Quantum Similarity Indices Research Articles

New findings on ligand series used as SARS-CoV-2 virus inhibitors within the frameworks of molecular docking, molecular quantum similarity and chemical reactivity indices

Background The severe acute respiratory syndrome coronavirus (SARS-CoV)-2 virus causes an infectious illness named coronavirus disease 2019 (COVID-19). SARS-CoV is a positive-sense single-stranded RNA virus from the Betacoronavirus genus. The SARS-CoV-2 RNA-dependent RNA polymerase (RdRp) has an important role in the viral life cycle and its active site is a very accessible region, thus a potential therapeutic approach may be to target this region to study the inhibition of viral replication. Various preexisting drugs have been proposed for the treatment of COVID-19 and the use of existing antiviral agents may reduce the time and cost of new drug discoveries, but the efficacy of these drugs is limited. Therefore, the aim of the present study was to evaluate a number of ligands used as SARS-CoV-2 virus inhibitors to determine the suitability of them for potential COVID-19 treatment. Methods In this study, we selected a series of ligands used as SARS-CoV-2 virus inhibitors such as: abacavir, acyclovir, amprenavir, ascorbic acid vitamin C, azithromycin, baloxavir, boceprevir, cholecalciferol vitamin D, cidofovir, edoxudine, emtricitabine, hydroxychloroquine and remdesivir. These ligands were analyzed using molecular docking, molecular quantum similarity, and chemical reactivity indices defined within a conceptual density functional theory framework. Results The analysis of molecular quantum similarity indices on inhibitors showed a high number of differences from a structural point of view. However, they are quite similar in their electronic density, obtaining the highest values in the electronic similarity index. Global and local chemical reactivity indices were analyzed. Conclusions These studies allowed for the identification of the main stabilizing interactions using the crystal structure of SARS-CoV-2 RdRp. The molecular quantum similarity and chemical reactivity descriptors provide novel insights into these ligands that can be used in the design of new COVID-19 treatments.

Philicity scales using molecular quantum similarity and chemical reactivity indices within density functional theory

AbstractIn this manuscript, we postulate a possible relationship of philicity within a molecular set of electrocyclic reactions. Philicity has been studied by Chattaraj and co‐workers (J. Phys. Chem. A. 2003, 107, 25). This important concept was obtained using the electrophilicity index and Fukui functions. Recently, the present author has published a possible way to quantify philicity using molecular quantum similarity and chemical reactivity indices (see, J. Math. Chem. 2023, 61, 165). In this work, philicity was related with the molecular quantum similarity framework to obtain a possible way to relate philicity using 21 electrocyclic reactions using the cyclobutene reaction as a reference. The main idea is to postulate philicity scales. This methodology can open up a possible path to find systematic relationships in each molecular ensemble using the selectivity defined in the density functional theory context. With these scales, we can relate the effect of the substituent on the electrocyclic opening reaction on the molecular set.

New findings on ligand series used as SARS-CoV-2 virus inhibitors within the frameworks of molecular docking, molecular quantum similarity and chemical reactivity indices

