Simultaneous observation of positive and negative NOE in biomolecules: a bistable jump model for segmental motion with modulation of internuclear distances

Abstract

Recently a negative nuclear Overhauser effect (NOE) among the backbone protons as well as a positive NOE between the backbone and ring protons of tryptophan in a peptide was reported. While the negative NOE is indicative of slow overall reorientation of the molecule, simultaneous Occurrence of a positive NOE is indicative of internal motions in the molecule. To explain these observations we develop here a model in which the overall motion is anisotropic reorientation and the internal motion modulates the internuclear distance. Analytical expressions for the spectral density functions for dipole-dipole relaxation are obtained when the internal motion is a bistable jump. Steady-state and transient NOE calculations are performed for two relaxation-coupled spins. The results confirm that when the overall motion is in the slow motion limit and the side chain internal motion is in the fast motion limit, the NOE within the backbone protons is negative and that between the backbone and the side chain protons is positive. This model further shows that the NOE between the backbone and the side chain is proportional to the weighted average of the inverse sixth power of the distance between the interacting spins only when the overall motion is isotropic, dominates the relaxation process and is much faster than the internal motion. With use of this model, multispin steady-state NOES are computed to explain the experimental observation of positive and negative NOE's and their temperature dependence in a tryptophan-containing polypeptide.