Structural compromise of disallowed conformations in peptide and protein structures

Using a data set of 454 crystal structures of peptides and 80 crystal structures of non-homologous proteins solved at ultra high resolution of 1.2 A or better we have analyzed the occurrence of disallowed Ramachandran (phi, psi) angles. Out of 1492 and 13508 non-glycyl residues in peptides and proteins respectively 12 and 76 residues in the two datasets adopt clearly disallowed combinations of Ramachandran angles. These examples include a number of conformational points which are far away from any of the allowed regions in the Ramachandran map. According to the Ramachandran map a given (phi, psi) combination is considered disallowed when two non-bonded atoms in a system of two-linked peptide units with ideal geometry are prohibitively proximal in space. However, analysis of the disallowed conformations in peptide and protein structures reveals that none of the observations of disallowed conformations in the crystal structures correspond to a short contact between non-bonded atoms. A further analysis of deviations of bond lengths and angles, from the ideal peptide geometry, at the residue positions of disallowed conformations in the crystal structures suggest that individual bond lengths and angles are all within acceptable limits. Thus, it appears that the rare tolerance of disallowed conformations is possible by gentle and acceptable deviations in a number of bond lengths and angles, from ideal geometry, over a series of bonds resulting in a net gross effect of acceptable non-bonded inter-atomic distances.     

Protein loop modeling by using fragment assembly and analytical loop closure

Protein loops are often involved in important biological functions such as molecular recognition, signal transduction, or enzymatic action. The three dimensional structures of loops can provide essential information for understanding molecular mechanisms behind protein functions. In this article, we develop a novel method for protein loop modeling, where the loop conformations are generated by fragment assembly and analytical loop closure. The fragment assembly method reduces the conformational space drastically, and the analytical loop closure method finds the geometrically consistent loop conformations efficiently. We also derive an analytic formula for the gradient of any analytical function of dihedral angles in the space of closed loops. The gradient can be used to optimize various restraints derived from experiments or databases, for example restraints for preferential interactions between specific residues or for preferred backbone angles. We demonstrate that the current loop modeling method outperforms previous methods that employ residue‐based torsion angle maps or different loop closure strategies when tested on two sets of loop targets of lengths ranging from 4 to 12. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Discrete restraint-based protein modeling and the Calpha-trace problem

We present a novel de novo method to generate protein models from sparse, discretized restraints on the conformation of the main chain and side chain atoms. We focus on Calpha-trace generation, the problem of constructing an accurate and complete model from approximate knowledge of the positions of the Calpha atoms and, in some cases, the side chain centroids. Spatial restraints on the Calpha atoms and side chain centroids are supplemented by constraints on main chain geometry, phi/xi angles, rotameric side chain conformations, and inter-atomic separations derived from analyses of known protein structures. A novel conformational search algorithm, combining features of tree-search and genetic algorithms, generates models consistent with these restraints by propensity-weighted dihedral angle sampling. Models with ideal geometry, good phi/xi angles, and no inter-atomic overlaps are produced with 0.8 A main chain and, with side chain centroid restraints, 1.0 A all-atom root-mean-square deviation (RMSD) from the crystal structure over a diverse set of target proteins. The mean model derived from 50 independently generated models is closer to the crystal structure than any individual model, with 0.5 A main chain RMSD under only Calpha restraints and 0.7 A all-atom RMSD under both Calpha and centroid restraints. The method is insensitive to randomly distributed errors of up to 4 A in the Calpha restraints. The conformational search algorithm is efficient, with computational cost increasing linearly with protein size. Issues relating to decoy set generation, experimental structure determination, efficiency of conformational sampling, and homology modeling are discussed.     

Structure in solution of a four-helix lipid binding protein.

