Conformational Entropy from NMR Relaxation in Proteins: The SRLS Perspective

Conformational entropy changes associated with bond-vector motions in proteins contribute to the free energy of ligand-binding. To derive such contributions, we apply the slowly relaxing local structure (SRLS) approach to NMR relaxation from ¹⁵N-H bonds or C-CDH₂ moieties of several proteins in free and ligand-bound form. The spatial restraints on probe motion, which determine the extent of local order, are expressed in SRLS by a well-defined potential, u(θ). The latter yields the orientational probability density, P_eq = exp(-u(θ)), and hence the related conformational entropy, Ŝ = -∫P_eq(θ) ln[P_eq(θ)] sin θ dθ (Ŝ is "entropy" in units of k_BT, and θ represents the bond-vector orientation in the protein). SRLS is applied to 4-oxalocrotonate tautomerase (4-OT), the acyl-coenzyme A binding protein (ACBP), the C-terminal SH2 domain of phospholipase C_γ1 (PLC_γ1C SH2), the construct dihydrofolate reductase-E:folate (DHFR-E:folate), and their complexes with appropriate ligands, to determine ΔŜ. Eglin C and its V18A and V34A mutants are also studied. Finally, SRLS is applied to the structurally homologous proteins TNfn3 and FNfn10 to characterize within its scope the unusual "dynamics" of the TNfn3 core. Upon ligand-binding, the backbones of 4-OT, ACBP, and PLC_γ1C SH2 show limited, increased, and decreased order, respectively; the cores of DHFR-E:folate and PLC_γ1C SH2 become more ordered. The V18A (V34A) mutation increases (decreases) the order within the eglin C core. The core of TNfn3 is less ordered structurally and more mobile kinetically. Secondary structure versus loops, surface-binding versus core insertion, and ligand size emerged as being important in rationalizing ΔŜ. The consistent and general tool developed herein is expected to provide further insights in future work.