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(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.

It is shown how the equilibrium pair correlation function between spin-bearing molecules in liquids may be incorporated as an effective force in the relative diffusion expressions, and how one may solve for the resulting time correlation functions and spectral densities needed for studies of spin relaxation by translational diffusion. The use of finite difference methods permits the solution no matter how complex the form of the pair correlation function (pcf) utilized. In particular, a Percus–Yevick pcf as well as one corrected from computer dynamics, both for hard spheres, are utilized. Good agreement with the experiments of Harmon and Muller on dipolar relaxation in liquid ethane is obtained from this analysis. Effects of ionic interactions in electrolyte solutions upon dipolar relaxation are also obtained in terms of Debye–Hückel theory for the pcf. Analytic solutions are given which are appropriate for the proper boundary-value problem for the relative diffusion of molecules (i.e., a distance of minimum approach) that has usually been neglected in the spin relaxation theories. Other molecular dynamics aspects of spin relaxation by translational diffusion in liquids are briefly discussed.

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.

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Publication costs assisted by the Petroleum Research Fund A detailed study of anisotropic ordering, line shapes, and relaxation is reported for the perdeuterated 2,2,6,6-tetramethyl-4-piperidone N-oxide (PD-Tempone) nitroxide radical in several liquid crystal solvents. The line width results are analyzed in terms of the Polnaszek, Bruno, and Freed (PBF) theory appropriately modified for anisotropic ordering both in the motional narrowing and slow tumbling region. The motional narrowing results are usually consistent with isotropic rotational diffusion, but under a weak (asymmetric) ordering potential, (Doo) 88 -0.1, and activation energies characteristic of the twist viscous properties of the liquid crystal. Anomalous line shape behavior in the incipient slow tumbling region is observed, which is not explained by the extrapolation of the appropriate parameters from the motional narrowing region. This anomaly is discussed in terms of anisotropic viscosity and director fluctuations. The latter is predicted to be of negligible importance for the weakly ordered spin probe, as well as qualitatively of the wrong behavior. Anisotropic viscosity, while apparently able to "explain" the anomaly, leads to physically untenable conclusions. The anomaly is then discussed in terms of slowly fluctuating intermolecular torques, leading to a frequency-dependent diffusion coefficient. While this latter may in part offer an explanation (when one distinguishes between torque components parallel and perpendicular to the director), the implied slowness of the fluctuating torques suggests, from general theory, a new model based upon a local solvent structure around the spin probe which may persist over longer periods than the reorientation time of the spin probe. A simple model calculation of the effects on the ESR relaxation is given. This limiting model is also appropriate for highly structured isotropic liquids. It is shown that such a model could have the same formal spectral effects as anisotropic rotational diffusion, and it would yield non-Debye-like spectral densities of the type that could potentially "explain" the observed incipient slow tumbling anomaly. More general theoretical approaches for the analysis of these effects are briefly discussed.