Molecular modeling of proteins including homology modeling, structure determination, and knowledge-based protein design requires tools to evaluate and refine three-dimensional protein structures. Steric clash is one of the artifacts prevalent in low-resolution structures and homology models. Steric clashes arise due to the unnatural overlap of any two non-bonding atoms in a protein structure. Usually, removal of severe steric clashes in some structures is challenging since many existing refinement programs do not accept structures with severe steric clashes. Here, we present a quantitative approach of identifying steric clashes in proteins by defining clashes based on the Van der Waals repulsion energy of the clashing atoms. We also define a metric for quantitative estimation of the severity of clashes in proteins by performing statistical analysis of clashes in high-resolution protein structures. We describe a rapid, automated and robust protocol, Chiron, which efficiently resolves severe clashes in low-resolution structures and homology models with minimal perturbation in the protein backbone. Benchmark studies highlight the efficiency and robustness of Chiron compared to other widely used methods. We provide Chiron as an automated web server to evaluate and resolve clashes in protein structures that can be further used for more accurate protein design.
Homology modeling; refinement; Chiron; Discrete Molecular Dynamics; Protein Design
We have developed and tested a complete set of nonbonded parameters for a continuum polarizable force field. Our analysis shows that the new continuum polarizable model is consistent with B3LYP/cc-pVTZ in modeling electronic response upon variation of dielectric environment. Comparison with experiment also shows that the new continuum polarizable model is reasonable, with similar accuracy as B3LYP/cc-pVTZ in reproduction of dipole moments of selected organic molecules in the gas phase. We have further tested the validity to interchange the Amber van der Waals parameters between the explicit and continuum polarizable force fields with a series of dimers. It can be found that the continuum polarizable model agrees well with MP2/cc-pVTZ, with deviations in dimer binding energies less than 0.9 kcal/mol in the aqueous dielectric environment. Finally we have optimized atomic cavity radii with respect to experimental solvation free energies of 177 training molecules. To validate the optimized cavity radii, we have tested these parameters against 176 test molecules. It is found that the optimized PB atomic cavity radii transfer well from the training set to the test set, with an overall root-mean-squared deviation of 1.30 kcal/mol, unsigned average error of 1.07 kacl/mol, and correlation coefficient of 92% for all 353 molecules in both the training and test sets. Given the development documented here, the next natural step is the construction of a full protein/nucleic acid force field within the new continuum polarization framework.
In the title complex, [Ni(C21H24N2O4)]·1.78H2O, the NiII ion has a slightly distorted planar geometry, coordinated by the two N and two O atoms of the tetradentate Schiff base ligand, with a mean deviation of 0.272 Å from the NiN2O2 plane. The N and O donor atoms are mutually cis. The dihedral angle between two benzene rings of the ligand is 38.86 (8)°. There are also three solvent water molecules, two of which lie across different crystallographic twofold rotation axes; one of these is partially occupied with a refined occupancy factor of 0.570 (7). The water molecules are linked together as tetramers in R
2(8) ring motifs, which also connect two neighbouring molecules of the complex through a network of O—H⋯O hydrogen bonds. The crystal structure is further stabilized by intermolecular C—H⋯O and C—H⋯π interactions, which link neighbouring molecules into extended chains along the b axis. Other interesting features of the crystal structure are the short intermolecular C⋯C [3.204 (3)–3.365 (3) Å] and the C⋯O [3.199 (2)–3.205 (2) Å] contacts which are shorter than the sum of the van der Waals radii of these atoms.
Specific binding between proteins plays a crucial role in molecular functions and biological processes. Protein binding interfaces and their atomic contacts are typically defined by simple criteria, such as distance-based definitions that only use some threshold of spatial distance in previous studies. These definitions neglect the nearby atomic organization of contact atoms, and thus detect predominant contacts which are interrupted by other atoms. It is questionable whether such kinds of interrupted contacts are as important as other contacts in protein binding. To tackle this challenge, we propose a new definition called beta (β) atomic contacts. Our definition, founded on the β-skeletons in computational geometry, requires that there is no other atom in the contact spheres defined by two contact atoms; this sphere is similar to the van der Waals spheres of atoms. The statistical analysis on a large dataset shows that β contacts are only a small fraction of conventional distance-based contacts. To empirically quantify the importance of β contacts, we design βACV, an SVM classifier with β contacts as input, to classify homodimers from crystal packing. We found that our βACV is able to achieve the state-of-the-art classification performance superior to SVM classifiers with distance-based contacts as input. Our βACV also outperforms several existing methods when being evaluated on several datasets in previous works. The promising empirical performance suggests that β contacts can truly identify critical specific contacts in protein binding interfaces. β contacts thus provide a new model for more precise description of atomic organization in protein quaternary structures than distance-based contacts.
