Crystal packing of pyrimidine nucleosides--a study in terms of empirical van der Waals' potential energy

Molecular interactions in 32 crystal structures of pyrimidine nucleosides and nucleoside derivatives have been studied in terms of empirical van der Waals' energy. The stacking patterns have been classified into three types according to the symmetry operations involved within the pattern. Halogen and sulphur atoms were included in the calculations where necessary. Model columns of stacked molecules were set up in a computer calculation giving the energy for different amounts of base overlap. There was a tendency for the crystal positions of the molecules to agree with the minima of the energy maps, which showed the predominance of the van der Waals' forces in determining the base-stacking arrangement. The position of the energy minimum was correlated with the molecular conformation defined by the C-N glycosidic torsion angle.     

Optimization of van der Waals energy for protein side-chain placement and design

Computational determination of optimal side-chain conformations in protein structures has been a long-standing and challenging problem. Solving this problem is important for many applications including homology modeling, protein docking, and for placing small molecule ligands on protein-binding sites. Programs available as of this writing are very fast and reasonably accurate, as measured by deviations of side-chain dihedral angles; however, often due to multiple atomic clashes, they produce structures with high positive energies. This is problematic in applications where the energy values are important, for example when placing small molecules in docking applications; the relatively small binding energy of the small molecule is drowned by the large energy due to atomic clashes that hampers finding the lowest energy state of the docked ligand. To address this we have developed an algorithm for generating a set of side-chain conformations that is dense enough that at least one of its members would have a root mean-square deviation of no more than R Å from any possible side-chain conformation of the amino acid. We call such a set a side-chain cover set of order R for the amino acid. The size of the set is constrained by the energy of the interaction of the side chain to the backbone atoms. Then, side-chain cover sets are used to optimize the conformation of the side chains given the coordinates of the backbone of a protein. The method we use is based on a variety of dead-end elimination methods and the recently discovered dynamic programming algorithm for this problem. This was implemented in a computer program called Octopus where we use side-chain cover sets with very small values for R, such as 0.1 Å, which ensures that for each amino-acid side chain the set contains a conformation with a root mean-square deviation of, at most, R from the optimal conformation. The side-chain dihedral-angle accuracy of the program is comparable to other implementations; however, it has the important advantage that the structures produced by the program have negative energies that are very close to the energies of the crystal structure for all tested proteins.     

Sequence Structure of van der Waals Locks in Proteins

Abstract

Recent works has suggested that proteins in early evolution have gone through a stage of closed loop elements with a typical contour size of 25–35 residues. These closed loops are still the elementary protein units to these days, and can be used to spell out protein sequence/structure relationship through a relatively small number of protein prototypes. In this study we aimed to identify the sequences that are used to lock the loop ends to one another, and to show how an extensive dictionary of such locking pairs can be created using positional correlation data from a large proteome database, and structural data from PDB databases. Such a dictionary can be used in reconstructing the evolutionary pathway the modern proteins have gone through, and in identifying closed loop elements in modern proteins with yet unknown 3D structure.     

Sequence structure of van der Waals locks in proteins

Recent works has suggested that proteins in early evolution have gone through a stage of closed loop elements with a typical contour size of 25-35 residues. These closed loops are still the elementary protein units to these days, and can be used to spell out protein sequence/structure relationship through a relatively small number of protein prototypes. In this study we aimed to identify the sequences that are used to lock the loop ends to one another, and to show how an extensive dictionary of such locking pairs can be created using positional correlation data from a large proteome database, and structural data from PDB databases. Such a dictionary can be used in reconstructing the evolutionary pathway the modern proteins have gone through, and in identifying closed loop elements in modern proteins with yet unknown 3D structure.     

van der Waals forces influencing adhesion of cells

Adhesion molecules, often thought to be acting by a ‘lock and key’ mechanism, have been thought to control the adhesion of cells. While there is no doubt that a coating of adhesion molecules such as fibronectin on a surface affects cell adhesion, this paper aims to show that such surface contamination is only one factor in the equation. Starting from the baseline idea that van der Waals force is a ubiquitous attraction between all molecules, and thereby must contribute to cell adhesion, it is clear that effects from geometry, elasticity and surface molecules must all add on to the basic cell attractive force. These effects of geometry, elasticity and surface molecules are analysed. The adhesion force measured between macroscopic polymer spheres was found to be strongest when the surfaces were absolutely smooth and clean, with no projecting protruberances. Values of the measured surface energy were then about 35 mJ m⁻², as expected for van der Waals attractions between the non-polar molecules. Surface projections such as abrasion roughness or dust reduced the molecular adhesion substantially. Water cut the measured surface energy to 3.4 mJ m⁻². Surface active molecules lowered the adhesion still further to less than 0.3 mJ m⁻². These observations do not support the lock and key concept.     