Because of the low solubility of lipids in water, intercellular and intracellular pathways of lipid transfer are necessary, e.g., for membrane formation. The mechanism by which lipids in vivo are transported from their site of biogenesis (endoplasmatic reticulum and the chloroplasts) to their place of action is unknown. Several small plant proteins with the ability to mediate transfer of radiolabeled phospholipids in vitro from liposomal donor membranes to mitochondrial and chloroplast acceptor membranes have been isolated, and a protein with this ability, the nonspecific lipid transfer protein (nsLTP) isolated from barley seeds (bLTP), has been studied here. The structure and the protein lipid interactions of lipid transfer proteins are relevant for the understanding of their function, and here we present the three-dimensional structure in solution of bLTP as determined by NMR spectroscopy. The 1H NMR spectrum of the 91-residue protein was assigned for more than 97% of the protein 1H atoms, and the structure was calculated on the basis of 813 distance restraints from 1H-1H nuclear Overhauser effects, four disulfide bond restraints, from dihedral angle restraints for 66 phi-angles, 61 chi 1 angles, and 2 chi 2 angles, and from 31 sets of hydrogen bond restraints. The solution structure of bLTP consists of four well-defined alpha-helices A-D (A, Cys 3-Gly 19; B, Gly 25-Ala 38; C, Arg 44-Gly 57; D, Leu 63-Cys 73), separated by three short loops that are less well defined and concluded by a well defined C-terminal peptide segment with no observable regular secondary structure. For the 17 structures that are used to represent the solution structure of bLTP, the RMS deviation to an average structure is 0.63 A +/- 0.04 A for backbone atoms and 0.93 A +/- 0.06 A for all heavy atoms. The secondary structure elements and their locations in the sequence resemble those of nsLTP from two other plant species, wheat and maize, whose structures were previously determined (Gincel E et al, 1995, Eur J Biochem 226:413-422; Shin DH et al, 1995, Structure 3:189-199). In bLTP, the residues analogous to those in maize nsLTP that constitute the palmitate binding site are forming a similar hydrophobic cavity and a potential acyl group binding site. Analysis of the solution structure of bLTP and bLTP in complex with a ligand might provide information on the conformational changes in the protein upon ligand binding and subsequently provide information on the mode of ligand uptake and release. In this work, we hope to establish a foundation for further work of determining the solution structure of bLTP in complex with palmitoyl coenzyme A, which is a suitable ligand, and subsequently to outline the mode of ligand binding.     

The normal modes of the gramicidin-A dimer channel.

The dynamics of the gramicidin-A dimer channel is studied in the harmonic approximation by a vibrational analysis of the atomic motions relative to their equilibrium positions. The system is represented by an empirical potential energy function, and all degrees of freedom (bonds lengths, bond angles, and torsional angles) are allowed to vary. The thermal fluctuations in the backbone dihedral angles phi and psi, atomic root mean square displacements, and the correlations between the different amide planes are computed. It is found that only adjacent dihedral psi i and phi i+1 are strongly correlated, while different hydrogen-bonded amide planes are only weakly correlated. Modes with relatively low vibrational frequencies (75-175 cm-1) make the dominant contributions to the carbonyl librations. The general flexibility of the structure and the role of carbonyl librations in the ion transport mechanism are discussed.     

Determination of three-dimensional structures of proteins by simulated annealing with interproton distance restraints. Application to crambin, potato carboxypeptidase inhibitor and barley serine proteinase inhibitor 2

An automated method, based on the principle of simulated annealing, is presented for determining the three-dimensional structures of proteins on the basis of short (less than 5 A) interproton distance data derived from nuclear Overhauser enhancement (NOE) measurements. The method makes use of Newton's equations of motion to increase temporarily the temperature of the system in order to search for the global minimum region of a target function comprising purely geometric restraints. These consist of interproton distances supplemented by bond lengths, bond angles, planes and soft van der Waals repulsion terms. The latter replace the dihedral, van der Waals, electrostatic and hydrogen-bonding potentials of the empirical energy function used in molecular dynamics simulations. The method presented involves the implementation of a number of innovations over our previous restrained molecular dynamics approach [Clore, G.M., Brünger, A.T., Karplus, M. and Gronenborn, A.M. (1986) J. Mol. Biol., 191, 523-551]. These include the development of a new effective potential for the interproton distance restraints whose functional form is dependent on the magnitude of the difference between calculated and target values, and the design and implementation of robust and fully automatic protocol. The method is tested on three systems: the model system crambin (46 residues) using X-ray structure derived interproton distance restraints, and potato carboxypeptidase inhibitor (CPI; 39 residues) and barley serine proteinase inhibitor 2 (BSPI-2; 64 residues) using experimentally derived interproton distance restraints. Calculations were carried out starting from the extended strands which had atomic r.m.s. differences of 57, 38 and 33 A with respect to the crystal structures of BSPI-2, crambin and CPI respectively. Unbiased sampling of the conformational space consistent with the restraints was achieved by varying the random number seed used to assign the initial velocities. This ensures that the different trajectories diverge during the early stages of the simulations and only converge later as more and more interproton distance restraints are satisfied. The average backbone atomic r.m.s. difference between the converged structures is 2.2 +/- 0.3 A for crambin (nine structures), 2.4 +/- 0.3 A for CPI (eight structures) and 2.5 +/- 0.2 A for BSPI-2 (five structures). The backbone atomic r.m.s. difference between the mean structures derived by averaging the coordinates of the converged structures and the corresponding X-ray structures is 1.2 A for crambin, 1.6 A for CPI and 1.7 A for BSPI-2.     