Background: The severe acute respiratory syndrome coronavirus (SARS-CoV)-2 virus causes an infectious illness named coronavirus disease 2019 (COVID-19). SARS-CoV is a positive-sense single-stranded RNA virus from the Betacoronavirus genus. The SARS-CoV-2 RNA-dependent RNA polymerase (RdRp) has an important role in the viral life cycle and its active site is a very accessible region, thus a potential therapeutic approach may be to target this region to study the inhibition of viral replication. Various preexisting drugs have been proposed for the treatment of COVID-19 and the use of existing antiviral agents may reduce the time and cost of new drug discoveries, but the efficacy of these drugs is limited. Therefore, the aim of the present study was to evaluate a number of ligands used as SARS-CoV-2 virus inhibitors to determine the suitability of them for potential COVID-19 treatment. Methods: In this study, we selected a series of ligands used as SARS-CoV-2 virus inhibitors such as: abacavir, acyclovir, amprenavir, ascorbic acid vitamin C, azithromycin, baloxavir, boceprevir, cholecalciferol vitamin D, cidofovir, edoxudine, emtricitabine, hydroxychloroquine and remdesivir. These ligands were analyzed using molecular docking, molecular quantum similarity, and chemical reactivity indices defined within a conceptual density functional theory framework. Results: The analysis of molecular quantum similarity indices on inhibitors showed a high number of differences from a structural point of view. However, they are quite similar in their electronic density, obtaining the highest values in the electronic similarity index. Global and local chemical reactivity indices were analyzed. Conclusions: These studies allowed for the identification of the main stabilizing interactions using the crystal structure of SARS-CoV-2 RdRp. The molecular quantum similarity and chemical reactivity descriptors provide novel insights into these ligands that can be used in the design of new COVID-19 treatments.

New findings on ligand series used as SARS-CoV-2 virus inhibitors within the frameworks of molecular docking, molecular quantum similarity and chemical reactivity indices

Background: The severe acute respiratory syndrome coronavirus (SARS-CoV)-2 virus causes an infectious illness named coronavirus disease 2019 (COVID-19). SARS-CoV is a positive-sense single-stranded RNA virus from the Betacoronavirus genus. The SARS-CoV-2 RNA-dependent RNA polymerase (RdRp) has an important role in the viral life cycle and its active site is a very accessible region, thus a potential therapeutic approach may be to target this region to study the inhibition of viral replication. Various preexisting drugs have been proposed for the treatment of COVID-19 and the use of existing antiviral agents may reduce the time and cost of new drug discoveries, but the efficacy of these drugs is limited. Therefore, the aim of the present study was to evaluate a number of ligands used as SARS-CoV-2 virus inhibitors to determine the suitability of them for potential COVID-19 treatment. Methods: In this study, we selected a series of ligands used as SARS-CoV-2 virus inhibitors such as: abacavir, acyclovir, amprenavir, ascorbic acid vitamin C, azithromycin, baloxavir, boceprevir, cholecalciferol vitamin D, cidofovir, edoxudine, emtricitabine, hydroxychloroquine and remdesivir. These ligands were analyzed using molecular docking, molecular quantum similarity, and chemical reactivity indices defined within a conceptual density functional theory framework. Results: The analysis of molecular quantum similarity indices on inhibitors showed a high number of differences from a structural point of view. However, they are quite similar in their electronic density, obtaining the highest values in the electronic similarity index. Global and local chemical reactivity indices were analyzed. Conclusions: These studies allowed for the identification of the main stabilizing interactions using the crystal structure of SARS-CoV-2 RdRp. The molecular quantum similarity and chemical reactivity descriptors provide novel insights into these ligands that can be used in the design of new COVID-19 treatments.

Study of interaction energies between residues of the active site of Hsp90 and geldanamycin analogues using quantum mechanics/molecular mechanics methods

Background:Heat shock protein (Hsp90KDa) is a molecular chaperone involved in the process of cellular oncogenesis, hence its importance as a therapeutic target in clinical trials. Geldanamycin is an inhibitor of Hsp90 chaperone activity, which binds to the ATP binding site in the N-terminal domain of Hsp90. However, geldanamycin has shown hepatotoxic damage in clinical trials; for this reason, its use is not recommended. Taking advantage that geldanamycin binds successfully to Hsp90, many efforts have focused on the search for similar analogues, which have the same or better biological response and reduce the side effects of its predecessor; 17-AAG and 17-DMAG are examples of these analogues.Methods:In order to know the chemical factors influencing the growth or decay of the biological activity of geldanamycin analogues, different computational techniques such as docking, 3DQSAR and quantum similarity were used. Moreover, the study quantified the interaction energy between amino acids residues of active side and geldanamycin analogues, through hybrid methodologies and density functional theory (DFT) indexes.Results:The evaluation of interaction energies showed that the interaction with Lys58 residue is essential for the union of the analogues to the active site of Hsp90, and improves its biological activity. This union is formed through a substituent on C-11 of the geldanamycin macrocycle. A small and attractor group was found as the main steric and electrostatic characteristic that substituents on C11 need in order to interact with Lys 58; behavior was observed with hydroxy and methoxy series of geldanamycin analogues, under study.Conclusion:These outcomes were supported with quantum similarity and reactivity indices calculations using DFT in order to understand the non-covalent stabilization in the active site of these compounds.

