Normal mode analysis with molecular geometry restraints: bridging molecular mechanics and elastic models

A new method for normal mode analysis is reported for all-atom structures using molecular geometry restraints (MGR). Similar to common molecular mechanics force fields, the MGR potential contains short- and long-range terms. The short-range terms are defined by molecular geometry, i.e., bond lengths, angles and dihedrals; the long-range term is similar to that in elastic network models. Each interaction term uses a single force constant parameter, and is determined by fitting against a set of known structures. Tests on proteins/non-proteins show that MGR can produce low frequency eigenvectors closer to all-atom force-field-based methods than conventional elastic network models. Moreover, the “tip effect”, found in low frequency eigenvectors in elastic network models, is reduced in MGR to the same level of the modes produced by force-field-based methods. The results suggest that molecular geometry plays an important role, in addition to molecular shape, in determining low frequency deformational motions. MGR does not require initial energy minimization, and is applicable to almost any structure, including the one with missing atoms, bad contacts, or bad geometries, frequently observed in low-resolution structure determination and refinement. The method bridges the two major representations in normal mode analyses, i.e., the molecular mechanics models and elastic network models.     

Protein Loop Modeling Using a New Hybrid Energy Function and Its Application to Modeling in Inaccurate Structural Environments

Protein loop modeling is a tool for predicting protein local structures of particular interest, providing opportunities for applications involving protein structure prediction and de novo protein design. Until recently, the majority of loop modeling methods have been developed and tested by reconstructing loops in frameworks of experimentally resolved structures. In many practical applications, however, the protein loops to be modeled are located in inaccurate structural environments. These include loops in model structures, low-resolution experimental structures, or experimental structures of different functional forms. Accordingly, discrepancies in the accuracy of the structural environment assumed in development of the method and that in practical applications present additional challenges to modern loop modeling methods. This study demonstrates a new strategy for employing a hybrid energy function combining physics-based and knowledge-based components to help tackle this challenge. The hybrid energy function is designed to combine the strengths of each energy component, simultaneously maintaining accurate loop structure prediction in a high-resolution framework structure and tolerating minor environmental errors in low-resolution structures. A loop modeling method based on global optimization of this new energy function is tested on loop targets situated in different levels of environmental errors, ranging from experimental structures to structures perturbed in backbone as well as side chains and template-based model structures. The new method performs comparably to force field-based approaches in loop reconstruction in crystal structures and better in loop prediction in inaccurate framework structures. This result suggests that higher-accuracy predictions would be possible for a broader range of applications. The web server for this method is available at http://galaxy.seoklab.org/loop with the PS2 option for the scoring function.     

Protein structure prediction force fields: Parametrization with quasi-newtonian dynamics

We present an unusual method for parametrizing low-resolution force fields of the type used for protein structure prediction. Force field parameters were-determined by assigning each a fictitious mass and using a quasi-molecular dynamics algorithm in parameter space. The quasi-energy term favored folded native structures and specifically penalized folded nonnative structures. The force field was generated after optimizing less than 70 adjustable parameters, but shows a strong ability to discriminate between native structures and compact misfolded-alternatives. The functional form of the force field was chosen as in molecular mechanics and is not table-driven. It is continuous with continuous derivatives and is thus suitable for use with algorithms such as energy minimization or newtonian dynamics. Proteins 27:367–384, 1997. © 1997 Wiley-Liss, Inc.     

Major groove width variations in RNA structures determined by NMR and impact of <Superscript>13</Superscript>C residual chemical shift anisotropy and <Superscript>1</Superscript>H–<Superscript>13</Superscript>C residual dipolar coupling on refinement

Ribonucleic acid structure determination by NMR spectroscopy relies primarily on local structural restraints provided by ¹H– ¹H NOEs and J-couplings. When employed loosely, these restraints are broadly compatible with A- and B-like helical geometries and give rise to calculated structures that are highly sensitive to the force fields employed during refinement. A survey of recently reported NMR structures reveals significant variations in helical parameters, particularly the major groove width. Although helical parameters observed in high-resolution X-ray crystal structures of isolated A-form RNA helices are sensitive to crystal packing effects, variations among the published X-ray structures are significantly smaller than those observed in NMR structures. Here we show that restraints derived from aromatic ¹H– ¹³C residual dipolar couplings (RDCs) and residual chemical shift anisotropies (RCSAs) can overcome NMR restraint and force field deficiencies and afford structures with helical properties similar to those observed in high-resolution X-ray structures.     

