Protein Dynamics by NMR Spin Relaxation: The Slowly Relaxing Local Structure Perspective

The two-body (protein and probe) coupled rotator slowly relaxing local structure (SRLS) approach, implemented for NMR spin relaxation in proteins, is presented. SRLS is based on a Smoluchowki equation that includes the tensorial descriptions of the diffusing rotators and (via the local ordering) their dynamical coupling. This yields spectral densities that enter the expressions for the experimentally measured relaxation parameters. The constrained motion of the probe is treated by analogy with the standard treatments of restricted motions in liquids. Such restricted motions are largely recovered in the limit of large time scale separation between the rotators, i.e., when mode-coupling is not important. We found that the tensorial properties are not simple for proteins even in this limit. Their complexity has to be accounted for to obtain physically insightful pictures of protein dynamics. The traditional method for analyzing NMR spin relaxation in proteins is model-free (MF). This method treats only the simplest tensorial properties and implies large time-scale separation. Only when these conditions are fulfilled the analytical MF spectral densities, which are limiting cases of SRLS, may be used. Since they are not fulfilled in most actual cases, the MF-based pictures of protein dynamics are unreliable.