The building of protein structures from alpha-carbon coordinates

A procedure for the construction of complete protein structures from only alpha-carbon coordinates is described. This involves building the backbone by sequential addition of Pro, Gly, or Ala residues. This main chain structure is then refined using molecular dynamics. Side chains are constructed by sequential addition of atoms with intermediate molecular dynamics refinement. For alpha lytic protease (a structure that is mostly beta sheet) a backbone root mean square deviation (RMSD) of 0.19 A and an overall RMSD of 1.24 A from the crystallographic coordinates are attained. For troponin C (67% alpha-helix), where the coordinates are available only for the alpha-carbons, a backbone RMSD of 0.41 A and an overall RMSD of 1.68 A are attained (fits kindly provided by Dr. Michael James and Natalie Strynadka). For flavodoxin a backbone RMSD of 0.49 A and an overall RMSD of 1.64 A were attained.     

Building proteins from C alpha coordinates using the dihedral probability grid Monte Carlo method.

Dihedral probability grid Monte Carlo (DPG-MC) is a general-purpose method of conformational sampling that can be applied to many problems in peptide and protein modeling. Here we present the DPG-MC method and apply it to predicting complete protein structures from C alpha coordinates. This is useful in such endeavors as homology modeling, protein structure prediction from lattice simulations, or fitting protein structures to X-ray crystallographic data. It also serves as an example of how DPG-MC can be applied to systems with geometric constraints. The conformational propensities for individual residues are used to guide conformational searches as the protein is built from the amino-terminus to the carboxyl-terminus. Results for a number of proteins show that both the backbone and side chain can be accurately modeled using DPG-MC. Backbone atoms are generally predicted with RMS errors of about 0.5 A (compared to X-ray crystal structure coordinates) and all atoms are predicted to an RMS error of 1.7 A or better.     

Building protein backbones from C alpha coordinates.

An automatic procedure for building polyalanine backbones from guiding alpha-carbon positions is presented. Polyalanine backbones are built based on the geometric restraints of angle N-C alpha-C and the knowledge of main-chain dihedral angle distributions. A building module constructs a list of polyalanine backbones that follow exactly the C alpha trace. Then a selection module selects one backbone with the largest portion of phi-psi pairs in favoured regions. Several test cases on C alpha coordinates from X-ray refined structures give acceptable results. Less than 10% of the peptide planes are incorrectly built, and the result is not sensitive to random shift up to 0.5 A of C alpha coordinates.     

Rebuilding flavodoxin from C alpha coordinates: a test study

The tertiary structure of flavodoxin has been model built from only the X-ray crystallographic alpha-carbon coordinates. Main-chain atoms were generated from a dictionary of backbone structures. Side-chain conformations were initially set according to observed statistical distributions, clashes were resolved with reference to other knowledge-based parameters, and finally, energy minimization was applied. The RMSD of the model was 1.7 A across all atoms to the native structure. Regular secondary structural elements were modeled more accurately than other regions. About 40% of the chi 1 torsional angles were modeled correctly. Packing of side chains in the core was energetically stable but diverged significantly from the native structure in some regions. The modeling of protein structures is increasing in popularity but relatively few checks have been applied to determine the accuracy of the approach. In this work a variety of parameters have been examined. It was found that close contacts, and hydrogen-bonding patterns could identify poorly packed residues. These tests, however, did not indicate which residues had a conformation different from the native structure or how to move such residues to bring them into agreement. To assist in the modeling of interacting side chains a database of known interactions has been prepared.     

Calculation of protein backbone geometry from alpha-carbon coordinates based on peptide-group dipole alignment.

