Promolecular Electron Density Research Articles

Why pay more? QTAIM descriptors of non-covalent interactions in S22 from promolecular electron density

Based on the comparative analysis of electron density topological features obtained by different methods for the model set of bimolecular associates it is shown that the simplest promolecule model can be an efficient tool in studies of non-covalent interactions

Description of non-covalent interactions in benzyl chalcocyanate crystals from smoothed Cromer–Mann electron density distribution functions

A well-known method to characterize non-covalent interactions consists in the topological analysis of electron density distribution (EDD) functions, complemented by the search for minima in the reduced density gradient (RDG) distributions. Here, we characterize intermolecular interactions occurring in crystals of benzyl chalcocyanate compounds through bond critical points (BCP) of the promolecular electron density (ED) built from the crystallographic Cromer–Mann parameters, at several smoothing levels t. The trajectories formed by the t-dependent BCP locations are interpreted in terms of the intermolecular interactions occurring within the crystal arrangements. Chalcogen…nitro BCPs are clearly present in the unsmoothed EDDs but are annihilated as t increases, while chalcogen…chalcogen BCPs appear and are among the only BCPs left at the highest smoothing level. The chalcogen bonds are differentiated from the other chalcogen interactions through the linear chalcogen…BCP…nitro geometry at low smoothing level and their more negative Laplacian values. The annihilation of CPs can be followed by the apparition of a RDG minimum, associated with a very weak interaction. Along the BCP trajectories, the Laplacian shows a progressive concentration of the ED in the intermolecular space within the crystals and adopts the most negative values at the shortest atom…atom separations. At the termination point of a BCP trajectory, the drastic increase of the ellipticity value illustrates the flattening of the EDD.

Synthesis, X-ray crystallography, molecular electronic property investigation, and leukopoiesis activity of novel 4,6-dimethyl-1,6-dihydropyridin-2-amino nitrate hybrid material

Herein, a new hybrid organic-inorganic material: 4,6-dimethyl-1,6-dihydropyridin-2-amino nitrate (I) has been synthesized and characterized by X-ray diffraction technique and Fourier transform infrared (FT-IR) spectroscopy. The structural, electronic and topological properties were investigated by a theoretical approach along with a validation of vibrational properties using the dispersion-corrected density functional theory (DFT-D3) method (PWPB95 D3(BJ)) along with the meta-generalized gradient approximation (Meta-GGA) functional of the Minnesota family (M06–2x). All computations were conducted with the 6–311++G(2df,2pd) and def2-TZVP basis set. A visual study of weak interactions was achieved via Bader's Quantum theory of atoms in molecules (QTAIM), non-covalent interaction (NCI) using the promolecular electron density approach, Electron localization function and molecular electrostatic potential. Natural orbital analysis and charge delocalization were equally considered to comprehend and appraise the various intermolecular stabilization mechanisms in the studied system. Molecular electronic properties (quantum descriptors) were also investigated to assess the reactive nature and stability index of the synthesized structure. Due to the ionic nature and structural similarity of the studied compound with methyluracil, molecular docking investigations of the Leukopoiesis stimulating activity of (I) were assessed and compared with a series of Krebs ’regulating enzymes. These studies divulged that the synthesized compound has the potential to stimulate the synthesis of nucleic acids, proteins, cell division, and leukopoiesis.

Correction to: Multiresolution non-covalent interaction analysis for ligand–protein promolecular electron density distributions

Correction to: Multiresolution non-covalent interaction analysis for ligand–protein promolecular electron density distributions

Multiresolution non-covalent interaction analysis for ligand–protein promolecular electron density distributions

