Molecular Structure Descriptors Research Articles

Comparative analysis of symmetric division deg index as potentially useful molecular descriptor

AbstractThere are several dozens of vertex–degree–based (VDB) molecular structure descriptors currently studied and proposed to be used in quantitative structure‐property/activity relationships (QSPR/QSAR) researches. Among them, just a couple are recognized as promising and worth of practical applications. One of the newest is the symmetric division deg index (SDD). This article is devoted to a thorough multifaceted analysis of SDD and its comparison with other VDB topological indices. We show that the applicative potential of SDD is comparable to already well‐established VDB structure descriptors. Additionally, some of conducted tests indicate its supremacy over other VDB molecular indices.

Synthesis and structural characterization of a 8-hydroxyquinoline derivative coordinated to Zn(II)

In this work, a 8-hydroxyquinoline derivative, named 8-hydroxyquinoline-2-carboxaldehyde 2-furoyl hydrazone (HQFUH), was obtained. The respective compound was successfully synthesized as well as its respective Zn(II) coordination compound. Both compounds were structurally characterized, by experimental and theoretical IR and Raman spectra, XRD. Single crystal XRD showed that Zn(II) adopts a tetrahedral geometry, in which the neutral chelating ligand coordinates bidentaded by two N-atoms and the neutrality charge is achieved by two coordinated chloride ions. Topological analysis using Quantum Theory of Atoms in Molecules (QTAIM) was performed to investigate ligand interaction through O-atoms. This investigation is important regarding the determination of complex formation constant. The crystal structures of the ligand and complex are arranged according to an orthorhombic system with P212121 and Aea2 space groups, respectively. Ligand displays a E configuration around to C10 = N2 bond, while after the coordination of metal, a Z configuration is observed. Besides molecular structure description of complex, the intermolecular environment was analyzed by Hirshfeld Surface.

The minimal-ABC trees with B1-branches.

The atom-bond connectivity index (or, for short, ABC index) is a molecular structure descriptor bridging chemistry to graph theory. It is probably the most studied topological index among all numerical parameters of a graph that characterize its topology. For a given graph G = (V, E), the ABC index of G is defined as , where di denotes the degree of the vertex i, and ij is the edge incident to the vertices i and j. A combination of physicochemical and the ABC index properties are commonly used to foresee the bioactivity of different chemical composites. Additionally, the applicability of the ABC index in chemical thermodynamics and other areas of chemistry, such as in dendrimer nanostars, benzenoid systems, fluoranthene congeners, and phenylenes is well studied in the literature. While finding of the graphs with the greatest ABC-value is a straightforward assignment, the characterization of the tree(s) with minimal ABC index is a problem largely open and has recently given rise to numerous studies and conjectures. A B1-branch of a graph is a pendent path of order 2. In this paper, we provide an important step forward to the full characterization of these minimal trees. Namely, we show that a minimal-ABC tree contains neither 4 nor 3 B1-branches. The case when the number of B1-branches is 2 is also considered.

The InChI Code

The International Union of Pure and Applied Chemistry has developed a computer algorithmic scheme for unambiguously coding molecular structure into relatively short alphabetic tags. These are now ubiquitous in many descriptions of molecular structure, yet the ease with which they are recognized and used is suppressed by their opaqueness even to the chemically knowledgeable reader. We present a short description of the structure, utility, advantages, and disadvantages of the code to ease familiarization.

Valency-based topological descriptors of chemical networks and their applications

A topological descriptor/index (or molecular structure descriptor) is a numerical value associated with chemical constitution for correlation of chemical structure/network with various physical properties, chemical reactivity or biological activity. Quantitative structure–activity and structure–property relationships of chemical networks require expressions for the topological properties of these networks. Topological indices provide these expressions of topological properties. Valency-based topological descriptors are the oldest and most successful class of descriptors so far. A chemical graph/network is a representation of the structural formula of a chemical compound whose vertices correspond to the atoms of the compound and edges correspond to chemical bonds. In this paper, we study valency-based topological indices of chemical networks. By using some real world data, we performed certain comparative testings to investigate the performance of almost all well-known valency-based indices. Dependence on the molecular structure is studied for topological indices which are best in performance. We calculated explicit formulas for well-performed indices of some infinite families of carbon nanotubes, carbon nanocones and a newly proposed family of organic networks called tetrahedral diamond networks. Tetrahedral diamond networks arises by recurrently joining graphene layers in a diamond cluster. Significance and applicability of the obtained results are reported.