Discrete structure of van der Waals domains in globular proteins

Most globular proteins are divisible by domains, distinct substructures of the globule. The notion of hierarchy of the domains was introduced earlier via van der Waals energy profiles that allow one to subdivide the proteins into domains (subdomains). The question remains open as to what is the possible structural connection of the energy profiles. The recent discovery of the loop-n-lock elements in the globular proteins suggests such a structural connection. A direct comparison of the segmentation by van der Waals energy criteria with the maps of the locked loops of nearly standard size reveals a striking correlation: domains in general appear to consist of one to several such loops. In addition, it was demonstrated that a variety of subdivisions of the same protein into domains is just a regrouping of the loop-n-lock elements.     

ProteinVolume: calculating molecular van der Waals and void volumes in proteins

Background

Voids and cavities in the native protein structure determine the pressure unfolding of proteins. In addition, the volume changes due to the interaction of newly exposed atoms with solvent upon protein unfolding also contribute to the pressure unfolding of proteins. Quantitative understanding of these effects is important for predicting and designing proteins with predefined response to changes in hydrostatic pressure using computational approaches. The molecular surface volume is a useful metric that describes contribution of geometrical volume, which includes van der Waals volume and volume of the voids, to the total volume of a protein in solution, thus isolating the effects of hydration for separate calculations.

Results

We developed ProteinVolume, a highly robust and easy-to-use tool to compute geometric volumes of proteins. ProteinVolume generates the molecular surface of a protein and uses an innovative flood-fill algorithm to calculate the individual components of the molecular surface volume, van der Waals and intramolecular void volumes. ProteinVolume is user friendly and is available as a web-server or a platform-independent command-line version.

Conclusions

ProteinVolume is a highly accurate and fast application to interrogate geometric volumes of proteins. ProteinVolume is a free web server available on http://gmlab.bio.rpi.edu. Free-standing platform-independent Java-based ProteinVolume executable is also freely available at this web site.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-015-0531-2) contains supplementary material, which is available to authorized users.     

Simple benzene derivatives adsorption on defective single-walled carbon nanotubes: a first-principles van der Waals density functional study

We have investigated the interaction between open-ended zig-zag single-walled carbon nanotube (SWCNT) and a few benzene derivatives using the first-principles van der Waals density functional (vdW-DF) method, involving full geometry optimization. Such sp ²-like materials are typically investigated using conventional DFT methods, which significantly underestimate non-local dispersion forces (vdW interactions), therefore affecting interactions between respected molecules. Here, we considered the vdW forces for the interacting molecules that originate from the interacting π electrons of the two systems. The ?0.54 eV adsorption energy reveals that the interaction of benzene with the side wall of the SWCNT is typical of the strong physisorption and comparable with the experimental value for benzene adsorption onto the graphene sheet. It was found that aromatics are physisorbed on the sidewall of perfect SWCNTs, as well as at the edge site of the defective nanotube. Analysis of the electronic structures shows that no orbital hybridization between aromatics and nanotubes occurs in the adsorption process. The results are relevant in order to identify the potential applications of noncovalent functionalized systems.

Display of quantum mechanical properties on van der Waals surfaces

A technique is described for comparing graphically the electrostatic properties of molecules. Results from quantum mechanical calculations are mapped onto the van der Waals surface. The surface is defined by CSG (constructive solid geometry), a technique used in CAD (computer-aided design). Colour is used to represent the electrostatic properties and the results are displayed on a high resolution raster device as a ‘realistic’ model. This technique is expected to be of value in discriminating qualitatively between compounds of different biological activities.     

A new approach for the calculation of the energy of van der Waals interactions in macromolecules of globular proteins

Van der Waals interaction energy in globular proteins is presented by the interaction energies between regions of protein spatial structure with homogenous medium density distribution. We introduce a notion of the local medium permittivity as a function of absorptance of molecular groups with particular conformation. Proposed theory avoids shortcomings which are typical for the calculations on the basis of the pairwise additive approximation. The approach takes into account local peculiarities of protein spatial structure and physical-chemical characteristics of amino acid residues and molecular groups.     

