A novel view of domain flexibility in E. coli adenylate kinase based on structural mode-coupling ¹⁵N NMR relaxation

Adenylate kinase from Escherichia coli (AKeco), consisting of a single 23.6 kDa polypeptide chain folded into domains CORE, AMPbd and LID, catalyzes the reaction AMP + ATP → 2ADP. In the ligand-free enzyme the domains AMPbd and LID execute large-amplitude movements controlling substrate binding and product release during catalysis. Domain flexibility is investigated herein with the slowly relaxing local structure (SRLS) model for ¹⁵N relaxation. SRLS accounts rigorously for coupling between the global and local N-H motions through a local ordering potential exerted by the protein structure at the N-H bond. The latter reorients with respect to its protein surroundings, which reorient on the slower time scale associated with the global protein tumbling. AKeco diffuses globally with correlation time τ_m 15.1 ns, while locally two different dynamic cases prevail. The domain CORE features ordering about the equilibrium N-H bond orientation with order parameters, S², of 0.8-0.9 and local motional correlation times, τ, mainly between 5-130 ps. This represents a conventional rigid protein structure with rapid small-amplitude N-H fluctuations. The domains AMPbd and LID feature small parallel (Z_M) ordering of S² 0.2-0.5 which can be reinterpreted as high perpendicular (Y_M) ordering. M denotes the local ordering/local diffusion frame. Local motion about Z_M is given by τ_∥ ≈ 5 ps and local motion of the effective Z_M axis about Y_M by τ_⊥ = 6-11 ns. Z_M is tilted at approximately 20° from the N-H bond. The orientation of the Y_M axis may be considered parallel to the C_{i - 1}^α-C_i^α axis. The τ_⊥ mode reflects collective nanosecond peptide-plane motions, interpretable as domain motion. A powerful new model of protein flexibility/domain motion has been established. Conformational exchange (R_ex) processes accompany the τ_⊥ mode. The SRLS analysis is compared with the conventional model-free analysis.