15N relaxation

For folded proteins, relaxation data are commonly interpreted within the framework of the model-free formalism, in which the dynamics are described by an overall rotational correlation time rm, an internal correlation time xe, and an order parameter. S 2 describing the amplitude of the internal motions (Lipari and Szabo, 1982a,b). Model-free analysis is popular because it describes molecular motions in terms of a set of intuitive physical parameters. However, the underlying assumptions of model-free analysis—that the molecule tumbles with a single isotropic correlation time and that internal motions are very much faster than overall tumbling—are of questionable validity for unfolded or partly folded proteins. Nevertheless, qualitative insights into the dynamics of unfolded states can be obtained by model-free analysis (Alexandrescu and Shortle, 1994 Buck etal., 1996 Farrow etal., 1995a). An extension of the model-free analysis to incorporate a spectral density function that assumes a distribution of correlation times on the nanosecond time scale has recently been reported (Buevich et al., 2001 Buevich and Baum, 1999) and better fits the experimental 15N relaxation data for an unfolded protein than does the conventional model-free approach. 

Determination of Protein Dynamics Using 15N Relaxation Measurements David Fushman 283... 

Strategies for the Analysis of Protein Dynamics from 15N Relaxation Data 291 ... 

Solid-phase peptide synthesis offers a fast and convenient route for many peptides when isotope-enriched compounds are not required. Classical synthesis additionally permits the use of non-natural amino acids and allows site-specific isotope labeling. Although Fmoc protected 15N-labeled amino adds are commercially available, the cost of such synthesis is usually prohibitive, and the peptides from chemical synthesis require perdeuterated detergents and unfortunately exclude investigation of internal dynamics through measurement of 15N relaxation. 

As another example, the three-dimensional structure of Cytochrome c has been determined on the basis of structural information from pseudocontact paramagnetic chemical shifts, Curie-Dipolar cross-correlation, secondary structure constraints, dipolar couplings and 15N relaxation data [103]. This protein has a paramagnetic center, and therefore the above-mentioned conformational restraints can be derived from this feature. Dipolar couplings do not average to zero because of the susceptibility tensor anisotropy of the protein. The structure determination of this protein without NOE data gives an RMSD (root... 

Cross-correlation effects between 15N CSA and 1H-15N dipolar interactions [10] will result in different relaxation rates for the two components of the 15N spin doublet, which could significantly complicate the analysis of the resulting bi-exponential decay of the decoupled signal in T, or T2 experiments. To avoid this problem, 180° 1H pulses are applied during the 15N relaxation period [3, 4], which effectively averages the relaxation rates for the two components of the 15N spin doublet... 

Fig. 12.1 Illustration of the temperature sensitivity of 15N relaxation parameters, Rlf R2t and NOE, as indicated. Shown are the relative deviations in these relaxation parameters from their values at 25 °C as a function of temperature in the range of + 3 °C. The expected variations in / ] and R2 due to temperature deviations of as little as +1 °C are already greater than the typical level of experimental precision ( % ) of these measurements (indicated by the dashed horizontal lines). For simplicity, only temperature variation of the overall tumbling time of the molecule (due to temperature dependence of the viscosity of water) is taken into account the effect of temperature variations on local dynamics is not considered here.

The overall tumbling of a protein molecule in solution is the dominant source of NH-bond reorientations with respect to the laboratory frame, and hence is the major contribution to 15N relaxation. Adequate treatment of this motion and its separation from the local motion is therefore critical for accurate analysis of protein dynamics in solution [46]. This task is not trivial because (i) the overall and internal dynamics could be coupled (e. g. in the presence of significant segmental motion), and (ii) the anisotropy of the overall rotational diffusion, reflecting the shape of the molecule, which in general case deviates from a perfect sphere, significantly complicates the analysis. Here we assume that the overall and local motions are independent of each other, and thus we will focus on the effect of the rotational overall anisotropy. 

Several approaches to determination of the overall rotational diffusion tensor from 15N relaxation data were suggested in the literature [15, 47, 49, 51-53]. The approach described here uses the orientational dependence of the ratio of spin-relaxation rates [49]... 

The isotropic model is justified when the estimated degree of the overall rotational anisotropy is small. A D /D l ratio of less than 1.1-1.2 could probably be considered as a reasonable value for the isotropic model, although an anisotropy as small as 1.17 can be reliably determined from 15N relaxation measurements, as demonstrated in Ref. [15]. 

Here we describe the model selection algorithm that is used to derive microdynamic (model-free) parameters for each NH group from 15N relaxation data. It is implemented in our program DYNAMICS [9]. Given the overall rotational diffusion tensor parameters (isotropic or anisotropic) derived as described above, this analysis is performed independently for each NH-group in order to characterize its local mobility. 

The summary of microdynamic parameters derived from 15N relaxation data for the / ARK PH domain is presented in Fig. 12.5. 

Fushman, D. (2003). Determination of protein dynamics using 15N relaxation measurements. Meth. Principles Med. Chem., 16,283-308. 

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