Structural Dynamics from NMR Relaxation by SRLS Analysis: Local Geometry, Potential Energy Landscapes, and Spectral...

We have developed the two-body coupled-rotator slowly relaxing local structure (SRLS) approach for elucidating protein dynamics by nuclear magnetic resonance (NMR) relaxation. The rotators are represented by diffusion tensors for overall protein tumbling and for locally ordered probe motion. and are coupled dynamically by a potential, u, typically given by linear combinations of the Wigner functions D₀₀² and (D₀₂² + D_0-2²). Until now, our SRLS analyses provided the tensors, and , the potential, u, and the geometric link between SRLS and NMR. Here we enhance this description by also examining the SRLS spectral densities obtained by solving the SRLS Smoluchowski equation. In addition, we show that the form of u specified above complies with two NMR-detected potential energy landscapes representing preferential ordering along N-H or C^α-C^α. Pictorial illustrations thereof are provided. The extended SRLS analysis is applied to ¹⁵N-H relaxation from the carbohydrate recognition domain of galectin-3 (Gal3C) in complex with two diastereomeric ligands, S and R. We find that is isotropic with a principal value, D₂, of 10¹⁰ s^-1 on average, and it is faster in the strands β₃, β₅, and β₈. The potential, u, is strong (∼20 kT); it is slightly rhombic when N-H is the main ordering axis and highly rhombic when C^α-C^α is the main ordering axis. Gal3C-S exhibits primarily preferential ordering along C^α-C^α; Gal3C-R exhibits both types of ordering. The binding-associated polypeptide chain segment of Gal3C-S is homogeneous, whereas that of Gal3C-R is diversified, with regard to D₂ and ordering preference. We associate these features with the previously determined diminished binding constant of Gal3C-R in comparison with Gal3C-S. Thus, the present study enhances the SRLS analysis, in general, and provides new insights into the dynamic structure and binding properties of Gal3C-S and Gal3C-R, in particular.