Nowadays, the topology of electron density (ED) distributions as well as the non-covalent interaction (NCI) analysis of reduced density gradient (RDG) distributions, are extensively used to characterize intermolecular contacts. Here, topological and NCI-based analyses are combined for the multiresolution study of the intermolecular interactions occurring in a drug-protein system (PDB access code: 3UNK). The method involves the search for the critical points (CP) of the well-known PASA model developed by Carbo-Dorca and co-workers, and the minima in the corresponding RDG grids. The CP-based representation of the intermolecular contacts enriches the geometry-based interactions found using a Web server. The stability of the intermolecular interactions is studied by following their corresponding CP trajectory in space at several degrees of the ED smoothing, and by the evaluation of the local potential energy density (LPDE). It is observed that several RDG minima are located at the meeting point of CP trajectories initiated in the unsmoothed ED distribution. At high smoothing levels, the accumulation of ED charges at the ligand–protein interface progressively emerges and is detected through the study of the Laplacian values at the CPs and RDG minima. In parallel, the distance-dependency of the LPED values is less and less clear while the density-dependency is favored. The CP networks and their descriptors are seen as a signature of the ligand–protein arrangement, which is proposed to be further used in the characterization of ligand–protein stackings obtained from, e.g., crystal structures, docking calculations, Molecular Dynamics simulations, and pharmacophore designs.

Hirshfeld Surface Analysis of Stable and Metastable Polymorphs of Vanillin

AbstractThe intermolecular interactions and the properties of voids present in the stable Form‐I and metastable Form‐II polymorphs of vanillin, a significant pharmaceutical and food material, are investigated through Hirshfeld surface analysis. Form‐I and Form‐II polymorphs of vanillin are separately grown through a template‐induced heterogeneous nucleation process from aqueous solution in the absence and presence of nickel foam as template and their structural parameters are obtained through single crystal X‐ray diffraction (SCXRD) analysis. With this SCXRD data as input, the intermolecular interactions within the grown polymorphs are analyzed by Hirshfeld surface analysis with detailed finger print plot and the area, volume, and percentage of voids present inside the polymorphic structures are identified through the isosurface of the spherical promolecular electron density. The 2D finger print analysis of each of the polymorphs reveals that besides the (H─H) interaction, the (O─H) interaction contributes more to the generation of polymorphs. Furthermore the percentage of volume occupied by the voids in the Form‐I and Form‐II are found to be 11.55% and 19.92%, respectively.

Reconstructing the Electron Density of Intermediates of the Hydrolysis of N-Acetylaspartate by Aspartoacylase

The hydrolysis of N-acetylaspartate by human aspartoacylase shows that using promolecular electron density (superpositions of the densities of spherical atoms) is insufficient for describing intermediates of reactions of enzyme catalysis. The deformation of electron density caused by the formation of covalent and coordination bonds inside a system must be considered, creating the need to develop new approaches in protein crystallography for better interpretation of observed electron density and more precise determination of the geometrical parameters of reaction intermediates.

The Independent Gradient Model: A New Approach for Probing Strong and Weak Interactions in Molecules from Wave Function Calculations.

Extraction of the chemical interaction signature from local descriptors based on electron density (ED) is still a fruitful field of development in chemical interpretation. In a previous work that used promolecular ED (frozen ED), the new descriptor, δg , was defined. It represents the difference between a virtual upper limit of the ED gradient (∇ρIGM , IGM=independent gradient model) that represents a noninteracting system and the true ED gradient (∇ρ ). It can be seen as a measure of electron sharing brought by ED contragradience. A compelling feature of this model is to provide an automatic workflow that extracts the signature of interactions between selected groups of atoms. As with the noncovalent interaction (NCI) approach, it provides chemists with a visual understanding of the interactions present in chemical systems. ∇ρIGM is achieved simply by using absolute values upon summing the individual gradient contributions that make up the total ED gradient. Hereby, we extend this model to relaxed ED calculated from a wave function. To this end, we formulated gradient-based partitioning (GBP) to assess the contribution of each orbital to the total ED gradient. We highlight these new possibilities across two prototypical examples of organic chemistry: the unconventional hexamethylbenzene dication, with a hexa-coordinated carbon atom, and β-thioaminoacrolein. It will be shown how a bond-by-bond picture can be obtained from a wave function, which opens the way to monitor specific interactions along reaction paths.