Increasing the precision of comparative models with YASARA NOVA--a self-parameterizing force field

One of the conclusions drawn at the CASP4 meeting in Asilomar was that applying various force fields during refinement of template-based models tends to move predictions in the wrong direction, away from the experimentally determined coordinates. We have derived an all-atom force field aimed at protein and nucleotide optimization in vacuo (NOVA), which has been specifically designed to avoid this problem. NOVA resembles common molecular dynamics force fields but has been automatically parameterized with two major goals: (i) not to make high resolution X-ray structures worse and (ii) to improve homology models built by WHAT IF. Force-field parameters were not required to be physically correct; instead, they were optimized with random Monte Carlo moves in force-field parameter space, each one evaluated by simulated annealing runs of a 50-protein optimization set. Errors inherent to the approximate force-field equation could thus be canceled by errors in force-field parameters. Compared with the optimization set, the force field did equally well on an independent validation set and is shown to move in silico models closer to reality. It can be applied to modeling applications as well as X-ray and NMR structure refinement. A new method to assign force-field parameters based on molecular trees is also presented. A NOVA server is freely accessible at http://www.yasara.com/servers     

Rapid and accurate structure determination of coiled-coil domains using NMR dipolar couplings: application to cGMP-dependent protein kinase Ialpha

Coiled-coil motifs play essential roles in protein assembly and molecular recognition, and are therefore the targets of many ongoing structural and functional studies. However, owing to the dynamic nature of many of the smaller coiled-coil domains, crystallization for X-ray studies is very challenging. Determination of elongated structures using standard NMR approaches is inefficient and usually yields low-resolution structures due to accumulation of small errors over long distances. Here we describe a solution NMR approach based on residual dipolar couplings (RDCs) for rapid and accurate structure determination of coiled-coil dimers. Using this approach, we were able to determine the high-resolution structure of the coiled-coil domain of cGMP-dependent protein kinase Ialpha, a protein of previously unknown structure that is critical for physiological relaxation of vascular smooth muscle. This approach can be extended to solve coiled-coil structures with higher order assemblies.     

Applying an empirical hydropathic forcefield in refinement may improve low-resolution protein X-ray crystal structures

Background

The quality of X-ray crystallographic models for biomacromolecules refined from data obtained at high-resolution is assured by the data itself. However, at low-resolution, >3.0 Å, additional information is supplied by a forcefield coupled with an associated refinement protocol. These resulting structures are often of lower quality and thus unsuitable for downstream activities like structure-based drug discovery.

Methodology

An X-ray crystallography refinement protocol that enhances standard methodology by incorporating energy terms from the HINT (Hydropathic INTeractions) empirical forcefield is described. This protocol was tested by refining synthetic low-resolution structural data derived from 25 diverse high-resolution structures, and referencing the resulting models to these structures. The models were also evaluated with global structural quality metrics, e.g., Ramachandran score and MolProbity clashscore. Three additional structures, for which only low-resolution data are available, were also re-refined with this methodology.

Results

The enhanced refinement protocol is most beneficial for reflection data at resolutions of 3.0 Å or worse. At the low-resolution limit, ≥4.0 Å, the new protocol generated models with Cα positions that have RMSDs that are 0.18 Å more similar to the reference high-resolution structure, Ramachandran scores improved by 13%, and clashscores improved by 51%, all in comparison to models generated with the standard refinement protocol. The hydropathic forcefield terms are at least as effective as Coulombic electrostatic terms in maintaining polar interaction networks, and significantly more effective in maintaining hydrophobic networks, as synthetic resolution is decremented. Even at resolutions ≥4.0 Å, these latter networks are generally native-like, as measured with a hydropathic interactions scoring tool.     

Application of a genetic algorithm in the conformational analysis of methylene-acetal-linked thymine dimers in DNA: Comparison with distance geometry calculations

The three-dimensional spatial structure of a methylene-acetal-linked thymine dimer presentin a 10 base-pair (bp) sense–antisense DNA duplex was studied with a geneticalgorithm designed to interpret NOE distance restraints. Trial solutions were represented bytorsion angles. This means that bond angles for the dimer trial structures are kept fixed duringthe genetic algorithm optimization. Bond angle values were extracted from a 10 bpsense–antisense duplex model that was subjected to energy minimization by means ofa modified AMBER force field. A set of 63 proton–proton distance restraints definingthe methylene-acetal-linked thymine dimer was available. The genetic algorithm minimizesthe difference between distances in the trial structures and distance restraints. A largeconformational search space could be covered in the genetic algorithm optimization byallowing a wide range of torsion angles. The genetic algorithm optimization in all cases ledto one family of structures. This family of the methylene-acetal-linked thymine dimer in theduplex differs from the family that was suggested from distance geometry calculations. It isdemonstrated that the bond angle geometry around the methylene-acetal linkage plays animportant role in the optimization.     