An algorithm is proposed for the conversion of a virtual-bond polypeptide chain (connected C alpha atoms) to an all-atom backbone, based on determining the most extensive hydrogen-bond network between the peptide groups of the backbone, while maintaining all of the backbone atoms in energetically feasible conformations. Hydrogen bonding is represented by aligning the peptide-group dipoles. These peptide groups are not contiguous in the amino acid sequence. The first dipoles to be aligned are those that are both sufficiently close in space to be arranged in approximately linear arrays termed dipole paths. The criteria used in the construction of dipole paths are: to assure good alignment of the greatest possible number of dipoles that are close in space; to optimize the electrostatic interactions between the dipoles that belong to different paths close in space; and to avoid locally unfavorable amino acid residue conformations. The equations for dipole alignment are solved separately for each path, and then the remaining single dipoles are aligned optimally with the electrostatic field from the dipoles that belong to the dipole-path network. A least-squares minimizer is used to keep the geometry of the alpha-carbon trace of the resulting backbone close to that of the input virtual-bond chain. This procedure is sufficient to convert the virtual-bond chain to a real chain; in applications to real systems, however, the final structure is obtained by minimizing the total ECEPP/2 (empirical conformational energy program for peptides) energy of the system, starting from the geometry resulting from the solution of the alignment equations. When applied to model alpha-helical and beta-sheet structures, the algorithm, followed by the ECEPP/2 energy minimization, resulted in an energy and backbone geometry characteristic of these alpha-helical and beta-sheet structures. Application to the alpha-carbon trace of the backbone of the crystallographic 5PTI structure of bovine pancreatic trypsin inhibitor, followed by ECEPP/2 energy minimization with C alpha-distance constraints, led to a structure with almost as low energy and root mean square deviation as the ECEPP/2 geometry analog of 5PTI, the best agreement between the crystal and reconstructed backbone being observed for the residues involved in the dipole-path network.     

Progress in protein-protein docking: atomic resolution predictions in the CAPRI experiment using RosettaDock with an improved treatment of side-chain flexibility

RosettaDock uses real-space Monte Carlo minimization (MCM) on both rigid-body and side-chain degrees of freedom to identify the lowest free energy docked arrangement of 2 protein structures. An improved version of the method that uses gradient-based minimization for off-rotamer side-chain optimization and includes information from unbound structures was used to create predictions for Rounds 4 and 5 of CAPRI. First, large numbers of independent MCM trajectories were carried out and the lowest free energy docked configurations identified. Second, new trajectories were started from these lowest energy structures to thoroughly sample the surrounding conformation space, and the lowest energy configurations were submitted as predictions. For all cases in which there were no significant backbone conformational changes, a small number of very low-energy configurations were identified in the first, global search and subsequently found to be close to the center of the basin of attraction in the free energy landscape in the second, local search. Following the release of the experimental coordinates, it was found that the centers of these free energy minima were remarkably close to the native structures in not only the rigid-body orientation but also the detailed conformations of the side-chains. Out of 8 targets, the lowest energy models had interface root-mean-square deviations (RMSDs) less than 1.1 A from the correct structures for 6 targets, and interface RMSDs less than 0.4 A for 3 targets. The predictions were top submissions to CAPRI for Targets 11, 12, 14, 15, and 19. The close correspondence of the lowest free energy structures found in our searches to the experimental structures suggests that our free energy function is a reasonable representation of the physical chemistry, and that the real space search with full side-chain flexibility to some extent solves the protein-protein docking problem in the absence of significant backbone conformational changes. On the other hand, the approach fails when there are significant backbone conformational changes as the steric complementarity of the 2 proteins cannot be modeled without incorporating backbone flexibility, and this is the major goal of our current work.     

Crystal structure of yeast tRNAAsp: atomic coordinates

The atomic coordinates of yeast aspartic acid transfer RNA, as determined from a crystallographic investigation to 3 A resolution, are presented. In the ribose phosphate backbone sugars are in the C(3')-endo pucker, except for residues A7, A9, D16, G17, G18, D19, C20, U48, A58, and U60 which are in the C(2')-endo pucker. A least-squares superposition of the phosphorus atoms of yeast tRNAAsp and yeast tRNAPhe enlightens both an overall structural similarity and significant conformational differences. The largest deviations occur in the D-loop and the anticodon region.     