Adenosine Derivates as Antioxidant Agents: Synthesis, Characterization, in Vitro Activity, and Theoretical Insights.

In this work, we present results about the synthesis and the antioxidant properties of seven adenosine derivatives. Four of these compounds were synthesized by substituting the N6-position of adenosine with aliphatic amines, and three were obtained by modification of the ribose ring. All compounds were obtained in pure form using column chromatography, and their structures were elucidated by infrared spectroscopy (IR) and Nuclear Magnetic Resonance (NMR). All adenosine derivatives were further evaluated in vitro as free radical scavengers. Our results show that compounds 1c, 3, and 5 display a potent antioxidant effect compared with the reference compound ascorbic acid. In addition, the absorption, distribution, metabolism and excretion (ADME) calculations show favorable pharmacokinetic parameters for the set of compounds analyzed, which guarantees their suitability as potential antioxidant drugs. Furthermore, theoretical analyses using Molecular Quantum Similarity and reactivity indices were performed in order to discriminate the different reactive sites involved in oxidative processes.

Efficient synthesis and antioxidant activity of novel N-propargyl tetrahydroquinoline derivatives through the cationic Povarov reaction

New N-propargyl tetrahydroquinolines 6a-g have been synthesized efficiently through the cationic Povarov reaction (a domino Mannich/Friedel-Crafts reaction), catalyzed by Indium (III) chloride (InCl3), from the corresponding N-propargylanilines preformed, formaldehyde and N-vinylformamide, with good to moderate yields. All tetrahydroquinoline derivatives obtained were evaluated in vitro as free radical scavengers. Results showed that compound 6c presents a potent antioxidant effect compared with ascorbic acid, used as a reference compound. ADME predictions also revealed favorable pharmacokinetic parameters for the synthesized compounds, which warrant their suitability as potentials antioxidant. Additionally, a theoretical study using Molecular Quantum Similarity and reactivity indices were developed to discriminate different reactive sites in the new molecules in which the oxidative process occurs.

Study of interactions energies between residues of the active site of Hsp90 and the geldanamycin analogues using Quantum Mechanics/Molecular Mechanics (QM/MM) methods

Background: (Hsp90) 90KDa heat shock proteins are molecular chaperone involved in process of cellular oncogenesis, hence its marked importance as a therapeutic target. An inhibitor of Hsp90 chaperone activity is the geldanamycin, a thready compound that has the power to bind to the binding of ATP in the N-terminal of Hsp90 domain site, however this reported in clinical trials hepatotoxic damage, which I pitting to its disuse. On the other hand, taking advantage that the geldanamycin joins successfully Hsp90, efforts have focused on the search for similar that they have the same or better effect and both exhibited lower effects than its predecessor, as it has been the case with the similar 17-AAG and 17-DMAG. Methods: In order to know the chemical factors influencing the growth or decay of the biological activity of such compounds have been evaluated different computational techniques such as docking and 3DQSAR, however it has not been considered in a quantitative way what happens within the active site represented in terms of interaction energy, as it has been evaluated in this work. Results: To evaluate interaction energies found that the Lys58 is essential for the union of the analogs to the active site of Hsp90, and that the activity of these will depend on if these have on the C-11 position of the macrocycle a group of small and at the same time attractor of electrons, as it is reflected with the series C-11 hydroxy and methoxy C-11. Conclusion: Theses outcomes were supported with Quantum Similarity and reactivity indices using the Density Funtional Theory in order to understand the non-covalent stabilization in the active site for theses compounds.

