The anisotropy of rapid fluctuations of the peptide planes in ubiquitin is explored by combined 15N and 13C‘ nuclear spin relaxation measurements and molecular dynamics (MD) computer simulation. T 1, T 2, and NOE data were collected at B 0-field strenghts corresponding to 400 and 600 MHz proton resonance. A 1.5-ns simulation of ubiquitin in an explicit water environment was performed using CHARMM 24. The simulation suggests that, for 76% of the peptide planes, the relaxation-active motion of the backbone 15N and 13C‘ spins is dominated by anisotropic Gaussian axial fluctuations of the peptide planes about three orthogonal axes. The dominant fluctuation axes are nearly parallel to the − axes. The remaining peptide planes belong to more flexible regions of the backbone and cannot be described by this type of motion alone. Based on the results of the computer simulation, an analytical 3D GAF motional model (Bremi, T.; Brüschweiler, R. J. Am. Chem. Soc. 1997, 119, 6672−6673) was applied to the experimental relaxation data. The fluctuation amplitudes of the peptide planes show a significant anisotropy of the internal motion. This analysis demonstrates that a combined interpretation of 15N and 13C‘ relaxation data by a model derived from a computer simulation may provide detailed insight into the fast time-scale backbone dynamics that goes beyond the results of a standard model-free analysis.

The interpretation of nuclear spin relaxation data of biomolecules often requires the accurate knowledge of chemical shielding anisotropy (CSA) tensors, which significantly depend on the environment and on intramolecular dynamics. CSA tensors are studied in this work by density functional theory and by molecular dynamics simulations. It is demonstrated that density functional theory yields CSA tensors for 15 N nuclei in the side chain of crystalline asparagine and in the peptide bond of crystalline alanine-alanine dipeptide with an accuracy comparable to that of solid-state NMR. In these calculations, the molecular fragment containing the nucleus of interest is treated with an IGLO-II and IGLO-III basis set while neighboring fragments exhibiting close contacts are represented by a DZVP set. In addition, electrostatic effects are taken into account by explicit partial point charges. The dynamical averaging of CSA tensors is investigated by applying density functional theory to snapshots of a molecular dynamics trajectory of the protein ubiquitin. The fluctuation properties of the 15 N CSA tensors of two glutamine side chains are assessed. Computed auto-and cross-correlated relaxation parameters using these CSA tensors are found to be in good agreement with the experiment. Local charges and close contacts can have a significant effect on 15 N CSA tensors and have to be taken into account when transferring CSA parameters from model compounds to proteins.

Intramolecular reorientational dynamics of proteins are described in terms of reorientational quasiharmonic modes. These modes provide important insight into anisotropic and collective axial fluctuations of distinct molecular fragments, and they represent a highly compact description of intramolecular protein motions that are spectroscopically observable via nuclear spin relaxation. The method is applied to a molecular dynamics computer simulation of the protein ubiquitin.

No abstract

A theoretical analysis is presented for liquid-state T1ρ relaxation in a coupled two-spin system I=1/2, S=1 in the presence of two radio-frequency fields applied to each of the spins individually. It is demonstrated that the relaxation rate constant T1ρ−1 of the spin I due to scalar relaxation sharply increases when the two radio-frequency fields are matched according to the Hartmann–Hahn condition. Relaxation measurements on the amino-protons of 3-nitroaniline show good agreement with theory.