The title compound, C14H11BrN4O4, comprises two crystallographically independent molecules (A and B) in the asymmetric unit. In molecule B, intramolecular bifurcated N—H⋯O and N—H⋯Br hydrogen bonds and in molecule A, an intramolecular N—H⋯O hydrogen bond generate S(6) ring motifs. The dihedral angle between the phenyl and benzene rings is 5.44 (6) in molecule A and 7.63 (6)° in molecule B. The ortho- and meta-nitro substituents make dihedral angles of 6.67 (15) and 2.26 (15)° to the attached benzene ring in molecule A and 6.37 (17) and 5.81 (16)° in molecule B. The Br atom in molecule B is disordered over two positions with a refined site-occupancy ratio of 0.61 (3):0.39 (3). Interesting features of the crystal structure are the short Br⋯N [3.257 (3)–3.294 (4) Å], Br⋯O [3.279 (3)–3.307 (4) Å] and O⋯O [2.9319 (16)–2.9995 (16) Å] contacts, which are shorter than the sum of the van der Waals radii of these atoms. The crystal structure is further stabilized by intermolecular C—H⋯O and π–π interactions [centroid–centroid distances = 3.6643 (8)–3.8514 (8) Å].
Contradicting evidence has been presented in the literature concerning the effectiveness of empirical contact energies for fold recognition. Empirical contact energies are calculated on the basis of information available from selected protein structures, with respect to a defined reference state, according to the quasi-chemical approximation. Protein-solvent interactions are estimated from residue solvent accessibility.
In the approach presented here, contact energies are derived from the potential of mean force theory, several definitions of contact are examined and their performance in fold recognition is evaluated on sets of decoy structures. The best definition of contact is tested, on a more realistic scenario, on all predictions including sidechains accepted in the CASP4 experiment. In 30 out of 35 cases the native structure is correctly recognized and best predictions are usually found among the 10 lowest energy predictions.
The definition of contact based on van der Waals radii of alpha carbon and side chain heavy atoms is seen to perform better than other definitions involving only alpha carbons, only beta carbons, all heavy atoms or only backbone atoms. An important prerequisite for the applicability of the approach is that the protein structure under study should not exhibit anomalous solvent accessibility, compared to soluble proteins whose structure is deposited in the Protein Data Bank. The combined evaluation of a solvent accessibility parameter and contact energy allows for an effective gross screening of predictive models.
The asymmetric unit of the title complex, [PdCl2(C12H16N3O)]·0.5C4H8O, consists of one palladium complex in a general position and one half tetrahydrofuran (THF) solvent molecule, with the O atom lying on a twofold rotation axis. The PdII atom is bound to one chelating imino nitroxide radical through two N atoms, one from the pyridyl ring and the other from the imidazoline ring. The coordination of the metal centre is completed by two Cl atoms in a cis configuration, leading to a quasi-square-planar coordination of the metal centre. The four atoms that define the PdII coordination environment and the eight atoms that belong to the pyridylimine fragment are coplanar, with no deviation larger than 0.087 (5) Å. In the crystal structure, intermolecular interactions shorter than the corresponding van der Waals radii sum are observed only between PdII complexes, and no short contact is observed around the THF molecule. Weak C—H⋯O and C—H⋯Cl interactions yield a two-dimensional network of complexes in the (101) plane.
