Computationally efficient gradients for relaxation matrix-based structure refinement including the accommodation of internal motions.

A general method for deriving analytical gradients based on NOESY cross-peak intensities is presented. This method allows for very rapid calculation of exact gradients of cross-peak intensities with respect to parameters directly related to the pairwise dipole-dipole interaction giving rise to the cross peak. In the simplest case, gradients with respect to internuclear separation can be calculated, which allows for the rational modification of distance constraints used in structural refinement. In the general case, any arbitrary level of knowledge of the internal dynamics of the molecule can be introduced, thereby providing a pathway for the experimental determination of motional parameters. The motional characteristics of the internuclear vectors defining dipole-dipole interactions are cast in model-free terms. The form of the gradient circumvents many of the limitations of gradients expressed in terms of Cartesian or dihedral variables. The gradients presented are simple, direct, and exact and require little computational effort to calculate.

Fast internal main-chain dynamics of human ubiquitin.

The fast internal dynamics of human ubiquitin have been studied by the analysis of 15N relaxation of backbone amide nitrogens. The amide 15N resonances have been assigned by use of heteronuclear multiple-quantum spectroscopy. Spin lattice relaxation times at 60.8 and 30.4 MHz and the steady-state nuclear Overhauser effect at 60.8 MHz have been determined for 67 amide 15N sites in the protein using two-dimensional spectroscopy. These data have been analyzed in terms of the model free treatment of Lipari and Szabo [Lipari, G., & Szabo, A. (1982) J. Am. Chem. Soc. 104, 4546-4559]. The global motion of the protein is shown to be isotropic and is characterized by a correlation time of 4.1 ns rad-1. The generalized order parameters (S2) of backbone amide N-H vectors in the globular region of the protein range from 0.5 to 0.95. No apparent correlation between secondary structure and generalized order parameters is observed. There is, however, a strong correlation between the magnitude of the generalized order parameters of a given N-H vector and the presence of hydrogen bonding of the amide hydrogen or its peptide bond associated carbonyl. Using a chemical shift tensor breadth of 160 ppm, the N-H vectors of peptide linkages participating in one or more hydrogen bonds to the main chain show an average generalized order parameter of 0.80 (SD 0.06), while those amide NH of peptide linkages free of hydrogen-bonding interactions with the main chain show an average order parameter of 0.69 (SD 0.06).(ABSTRACT TRUNCATED AT 250 WORDS)

Modifications of the rate matrix required for the quantitative analysis of NOESY spectra of proteins.

The introduction of rate matrix analysis to protocols for the refinement of solution structures of biopolymers on the basis of NMR-derived structural constraints has greatly enhanced the self-consistency of the general approach. However, current implementations of this strategy appear not to consider several issues arising from various commonly employed experimental conditions and sample characteristics which can prevent the quantitative interpretation of NOESY spectra of proteins. Here, a number of these effects are considered, including the influence of nonequilibrium populations generated by over-pulsing and solvent presaturation, the presence of heteronuclei, and the equilibration of exchangeable sites with deuterium in solvent. The modifications of the rate matrix that are required to treat these effects are summarized and simulations presented to illustrate the relative importance of each. The computational effort required to rigorously accommodate each effect is described along with several simple experimental modifications that reduce the computational burden.

Assignments and structure determination of the catalytic domain of human fibroblast collagenase using 3D double and triple resonance NMR spectroscopy.

We report here the backbone 1HN, 15N, 13C alpha, 13CO, and 1H alpha NMR assignments for the catalytic domain of human fibroblast collagenase (HFC). Three independent assignment pathways (matching 1H, 13C alpha, and 13CO resonances) were used to establish sequential connections. The connections using 13C alpha resonances were obtained from HNCOCA and HNCA experiments; 13CO connections were obtained from HNCO and HNCACO experiments. The sequential proton assignment pathway was established from a 3D (1H/15N) NOESY-HSQC experiment. Amino acid typing was accomplished using 13C and 15N chemical shifts, specific labeling of 15N-Leu, and spin pattern recognition from DQF-COSY. The secondary structure was determined by analyzing the 3D (1H/15N) NOESY-HSQC. A preliminary NMR structure calculation of HFC was found to be in agreement with recent X-ray structures of human fibroblast collagenase and human neutrophil collagenase as well as similar to recent NMR structures of a highly homologous protein, stromelysin. All three helices were located; a five-stranded beta-sheet (four parallel strands, one antiparallel strand) was also determined. beta-Sheet regions were identified by cross-strand d alpha N and d NN connections and by strong intraresidue d alpha N correlations, and were corroborated by observing slow amide proton exchange. Chemical shift changes in a selectively 15N-labeled sample suggest that substantial structural changes occur in the active site cleft on the binding of an inhibitor.