Discriminating Drug-Like Compounds by Partition Trees with Quantum Similarity Indices and Graph Invariants.

The search for new drug candidates in databases is of paramount importance in pharmaceutical chemistry. The selection of molecular subsets is greatly optimized and much more promising when potential drug-like molecules are detected a priori. In this work, about one hundred thousand molecules are ranked following a new methodology: a drug/non-drug classifier constructed by a consensual set of classification trees. The classification trees arise from the stochastic generation of training sets, which in turn are used to estimate probability factors of test molecules to be drug-like compounds. Molecules were represented by Topological Quantum Similarity Indices and their Graph Theoretical counterparts. The contribution of the present paper consists of presenting an effective ranking method able to improve the probability of finding drug-like substances by using these types of molecular descriptors.

Communications on quantum similarity (4): collective distances computed by means of similarity matrices, as generators of intrinsic ordering among quantum multimolecular polyhedra

This study generalizes the notion of distance via defining an axiomatic collective distance, between arbitrary vector sets. A first part discusses conceptual tools, which can be later useful for general mathematical practice or as computational quantum similarity indices. After preliminary definitions, two elements, which can be associated with arbitrary sets of a vector space, are described: the centroid and the variance vectors. The Minkowski norm of the variance vector is shown to comply with the axioms of a collective distance. The role of the Gram matrix, associated with a vector set, is linked to the definition of numerical variance. Several simple application examples involving linear algebra and N‐dimensional geometry are given. In a second part, all previous definitions are applied to quantum multimolecular polyhedra (QMP), where a set of molecular quantum mechanical density functions act as vertices. The numerical Minkowski norm of the variance vector in any QMP could be considered as a superposition of molecular contributions, corresponding to a new set of quantum similarity indices, which can generate intrinsic ordering among QMP vertices. In this way, the role of quantum similarity matrix elements is evidenced. Application to collections of molecular structures is analyzed as an illustrative practical exercise. The connection of the QMP framework with classical and quantum quantitative structure–properties relation (QSPR) becomes evident with the aid of numerical examples computed over several molecular sets acting as QMP. WIREs Comput Mol Sci 2015, 5:380–404. doi: 10.1002/wcms.1223This article is categorized under: Structure and Mechanism > Molecular Structures Computer and Information Science > Chemoinformatics Computer and Information Science > Computer Algorithms and Programming

Electron-pair shell density approximation applied to inner and outer densities of atoms

The shell density approximation to the electron-pair radial density of atoms is applied to the inner \(D_ (r)\) densities, which are two components of the single-electron density \(D(r)\). The inner and outer densities are found to be expressed by product sums of shell densities and shell distributions or their complements. The expressions clarify physical meaning of the two densities and give examples for constructing two-electron properties from single-electron properties. Examination of the 53 atoms He through Xe shows that the quantum similarity indices between the original and approximate densities, bounded by 0 (complete dissimilarity) and 1 (complete similarity), are never smaller than 0.99998 and 0.99987 for the inner and outer densities, respectively. The local nature of the shell density and the monotonically increasing property of the shell distribution are used to derive simple shellwise lower and upper bounds to \(D_ (r)\) in terms of \(D(r)\) and the numbers of shell electrons. Numerical tests of the bounds demonstrate their utility.