Prediction of Dispersive Liquid–Liquid Microextraction Enrichment Effect of Aromatic Organics by [OMIM] [PF6] Ionic Liquid Based on Atom-Type Electrotopological State Indices

In this work, a quantitative structure–property relationship (QSPR) model based on atom-type electrotopological state (E-state) indices has been developed for predicting the dispersive liquid–liquid microextraction (DLLME) enrichment effect for aromatic organics by using 1-octyl-3-methylimidazolium hexafluorophosphate ([OMIM][PF6]) ionic liquid as extractant. The enrichment factors of the aromatic organics obtained through DLLME-IL process were used as the dependent variable of the multiple linear regression (MLR) equation. The E-state indices of those organic compounds which combined together both electronic and topological characteristics of the analyzed molecules were used as molecular structure descriptors and the independent variable of the equation. The squared correlation coefficient R2 for the MLR was 0.992 for the training set of 33 compounds. For the test set of 8 compounds, the linear regression coefficient was R2 = 0.985. The results of this study showed that it can successfully predict enrichment factors of [OMIM][PF6] in DLLME by using atom-type E-state indices, which can provide one more way for predicting the ability of ionic liquid to extract organic compounds based on their molecular structures.

The Minimal-ABC Trees With <inline-formula> <tex-math notation="LaTeX">${B}1$ </tex-math> </inline-formula>-Branches II

The atom-bond connectivity (ABC) index is one of the most investigated degree-based molecular structure descriptors with a variety of chemical applications. For a given graph $G=(V,E)$ , the ABC index is defined as $ABC(G)=\sum _{uv\in E} {(d_{u}+d_{v}-2)/(d_{u}d_{v})}^{1/2}$ , where $d_{u}$ denotes the degree of the vertex $u$ , and $uv$ is the edge incident to the vertices $u$ and $v$ . It is known that a minimal-ABC tree (a tree with the minimal value of the ABC index) cannot contain more than four so-called $B_{1}$ -branches (the figuration for $B_{1}$ -branch see Fig. 1 ). Recently, it was shown that a minimal-ABC tree of order larger than 19 contains neither three nor four $B_{1}$ -branches. Here, we further improve those results by showing that a minimal-ABC tree of order larger than 122 cannot contain also one $B_{1}$ -branch. Moreover, we have proven that a minimal-ABC tree of order larger than 122 can contain only two $B_{1}$ -branches and that only in a combination with one $B_{2}$ -branch (the figuration can also see $B_{3}^{**}$ -branch in Fig. 1 ).

Clustering pesticides according to their molecular properties, fate, and effects by considering additional ecotoxicological parameters in the TyPol method.

Understanding the fate and ecotoxicological effects of pesticides largely depends on their molecular properties. We recently developed "TyPol" (Typology of Pollutants), a classification method of organic compounds based on statistical analyses. It combines several environmental (sorption coefficient, degradation half-life) and one ecotoxicological (bioconcentration factor) parameters, to structural molecular descriptors (number of atoms in the molecule, molecular surface, dipole moment, energy of orbitals, etc.). The present study attempts to extend TyPol to the ecotoxicological effects of pesticides on non-target organisms, based on data analysis from available literature and databases. It revealed that relevant ecotoxicological endpoints for terrestrial organisms (e.g., soil microorganisms, invertebrates) that support a range of ecosystemic services are lacking as compared to aquatic organisms. The availability of ecotoxicological parameters was also lower for chronic than for acute ecotoxicity endpoints. Consequently, seven parameters were included for acute (EC50, LC50) and chronic (NOEC) ecotoxicological effects for one terrestrial (Eisenia sp.) and three aquatic (Daphnia sp., algae, Lemna sp.) organisms. In this new configuration, we used TyPol to classify 50 pesticides into different clusters that gather molecules with similar environmental behaviors and ecotoxicological effects. The classification results evidenced relationships between molecular descriptors, environmental parameters, and the added ecotoxicological endpoints. This proof-of-concept study also showed that TyPol in silico classification can successfully address new scientific questions and be expanded with other parameters of interest.

Experimental and QSAR study on the surface activities of alkyl imidazoline surfactants

15 alkyl imidazoline surfactants with different structures were synthesized and their critical micelle concentration (CMC) and surface tension under the CMC (σcmc) in aqueous solution were measured at 298 K. 54 kinds of molecular structure descriptors were selected as independent variables and the quantitative structure-activity relationship (QSAR) between surface activities of alkyl imidazoline and molecular structure were built through the genetic function approximation (GFA) method. Experimental results showed that the maximum surface excess of alkyl imidazoline molecules at the gas-liquid interface increased and the area occupied by each surfactant molecule and the free energies of micellization ΔGm decreased with increasing carbon number (NC) of the hydrophobic chain or decreasing hydrophilicity of counterions, which resulted in a CMC and σcmc decrease, while the log CMC and NC had a linear relationship and a negative correlation. The GFA-QSAR model, which was generated by a training set composed of 13 kinds of alkyl imidazoline though GFA method regression analysis, was highly correlated with predicted values and experimental values of the CMC. The correlation coefficient R was 0.9991, which means high prediction accuracy. The prediction error of 2 kinds of alkyl imidazoline CMCs in the Validation Set that quantitatively analyzed the influence of the alkyl imidazoline molecular structure on the CMC was less than 4%.