A fast method to sample real protein conformational space

A fast computer program, FOLDTRAJ, to generate plausible random protein structures is reported. All-atom proteins are made directly in continuous three-dimensional space starting from primary sequence with an N to C directed build-up method. The method uses a novel pipelined residue addition approach in which the leading edge of the protein is constructed three residues at a time for optimal protein geometry, including the placement of cis proline. Build-up methods represent a classic N-body problem, expected to scale as N(2). When proteins become more collapsed, build-up methods are susceptible to backtracking problems which can scale exponentially with the number of residues required to back out of a trapped walk. We have provided solutions to both these problems, using a multiway binary tree that makes the N-body problem of bump-checking scale as NlogN, and speeding up backtracking by varying the number of tries before backtracking based on available conformational space. FOLDTRAJ is independent of energy potentials, other than that implicit in the geometrical properties derived by statistical studies of known structures, and in atomic Van der Waals radii. WHAT-CHECK shows that the program generates chirally and physically valid proteins with all bond lengths, angles and dihedrals within allowable tolerances. Random structures built using sequences from PDB files 1SEM, 2HPR, and 1RTP typically have 5-15% alpha-helical content (according to DSSP) and on the order of 20% beta-strand/extended content. Ensembles of random structures are compared with polymer theory and with experimentally determined fluorescence resonance energy transfer distances. Reasonably sized structure ensembles do sample most of the conformational space available to proteins. The method is also capable of protein reconstruction using Calpha--Calpha direction vectors, and it compares favorably with methods that reconstruct protein backbones based on alpha-carbon coordinates, having an average backbone and Cbeta root mean square deviation of 0.63 A for nine different protein folds. Proteins 2000;39:112-131.     

Multiple structure alignment and consensus identification for proteins

Background  

An algorithm is presented to compute a multiple structure alignment for a set of proteins and to generate a consensus (pseudo) protein which captures common substructures present in the given proteins. The algorithm represents each protein as a sequence of triples of coordinates of the alpha-carbon atoms along the backbone. It then computes iteratively a sequence of transformation matrices (i.e., translations and rotations) to align the proteins in space and generate the consensus. The algorithm is a heuristic in that it computes an approximation to the optimal alignment that minimizes the sum of the pairwise distances between the consensus and the transformed proteins.     

Elucidating protein secondary structures using alpha-carbon recurrence quantifications.

Secondary structures of proteins were studied by recurrence quantification analysis (RQA). High-resolution, 3-dimensional coordinates of alpha-carbon atoms comprising a set of 68 proteins were downloaded from the Protein Data Bank. By fine-tuning four recurrence parameters (radius, line, residue, separation), it was possible to establish excellent agreement between percent contribution of alpha-helix and beta-sheet structures determined independently by RQA and that of the DSSP algorithm (Define Secondary Structure of Proteins). These results indicate that there is an equivalency between these two techniques, which are based upon totally different pattern recognition strategies. RQA enhances qualitative contact maps by quantifying the arrangements of recurrent points of alpha carbons close in 3-dimensional space. For example, the radius was systematically increased, moving the analysis beyond local alpha-carbon neighborhoods in order to capture super-secondary and tertiary structures. However, differences between proteins could only be detected within distances up to about 6-11 A, but not higher. This result underscores the complexity of alpha-carbon spacing when super-secondary structures appear at larger distances. Finally, RQA-defined secondary structures were found to be robust against random displacement of alpha carbons upwards of 1 A. This finding has potential import for the dynamic functions of proteins in motion.     

Continuous metadynamics in essential coordinates as a tool for free energy modelling of conformational changes

Modelling of conformational changes in biopolymers is one of the greatest challenges of molecular biophysics. Metadynamics is a recently introduced free energy modelling technique that enhances sampling of configurational (e.g. conformational) space within a molecular dynamics simulation. This enhancement is achieved by the addition of a history-dependent bias potential, which drives the system from previously visited regions. Discontinuous metadynamics in the space of essential dynamics eigenvectors (collective motions) has been proposed and tested in conformational change modelling. Here, we present an implementation of two continuous formulations of metadynamics in the essential subspace. The method was performed in a modified version of the molecular dynamics package GROMACS. These implementations were tested on conformational changes in cyclohexane, alanine dipeptide (terminally blocked alanine, Ace-Ala-Nme) and SH3 domain. The results illustrate that metadynamics in the space of essential coordinates can accurately model free energy surfaces associated with conformational changes. Figure The conformational free energy surface of cyclohexane in the space of the two most intensive collective motions.

