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.     

General van der Waals potential for common organic molecules

This work presents a systematic development of a new van der Waals potential (vdW2016) for common organic molecules based on symmetry-adapted perturbation theory (SAPT) energy decomposition. The Buf-14-7 function, as well as Cubic-mean and Waldman–Hagler mixing rules were chosen given their best performance among other popular potentials. A database containing 39 organic molecules and 108 dimers was utilized to derive a general set of vdW parameters, which were further validated on nucleobase stacking systems and testing organic dimers. The vdW2016 potential is anticipated to significantly improve the accuracy and transferability of new generations of force fields for organic molecules.     

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.     

A New Spatial Representation of Amino Acid Residues in Globular Proteins

Abstract

For the globular proteins with known three-dimensional structures, an ellipsoid model of each protein was constructed with least volume and its dimensions were derived. The spatial arrangements were made for the C_α and side chain atoms of that protein within that ellipsoid. This new spatial representation shows the residue position from the centroid, as well as the depth from the surface. The average spatial parameters were then calculated. The correlations between these new spatial parameters and the existing parameters of the amino acid residues were then derived.     

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.     

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.     

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.     

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.     

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.     

Influence of Medium and Long Range Interactions in Different Structural Classes of Globular Proteins

An analysis of the dependence known three dimensional structure ofglobular proteins on their residue contacts and their interactions providesmuch information about their folding and stability. In this work, we analysethe residue-residue contacts and the role of medium and long rangeinteractions in globular proteins belonging to different structural classes.The results show that while medium range interactions predominate in allalpha class proteins, long range interactions predominate in all beta class.The residues Pro and Gly are found to have lowest medium range contacts,probably due to their helix breaking tendency. The hydrophobic residues Ile,Val and Tyr have higher long range contacts, and hence may serve as goodnucleation centres. Further, the role of charged residues and disulfidebridges in these interactions are also discussed.     

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 model for the recognition of protein kinases based on the entropy of 3D van der Waals interactions

The study and prediction of kinase function (kinomics) is of major importance for proteome research due to the widespread distribution of kinases. However, the prediction of protein function based on the similarity between a functionally annotated 3D template and a query structure may fail, for instance, if a similar protein structure cannot be identified. Alternatively, function can be assigned using 3D-structural empirical parameters. In previous studies, we introduced parameters based on electrostatic entropy (Proteins 2004, 56, 715) and molecular vibration entropy (Bioinformatics 2003, 19, 2079) but ignored other important factors such as van der Waals (vdw) interactions. In the work described here, we define 3D-vdw entropies (degrees theta(k)) and use them for the first time to derive a classifier for protein kinases. The model classifies correctly 88.0% of proteins in training and more than 85.0% of proteins in validation studies. Principal components analysis of heterogeneous proteins demonstrated that degrees theta(k) codify information that is different to that described by other bulk or folding parameters. In additional validation experiments, the model recognized 129 out of 142 kinases (90.8%) and 592 out of 677 non-kinases (87.4%) not used above. This study provides a basis for further consideration of degrees theta(k) as parameters for the empirical search for structure-function relationships.     

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.     

Nature of Novel 2D van der Waals Heterostructures for Superior Potassium Ion Batteries

Novel 2D van der Waals heterostructures with innovative bimetallic oxychloride (Bi‐ and Sb‐based oxychloride) nanosheets that are well dispersed on reduced graphene oxide nanosheets, are established through element engineering for superior potassium ion battery (PIBs) anodes. This material displays an exceptional electrochemical performance, obtaining a discharge capacity as high as 360 mAh g^?1 at 100 mA g^?1 after running 1000 cycles for over 9 months with a capacity preservation percentage of 88.5% and achieving a discharge capacity as high as 319 mAh g^?1 at 1000 mA g^?1, in addition to the low charge/discharge plateaus for anodes and promising full cell performance. More significantly, the nature of such 2D van der Waals heterostructures, including the element engineering for morphology control, the function of each component of heterostructures, the mechanism of potassium ion storage, and the process of K⁺ intercalation accompanied with the lattice distortion and chemical bond breakages, is explored in depth. This study is critical for not only paving the way for the practical application of PIBs but also shedding light on fundamentals of potassium ion storage in 2D van der Waals heterostructures.     

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 Prediction of Folding Nuclei in Globular Proteins

An approach to predicting folding nuclei in globular proteins with known three-dimensional structures is proposed. This approach is based on the pinpointing of the lowest saddle points on the barrier between the unfolded state and native structure on the free-energy landscape of a protein chain; the proposed technique uses the dynamic programming method. A comparison of calculation results with experimental data on the folding nuclei of 21 proteins shows that the model provides good Φ value predictions for protein structures determined by X-ray analysis and, less successfully, in structures determined by nuclear magnetic resonance. Consideration of the whole ensemble of transition states provides a better prediction of folding nuclei than consideration of only transition states with lowest free energies. In addition, we predict the location of folding nuclei in three-dimensional structures of some proteins whose folding kinetics is being studied, but there is no experimental evidence concerning their folding nuclei.