Strategy for supplementing structure calculations using limited data with hydrophobic distance restraints

Introductory biochemistry texts often note that the fold of a protein is completely defined when the dihedral angles phi and psi are known for each amino acid. This assertion was examined with torsion angle dynamics and simulated annealing (TAD/SA) calculations of protein G using only dihedral angle restraints. When all dihedral angles were restrained to within 1 degrees of the values of the X-ray structure, the TAD/SA structures gave a backbone root mean square deviation to the target of 4 A. Factors that contributed to divergence from the correct solution include deviations of peptide bonds from planarity, internal conflicts resulting from the nonuniform energies of different phi, psi combinations, and relaxation to extended conformations in the absence of long-range constraints. Simulations including hydrogen-bond restraints showed that even a few long-range contacts constrain the fold better than a complete set of accurate dihedral restraints. A procedure is described for TAD/SA calculations using hydrogen-bond restraints, idealized dihedral restraints for residues in regular secondary structures, and "hydrophobic distance restraints" derived from the positions of hydrophobic residues in the amino acid sequence. The hydrogen-bond restraints are treated as inviolable, whereas violated hydrophobic restraints are removed following reduction of restraint upper bounds from 2 to 1 times the predicted radius of gyration. The strategy was tested with simulated restraints from X-ray structures of proteins from different fold classes and NMR data for cold shock protein A that included only backbone chemical shifts and hydrogen bonds obtained from a long-range HNCO experiment.     

An atomic environment potential for use in protein structure prediction

We describe the derivation and testing of a knowledge-based atomic environment potential for the modeling of protein structural energetics. An analysis of the probabilities of atomic interactions in a dataset of high-resolution protein structures shows that the probabilities of non-bonded inter-atomic contacts are not statistically independent events, and that the multi-body contact frequencies are poorly predicted from pairwise contact potentials. A pseudo-energy function is defined that measures the preferences for protein atoms to be in a given microenvironment defined by the number of contacting atoms in the environment and its atomic composition. This functional form is tested for its ability to recognize native protein structures amongst an ensemble of decoy structures and a detailed relative performance comparison is made with a number of common functions used in protein structure prediction.     

Modeling of loops in protein structures

Comparative protein structure prediction is limited mostly by the errors in alignment and loop modeling. We describe here a new automated modeling technique that significantly improves the accuracy of loop predictions in protein structures. The positions of all nonhydrogen atoms of the loop are optimized in a fixed environment with respect to a pseudo energy function. The energy is a sum of many spatial restraints that include the bond length, bond angle, and improper dihedral angle terms from the CHARMM-22 force field, statistical preferences for the main-chain and side-chain dihedral angles, and statistical preferences for nonbonded atomic contacts that depend on the two atom types, their distance through space, and separation in sequence. The energy function is optimized with the method of conjugate gradients combined with molecular dynamics and simulated annealing. Typically, the predicted loop conformation corresponds to the lowest energy conformation among 500 independent optimizations. Predictions were made for 40 loops of known structure at each length from 1 to 14 residues. The accuracy of loop predictions is evaluated as a function of thoroughness of conformational sampling, loop length, and structural properties of native loops. When accuracy is measured by local superposition of the model on the native loop, 100, 90, and 30% of 4-, 8-, and 12-residue loop predictions, respectively, had <2 A RMSD error for the mainchain N, C(alpha), C, and O atoms; the average accuracies were 0.59 +/- 0.05, 1.16 +/- 0.10, and 2.61 +/- 0.16 A, respectively. To simulate real comparative modeling problems, the method was also evaluated by predicting loops of known structure in only approximately correct environments with errors typical of comparative modeling without misalignment. When the RMSD distortion of the main-chain stem atoms is 2.5 A, the average loop prediction error increased by 180, 25, and 3% for 4-, 8-, and 12-residue loops, respectively. The accuracy of the lowest energy prediction for a given loop can be estimated from the structural variability among a number of low energy predictions. The relative value of the present method is gauged by (1) comparing it with one of the most successful previously described methods, and (2) describing its accuracy in recent blind predictions of protein structure. Finally, it is shown that the average accuracy of prediction is limited primarily by the accuracy of the energy function rather than by the extent of conformational sampling.     