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Criteria that discriminate between native proteins and incorrectly folded models

Various theoretical concepts, such as free energy potentials, electrostatic interaction potentials, atomic packing, solvent-exposed surface, and surface charge distribution, were tested for their ability to discriminate between native proteins and misfolded protein models. Misfolded models were constructed by introducing incorrect side chains onto polypeptide backbones: side chains of the alpha-helical hemerythrin were modeled on the beta-sheeted backbone of immunoglobulin VL domain, whereas those of the VL domain were similarly modeled on the hemerythrin backbone. CONGEN, a conformational space sampling program, was used to construct the side chains, in contrast to the previous work, where incorrect side chains were modeled in all trans conformations. Capability of the conformational search procedure to reproduce native conformations was gauged first by rebuilding (the correct) side chains in hemerythrin and the VL domain: constructs with r.m.s. differences from the x-ray side chains 2.2-2.4 A were produced, and many calculated conformations matched the native ones quite well. Incorrectly folded models were then constructed by the same conformational protocol applied to incorrect amino acid sequences. All CONGEN constructs, both correctly and incorrectly folded, were characterized by exceptionally small molecular surfaces and low potential energies. Surface charge density, atomic packing, and Coulomb formula-based electrostatic interactions of the misfolded structures and the correctly folded proteins were similar, and therefore of little interest for diagnosing incorrect folds. The following criteria clearly favored the native structures over the misfolded ones: 1) solvent-exposed side-chain nonpolar surface, 2) number of buried ionizable groups, and 3) empirical free energy functions that incorporate solvent effects.     

The reconstruction of side-chain conformations from protein Cα coordinates

A model of nine proteins including side-chain atoms have been built from the known C^α coordinates and amino acid sequences using a Monte Carlo Protein Building Annealing method. The Cartesian coordinates for the side-chain atoms were established with bond lengths and angles selected randomly from within previously determined ranges. A simulated annealing technique is used to generate some 300 structures with differing side-chain conformations. The atomic coordinates of the backbone atoms are fixed during the simulated annealing process. The coordinates of the side-chain atoms of 300 low energy conformations are averaged to obtain a mean structure that is minimized with the C^α atoms constrained to their position in the x-ray structure using the OPLS/AMBER force field with the GB/SA water model. The rms deviation of the main-chain atoms (without C^β) compared with the corresponding crystal structures is in the range 0.20–0.64 Å. The rms deviation of the side-chain atoms is between 1.72 and 2.71 Å and for all atoms is between 1.19 and 1.99 Å. The method is insensitive to random errors in the C^α positions and the computational requirement is modest. © 1997 John Wiley & Sons, Inc.     

Distributions in protein conformation space: implications for structure prediction and entropy

By considering how polymer structures are distributed in conformation space, we show that it is possible to quantify the difficulty of structural prediction and to provide a measure of progress for prediction calculations. The critical issue is the probability that a conformation is found within a specified distance of another conformer. We address this question by constructing a cumulative distribution function (CDF) for the average probability from observations about its limiting behavior at small displacements and numerical simulations of polyalanine chains. We can use the CDF to estimate the likelihood that a structure prediction is better than random chance. For example, the chance of randomly predicting the native backbone structure of a 150-amino-acid protein to low resolution, say within 6 A, is 10(-14). A high-resolution structural prediction, say to 2 A, is immensely more difficult (10(-57)). With additional assumptions, the CDF yields the conformational entropy of protein folding from native-state coordinate variance. Or, using values of the conformational entropy change on folding, we can estimate the native state's conformational span. For example, for a 150-mer protein, equilibrium alpha-carbon displacements in the native ensemble would be 0.3-0.5 A based on T Delta S of 1.42 kcal/(mol residue).     