Quantum molecular similarity analysis and quantitative definition of catecholamines with respect to biogenic monoamines associated: Scale alpha and beta of quantitative convergence

AbstractIn this article, we propose to make a quantitative definition of catecholamines with respect monoamine biogenic associated, this quantification allows define the alpha and beta scales, which expresses mathematically the correlation group of catecholamines with respect to their common fragment (phenylethylamine) and the tyrosine precursor, in addition performed quantum molecular similarity analysis using four descriptors, quantified by: molecular quantum similarity indices of overlap, Coulomb, overlap‐interaction, Coulomb‐interaction, overlap‐distances Euclidian, and Coulomb‐distances Euclidian, using the topo‐geometrical superposition approach as method of alignment, also proposes a methodology for defining individual groups quantitatively, based on quantum similarity descriptors and supporting the interpretations with experimental results of structural path of reaction. Take in account the importance of creating tools that allow the quantification of biological relationships, and allow the creation of scales of group relations, this scales may be useful in organic synthesis of catecholamines for determine similarities, considering the search for experimental conditions as an area of growing scientific interest. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Relativistic quantum similarities in atoms in position and momentum spaces

A study of different quantum similarity measures and their corresponding quantum similarity indices is carried out for the atoms from H to Lr ( Z = 1 – 103 ). Relativistic effects in both position and momentum spaces have been studied by comparing the relativistic values to the non-relativistic ones. We have used the atomic electron density in both position and momentum spaces obtained within relativistic and non-relativistic numerical-parameterized optimized effective potential approximations.

Formal theory of the comparative relations: its application to the study of quantum similarity and dissimilarity measures and indices

The study proposes a formal theory of comparative relations characterized by a group of abstract definitions and axioms. This abstract characterization allows us to rigorously define in a very general form what a comparative relation is, which can in turn be used as starting point in every case where comparative analysis is used. Some of the consequences of this formalization—when applied to existing results- are analyzed, particularly those related with the consistency of the results of the comparisons. Following, a study was conducted of descriptors of Quantum Quantitative Structure–Property Relationships models proposed by Carbo-Dorca et al. Several quantum comparative indices such as: Carbo, Hodgkin–Richards, Petke, Tanimoto, conjugate Petke and conjugate Hodgkin–Richards were also analyzed. The proposed theory gives a solid theoretical basis for comparative analysis that will have a positive impact on a broad spectrum of disciplines, where the field of chemistry could be one of the most important beneficiaries.

INTERNAL TEST SET (ITS) METHOD: A NEW CROSS-VALIDATION TECHNIQUE TO ASSESS THE PREDICTIVE CAPABILITY OF QSAR MODELS. APPLICATION TO A BENCHMARK SET OF STEROIDS

A new internal cross-validation method is presented for assessing the true predictive capability of QSAR models. The test is general and can be applied in many QSAR/QSPR approaches. In this work, the method is tested on a well-known benchmark set of steroids. In order to make the calculations, Topological Quantum Similarity Indices and Multiple Linear Regression models were considered. warned that these simple aspects of paramount importance for method reliability must be well taken care of. In this work an internal validation method inspired by the concept of the external validation test set is described. The method is general and applicable to many QSAR approaches. It can be easily generalized to any LMO cross-validation protocol but, for the sake of simplicity, the algorithm presented here lies within the context of a simpler approach: the LOO procedure. In its basic formulation, the LOO-CV procedure can be applied when a fixed set of descriptors is considered for a set of n molecules. For each molecule, a model is built considering the experimental property value of the n- 1 remaining compounds and the respective descriptors. Then, this model is used to make a prediction for the molecule left out. The above primary algorithm is named here the kernel of the standard LOO-CV method. This kernel algorithm can be applied using linear or non-linear methods such as Neural Networks 5,6

3D-chiral (2.5) atom-based TOMOCOMD-CARDD descriptors: theory and QSAR applications to central chirality codification