Single-structure models derived from X-ray data do not adequately account for the inherent, functionally important dynamics of protein molecules. We generated ensembles of structures by time-averaged refinement, where local molecular vibrations were sampled by molecular-dynamics (MD) simulation whilst global disorder was partitioned into an underlying overall translation–libration–screw (TLS) model. Modeling of 20 protein datasets at 1.1–3.1 Å resolution reduced cross-validated Rfree values by 0.3–4.9%, indicating that ensemble models fit the X-ray data better than single structures. The ensembles revealed that, while most proteins display a well-ordered core, some proteins exhibit a ‘molten core’ likely supporting functionally important dynamics in ligand binding, enzyme activity and protomer assembly. Order–disorder changes in HIV protease indicate a mechanism of entropy compensation for ordering the catalytic residues upon ligand binding by disordering specific core residues. Thus, ensemble refinement extracts dynamical details from the X-ray data that allow a more comprehensive understanding of structure–dynamics–function relationships.
It has been clear since the early days of structural biology in the late 1950s that proteins and other biomolecules are continually changing shape, and that these changes have an important influence on both the structure and function of the molecules. X-ray diffraction can provide detailed information about the structure of a protein, but only limited information about how its structure fluctuates over time. Detailed information about the dynamic behaviour of proteins is essential for a proper understanding of a variety of processes, including catalysis, ligand binding and protein–protein interactions, and could also prove useful in drug design.
Currently most of the X-ray crystal structures in the Protein Data Bank are ‘snap-shots’ with limited or no information about protein dynamics. However, X-ray diffraction patterns are affected by the dynamics of the protein, and also by distortions of the crystal lattice, so three-dimensional (3D) models of proteins ought to take these phenomena into account. Molecular-dynamics (MD) computer simulations transform 3D structures into 4D ‘molecular movies’ by predicting the movement of individual atoms.
Combining MD simulations with crystallographic data has the potential to produce more realistic ensemble models of proteins in which the atomic fluctuations are represented by multiple structures within the ensemble. Moreover, in addition to improved structural information, this process—which is called ensemble refinement—can provide dynamical information about the protein. Earlier attempts to do this ran into problems because the number of model parameters needed was greater than the number of observed data points. Burnley et al. now overcome this problem by modelling local molecular vibrations with MD simulations and, at the same time, using a course-grain model to describe global disorder of longer length scales.
Ensemble refinement of high-resolution X-ray diffraction datasets for 20 different proteins from the Protein Data Bank produced a better fit to the data than single structures for all 20 proteins. Ensemble refinement also revealed that 3 of the 20 proteins had a ‘molten core’, rather than the well-ordered residues core found in most proteins: this is likely to be important in various biological functions including ligand binding, filament formation and enzymatic function. Burnley et al. also showed that a HIV enzyme underwent an order–disorder transition that is likely to influence how this enzyme works, and that similar transitions might influence the interactions between the small-molecule drug Imatinib (also known as Gleevec) and the enzymes it targets. Ensemble refinement could be applied to the majority of crystallography data currently being collected, or collected in the past, so further insights into the properties and interactions of a variety of proteins and other biomolecules can be expected.
protein; crystallography; structure; function; dynamics; None
Molecular dynamics (MD) simulations of cellulose microfibrils are pertinent to the paper, textile, and biofuels industries for their unique capacity to characterize dynamic behavior and atomic-level interactions with solvent molecules and cellulase enzymes. While high-resolution crystallographic data have established a solid basis for computational analysis of cellulose, previous work has demonstrated a tendency for modeled microfibrils to diverge from the linear experimental structure and adopt a twisted conformation. Here, we investigate the dependence of this twisting behavior on computational approximations and establish the theoretical basis for its occurrence. We examine the role of solvent, the effect of nonbonded force field parameters [partial charges and van der Waals (vdW) contributions], and the use of explicitly modeled oxygen lone pairs in both the solute and solvent. Findings suggest that microfibril twisting is favored by vdW interactions, and counteracted by both intrachain hydrogen bonds and solvent effects at the microfibril surface.
cellulose; microfibril twist; molecular dynamics; GLYCAM
The asymmetric unit of the title compound, [Mo(C19H16Cl4N2O2)O2], comprises two independent molecules (A and B). The geometry around the MoVI atom is distorted octahedral in each complex molecule, supported by two oxide O atoms and the N2O2 donor atoms of the coordinating ligand. The dihedral angle between the benzene rings is 74.96 (11) Å for molecule A and 76.05 (11) Å for molecule B. In the crystal, the B molecules are linked by pairs of C—H⋯Cl hydrogen bonds, forming inversion dimers. The crystal structure is further stabilized by C—H⋯π interactions. An interesting feature of the crystal structure is a Cl⋯Cl contact [3.3748 (18) Å], which is shorter than the sum of the van der Waals radii of Cl atoms (3.50 Å).