Theoretical conformational analysis of methylamide of N-acetyl-L-lysine]

The spatial structure of the methylamide of N-acetyl-L-lysine has been analysed taking into account non-bonded and electrostatic interactions, torsional energy, bond angles distortion and hydrogen bonding. Conformational capacities of the backbone and mutual dependence of spatial structures of the backbone and the side chain was described by conformational maps obtained by energy minimisation, the dihedral angles and the bond angles of the side chain being varied for every phi, psi point. Every possible combination for phi, psi, x1-x5-angles was used corresponding to the stable form of the backbone and to torsion potential minima of the initial approximations in the calculation of preferred conformations of the molecule. Comparisons are made between stable forms of the methylamide of N-acetyl-L-lysine and Lys residues in proteins with known structure.     

Local propensities and statistical potentials of backbone dihedral angles in proteins

The following three issues concerning the backbone dihedral angles of protein structures are presented. (1) How do the dihedral angles of the 20 amino acids depend on the identity and conformation of their nearest residues? (2) To what extent are the native dihedral angles determined by local (dihedral) potentials? (3) How to build a knowledge-based potential for a residue's dihedral angles, considering the identity and conformation of its nearest residues? We find that the dihedral angle distribution for a residue can significantly depend on the identity and conformation of its adjacent residues. These correlations are in sharp contrast to the Flory isolated-pair hypothesis. Statistical potentials are built for all combinations of residue triplets and depend on the dihedral angles between consecutive residues. First, a low-resolution potential is obtained, which only differentiates between the main populated basins in the dihedral angle density plots. Minimization of the dihedral potential for 125 test proteins reveals that most native alpha-helical residues (89%) and a large fraction of native beta-sheet residues (47%) adopt conformations close to their native one. For native loop residues, the percentage is 48%. It is also found that this fraction is higher for residues away from the ends of alpha or beta secondary structure elements. In addition, a higher resolution potential is built as a function of dihedral angles by a smoothing procedure and continuous functions interpolations. Monte Carlo energy minimization with this potential results in a lower fraction for native beta-sheet residues. Nevertheless, because of the higher flexibility and entropy of beta structures, they could be preferred under the influence of non-local interactions. In general, most alpha-helices and many beta-sheets are strongly determined by the local potential, while the conformations in loops and near the end of beta-sheets are more influenced by non-local interactions.     

CONFOLD: Residue‐residue contact‐guided ab initio protein folding

Predicted protein residue–residue contacts can be used to build three‐dimensional models and consequently to predict protein folds from scratch. A considerable amount of effort is currently being spent to improve contact prediction accuracy, whereas few methods are available to construct protein tertiary structures from predicted contacts. Here, we present an ab initio protein folding method to build three‐dimensional models using predicted contacts and secondary structures. Our method first translates contacts and secondary structures into distance, dihedral angle, and hydrogen bond restraints according to a set of new conversion rules, and then provides these restraints as input for a distance geometry algorithm to build tertiary structure models. The initially reconstructed models are used to regenerate a set of physically realistic contact restraints and detect secondary structure patterns, which are then used to reconstruct final structural models. This unique two‐stage modeling approach of integrating contacts and secondary structures improves the quality and accuracy of structural models and in particular generates better β‐sheets than other algorithms. We validate our method on two standard benchmark datasets using true contacts and secondary structures. Our method improves TM‐score of reconstructed protein models by 45% and 42% over the existing method on the two datasets, respectively. On the dataset for benchmarking reconstructions methods with predicted contacts and secondary structures, the average TM‐score of best models reconstructed by our method is 0.59, 5.5% higher than the existing method. The CONFOLD web server is available at http://protein.rnet.missouri.edu/confold/ . Proteins 2015; 83:1436–1449. © 2015 Wiley Periodicals, Inc.     