The history of the use of chiral descriptors in Quantitative structure–activity relationships (QSAR) studies is described, with a particular emphasis on several series of novel chirality descriptors that have been introduced in this field. Specifically, chiral topological indices that circumvent the inability of conventional (chiral insensitive) topological molecular descriptors are reviewed. These modified descriptors were applied to several well-know data sets in order to validate each one of them. Particularly, Cramer’s steroid data set has become a benchmark for the assessment of novel QSAR methods. This data set has been used by several researches using 3D-QSAR approaches such as Comparative Molecular Field Analysis (CoMFA), Comparative Molecular Similarity Indices Analysis (CoMSIA), Molecular Quantum Similarity Measures (MQSM), 3D-chiral (2.5) TOMOCOMD-CARDD descriptors, Topological Quantum Similarity Indices (TQSI), similarity matrixes, Comparative Molecular Moment Analysis (CoMMA), E-state, Mapping Property Distributions of Molecular Surfaces (MAP), EVA and so on. For that reason, it was selected for the shake of comparability by us. An extensive comparison between all these approaches was updated. In addition, to evaluate the effectiveness of this novel approach in drug design we have modelled the angiotensin-converting enzyme inhibitory activity of perindoprilate’s σ-stereoisomers combinatorial library as well as to codify information related to pharmacological property highly dependent on molecular symmetry of a set of seven pairs of chiral N-alkylated 3-(3-hydroxyphenyl)-piperidines that bind σ-receptors. The validation of this method was achieved by comparison with previous reports applied to the same data sets. The non-stochastic and stochastic 3D-chiral (2.5) bilinear indices appear to provide a very interesting alternative to other more common 3D-QSAR descriptors.

Geometric and electronic similarities between transition structures for electrocyclizations and sigmatropic hydrogen shifts

This paper reports new theoretical evidence that supports previous proposals concerning the similarity between transition structures for electrocyclizations and sigmatropic hydrogen shifts. This evidence was obtained using two recently proposed methodologies, namely the so-called generalized population analysis and the formalism of molecular quantum similarity indices. Analysis of multicenter bond indices shows that the transition structures for cationic [1,n] hydrogen shifts do indeed have three-center indices that are similar to those of other three-center carbocations. In addition, the close resemblance of the electronic structures of electrocyclic and sigmatropic transition structures that differ by only a proton is supported by the values of their quantum molecular similarity indices.

A Mathematical Discussion on Density and Shape Functions, Vector Semispaces and Related Questions

Density and shape functions are studied from the point of view of vector semispace structure and properties. Useful characteristics based on the shell structure of vector semispaces are used to analyze some properties of both functions. Fukui functions and quantum similarity indices are also studied when basic applications of the theory are discussed. Construction of approximate density functions and pseudo wave functions is also outlined. Finally, the original DFT variational theorem is reformulated within the frame of the shape function.

A Formal Comparison between Molecular Quantum Similarity Measures and Indices

In this paper two methods are described to establish a formal comparison between different molecular quantum similarity measures (MQSM) and indices (MQSI) to detect redundancies in the information produced. The methods used are the Procrustes analysis and a proximity measure involving standarized similarity vectors. A small set of molecules, the fluoro- and chloro-substituted methanes, are used as an illustrative example, and conclusions obtained by direct comparison of the similarity matrixes are retrieved.

Second-order quantum similarity measures from intracule and extracule densities

The calculation of quantum similarity measures from second-order density functions contracted to intracule and extracule densities obtained at the Hartree-Fock level is presented and applied to a series of atoms, (He, Li, Be, and Ne), isoelectronic molecules (C2H2, HCN, CNH, CO, and N2), and model hydrogen-transfer processes (H2/H+, H2/Hot, H2/H−). Second-order quantum similarity measures and indices are found to be suitable measures for quantitatively analyzing electron-pair density reorganizations in atoms, molecules, and chemical processes. For the molecular series, a comparative analysis between the topology of pairwise similarity functions as computed from one-electron, intracule, and extracule densities is carried out and the assignment of each particular local similarity maximum to a molecular alignment discussed. In the comparative study of the three hydrogen-transfer reactions considered, second-order quantum similarity indices are found to be more sensitive than first-order indices for analyzing the electron-density reorganization between the reactant complex and the transition state, thus providing additional insights for a better understanding of the mechanistic aspects of each process.