Comparison of reduced point charge models of proteins: Molecular Dynamics simulations of Ubiquitin

Reduced point charge models of amino acids are used to model Ubiquitin (PDB: 1UBQ). They are designed (i) from local extremum positions in charge density (CD) distribution functions built from the Poisson equation applied to smoothed molecular electrostatic potential functions, or (ii) from local maximum positions in promolecular electron density distribution (ED) functions. Charge values are fitted versus all-atom Amber99 molecular electrostatic potentials. The program GROMACS is used to generate molecular dynamics trajectories of the protein, under various implementation schemes, solvation, and temperature conditions. Point charges that are not located on atoms are considered as virtual sites with a null mass and radius. The results illustrate that secondary structure is best preserved with the CD-based model at low temperatures and in vacuum. This indicates that local potential energy wells are consistent with the all-atom model. However, at room temperature, the structure is best conserved when point charges are forced to be located on atoms, due to a better description of the Coulomb 1–4 energy terms. The ED-based model, generated at a lower resolution, led to the largest discrepancies versus the all-atom case. The CD-based model allows the formation of protein-water H-bonds with geometrical properties similar to the all-atom ones. Contrarily, intra-molecular H-bonds are not well described. Structural, thermodynamical, and dynamical properties of proteins modelled with reduced point charge models are also significantly affected by the choice of the solvent force field.

Evaluation of reduced point charge models of proteins through Molecular Dynamics simulations: Application to the Vps27 UIM-1–Ubiquitin complex

Reduced point charge models of amino acids are designed, (i) from local extrema positions in charge density distribution functions built from the Poisson equation applied to smoothed molecular electrostatic potential (MEP) functions, and (ii) from local maxima positions in promolecular electron density distribution functions. Corresponding charge values are fitted versus all-atom Amber99 MEPs. To easily generate reduced point charge models for protein structures, libraries of amino acid templates are built. The program GROMACS is used to generate stable Molecular Dynamics trajectories of an Ubiquitin-ligand complex (PDB: 1Q0W), under various implementation schemes, solvation, and temperature conditions. Point charges that are not located on atoms are considered as virtual sites with a nul mass and radius. The results illustrate how the intra- and inter-molecular H-bond interactions are affected by the degree of reduction of the point charge models and give directions for their implementation; a special attention to the atoms selected to locate the virtual sites and to the Coulomb-14 interactions is needed. Results obtained at various temperatures suggest that the use of reduced point charge models allows to probe local potential hyper-surface minima that are similar to the all-atom ones, but are characterized by lower energy barriers. It enables to generate various conformations of the protein complex more rapidly than the all-atom point charge representation.

Collective motions of rigid fragments in protein structures from smoothed electron density distributions

In this work, the Gaussian Network Model (GNM) and Anisotropic Network Model (ANM) approaches are applied to describe the dynamics of protein structure graphs built from calculated promolecular electron density (ED) distribution functions. A first set of analyses is carried out on results obtained from ED maxima calculated at various smoothing levels. A second set is achieved for ED networks whose edges are weighted by ED overlap integral values. Results are compared with those obtained through the classical GNM and ANM approaches applied to networks of C(alpha) atoms. It is shown how the network model and the consideration of crystal packing as well as of the side chains may lead to various improvements dependent upon the structure under study. The selected protein structures are Crambin and Pancreatic Trypsin Inhibitor because of their small size and numerous dynamical data obtained by other authors.

Collective motions in protein structures: Applications of elastic network models built from electron density distributions

In this work, the Gaussian Network Model (GNM) and Anisotropic Network Model (ANM) approaches are applied to describe the dynamics of Pancreatic Trypsin Inhibitor protein graphs built from smoothed promolecular electron density (ED) distribution functions. A specific smoothing degree is selected which provides a clear partitioning of the protein structure into fragments located either on the protein backbone or side chains. A first set of analyses is carried out on results obtained from ED maxima calculated at that specific smoothing level. A second set is achieved for a protein ED network whose edges are weighted by ED overlap integral values. Results are compared with those obtained through GNM, ANM, and Normal Mode Analysis approaches, applied to the network of C α atoms.

