(15)N-(1)H spin relaxation is a powerful method for deriving information on protein dynamics. The traditional method of data analysis is model-free (MF), where the global and local N-H motions are independent and the local geometry is simplified. The common MF analysis consists of fitting single-field data. The results are typically field-dependent, and multifield data cannot be fit with standard fitting schemes. Cases where known functional dynamics has not been detected by MF were identified by us and others. Recently we applied to spin relaxation in proteins the slowly relaxing local structure (SRLS) approach, which accounts rigorously for mode mixing and general features of local geometry. SRLS was shown to yield MF in appropriate asymptotic limits. We found that the experimental spectral density corresponds quite well to the SRLS spectral density. The MF formulas are often used outside of their validity ranges, allowing small data sets to be force-fitted with good statistics but inaccurate best-fit parameters. This paper focuses on the mechanism of force-fitting and its implications. It is shown that MF analysis force-fits the experimental data because mode mixing, the rhombic symmetry of the local ordering and general features of local geometry are not accounted for. Combined multifield multitemperature data analyzed with the MF approach may lead to the detection of incorrect phenomena, and conformational entropy derived from MF order parameters may be highly inaccurate. On the other hand, fitting to more appropriate models can yield consistent physically insightful information. This requires that the complexity of the theoretical spectral densities matches the integrity of the experimental data. As shown herein, the SRLS spectral densities comply with this requirement.

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.

Protein dynamics by NMR has been reviewed extensively in recent years. These surveys show decisively that information on structure should be complemented by information on motion both to properly characterize the protein, and to understand its function. The time scale accessible by NMR extends from picoseconds to days, with different methods accessing different parts of this time axis. Here we focus on heteronuclear NMR spin relaxation used to study ps to ns protein dynamics. The slow limit of this time regime is determined by the global tumbling of the protein, with the rates for internal motion of the probe being typically faster. Based on experience gained over nearly a decade we came to the conclusion that the traditional method of NMR spin relaxation analysis in proteins and nucleic acids, called “model-free” (MF), does not extract adequately and fully the information inherent in the experimental data largely because it is oversimplified. We have developed an approach that overcomes many of the MF deficiencies. This method, called the slowly relaxing local structure (SRLS) may be regarded as a generalization of MF. SRLS predates the MF approach, and even provided derivations of the exact equivalents of the MF equations . The issues brought up above will be addressed in detail in this review. It will be shown that analogous, but physically distinct, SRLS and MF analyses often yield substantially different results, indicating that the oversimplifications inherent in MF have unfavorable practical implications. Within a broader perspective, we illustrate the disadvantages of applying parameterization instead of setting forth models, using mathematical instead of physical parameter definitions, and not abiding by the assumptions underlying the various equations used. We offer the concepts that underlie SRLS as an alternative to the model-free point-of-view, and we describe and illustrate how SRLS can be implemented in a practical fashion. We also indicate how improvements to the current SRLS approach can be introduced

We developed in recent years the slowly relaxing local structure (SRLS) approach for analyzing NMR spin relaxation in proteins. SRLS is a two-body coupled rotator model which accounts rigorously for mode-coupling between the global motion of the protein and the local motion of the spin-bearing probe and allows for general properties of the second rank tensors involved. We showed that a general tool of data analysis requires both capabilities. Several important functionalities were missing in our previous implementations of SRLS in data fitting schemes, and in some important cases, the calculations were tedious. Here we present a general implementation which allows for asymmetric local and global diffusion tensors, distinct local ordering and local diffusion frames, and features a rhombic local potential which includes Wigner matrix element terms of ranks 2 and 4. A recently developed hydrodynamics-based approach for calculating global diffusion tensors has been incorporated into the data-fitting scheme. The computational efficiency of the latter has been increased significantly through object-oriented programming within the scope of the C++ programming language, and code parallelization. A convenient graphical user interface is provided. Currently autocorrelated (15)N spin relaxation data can be analyzed effectively. Adaptation to any autocorrelated and cross-correlated relaxation analysis is straightforward. New physical insight is gleaned on largely preserved local structure in solution, even in chain segments which experience slow local motion. Prospects associated with improved dynamic models, and new applications made possible by the current implementation of SRLS, are delineated.

The focus of structural biology is on studies of the highly populated, ground states of biological molecules; states that are only sparsely and transiently populated are more difficult to probe because they are invisible to most structural methods. Yet, such states can play critical roles in biochemical processes such as ligand binding, enzyme catalysis, and protein folding. A description of these states in terms of structure and dynamics is, therefore, of great importance. Here, we present a method, based on relaxation dispersion NMR spectroscopy of weakly aligned molecules in a magnetic field, that can provide such a description by direct measurement of backbone amide bond vector orientations in transient, low populated states that are not observable directly. Such information, obtained through the measurement of residual dipolar couplings, has until now been restricted to proteins that produce observable spectra. The methodology is applied and validated in a study of the binding of a target peptide to an SH3 domain from the yeast protein Abp1p and subsequently used in an application to protein folding of a mutational variant of the Fyn SH3 domain where 1 H-15 N dipolar couplings of the invisible unfolded state of the domain are obtained. The approach, which can be used to obtain orientational restraints at other sites in proteins as well, promises to significantly extend the available information necessary for providing a site-specific characterization of structural properties of transient, low populated states that have to this point remained recalcitrant to detailed analysis.olution NMR spectroscopy is a powerful technique for the study of biomolecular dynamics spanning a range of time scales from picoseconds for bond vector librations to many hours for hydrogen exchange in the buried interiors of proteins (1, 2). One very important approach, based on the concept of a ''spin-echo'' that was first described by Hahn in 1950 (3), is called the Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion method (4, 5). This class of experiment provides a window into processes with conformational exchange on the millisecond time scale (6), a time regime that is often the relevant one for the lifetimes of bound ligands (7,8), protein folding events (9), or molecular rearrangements that are important for the control of enzyme function (10-13). For systems in which the ground state exchanges with a minor conformer populated at 0.5% or higher and with exchange rates on the order of a hundred to a few thousand per second, the CPMG dispersion experiment provides a sensitive measure of the exchange dynamics (6). Rates of exchange, populations of exchanging states, and chemical shifts of nuclear spins in minor states can be obtained from fits of dispersion profiles to the appropriate model of exchange. Most importantly, information from potentially every residue is obtained in states that are often invisible in even the most sensitive of NMR spectra. Fig. 1a illustrates a simple case in which a loop of a protein, highlighted ...

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...

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