Evaluation of PM3(tm) as a Geometry Generator in Theoretical Studies of Transition-Metal-Based Catalysts for Polymerizing Olefins

The PM3(tm) method has been applied to several systems of relevance to catalytic polymerization of olefins, for catalysts containing Ti, Zr or Cr. With some exceptions, PM3(tm) calculations reproduce experimental geometries of stable, closed-shell, precursors well. For stationary points along the path of monomer insertion into a metal-alkyl bond, the comparison is made to structures obtained by optimization using various first-principle methods. Large errors are uncovered for the transient structures, in particular pertaining to metal-ethylene coordination and agostic interactions. The energy profiles for four insertion reactions are computed by gradient-corrected density functional (DFTG) methods, using molecular structures taken from PM3(tm) and first-principle geometry optimizations, respectively. The chromium case is promising, giving values for the barrier to monomer insertion of 11 and 9 kcal/mol based on PM3(tm) and DFTG geometries, respectively. The Ti- and Zr-based systems are predicted to proceed downhill based on PM3(tm) structures, whereas small barriers are found when using first-principle structures. A hybrid PM3(tm)-DFTG procedure is suggested for geometry optimization, which facilitates an accurate estimate of the barrier when applied to one of the zirconium systems.     

Determining protein topology from skeletons of secondary structures

We report a novel computational procedure for determining protein native topology, or fold, by defining loop connectivity based on skeletons of secondary structures that can usually be obtained from low to intermediate-resolution density maps. The procedure primarily involves a knowledge-based geometry filter followed by an energetics-based evaluation. It was tested on a large set of skeletons covering a wide range of protein architecture, including one modeled from an experimentally determined 7.6A cryo-electron microscopy (cryo-EM) density map. The results showed that the new procedure could effectively deduce protein folds without high-resolution structural data, a feature that could also be used to recognize native fold in structure prediction and to interpret data in fields like structure genomics. Most importantly, in the energetics-based evaluation, it was revealed that, despite the inevitable errors in the artificially constructed structures and limited accuracy of knowledge-based potential functions, the average energy of an ensemble of structures with slightly different configurations around the native skeleton is a much more robust parameter for marking native topology than the energy of individual structures in the ensemble. This result implies that, among all the possible topology candidates for a given skeleton, evolution has selected the native topology as the one that can accommodate the largest structural variations, not the one rigidly trapped in a deep, but narrow, conformational energy well.     

Accurate geometries for “Mountain pass” regions of the Ramachandran plot using quantum chemical calculations

Unusual local arrangements of protein in Ramachandran space are not well represented by standard geometry tools used in either protein structure refinement using simple harmonic geometry restraints or in protein simulations using molecular mechanics force fields. In contrast, quantum chemical computations using small poly‐peptide molecular models can predict accurate geometries for any well‐defined backbone Ramachandran orientation. For conformations along transition regions—ϕ from −60 to 60°—a very good agreement with representative high‐resolution experimental X‐ray (≤1.5 Å) protein structures is obtained for both backbone C⁻¹‐N‐C_α angle and the nonbonded O⁻¹…C distance, while “standard geometry” leads to the “clashing” of O…C atoms and Amber FF99SB predicts distances too large by about 0.15 Å. These results confirm that quantum chemistry computations add valuable support for detailed analysis of local structural arrangements in proteins, providing improved or missing data for less understood high‐energy or unusual regions.     

Protein structure determination using a database of interatomic distance probabilities

The accelerated pace of genomic sequencing has increased the demand for structural models of gene products. Improved quantitative methods are needed to study the many systems (e.g., macromolecular assemblies) for which data are scarce. Here, we describe a new molecular dynamics method for protein structure determination and molecular modeling. An energy function, or database potential, is derived from distributions of interatomic distances obtained from a database of known structures. X-ray crystal structures are refined by molecular dynamics with the new energy function replacing the Van der Waals potential. Compared to standard methods, this method improved the atomic positions, interatomic distances, and side-chain dihedral angles of structures randomized to mimic the early stages of refinement. The greatest enhancement in side-chain placement was observed for groups that are characteristically buried. More accurate calculated model phases will follow from improved interatomic distances. Details usually seen only in high-resolution refinements were improved, as is shown by an R-factor analysis. The improvements were greatest when refinements were carried out using X-ray data truncated at 3.5 A. The database potential should therefore be a valuable tool for determining X-ray structures, especially when only low-resolution data are available.     

