DOI: 10.1002/ijch.201300090 The Slowly Relaxing Local Structure Perspective of Protein Dynamics by NMR Relaxation Eva Meirovitch* [a] 1 Introduction There is ample evidence that information on structure has to be complemented by information on motion, both to properly characterize the protein and to understand its function. [1,2] Nuclear magnetic resonance (NMR) is a pow- erful method for studying protein dynamics. The time- scale accessible by NMR extends from picoseconds to days, with different experimental methods accessing dif- ferent parts of this time axis. [1,2] In this article, we focus on NMR relaxation from aqueous solutions of proteins; this method covers the picosecond to nanosecond time regime. The commonly used probes are the 15 N  1 H bond for studying backbone dynamics, and the 13 CDH 2 methyl group for studying side-chain dynamics. [1,2] The protein reorients in an unrestricted manner in iso- tropic solution. The probe reorients in a restricted manner, because the immediate protein surroundings exert anisotropic spatial restraints at the site of its motion. Restricted motions are usually associated with static directors (e.g., a rigid molecule reorienting in a nematic solvent is restricted by a liquid crystal director pointing along the space-fixed magnetic field). [3–8] Con- versely, the motion of the probe is restricted by a mobile local director – the equilibrium orientation of the probe, fixed in the protein, which tumbles in solution together with the protein. Therefore the rotational degrees of free- dom of the protein and the rotational degrees of freedom of the probe are in principle statistically dependent. This constitutes a two-body problem involving in the over- damped diffusion (Smoluchowski) limit diffusion and or- dering tensors . The challenge is to devise theoretical ap- proaches for treating this tensorial mode-coupling scenar- io that are realistic, general, computationally effective, and commensurate with the sensitivity of the experimen- tal data. Two conceptually different perspectives have been set forth: the standard perspective based on stochastic models [9–16] and the model-free viewpoint. [17–21] The objec- tive of this review is to clarify various matters associated with these diverging points of view, and provide compel- ling evidence in support of the standard established con- ceptualization. Abstract : NMR relaxation is a powerful method for elucidat- ing structural dynamics. Standard stochastic dynamic models generate time correlation functions (TCFs) that fea- ture physically well-defined parameters. We developed such a model, called the slowly relaxing local structure (SRLS) ap- proach, for proteins. SRLS is a two-body (protein and probe) coupled-rotator approach. Given that the protein (featuring diffusion tensor, D 1 ) restricts the probe (featuring diffusion tensor, D 2 ), the two “bodies” are inherently cou- pled dynamically. This is substantiated by a local potential, u, associated with a local ordering tensor, S. SRLS allows for general tensorial properties of D 1 , D 2 , S and the magnetic NMR tensors, and a general form of u. The TCFs are multi- exponential, in accordance with the degree of generality of the various tensors. The traditional model-free (MF) method is based on a different conceptualization. According to it a mode-decoupling bi-exponential (one term for each rota- tor) TCF captures adequately the detectable features of structural dynamics. Hence, stochastic approaches are un- necessary. Here, we show that this (amply proven) oversim- plification leads to physically vague constructs/composites as descriptors of structural dynamics. We illustrate mislead- ing results obtained with MF when mode coupling, or S tensor asymmetry, dominate the analysis. Finally, we delin- eate the substantial advantage in using SRLS TCF as quanti- ty to be compared with its atomistic molecular dynamics  based counterpart. Keywords: molecular dynamics · NMR relaxation · proteins · stochastic models · time correlation functions [a] E. Meirovitch The Mina and Everard Goodman Faculty of Life Sciences Bar-Ilan University Ramat-Gan 52900-02 (Israel) e-mail: eva.meirovitch@biu.ac.il Isr. J. Chem. 2014, 54, 47 – 59  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 47 Review