In the title complex, [Ni(C20H14N2O4)]·2H2O, the NiII ion is in an essentially square-planar geometry involving an N2O2 atom set of the tetradentate Schiff base ligand. The Ni atom lies on a crystallographic twofold rotation axis. The asymmetric unit contains one half-molecule of the complex and a water molecule. An intermolecular O—H⋯O hydrogen bond forms a four-membered ring, producing an R
2(4) ring motif involving a bifurcated hydrogen bond to the phenolate O atoms of the complex molecule. In the crystal structure, molecules are linked by π–π stacking interactions, with centroid–centroid distances in the range 3.5750 (11)–3.7750 (11) Å. As a result of the twofold symmetry, the central benzene ring makes the same dihedral angle of 15.75 (9)° with the two outer benzene rings. The dihedral angle between the two hydroxyphenyl rings is 13.16 (5)°. In the crystal structure, molecules are linked into infinite one-dimensional chains by directed four-membered O—H⋯O—H interactions along the c axis and are further connected by C—H⋯O and π–π stacking into a three-dimensional network. An interesting feature of the crystal structure is the short Ni⋯O, O⋯O and N⋯N interactions which are shorter than the sum of the van der Waals radii of the relevant atoms. The crystal structure is stabilized by intermolecular O—H⋯O and C—H⋯O hydrogen bonds and by π–π stacking interactions.
RCrane is a new tool for the partially automated building of RNA crystallographic models into electron-density maps of low or intermediate resolution. This tool helps crystallographers to place phosphates and bases into electron density and then automatically predicts and builds the detailed all-atom structure of the traced nucleotides.
RNA crystals typically diffract to much lower resolutions than protein crystals. This low-resolution diffraction results in unclear density maps, which cause considerable difficulties during the model-building process. These difficulties are exacerbated by the lack of computational tools for RNA modeling. Here, RCrane, a tool for the partially automated building of RNA into electron-density maps of low or intermediate resolution, is presented. This tool works within Coot, a common program for macromolecular model building. RCrane helps crystallographers to place phosphates and bases into electron density and then automatically predicts and builds the detailed all-atom structure of the traced nucleotides. RCrane then allows the crystallographer to review the newly built structure and select alternative backbone conformations where desired. This tool can also be used to automatically correct the backbone structure of previously built nucleotides. These automated corrections can fix incorrect sugar puckers, steric clashes and other structural problems.
RCrane; RNA model building
HIV-1 protease (PR) and two drug-resistant variants – PR with the V82A mutation (PRV82A) and PR with the I84V mutation (PRI84V) – were studied using reduced peptide analogs of five natural cleavage sites (CA-p2, p2-NC, p6pol-PR, p1-p6 and NC-p1) to understand the structural and kinetic changes. The common drug-resistant mutations V82A and I84V alter residues forming the substrate-binding site. Eight crystal structures were refined at resolutions of 1.10–1.60 Å. Differences in the PR–analog interactions depended on the peptide sequence and were consistent with the relative inhibition. Analog p6pol-PR formed more hydrogen bonds of P2 Asn with PR and fewer van der Waals contacts at P1′ Pro compared with those formed by CA-p2 or p2-NC in PR complexes. The P3 Gly in p1-p6 provided fewer van der Waals contacts and hydrogen bonds at P2–P3 and more water-mediated interactions. PRI84V showed reduced van der Waals interactions with inhibitor compared with PR, which was consistent with kinetic data. The structures suggest that the binding affinity for mutants is modulated by the conformational flexibility of the substrate analogs. The complexes of PRV82A showed smaller shifts of the main chain atoms of Ala82 relative to PR, but more movement of the peptide analog, compared to complexes with clinical inhibitors. PRV82A was able to compensate for the loss of interaction with inhibitor caused by mutation, in agreement with kinetic data, but substrate analogs have more flexibility than the drugs to accommodate the structural changes caused by mutation. Hence, these structures help to explain how HIV can develop drug resistance while retaining the ability of PR to hydrolyze natural substrates.
