Internal and Overall Peptide Group Motion in Proteins:  Molecular Dynamics Simulations for Lysozyme Compared with Results from X-ray and NMR Spectroscopy

The motions of the main-chain N−H vector and of the atoms which define the peptide plane in proteins have been analyzed by use of a 1.6 ns molecular dynamics simulation of hen lysozyme in explicit solvent. By use of both local and molecular superposition of the peptide plane, fluctuations of the peptide group atoms relative to one another are distinguished from motions of the group as a whole. Distortions of the peptide plane arise from changes in bond geometry at the nitrogen and carbonyl carbon center, as well as from twisting around the C−N bond. Probability distributions for the distortions obtained from the protein average structure were compared with the instantaneous distortions sampled in the simulation. For the peptide group ω angle, there is approximate agreement between these two ways of determining the potentials of mean force, providing support for the widespread use of the former to obtain information about the latter. Good agreement is obtained also with potentials of mean force derived from experimental data on peptide plane distortions in peptide crystal and high-resolution protein structures. By contrast, for the N−H vector probability distribution, the potentials of mean force do not agree with those obtained from the average distortion. The N−H vector, which is of primary interest for NMR, has an average position that is nearly in the peptide plane and antiparallel to the CO bond vector. The N−H bond vector undergoes rapid in-plane and out-of-plane fluctuations with average amplitudes of 4.7° ± 0.1° and 7.4° ± 0.4°, respectively. Since the N−H reorientational fluctuations occur on a subpicosecond time scale, their contribution to 15N relaxation can be described by a local order parameter Sloc2 whose average is 0.931 ± 0.005 for 126 peptide planes in hen lysozyme. For 16 of the N−H bond vectors, the calculated Sloc2 values are within 0.02 units of the overall N−H order parameters S2. For smaller values of S2, as found for the majority of the N−H vectors, the dominant contribution comes from overall peptide group motion. These results suggest that a renormalization of experimental order parameters should be used to extract the peptide group motions. The N−H bond-stretching motions are on the order of ±0.024 Å, and the average bond lengths are almost uniform along the protein sequence. Thus, given the correct average value, the N−H bond-stretching vibrations have a negligible effect on the calculation of order parameters from the simulation. Peptide planes which are involved in secondary structures show reduced fluctuations. They can also exhibit motions that are correlated with dihedral angle fluctuations involving the surrounding heavy atoms and adjacent peptide planes.