Mode-Coupling SRLS versus Mode-Decoupled Model-Free N-H Bond Dynamics: Mode-Mixing and Renormalization

The common approach to N-H motion in proteins is model-free (MF), where the global (RC) and local (RL) motions are assumed decoupled. We have recently applied to N-H bond dynamics the slowly relaxing local structure (SRLS) model, which accounts rigorously for mode-coupling. The original and extended MF formulas are perturbational expansions of SRLS with respect to the local ordering, (S0), when RL . RC. Their functional form, number of terms equal to the number of dynamic modes, is implied by mode-decoupling, and the free diffusion eigenvalue, 1/τ ) 6RL, by the absence of strong-potential-induced renormalization. However, for N-H motion, (S0) is high and in the extended MF regime R⊥ L ≈ RC. Although the functional form of the original MF formula is largely valid for RC/RL e 0.01 and (S0) g 0.8, τe MF represents the significantly reduced potential-dependent renormalized value of τ. Hence, the application of this formula to calculate NMR variables is appropriate in this parameter range, but associating τe with the local motion correlation time is inappropriate. Means to derive τ from τe are provided. For a cosine squared potential, the cone-model-based MF formula that relates τe to τ can also be used. Deriving τ from τe is important for proper characterization of the site-specific local motion and in the context of τ-dependent MF functionalities. Mode-coupling dominates the extended MF regime where SRLS must be invariably used. Eigenmode and spectral density analysis is provided in this study for the two parameter ranges associated with N-H bond motion.