catalysis; crystal structure; drug resistance; HIV-1 protease; substrate analog; Nle, norleucine; PR, wild type HIV-1 protease; PRV82A, PR with the V82A mutation; PRI84V, PR with the I84V mutation
A method to accelerate the computation of structure factors from an electron density described by anisotropic and aspherical atomic form factors via fast Fourier transformation is described for the first time.
Recent advances in computational chemistry have produced force fields based on a polarizable atomic multipole description of biomolecular electrostatics. In this work, the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field is applied to restrained refinement of molecular models against X-ray diffraction data from peptide crystals. A new formalism is also developed to compute anisotropic and aspherical structure factors using fast Fourier transformation (FFT) of Cartesian Gaussian multipoles. Relative to direct summation, the FFT approach can give a speedup of more than an order of magnitude for aspherical refinement of ultrahigh-resolution data sets. Use of a sublattice formalism makes the method highly parallelizable. Application of the Cartesian Gaussian multipole scattering model to a series of four peptide crystals using multipole coefficients from the AMOEBA force field demonstrates that AMOEBA systematically underestimates electron density at bond centers. For the trigonal and tetrahedral bonding geometries common in organic chemistry, an atomic multipole expansion through hexadecapole order is required to explain bond electron density. Alternatively, the addition of interatomic scattering (IAS) sites to the AMOEBA-based density captured bonding effects with fewer parameters. For a series of four peptide crystals, the AMOEBA–IAS model lowered R
free by 20–40% relative to the original spherically symmetric scattering model.
scattering factors; aspherical; anisotropic; force fields; multipole; polarization; AMOEBA; bond density; direct summation; FFT; SGFFT; Ewald; PME
Non-covalent interactions hold the key to understanding many chemical, biological, and technological problems. Describing these non-covalent interactions accurately, including their positions in real space, constitutes a first step in the process of decoupling the complex balance of forces that define non-covalent interactions. Because of the size of macromolecules, the most common approach has been to assign van der Waals interactions (vdW), steric clashes (SC), and hydrogen bonds (HBs) based on pairwise distances between atoms according to their van der Waals radii. We recently developed an alternative perspective, derived from the electronic density: the Non-Covalent Interactions (NCI) index [J. Am. Chem. Soc. 2010, 132, 6498]. This index has the dual advantages of being generally transferable to diverse chemical applications and being very fast to compute, since it can be calculated from promolecular densities. Thus, NCI analysis is applicable to large systems, including proteins and DNA, where analysis of non-covalent interactions is of great potential value. Here, we describe the NCI computational algorithms and their implementation for the analysis and visualization of weak interactions, using both self-consistent fully quantum-mechanical, as well as promolecular, densities. A wide range of options for tuning the range of interactions to be plotted is also presented. To demonstrate the capabilities of our approach, several examples are given from organic, inorganic, solid state, and macromolecular chemistry, including cases where NCI analysis gives insight into unconventional chemical bonding. The NCI code and its manual are available for download at http://www.chem.duke.edu/~yang/software.htm
In the title complex, [Ni(C26H26N2O4)]·2H2O, the NiII ion, lying on a twofold crystallographic rotation axis, has a square-planar geometry, being coordinated by the N2O2 unit of the tetradentate Schiff base ligand. The asymmetric unit of the title compound comprises one-half of the complex molecule and one of the water molecules of crystallization. The water H atoms form bifurcated O—H⋯(O,O) hydrogen bonds with the O atoms of the phenolato and ethoxy groups with R
2(5) and R
2(6) ring motifs. The dihedral angle between the central benzene ring and the two outer benzene rings are 4.07 (11) and 3.99 (12)°. The dihedral angle between the two O–Ni–N coordination planes is only 0.77 (11)°. In the crystal structure, the molecules are linked together into extended chains along the c axis by intermolecular O—H⋯O and C—H⋯O interactions. An interesting feature of the crystal structure is a short intermolecular C ⋯ C [3.355 (3) Å] contact, which is shorter than the sum of the van der Waals radii. The crystal structure may be further stabilized by intermolecular π–π interactions [centroid–centroid distances in the range 3.5758 (13)–3.6337 (13) Å].