QSAR modeling of dihydrofolate reductase inhibitors as a therapeutic target for multiresistant bacteria

Antibacterial resistance is a growing public health threat of major concern around the world so development of new therapeutic approaches to prevent bacterial multidrug resistance has become a primary consideration for medicinal chemistry research. QSAR models for the dihydrofolate reductase inhibition with 2,4-diamino-5-(substituted-benzyle)-pyramidine derivatives were developed with further computer-aided design of new derivatives with desired activity. The Monte Carlo method has been used as a computational tool for QSAR modeling. For the representation of molecular structure and optimal descriptor calculation, the simplified molecular input line entry system (SMILES) together with the molecular graph (hydrogen-suppressed graph—HSG, hydrogen-filled graph—HFG, and the graph of atomic orbitals-GAO) was used. One-variable models have been calculated for one data split into training, test, and validation set. The impact of Morgan’s extended connectivity index on built QSAR models and outliers was determined. Statistical parameters for the best QSAR model are satisfying. Structural indicators (molecular fragments) responsible for the increase and the decrease of the stated activity are defined, and with the application of defined structural alerts, the computer-aided design of new derivatives with desired activity is presented. Computational experiments presented and applied in this research can satisfactorily predict desired endpoint and can be used further for computer-aided antibacterial drug design.

Randić index and information

The Randić index RG is one of the classical graph-based molecular structure descriptors that found countless applications in chemistry and pharmacology. The mathematical background of this index is also well elaborated. We now point out a hitherto unnoticed feature of RG, namely its connection with the degree-based information content of a (molecular) graph. This connection is based on the linear correlation betweenRG and the logarithm of the multiplicative version of the Randić index.

On structural properties of trees with minimal atom-bond connectivity index IV: Solving a conjecture about the pendent paths of length three

The atom-bond connectivity (ABC) index is one of the most investigated degree-based molecular structure descriptors with a variety of chemical applications. It is known that among all connected graphs, the trees minimize the ABC index. However, a full characterization of trees with a minimal ABC index is still an open problem. By now, one of the proved properties is that a tree with a minimal ABC index may have, at most, one pendent path of length 3, with the conjecture that it cannot be a case if the order of a tree is larger than 1178. Here, we provide an affirmative answer of a strengthened version of that conjecture, showing that a tree with minimal ABC index cannot contain a pendent path of length 3 if its order is larger than 415.

Chemical structure and correlation analysis of HIV-1 NNRT and NRT inhibitors and database-curated, published inhibition constants with chemical structure in diverse datasets

Human immunodeficiency virus (HIV-1) reverse transcriptase is a major target for designing anti-HIV drugs. Developed inhibitors are divided into non-nucleoside analog reverse-transcriptase inhibitors (NNRTIs) and nucleoside analog reverse-transcriptase inhibitors (NRTIs) depending on their mechanism. Given that many inhibitors have been studied and for many of them binding affinity constants have been calculated, it is beneficial to analyze the chemical landscape of these families of inhibitors and correlate these inhibition constants with molecular structure descriptors. For this, the HIV-1 RT data was retrieved from the ChEMBL database, carefully curated, and original literature verified, grouped into NRTIs and NNRTIs, analyzed using a hierarchical scaffold classification method and modelled with best multi-linear regression approach. Analysis of the HIV-1 NNRTIs subset results in ten different common structural parent types of oxazepanone, piperazinone, pyrazine, oxazinanone, diazinanone, pyridine, pyrrole, diazepanone, thiazole, and triazine. The same analysis for HIV-1 NRTIs groups structures into four different parent types of uracil, pyrimide, pyrimidione, and imidazole. Each scaffold tree corresponding to the parent types has been carefully analyzed and examined, and changes in chemical structure favorable to potency and stability are highlighted. For both subsets, descriptive and predictive QSAR models are derived, discussed and externally validated, revealing general trends in relationships between molecular structure and binding affinity constants in structurally diverse datasets. Data and QSAR models are available at the QsarDB repository (http://dx.doi.org/10.15152/QDB.202).

Refinement of a generalized Fermat’s last theorem conjecture in natural vector spaces

This study, at the light of a systematic computational search, provides a refined generalized Fermat’s last theorem conjecture with respect to the one, which appeared in a recent paper in this journal dealing with a Fermat-like behavior, attached in turn to the Minkowski norms defined within natural vector spaces. The aim of this kind of studies is to connect vector spaces with Boolean Hypercubes. This pretends also uncover the inner structure of vector sets, which appear important for the vectorial description of molecular structures and in this manner lead to new QSPR developments.

