hairpin (BoxB17) (80). Nun... 

In order to characterize the active site structure of Ca ATPase from sarcoplasmic reticulum, we have employed Gd + as a paramagnetic probe of this system in a series of NMR and EPR investigations. Gadolinium and several other lanthanide ions have been used in recent years to characterize Ca + (and in some cases Mg2+) binding sites on proteins and enzymes using a variety of techniques, including water proton nuclear relaxation rate measurements (35,36,37), fluorescence (38) and electron spin resonance (39). In particular Dwek and Richards (35) as well as Cottam and his coworkers (36,37) have employed a series of nuclear relaxation measurements of both metal-bound water protons and substrate nuclei to characterize the interaction of Gd + with several enzyme systems. 

Aisen, P., A. Leibman, and H. A. Reich Studies on the Binding of Iron to Transferrin and Conalbumin. J. Biol. Chem. 241, 1666 (1966). They have found by electrophoretic studies that the stability constants of the two binding sites in ovotransferrin and human serum transferrin are equivalent. By proton magnetic relaxation rate measurements, they also found that the binding sites of ovotransferrin and human serum transferrin acted independently. 

While the different contributions to the shift may not always be easy to estimate, one expects the relaxation rate in any transition metal to be dominated by Dd- From relaxation-rate measurements across the spectrum, as, e.g., in Figure 11 for Pt in platinum/palladium alloys, we can immediately say that D is higher in... 

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