The title compound, C8H8F2, lies across a crystallographic inversion centre. The structure features short C⋯F [2.8515 (18) Å] and F⋯F [2.490 (4) Å] contacts, which are significantly shorter than the sum of the van der Waals radii of these atoms. The F atom and methylene H atoms are disordered over two positions with a site-occupancy ratio of 0.633 (3):0.367 (3). In the crystal structure, intermolecular C—H⋯F interactions link neighboring molecules into infinite chains along the b axis. In addition, C—H⋯π interactions link these molecules along , forming a two-dimensional network parallel to (101).
In the title complex, [Ni(C23H28N2O4)]·H2O, the NiII ion is coordinated by the N2O2 unit of the tetradentate Schiff base ligand in a slightly distorted planar geometry. The asymmetric unit of the title compound comprises one complex molecule and a water molecule of crystallization. The H atoms of the water molecule make bifurcated intermolecular hydrogen bonds with the O atoms of the phenolate and ethoxy groups with R
2(5) and R
2(6) ring motifs, which may, in part, influence the molecular configuration. The dihedral angle between the two benzene rings is 31.43 (5)°. The crystal structure is further stabilized by intermolecular C—H⋯O and C—H⋯π interactions, which link neighbouring molecules into one-dimensional extended chains along the a axis. An interesting feature of the crystal structure is the short intermolecular C⋯C [3.3044 (14) Å] contact which is shorter than the sum of the van der Waals radii.
In the crystal structure of the title compound, C20H23Br2N, the octyl chains are extended in an anti conformation and form a segregating bilayer, isolating rows of carbazole units. The carbazole moieties are engaged in offset π–π interactions; the smallest centroid-to-centroid distance is 4.2822 (11) Å. This offset packing motif allows the methylene group attached directly to the N atom to be involved in two short C—H⋯π interactions (H⋯centroid distances = 2.96 and 2.99 Å) with an adjacent carbazole. One of the Br atoms also participates in a short contact [3.5475 (3) Å] with a symmetry-related (−x, 1 − y, −z) Br atom. This value is significantly smaller than the sum of the van der Waals radii for bromine (3.70 Å).
The 3 centre-4 electrons (3c-4e) and the donor/acceptor or charge-transfer models for the
description of the chemical bond in linear three-body systems, such as I3− and related electron-rich (22 shell electrons) systems, are comparatively discussed on the
grounds of structural data from a search of the Cambridge Structural Database (CSD). Both models account for a total bond order of 1 in these systems, and while the former fits better symmetric systems, the latter describes better strongly asymmetric situations. The 3c-4e MO scheme shows that any linear system formed by three aligned closed-shell species (24 shell electrons overall) has reason to exist provided that two electrons are removed from it to afford a 22 shell electrons three-body system: all combinations of three closed-shell halides and/or chalcogenides are considered here. A survey of the literature shows that most of these three-body systems exist. With some exceptions, their structural features vary continuously from the symmetric situation showing two equal bonds to very asymmetric situations in which one bond approaches to the value corresponding to a single bond and the second one to the sum of the van der Waals radii of the involved atoms. This indicates that the potential energy surface of these three-body systems is fairly flat, and that the chemical surrounding of the chalcogen/halogen atoms can play an important role in freezing different structural situations; this is well documented for the I3− anion. The existence of correlations between the two bond distances and more importantly the linearity observed for all these systems, independently on the degree of their asymmetry, support the state of hypervalency of the central atom.
