## Abstract

The common approach to N-H motion in proteins is model-free (MF), where the global (R^{C}) and local (R^{L}) 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, (S_{0}^{2})^{2}, when R^{L} ≫ R^{C}. 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 = 6R^{L}, by the absence of strong-potential-induced renormalization. However, for N-H motion, (S _{0}^{2})^{2} is high and in the extended MF regime R_{⊥}^{L} ≈ R^{C}. Although the functional form of the original MF formula is largely valid for R^{C}/R^{L} ≤ 0.01 and (S_{0}^{2})^{2} ≥ 0.8, τ _{e} 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 τ_{e} with the local motion correlation time is inappropriate. Means to derive τ from τ_{e} are provided. For a cosine squared potential, the cone-model-based MF formula that relates τ_{e} to τ can also be used, Deriving τ from τ_{e} 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.

Original language | English |
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Pages (from-to) | 9898-9904 |

Number of pages | 7 |

Journal | Journal of Physical Chemistry B |

Volume | 107 |

Issue number | 36 |

DOIs | |

State | Published - 11 Sep 2003 |