Protein fold recognition without Boltzmann statistics or explicit physical basis.

We present a fast method for finding optimal parameters for a low-resolution (threading) force field intended to distinguish correct from incorrect folds for a given protein sequence. In contrast to other methods, the parameterization uses information from >10(7) misfolded structures as well as a set of native sequence-structure pairs. In addition to testing the resulting force field's performance on the protein sequence threading problem, results are shown that characterize the number of parameters necessary for effective structure recognition.     

A hierarchical approach to all-atom protein loop prediction

The application of all-atom force fields (and explicit or implicit solvent models) to protein homology-modeling tasks such as side-chain and loop prediction remains challenging both because of the expense of the individual energy calculations and because of the difficulty of sampling the rugged all-atom energy surface. Here we address this challenge for the problem of loop prediction through the development of numerous new algorithms, with an emphasis on multiscale and hierarchical techniques. As a first step in evaluating the performance of our loop prediction algorithm, we have applied it to the problem of reconstructing loops in native structures; we also explicitly include crystal packing to provide a fair comparison with crystal structures. In brief, large numbers of loops are generated by using a dihedral angle-based buildup procedure followed by iterative cycles of clustering, side-chain optimization, and complete energy minimization of selected loop structures. We evaluate this method by using the largest test set yet used for validation of a loop prediction method, with a total of 833 loops ranging from 4 to 12 residues in length. Average/median backbone root-mean-square deviations (RMSDs) to the native structures (superimposing the body of the protein, not the loop itself) are 0.42/0.24 A for 5 residue loops, 1.00/0.44 A for 8 residue loops, and 2.47/1.83 A for 11 residue loops. Median RMSDs are substantially lower than the averages because of a small number of outliers; the causes of these failures are examined in some detail, and many can be attributed to errors in assignment of protonation states of titratable residues, omission of ligands from the simulation, and, in a few cases, probable errors in the experimentally determined structures. When these obvious problems in the data sets are filtered out, average RMSDs to the native structures improve to 0.43 A for 5 residue loops, 0.84 A for 8 residue loops, and 1.63 A for 11 residue loops. In the vast majority of cases, the method locates energy minima that are lower than or equal to that of the minimized native loop, thus indicating that sampling rarely limits prediction accuracy. The overall results are, to our knowledge, the best reported to date, and we attribute this success to the combination of an accurate all-atom energy function, efficient methods for loop buildup and side-chain optimization, and, especially for the longer loops, the hierarchical refinement protocol.     

Force field parameters for S-nitrosocysteine and molecular dynamics simulations of S-nitrosated thioredoxin

Estimation of structural perturbation induced by S-nitrosation is important to understand the mode of cellular signal transduction mediated by nitric oxide. Crystal structures of S-nitrosated proteins have been solved only for a few cases, however, so that molecular dynamics simulation may provide an alternative tool for probing structural perturbation. In this study AMBER-99 force field parameters for S-nitrosocysteine were developed and applied to molecular dynamics simulations of S-nitrosated thioredoxin. Geometry optimization at the level of HF/6-31G∗ was followed by a restrained electrostatic potential charge-fitting to obtain the atomic charges of S-nitrosocysteine. Force constants for bonds and angles were obtained from generalized AMBER force field. Torsional force constants for CC-SN and CS-NO were determined by fitting the torsional profiles obtained from geometry optimization with those from molecular mechanical energy minimization. Finally molecular dynamics simulations were performed with theses parameters on oxidized and reduced thioredoxin with and without S-nitrosocysteine. In all cases the root-mean-square deviations of α-carbons yielded well-behaved trajectories. The CC-SH dihedral angle which fluctuated severely during the simulation became quiet upon S-nitrosation. In conclusion the force field parameters developed in this study for S-nitrosocysteine appear to be suitable for molecular dynamics simulations of S-nitrosated proteins.     

Positioning hydrogen atoms by optimizing hydrogen-bond networks in protein structures

A method is presented that positions polar hydrogen atoms in protein structures by optimizing the total hydrogen bond energy. For this goal, an empirical hydrogen bond force field was derived from small molecule crystal structures. Bifurcated hydrogen bonds are taken into account. The procedure also predicts ionization states of His, Asp, and Glu residues. During optimization, sidechain conformations of His, Gln, and Asn residues are allowed to change their last χ angle by 180° to compensate for crystallographic misassignments. Crystal structure symmetry is taken into account where appropriate. The results can have significant implications for molecular dynamics simulations, protein engineering, and docking studies. The largest impact, however, is in protein structure verification: over 85% of protein structures tested can be improved by using our procedure. Proteins 26:363–376 © 1996 Wiley-Liss, Inc.     