In the title compound, [ReBr(C16H12Cl2F2N2)(CO)3], the Re atom is in a slightly distorted octahedral coordination environment with the three carbonyl ligands having a fac configuration. The diimine ligand is equatorial and is bonded to the Re centre in an N,N′-bidentate chelating fashion, with a bite angle of 77.7 (2)°. The dihedral angle between the two benzene rings is 88.7 (6)°. In the crystal structure, there are F⋯O [2.856 (9) Å], Cl⋯C [3.150 (8) Å] and O⋯C [2.984 (10) Å] contacts which are shorter than the sum of the van der Waals radii for these atoms. In addition, symmetry-related molecules are linked via intermolecular C—H⋯O, C—H⋯Br and the F⋯O interactions into one-dimensional chains extending along the a axis. The crystal structure is further stabilized by intermolecular π–π interactions [centroid–centroid distance = 3.571 (5) Å].
The title compound, C24H25Br, packs efficiently in the crystal structure with no solvent-accessible voids and several intermolecular H⋯H contacts approximating the sum of the van der Waals radii. The molecule is quite crowded, with intramolecular Br⋯H and C⋯H contacts ca 0.38 and 0.30 Å, respectively, less than the sum of the corresponding van der Waals radii. All cyclohexyl rings adopt chair conformations with the ‘seat’ of the chair inclined at approximately 57–81° to the mean plane of the benzene ring, while those ortho to bromine have their centroids displaced in opposite directions from this plane.
The prediction of ligand binding or protein structure requires very accurate force field potentials – even small errors in force field potentials can make a 'wrong' structure (from the billions possible) more stable than the single, 'correct' one. However, despite huge efforts to optimize them, currently-used all-atom force fields are still not able, in a vast majority of cases, even to keep a protein molecule in its native conformation in the course of molecular dynamics simulations or to bring an approximate, homology-based model of protein structure closer to its native conformation.
A strict analysis shows that a specific coupling of multi-atom Van der Waals interactions with covalent bonding can, in extreme cases, increase (or decrease) the interaction energy by about 20–40% at certain angles between the direction of interaction and the covalent bond. It is also shown that on average multi-body effects decrease the total Van der Waals energy in proportion to the square root of the electronic component of dielectric permittivity corresponding to dipole-dipole interactions at small distances, where Van der Waals interactions take place.
The study shows that currently-ignored multi-atom Van der Waals interactions can, in certain instances, lead to significant energy effects, comparable to those caused by the replacement of atoms (for instance, C by N) in conventional pairwise Van der Waals interactions.
Hydrogen constitutes nearly half of all atoms in proteins and their positions are essential for analyzing hydrogen-bonding interactions and refining atomic-level structures. However, most protein structures determined by experiments or computer prediction lack hydrogen coordinates. We present a new algorithm, HAAD, to predict the positions of hydrogen atoms based on the positions of heavy atoms. The algorithm is built on the basic rules of orbital hybridization followed by the optimization of steric repulsion and electrostatic interactions. We tested the algorithm using three independent data sets: ultra-high-resolution X-ray structures, structures determined by neutron diffraction, and NOE proton-proton distances. Compared with the widely used programs CHARMM and REDUCE, HAAD has a significantly higher accuracy, with the average RMSD of the predicted hydrogen atoms to the X-ray and neutron diffraction structures decreased by 26% and 11%, respectively. Furthermore, hydrogen atoms placed by HAAD have more matches with the NOE restraints and fewer clashes with heavy atoms. The average CPU cost by HAAD is 18 and 8 times lower than that of CHARMM and REDUCE, respectively. The significant advantage of HAAD in both the accuracy and the speed of the hydrogen additions should make HAAD a useful tool for the detailed study of protein structure and function. Both an executable and the source code of HAAD are freely available at http://zhang.bioinformatics.ku.edu/HAAD.
The CuII atom in the title complex, [Cu(C18H21N2O2)(C2H3O2)], is tetracoordinated by two N atoms and two O atoms, of which one O atom is attributed to the acetate group and the other atoms are from the tridentate salicylideneiminate ligand, forming a slight distorted square-planar environment. The other acetate O atom exhibits a very weak intramolecular interaction toward the Cu atom, the Cu—O distance of 2.771 (2) Å being shorter than the van der Waals radii for Cu and O atoms (2.92 Å). Furthermore, there are weak intermolecular interactions, in which the bonding O atom of the acetate group can bridge to the Cu atom of another complex, and the distance of 2.523 (2) Å is about 0.4 Å shorter than the van der Waals Cu—O distance in other crystal structures.