Vibrational approach to the dynamics of an α-helix

The dynamics of a finite α-helix have been studied in the harmonic approximation by a vibrational analysis of the atomic motions about their equilibrium positions. The system were represented by an empirical potential energy function, and all degrees of freedom (bond lengths, bond angles, and torsional angles) were allowed to vary. The complete results were compared with a more restrictive model in which the peptide dihedral angle was kept rigid; also, a model potential excluding hydrogen bonds was examined. Thermal fluctuations in the backbone dihedral angles ? and ψ are 12° to 15°. The fluctuations of adjacent dihedral angles are highly correlated, and the correlation pattern is affected by the flexibility of the peptide dihedral angle. Time-dependent autocorrelations in the motion of ? and ψ appear to decay due to dephasing in less than 1 psec, while the motions of the carbonyl oxygen and amide hydrogens out of the peptide plane are more harmonic. Length fluctuations have been evaluated and exhibit a strong end effect; the calculated elastic modulus is in agreement with other values. Rigid and adiabatic total energy surfaces corresponding to dihedral angle rotations in the middle of the helix have been obtained and compared with the quadratic approximation to those surfaces. The magnitudes and correlations between the fluctuations obtained by averaging over the adiabatic energy surface most closely resemble the vibrational results. Of particular interest is the fact that hydrogen bonds play a relatively small role in the local dihedral angle fluctuations, though the hydrogen bonds are important in the energy of overall length changes.     

Determination of three-dimensional structures of proteins from interproton distance data by hybrid distance geometry-dynamical simulated annealing calculations

A new hybrid distance space-real space method for determining three-dimensional structures of proteins on the basis of interproton distance restraints is presented. It involves the following steps: (i) the approximate polypeptide fold is obtained by generating a set of substructures comprising only a small subset of atoms by projection from multi-dimensional distance space into three-dimensional cartesian coordinate space using a procedure known as 'embedding'; (ii) all remaining atoms are then added by best fitting extended amino acids one residue at a time to the substructures; (iii) the resulting structures are used as the starting point for real space dynamical simulated annealing calculations. The latter involve heating the system to a high temperature followed by slow cooling in order to overcome potential barriers along the pathway towards the global minimum region. This is carried out by solving Newton's equations of motion. Unlike conventional restrained molecular dynamics, however, the non-bonded interactions are represented by a simple van der Waals repulsion term. The method is illustrated by calculations on crambin (46 residues) and the globular domain of histone H5 (79 residues). It is shown that the hybrid method is more efficient computationally and samples a larger region of conformational space consistent with the experimental data than full metric matrix distance geometry calculations alone, particularly for large systems.     

Minimalist representations and the importance of nearest neighbor effects in protein folding simulations

In order to investigate the level of representation required to simulate folding and predict structure, we test the ability of a variety of reduced representations to identify native states in decoy libraries and to recover the native structure given the advanced knowledge of the very broad native Ramachandran basin assignments. Simplifications include the removal of the entire side-chain or the retention of only the Cbeta atoms. Scoring functions are derived from an all-atom statistical potential that distinguishes between atoms and different residue types. Structures are obtained by minimizing the scoring function with a computationally rapid simulated annealing algorithm. Results are compared for simulations in which backbone conformations are sampled from a Protein Data Bank-based backbone rotamer library generated by either ignoring or including a dependence on the identity and conformation of the neighboring residues. Only when the Cbeta atoms and nearest neighbor effects are included do the lowest energy structures generally fall within 4 A of the native backbone root-mean square deviation (RMSD), despite the initial configuration being highly expanded with an average RMSD > or = 10 A. The side-chains are reinserted into the Cbeta models with minimal steric clash. Therefore, the detailed, all-atom information lost in descending to a Cbeta-level representation is recaptured to a large measure using backbone dihedral angle sampling that includes nearest neighbor effects and an appropriate scoring function.     