MINRMS: an efficient algorithm for determining protein structure similarity using root-mean-squared-distance

MOTIVATION: Existing algorithms for automated protein structure alignment generate contradictory results and are difficult to interpret. An algorithm which can provide a context for interpreting the alignment and uses a simple method to characterize protein structure similarity is needed. RESULTS: We describe a heuristic for limiting the search space for structure alignment comparisons between two proteins, and an algorithm for finding minimal root-mean-squared-distance (RMSD) alignments as a function of the number of matching residue pairs within this limited search space. Our alignment algorithm uses coordinates of alpha-carbon atoms to represent each amino acid residue and requires a total computation time of O(m(3) n(2)), where m and n denote the lengths of the protein sequences. This makes our method fast enough for comparisons of moderate-size proteins (fewer than approximately 800 residues) on current workstation-class computers and therefore addresses the need for a systematic analysis of multiple plausible shape similarities between two proteins using a widely accepted comparison metric.     

Activated conformations of the ras-gene-encoded p21 protein. 1. An energy-refined structure for the normal p21 protein complexed with GDP.

A complete three-dimensional structure for the ras-gene-encoded p21 protein with Gly 12 and Gln 61, bound to GDP, has been constructed in four stages using the available alpha-carbon coordinates as deposited in the Brookhaven National Laboratories Protein Data Bank. No all-atom structure has been made available despite the fact that the first crystallographic structure for the p21 protein was reported almost four years ago. In the p21 protein, if amino acid substitutions are made at any one of a number of different positions in the amino acid sequence, the protein becomes permanently activated and causes malignant transformation of normal cells or, in some cell lines, differentiation and maturation. For example, all amino acids except Gly and Pro at position 12 result in an oncogenic protein; all amino acids except Gln, Glu and Pro at position 61 likewise cause malignant transformation of cells. We have constructed our all-atom structure of the non-oncogenic protein from the x-ray structure in order to determine how oncogenic amino acid substitutions affect the three-dimensional structure of this protein. In Stage 1 we generated a poly-alanine backbone (except at Gly and Pro residues) through the alpha-carbon structure, requiring the individual Ala, Pro or Gly residues to conform to standard amino acid geometry and to form trans-planar peptide bonds. Since no alpha-carbon coordinates for residues 60-65 have been determined, these residues were modeled by generating them in the extended conformation and then subjecting them to molecular dynamics using the computer application DISCOVER and energy minimization using DISCOVER and the ECEPP (Empirical Conformational Energies for Peptides Program). In Stage 2, the positions of residues that are homologous to corresponding residues of bacterial elongation factor Tu (EF-Tu) to which p21 bears an overall 40% sequence homology, were determined from their corresponding positions in a high-resolution structure of EF-Tu. Non-homologous loops were taken from the structure generated in Stage 1 and were placed between the appropriate homologous segments so as to connect them. In Stage 3, all bad contacts that occurred in this resulting structure were removed, and the coordinates of the alpha-carbon atoms were forced to superimpose as closely as possible on the corresponding atoms of the reference (x-ray) structure. Then the side chain positions of residues of the non-homologous loop regions were modeled using a combination of molecular dynamics and energy minimization using DISCOVER and ECEPP respectively.(ABSTRACT TRUNCATED AT 400 WORDS)     

Crystallisation and preliminary analysis of glucose isomerase from Streptomyces albus

The glucose isomerase of Streptomyces albus has been crystallised from a dilute solution of magnesium chloride buffered at a pH of 6.8-7.0. The crystals are in the space group I222 with cell dimensions a = 93.9 A, b = 99.5 A and c = 102.9 A. There is one monomer of the tetrameric molecule per asymmetric unit of the crystal and the packing density is 2.93 A3.Da-1. The tetramer sits on the 222 symmetry point of the crystal. Native data have been recorded to a resolution of 1.9 A and the crystals diffract to about 1.5 A. The alpha-carbon coordinates of the Arthrobacter glucose isomerase and the backbone coordinates of the S. olivochromogenes enzyme determined by other groups have been oriented in the present cell. The structure is currently being refined. The binding of several metal ions to the two metal sites has been analysed.