Similarity measures based on Gaussian‐type promolecular electron density models: Alignment of small rigid molecules

Various molecular similarity measures (overlap, Coulomb, kinetic, electrostatic energy) and similarity indices (Carbó, Hodgkin-Richards, Kulczynski, Shape Tanimoto) are applied to the superposition of 3D promolecular electron density (PED) distributions. The original aspect of the paper lies in the consideration of smoothed PEDs, which allow to decrease the number of local solutions to a superposition problem, together with the use of the less common kinetic and electrostatic energy similarity measures. Results are obtained for a family of five rigid endothiapepsin ligands that were already considered in previous applications, based on graph representations of their PED. In the present work, it is observed that the use of smoothed PED and the kinetic similarity measure, together with the Kulczynski or Shape Tanimoto index, performed the best to align molecules of different sizes.

Influence of conformation on the representation of small flexible molecules at low resolution: alignment of endothiapepsin ligands

In this contribution, we discuss a molecular representation mode for the generation of reduced descriptions of flexible molecules in various conformations. The representations of the endothiapepsin ligands are constituted by graphs of peaks obtained through a hierarchical merging algorithm which combines the location of promolecular electron density (ED) maxima with the decomposition of the molecular structures into fragments. The representations are then aligned through the use of a Monte Carlo/Simulated Annealing procedure. The evaluation function of the alignment solutions is based on the local density values of the peaks and their inter-distances. The applications show that the alignment of a given molecule onto itself, in a different conformation, is successful when a pseudo-topological path length is considered in the evaluation function of the solution, while Cartesian distances are more adapted to the scoring for alignments of two different molecules in their co-crystallized conformation. Results are compared with the available literature data.

Hierarchical description of protein structure fragments obtained from analyses of promolecular electron density distributions

Hierarchical description of protein structure fragments obtained from analyses of promolecular electron density distributions

Hierarchical analysis of promolecular full electron-density distributions: description of protein structure fragments.

A theoretical method is applied to describe protein structures in terms of hierarchically related substructures. The approach is based on the location of local maxima (peaks) in promolecular electron-density (ED) distributions established at various smoothing levels. Promolecular ED distributions are generated using either the Promolecular Atom Shell Approximation (PASA) representation or the ED are calculated using the Cromer-Mann coefficients. The analysis of the decomposition patterns of a protein structure in its native and hypothetical extended conformations showed that the amino-acid residues have a similar decomposition pattern regardless of their position in the protein sequence, the protein conformation and the influence of the crystal packing. A link is proposed with model-building tools in protein structure determination from diffraction data.

Structural Identification of Local Maxima in Low-Resolution Promolecular Electron Density Distributions

In this paper, we present a theoretical method to describe molecular structures in terms of hierarchically related substructures. The approach is based on the location of local maxima (peaks) in promolecular electron density distributions (EDD) established at continuously varying resolution levels. For each of the so-calculated EDD, the local maxima are determined by using a hierarchical clustering algorithm wherein peaks obtained at a given resolution are used as starting points for discovering peaks at the next lower resolution level through gradient trajectories of the EDD. The use of such an approach allows assignment of molecular fragments or chemical groups to peaks, at any resolution level. Results, obtained for a set of four benzodiazepine-related molecules and three thrombin inhibitors, are presented in terms of dendrograms wherein each node corresponds to a well-defined molecular substructure.

Application of multiresolution analyses to electron density maps of small molecules: Critical point representations for molecular superposition

Three different methods are applied to generate low resolution molecular electron density (ED) distribution functions: a crystallography-based formalism, an analytical approach which allows the calculation of a promolecular ED distribution in terms of a weighted summation over atomic ED distributions, and a wavelet-based multiresolution analysis approach. Critical point graph representations of the molecular ED distributions are then generated by locating points where the gradient of the density is equal to zero, and further considered for pairwise molecular superpositions of thrombin inhibitors using a Monte Carlo/Simulated Annealing technique.