An alternative approach to unifying chemistry with quantum mechanics

Harold Kincaid in Individualism and the Unity of Science postulates a model of unity-without-reduction in order to accurately describe the relation between individualism and macroeconomics. I present this model and apply it to the description of the relation between chemistry and quantum mechanics. I argue that, when it comes to the description of molecular structure, chemistry and quantum mechanics are unified in Kincaid’s sense. Specifically, the two disciplines contribute to the formation of a unified body of knowledge with respect to molecular structure.

Structural characterization and chromatographic retention time simulation for some aliphatic carboxylic acids

Molecular structural descriptors (MVEIs) are developed from the molecular vertex electronegativity interaction, and the molecular structures of 43 organic acids are characterized. Two quantitative structure-retention relationship models are built up by the multiple linear regression and the partial least squares regression. The correlation coefficients (R) of the two models are 0.990 and 0.988, and the standard deviations of them are 2.935 and 3.024, respectively. Then the two models are evaluated by the leave-one-out cross-validation and the correlation coefficients (R CV) are 0.985 and 0.976, the standard deviations are 3.527 and 3.628, respectively. It is confirmed that MVEIs are largely dependent on the properties of the organic molecules.

Extended energy and its dependence on molecular structure

The extended energy ([Formula: see text]) is a vertex degree based and spectrum-based molecular structure descriptor, shown to be well correlated with a variety of physicochemical molecular properties. We investigate the dependence of [Formula: see text] on molecular structure and establish its basic characteristics. In particular, we show how [Formula: see text] is related with the geometric–arithmetic (GA) topological index. Our main finding is that the difference between [Formula: see text] and the total π-electron energy is linearly proportional to the difference between the number of edges and the GA index.

Experimental and quantum chemical studies on poriferasterol – A natural phytosterol isolated from Cassia sophera Linn. (Caesalpiniaceae)

Poriferasterol, a biologically relevant phytosterol, has been isolated and identified first-time from Cassia sophera Linn. (family: Caesalpiniaceae) based on detailed spectral studies. Exhaustive theoretical studies on the molecular structure, vibrational spectra, HOMO, LUMO, MESP surfaces and reactivity descriptor of this plant-derived natural molecule have been performed. The experimentally observed FT-IR spectrum of the title compound has been compared with spectral data obtained by DFT-B3LYP/6-311 + G (d,p) method. The UV–visible spectrum of the title compound has also been recorded and the electronic properties, such as frontier orbitals and band gap energy are measured by TD-DFT approach. The 1H and 13C NMR spectrum has been calculated by using the gauge independent atomic orbital method and compared with the observed data.

Remarks on maximum atom-bond connectivity index with given graph parameters

The atom-bond connectivity (ABC) index is a degree-based molecular structure descriptor that can be used for modelling thermodynamic properties of organic chemical compounds. Motivated by its applicable potential, a series of investigations have been carried out in the past several years. In this note we first consider graphs with given edge-connectivity that attain the maximum ABC index. In particular, we give an affirmative answer to the conjecture about the structure of graphs with edge-connectivity equal to one that maximize the ABC index, which was recently raised by Zhang et al. (2016). In addition, we provide supporting evidence for another conjecture posed by the same authors which concerns graphs that maximize the ABC index among all graphs with chromatic number equal to some fixed χ≥3. Specifically, we confirm this conjecture in the case where the order of the graph is divisible by χ.

Constraint score for semi-supervised feature selection in ligand-and receptor-based QSAR on serine/threonine-protein kinase PLK3 inhibitors

Constraint score is a feature selection method based on pairwise constraints which is used in classification problems. To the best of our knowledge, no work has used pairwise constraints for feature selection in QSAR models which have continuous values for activity of inhibitors. This study presented a semi-supervised constraint score for feature selection in ligand-and receptor-based QSAR. The semi-supervise constraint score used the supervision information of a small number of inhibitors with known inhibitory activity in the form of pairwise constraints beside the local structure of inhibitors with unknown inhibitory activity to evaluate descriptor importance. This method was used for selection of molecular structural descriptors and docking derived descriptors to predict the inhibitory activity of serine/threonine-protein kinase PLK3 inhibitors. The selected descriptors preserved the pairwise constraints defined on the inhibitors with known inhibitory activity and the local structure of inhibitors with unknown inhibitory activity. Performance comparison of the semi-supervised constraint score with other feature selection methods using RMSE, R2, and Q2ext values indicated its superiority in selecting relevant descriptors when a small number of inhibitors with known inhibitory activity are available. The results of this study showed that using the inhibitor with unknown inhibitory activity and a small number of supervision information in the form of pairwise constraints can achieve comparable or better performance than supervised and unsupervised methods.