Comparison of different torsion angle approaches for NMR structure determination

Systematic Exploration of Protein Conformational Space Using a Distance Geometry Approach

The optimization approaches classically used during the determination of protein structure encounter various difficulties, especially when the size of the conformational space is large. Indeed, in such a case, algorithmic convergence criteria are more difficult to set up. Moreover, the size of the search space makes it difficult to achieve a complete exploration. The interval branch-and-prune (iBP) approach, based on the reformulation of the distance geometry problem (DGP) provides a theoretical frame for the generation of protein conformations, by systematically sampling the conformational space. When an appropriate subset of interatomic distances is known exactly, this worst-case exponential-time algorithm is provably complete and fixed-parameter tractable. These guarantees, however, immediately disappear as distance measurement errors are introduced. Here we propose an improvement of this approach: threading-augmented interval branch-and-prune (TAiBP), where the combinatorial explosion of the original iBP approach arising from its exponential complexity is alleviated by partitioning the input instances into consecutive peptide fragments and by using self-organizing maps (SOMs) to obtain clusters of similar solutions. A validation of the TAiBP approach is presented here on a set of proteins of various sizes and structures. The calculation inputs are a uniform covalent geometry extracted from force field covalent terms, the backbone dihedral angles with error intervals, and a few long-range distances. For most of the proteins smaller than 50 residues and interval widths of 20°, the TAiBP approach yielded solutions with RMSD values smaller than 3 Å with respect to the initial protein conformation. The efficiency of the TAiBP approach for proteins larger than 50 residues will require the use of nonuniform covalent geometry and may have benefits from the recent development of residue-specific force-fields.

BioMagResBank

The BioMagResBank (BMRB: www.bmrb.wisc.edu) is a repository for experimental and derived data gathered from nuclear magnetic resonance (NMR) spectroscopic studies of biological molecules. BMRB is a partner in the Worldwide Protein Data Bank (wwPDB). The BMRB archive consists of four main data depositories: (i) quantitative NMR spectral parameters for proteins, peptides, nucleic acids, carbohydrates and ligands or cofactors (assigned chemical shifts, coupling constants and peak lists) and derived data (relaxation parameters, residual dipolar couplings, hydrogen exchange rates, pK(a) values, etc.), (ii) databases for NMR restraints processed from original author depositions available from the Protein Data Bank, (iii) time-domain (raw) spectral data from NMR experiments used to assign spectral resonances and determine the structures of biological macromolecules and (iv) a database of one- and two-dimensional (1)H and (13)C one- and two-dimensional NMR spectra for over 250 metabolites. The BMRB website provides free access to all of these data. BMRB has tools for querying the archive and retrieving information and an ftp site (ftp.bmrb.wisc.edu) where data in the archive can be downloaded in bulk. Two BMRB mirror sites exist: one at the PDBj, Protein Research Institute, Osaka University, Osaka, Japan (bmrb.protein.osaka-u.ac.jp) and the other at CERM, University of Florence, Florence, Italy (bmrb.postgenomicnmr.net/). The site at Osaka also accepts and processes data depositions.

A comparative study of molecular dynamics in Cartesian and in internal coordinates: dynamical instability in the latter caused by nonlinearity of the equations of motion

The stability of a general molecular dynamics (MD) integration scheme is examined for simulations in generalized (internal plus external) coordinates (GCs). An analytic expression is derived for the local error in energy during each integration time step. This shows that the explicit dependence of the mass-matrix on GCs, which makes the system's Lagrange equations of motion nonlinear, causes MD simulations in GCs to be less stable than those in Cartesian coordinates (CCs). In terms of CCs, the corresponding mass-matrix depends only on atomic masses and thus atomistic motion is subject to the linear Newton equations, which makes the system more stable. Also investigated are two MD methods in GCs that utilize nonzero elements of the vibrational spectroscopic B-matrices. One updates positions and velocities in GCs that are iteratively adjusted so as to conform to the velocity Verlet equivalent in GCs. The other updates positions in GCs and velocities in CCs that are adjusted to satisfy the internal constraints of the new constrained WIGGLE MD scheme. The proposed methods are applied to an isolated n-octane molecule and their performances are compared with those of several CCMD schemes. The simulation results are found to be consistent with the analytic stability analysis. Finally, a method is presented for computing nonzero elements of B-matrices for external rotations without imposing the Casimir-Eckart conditions.

The conformational landscape of the ribosomal protein S15 and its influence on the protein interaction with 16S RNA

The interaction between the ribosomal protein S15 and its binding sites in the 16S RNA was examined from two points of view. First, the isolated protein S15 was studied by comparing NMR conformer sets, available in the PDB and recalculated using the CNS-ARIA protocol. Molecular dynamics (MD) trajectories were then recorded starting from a conformer of each set. The recalculation of the S15 NMR structure, as well as the recording of MD trajectories, reveals that several orientations of the N-terminal alpha-helix alpha1 with respect to the structure core are populated. MD trajectories of the complex between the ribosomal protein S15 and RNA were also recorded in the presence and absence of Mg(2+) ions. The Mg(2+) ions are hexacoordinated by water and RNA oxygens. The coordination spheres mainly interact with the RNA phosphodiester backbone, reducing the RNA mobility and inducing electrostatic screening. When the Mg(2+) ions are removed, the internal mobility of the RNA and of the protein increases at the interaction interface close to the RNA G-U/G-C motif as a result of a gap between the phosphate groups in the UUCG capping tetraloop and of the disruption of S15-RNA hydrogen bonds in that region. On the other hand, several S15-RNA hydrogen bonds are reinforced, and water bridges appear between the three-way junction region and S15. The network of hydrogen bonds observed in the loop between alpha1 and alpha2 is consequently reorganized. In the absence of Mg(2+), this network has the same pattern as the network observed in the isolated protein, where the helix alpha1 is mobile with respect to the protein core. The presence of Mg(2+) ions may thus play a role in stabilizing the orientation of the helix alpha1 of S15.