Derivation of class II force fields. VI. Carbohydrate compounds and anomeric effects

The methodology for deriving class II force fields has been applied to acetal, hemiacetal, and carbohydrate compounds. A set of eighteen model compounds containing one or more anomeric centers was selected for generating the quantum mechanical energy surface, from which the force field was derived and the functional form assessed. The quality of the fit was tested by comparing the energy surface predicted by the force field with ab initio results. Structural, energetic, and dynamic properties (vibrational frequencies) were analyzed. In addition, α and β anomeric equilibrium structures and energies of 2-methoxytetrahydropyran, 2-deoxyribose, and glucose were computed at the HF/6-31G* and higher ab initio levels. These calculations provide test data from molecules outside the training set used to derive the force field. The quantum calculations were used to assess the ability of the class II force field and two quadratic diagonal (class I) force fields, CVFF, and Homans' extension of the AMBER force field, to account for the anomeric effects on the structural and energetic properties of carbohydrate systems. These class I force fields are unable to account for observed structural and energetic trends, exhibiting deviations as large as 5 kcal/mol in relative energies. The class II force field, on the other hand, is shown to reproduce anomeric structural as well as energetic differences. An energy component analysis of this force field shows that the anomeric differences are dominated by torsional energies, although coupling terms, especially angle/torsion, also make significant contributions (roughly 1 kcal/mol in glucose). In addition, the force field accurately accounts for both anomeric and exo-anomeric energy differences in 2-methoxytetrahydropyran, and anomeric energy differences in 2-deoxyribose and glucose. © 1998 John Wiley & Sons, Inc. Biopoly 45: 435–468, 1998     

Protein-DNA docking with a coarse-grained force field

ABSTRACT: BACKGROUND: Protein-DNA interactions are important for many cellular processes, however structural knowledge for a large fraction of known and putative complexes is still lacking. Computational docking methods aim at the prediction of complex architecture given detailed structures of its constituents. They are becoming an increasingly important tool in the field of macromolecular assemblies, complementing particularly demanding protein-nucleic acids X ray crystallography and providing means for the refinement and integration of low resolution data coming from rapidly advancing methods such as cryoelectron microscopy. RESULTS: We present a new coarse-grained force field suitable for protein-DNA docking. The force field is an extension of previously developed parameter sets for protein-RNA and protein-protein interactions. The docking is based on potential energy minimization in translational and orientational degrees of freedom of the binding partners. It allows for fast and efficient systematic search for native-like complex geometry without any prior knowledge regarding binding site location. CONCLUSIONS: We find that the force field gives very good results for bound docking. The quality of predictions in the case of unbound docking varies, depending on the level of structural deviation from bound geometries. We analyze the role of specific protein-DNA interactions on force field performance, both with respect to complex structure prediction, and the reproduction of experimental binding affinities. We find that such direct, specific interactions only partially contribute to protein-DNA recognition, indicating an important role of shape complementarity and sequence-dependent DNA internal energy, in line with the concept of indirect protein-DNA readout mechanism.     

Conformational transitions of flanking purines in HIV-1 RNA dimerization initiation site kissing complexes studied by CHARMM explicit solvent molecular dynamics

Dimerization of HIV-1 genomic RNA is initiated by kissing loop interactions at the Dimerization Initiation Site (DIS). Dynamics of purines that flank the 5' ends of the loop-loop helix in HIV-1 DIS kissing complex were explored using explicit solvent molecular dynamics (MD) simulations with the CHARMM force field. Multiple MD simulations (200 ns in total) of X-ray structures for HIV-1 DIS Subtypes A, B, and F revealed conformational variability of flanking purines. In particular, the flanking purines, which in the starting X-ray structures are bulged-out and stack in pairs, formed a consecutive stack of four bulged-out adenines at the beginning of several simulations. This conformation is seen in the crystal structure of DIS Subtype F with no interference from crystal packing, and was frequently reported in our preceding MD studies performed with the AMBER force field. However, as CHARMM simulations progressed, the four continuously stacked adenines showed conformational transitions from the bulged-out into the bulged-in geometries. Although such an arrangement has not been seen in any X-ray structure, it has been suggested by a recent NMR investigation. In CHARMM simulations, in the longer time scale, the flanking purines display the tendency to move to bulged-in conformations. This is in contrast with the AMBER simulations, which indicate a modest prevalence for bulged-out flanking base positions in line with the X-ray data. The simulations also suggest that the intermolecular stacking between purines from the opposite hairpins can additionally stabilize the kissing complex.