Identification of Allosteric Disulfides from Prestress Analysis

Disulfide bonds serve to form physical cross-links between residues in protein structures, thereby stabilizing the protein fold. Apart from this purely structural role, they can also be chemically active, participating in redox reactions, and they may even potentially act as allosteric switches controlling protein functions. Specific types of disulfide bonds have been identified in static protein structures from their distinctive pattern of dihedral bond angles, and the allosteric function of such bonds is purported to be related to the torsional strain they store. Using all-atom molecular-dynamics simulations for ∼700 disulfide bonded proteins, we analyzed the intramolecular mechanical forces in 20 classes of disulfide bonds. We found that two particular classes, the −RHStaple and the −/+RHHook disulfides, are indeed more stressed than other disulfide bonds, but the stress is carried primarily by stretching of the S-S bond and bending of the neighboring bond angles, rather than by dihedral torsion. This stress corresponds to a tension force of magnitude ∼200 pN, which is balanced by repulsive van der Waals interactions between the cysteine Cα atoms. We confirm stretching of the S-S bond to be a general feature of the −RHStaples and the −/+RHHooks by analyzing ∼20,000 static protein structures. Given that forced stretching of S-S bonds is known to accelerate their cleavage, we propose that prestress of allosteric disulfide bonds has the potential to alter the reactivity of a disulfide, thereby allowing us to readily switch between functional states.     

Comparison of normal mode analyses on a small globular protein in dihedral angle space and Cartesian coordinate space

Normal mode analyses on the protein, bovine pancreatic trypsin inhibitor, in dihedral angle space and Cartesian coordinate space are compared. In Cartesian coordinate space it is found that modes of frequencies lower than 30 cm(-1) contribute 80% of the total mean-square fluctuation and are represented almost completely by motions in the dihedral angles. Bond angle and length fluctuations dominate in modes above 200 cm(-1), but contribute less than 2% to the total mean-square fluctuation. In the low-frequency modes a good correspondence between patterns of atomic displacements was found, but on average the root-mean-square fluctuations of the Cartesian coordinate modes are 13% greater than their dihedral angle counterparts. The main effect of fluctuations in the bond angles and lengths, therefore, is to allow the dihedral angles to become more flexible. As the important subspaces determined from the two methods overlap considerably, dihedral angle space analysis can be applied to proteins too large for Cartesian coordinate space analysis.     

Geno3D: automatic comparative molecular modelling of protein

Geno3D (http://geno3d-pbil.ibcp.fr) is an automatic web server for protein molecular modelling. Starting with a query protein sequence, the server performs the homology modelling in six successive steps: (i) identify homologous proteins with known 3D structures by using PSI-BLAST; (ii) provide the user all potential templates through a very convenient user interface for target selection; (iii) perform the alignment of both query and subject sequences; (iv) extract geometrical restraints (dihedral angles and distances) for corresponding atoms between the query and the template; (v) perform the 3D construction of the protein by using a distance geometry approach and (vi) finally send the results by e-mail to the user.     

The solution structure of a B-DNA undecamer comprising a portion of the specific target site for the cAMP receptor protein in the gal operon. Refinement on the basis of interproton distance data.

A restrained least squares refinement of the solution structure of the double-stranded DNA undecamer 5'd(AAGTGT-GACAT).5'd(ATGTCACACTT) comprising a portion of the specific target site of the cAMP receptor protein in the gal operon is presented. The structure is refined on the basis of both distance and planarity restraints, 2331 in all. The distance restraints comprise 150 interproton distances determined from pre-steady state nuclear Overhauser enhancement measurements and 2159 other interatomic distances derived from idealized geometry (i.e., distances between covalently bonded atoms, between atoms defining fixed bond angles, and between atoms defining hydrogen bonding in AT and GC base pairs). Two refinements were carried out and in both cases the final RMS difference between the experimental and calculated interproton distances was 0.2 A. The difference between the two refined structures is small (overall RMS difference of 0.23 A) and represents the error in the refined coordinates. Although the refined structures have an overall B-type conformation there are large variations in many of the local conformational parameters including backbone and glycosidic bond torsion angles, helical twist and propellor twist, base roll and base tilt angles.