Computing van der Waals energies in the context of the rotamer approximation

The rotamer approximation states that protein side-chain conformations can be described well using a finite set of rotational isomers. This approximation is often applied in the context of computational protein design and structure prediction to reduce the complexity of structural sampling. It is an effective way of reducing the structure space to the most relevant conformations. However, the appropriateness of rotamers for sampling structure space does not imply that a rotamer-based energy landscape preserves any of the properties of the true continuous energy landscape. Specifically, because the energy of a van der Waals interaction can be very sensitive to small changes in atomic separation, meaningful van der Waals energies are particularly difficult to calculate from rotamer-based structures. This presents a problem for computational protein design, where the total energy of a given structure is often represented as a sum of precalculated rigid rotamer self and pair contributions. A common way of addressing this issue is to modify the van der Waals function to reduce its sensitivity to atomic position, but excessive modification may result in a strongly nonphysical potential. Although many different van der Waals modifications have been used in protein design, little is known about which performs best, and why. In this paper, we study 10 ways of computing van der Waals energies under the rotamer approximation, representing four general classes, and compare their performance using a variety of metrics relevant to protein design and native-sequence repacking calculations. Scaling van der Waals radii by anywhere from 85 to 95% gives the best performance. Linearizing and capping the repulsive portion of the potential can give additional improvement, which comes primarily from getting rid of unrealistically large clash energies. On the other hand, continuously minimizing individual rotamer pairs prior to evaluating their interaction works acceptably in native-sequence repacking, but fails in protein design. Additionally, we show that the problem of predicting relevant van der Waals energies from rotamer-based structures is strongly nonpairwise decomposable and hence further modifications of the potential are unlikely to give significant improvement.     

Many-atom van der Waals interactions lead to direction-sensitive interactions of covalent bonds

Strict physical theory and numerical calculations show that a specific coupling of many-atom van der Waals interactions with covalent bonding can significantly (half as much) increase the strength of attractive dispersion interactions when the direction of interaction coincides with the direction of the covalent bond, and decrease this strength when the direction of interaction is perpendicular to the direction of the covalent bond. The energy effect is comparable to that caused by the replacement of atoms (e.g. N by C or O) in conventional pairwise van der Waals interactions. Analysis of protein structures shows that they bear an imprint of this effect. This means that many-atom van der Waals interactions cannot be ignored in refinement of protein structures, in simulations of their folding, and in prediction of their binding affinities.     

On the importance of van der Waals interaction in the groove binding of DNA with ligands: restrained molecular dynamics study

Comparison of interaction energy between an oligonucleotide and a DNA-binding ligand in the minor and major groove modes was made by use of restrained molecular dynamics. Distortion in DNA was found for the major groove mode whereas less significant changes for both ligand and DNA were detected for the minor groove binding after molecular dynamics simulation. The conformation of the ligand obtained from the major groove mode resembles that computed with the ligand soaked in water. The van der Waals contact energy was found to be as significant as electrostatic energy and more important for difference in binding energy between these two binding modes. The importance of van der Waals force in groove binding was supported by computations on the complex formed by the repressor peptide fragment from the bacteriophage 434 and its operator oligonucleotide.     

van der Waals forces between cylinders: Arrays of thin cylinders and three body forces

We study the van der Waals energy of interaction of an array of parallel dielectric cylinders immersed in a dielectric medium. We consider only “thin” cylinders which have radius small compared to the separation of the cylinders. The energy is calculated as a sum of two body plus three body interactions. The case of hexagonally close packed cylinders is studied in more detail. Some biophysical applications are discussed and in particular the van der Waals energy of the myosin lattice in striated muscle is examined.     

van der Waals Forces between Cylinders: II. Retarded Interaction between Thin Isotropic Rods

We derive the retarded van der Waals interaction between two long thin parallel dielectric cylinders immersed in a solvent. The result shows that the ultraviolet interactions which may be responsible for the specificity of macromolecular interactions do not operate strongly over distances R ≥ 50 Å. For greater distances the contribution of these frequencies ξ is damped by a factor ∞ e^-ξR/c.     

Calibration of effective van der Waals atomic contact radii for proteins and peptides

Effective van der Waals radii were calibrated in such a way that molecular models built from standard bond lengths and bond angles reproduced the amino acid conformations observed by crystallography in proteins and peptides. The calibrations were based on the comparison of the Ramachandran plots prepared from high-resolution X-ray data of proteins and peptides with the allowed phi, psi torsional angle space for the dipeptide molecular models. The calibrated radii are useful as criteria with which to filter energetically improbable conformations in molecular modeling studies of proteins and peptides.     

A new approach to calculation of the energy from van der Waals interactions in macromolecular proteins. Dielectric permeability as a physical parameter for calculations

The problem in the calculation of Van der Waals interactions in protein globules based on the theory of condensed media was considered. The Van der Waals interactions are represented as energies of interaction of regions with a uniform density distribution. A definition of the local dielectric constant as a function of coefficients of absorption of molecular groups with a particular conformation was introduced. The applicability of this approach was estimated. The theory enables one to circumvent the problems arising in calculations based on pairwise additive approximation. The methods provides a high accuracy in determining the local features of spatial structures of globular proteins and physicochemical characteristics of their constituent amino acids and molecular groups.