The two-body Slowly Relaxing Local Structure (SRLS) model was applied to (15)N NMR spin relaxation in proteins and compared with the commonly used original and extended model-free (MF) approaches. In MF, the dynamic modes are assumed to be decoupled, local ordering at the N-H sites is represented by generalized order parameters, and internal motions are described by effective correlation times. SRLS accounts for dynamical coupling between the global diffusion of the protein and the internal motion of the N-H bond vector. The local ordering associated with the coupling potential and the internal N-H diffusion are tensors with orientations that may be tilted relative to the global diffusion and magnetic frames. SRLS generates spectral density functions that differ from the MF formulas. The MF spectral densities can be regarded as limiting cases of the SRLS spectral density. SRLS-based model-fitting and model-selection schemes similar to the currently used MF-based ones were devised, and a correspondence between analogous SRLS and model-free parameters was established. It was found that experimental NMR data are sensitive to the presence of mixed modes. Our results showed that MF can significantly overestimate order parameters and underestimate local motion correlation times in proteins. The extent of these digressions in the derived microdynamic parameters is estimated in the various parameter ranges, and correlated with the time scale separation between local and global motions. The SRLS-based analysis was tested extensively on (15)N relaxation data from several isotropically tumbling proteins. The results of SRLS-based fitting are illustrated with RNase H from E. coli, a protein extensively studied previously with MF.

It is shown that the commonly used models for analyzing ESR spectra from nitroxide spin-labeled proteins or DNA systems are special cases of the more general slowly relaxing local structure (SRLS) model, wherein the nitroxide spin probe is taken as reorienting in a restricted local environment, which itself is relaxing on a longer time scale. This faster motion describes the internal dynamics, while the slower motion describes the global tumbling of the macromolecule. By using the SRLS model as the reference, it is shown (1) under what conditions the microscopic-order macroscopic-disorder (MOMD) model, wherein the global tumbling of the macromolecule is in the rigid limit, is valid, and (2) when the fast internal motion (FIM) model, wherein the internal motion is so rapid as to lead to partial averaging of the magnetic tensors, is valid. The frequency dependence of these models is studied. A key general property of high frequency ESR that emerges is that it reports on a faster motional time scale, whereas low frequency ESR reports on a slower motional time scale. It is shown that, in general, the MOMD model is a better approximation for ESR spectra obtained at high frequency (250 GHz), whereas, in general, the FIM model is a better approximation for low frequency (9 GHz) ESR spectra. However, in general, one does not find that the simpler model fits, at a single ESR frequency, to the more complete SRLS model, return correct motional and ordering parameters. The simultaneous fitting of both low and high frequency ESR spectra is thus required to remove such ambiguities and to return all the various dynamic, ordering, and geometric factors that characterize the complex dynamics. This approach is briefly related to recent ESR spectra from the spin-labeled protein, T4 lysozyme, and from spin-labeled DNA nucleosides. In order to better apply the slow-motional SRLS model to macromolecular dynamics, the Polimeno-Freed theory has been extended to the case where the global tumbling is anisotropic and where the angle between the principal axis of the global motion and the preferred orientation of the internal modes of motion is arbitrary.

Adenylate kinase from Escherichia coli (AKeco), consisting of a 23.6-kDa polypeptide chain folded into domains CORE, AMPbd, and LID catalyzes the reaction AMP + ATP T 2ADP. The domains AMPbd and LID execute large-amplitude movements during catalysis. Backbone dynamics of ligandfree and AP 5 A-inhibitor-bound AKeco is studied with slowly relaxing local structure (SRLS) 15 N relaxation, an approach particularly suited when the global (τ m ) and the local (τ) motions are likely to be coupled. For AKeco τ m ) 15.1 ns, whereas for AKeco*AP 5 A τ m ) 11.6 ns. The CORE domain of AKeco features an average squared order parameter, , of 0.84 and correlation times τ f ) 5-130 ps. Most of the AKeco*AP 5 A backbone features ) 0.90 and τ f ) 33-193 ps. These data are indicative of relative rigidity. Domains AMPbd and LID of AKeco, and loops 1 /R 1 , R 2 /R 3 , R 4 / 3 , R 5 / 4 , and 8 /R 7 of AKeco*AP 5 A, feature a novel type of protein flexibility consisting of nanosecond peptide plane reorientation about the C i-1 R -C i R axis, with correlation time τ ⊥ ) 5.6-11.3 ns. The other microdynamic parameters underlying this dynamic model include S 2 ) 0.13-0.5, τ || on the ps time scale, and a diffusion tilt MD ranging from 12 to 21°. For the ligand-free enzyme the τ ⊥ mode was shown to represent segmental domain motion, accompanied by conformational exchange contributions R ex e 4.4 s -1 . Loop R 4 / 3 and R 5 / 4 dynamics in AKeco*AP 5 A is related to the "energetic counter-balancing of substrate binding" effect apparently driving kinase catalysis. The other flexible AKeco*AP 5 A loops may relate to domain motion toward product release.The ability to interpret nuclear spin relaxation properties in terms of microdynamic parameters turned NMR into a powerful method for elucidating protein dynamics (1, 2). The amide 15 N spin in proteins is a particularly useful probe, relaxed predominantly by dipolar coupling to the amide proton and 15 N chemical shift anisotropy (CSA) 1 (3). The experimental NMR observables are controlled by the global and local dynamic processes experienced by protein N-H bond vectors, which determine the spectral density function, J(ω). 15 N relaxation data in proteins are commonly analyzed with the model-free (MF) approach, where the global and local motions are assumed to be decoupled (4-6). In a recent study (7), we applied the two-body slowly relaxing local structure (SRLS) approach developed by Freed and coworkers (8, 9) to 15 N relaxation in proteins. SRLS accounts rigorously for dynamical coupling between the local and global motions, and treats the global diffusion, the local diffusion, the local ordering, and the magnetic interactions as tensors that may be tilted relative to one another, providing thereby important information related to protein structure (10-12). The MF spectral density functions constitute asymptotic solutions of the SRLS spectral densities (7,8,13). It was found that currently available experimental 15 N relaxation data are sensitive to the coupling-induce...