Molecular Quantum Similarity Measures Research Articles

Understanding the comparative molecular field analysis (CoMFA) in terms of molecular quantum similarity and DFT-based reactivity descriptors.

The three-dimensional quantitative structure-activity relationship (3D QSAR) models have many applications, although the inherent complexity to understand the results coming from 3D-QSAR arises the necessity of new insights in the interpretation of them. Hence, the quantum similarity field as well as reactivity descriptors based on the density functional theory were used in this work as a consistent approach to better understand the 3D-QSAR studies in drug design. For this purpose, the quantification of steric and electrostatic effects on a series of bicycle [4.1.0] heptane derivatives as melanin-concentrating hormone receptor 1 antagonists were performed on the basis of molecular quantum similarity measures. The maximum similarity superposition and the topo-geometrical superposition algorithms were used as molecular alignment methods to deal with the problem of relative molecular orientation in quantum similarity. In addition, a chemical reactivity analysis using global and local descriptors such as chemical hardness, softness, electrophilicity, and Fukui functions, was developed. Overall, our results suggest that the application of this methodology in drug design can be useful when the receptor is known or even unknown.

ChemInform Abstract: Molecular Quantum Similarity Measures Tuned 3D QSAR: An Antitumoral Family Validation Study.

In this work, a new methodology to construct a tuned QSAR model is presented, which is based on a convex set formalism. The present procedure continues previous 3D QSAR studies, performed using molecular quantum similarity measures (MQSM). With this new computational tool, the efficiency of MQSM applied to QSAR analysis is significantly improved. A reliable QSAR model is obtained using convex linear combinations of different kinds of MQSM, corresponding to different quantum-mechanical operators related to the quantum similarity integral. The active compounds studied here, as a case study, are a set of antitumor agents, the camptothecin molecule and analogues, and the property evaluated is the topoisomerase-I inhibition activity. Before performing a tuned QSAR analysis with this particular molecular set, a simple QSAR study for all the different possible types of MQSM is carried out. In addition, another application of MQSM is presented, to determine which method can be used to optimize molecular structure...

Quantitative assessment of the effect of basis set superposition error on the electron density of molecular complexes by means of quantum molecular similarity measures

AbstractThe Chemical Hamiltonian Approach (CHA) method is applied to obtain Basis Set Superposition Error (BSSE)‐free molecular orbitals at the Hartree–Fock (HF) and Density Functional Theory (DFT) levels of theory. To assess qualitatively the effect of the BSSE on the first‐order electron density, we had previously applied Bader's analysis of the intermolecular critical points located on the electron density, as well as density difference maps for several hydrogen bonded complexes. In this work, Quantum Molecular Similarity Measures are probed as an alternative avenue to properly quantify the electronic relaxation due to the BSSE removal by means of distance indices between the uncorrected and corrected charge densities. It is shown that BSSE contamination is more important at the DFT level of theory, and in some cases, changes on the topology of the electron density are observed upon BSSE correction. Inclusion of diffuse functions have been found to dramatically decrease the BSSE effect in both geometry and electron density. The CHA method represents a good compromise to obtain accurate results with small basis sets. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Brominated phenols as auxin-like molecules

2,6-Dibromophenol (DBP) was reported as an auxin-like molecule using molecular quantum similarity measures. In this study, the auxin activity of this molecule and its chlorinated homologue is further determined using a bacterial biosensor: the auxin-inducible ipdC promoter of Azospirillum brasilense. We were able to demonstrate that DBP can induce gene expression, but to a lesser extent than the auxin indole-3-acetic acid (IAA) and that DBP is not an antagonist for the IAA signalling pathway. To investigate the role of the bromine groups, the molecule 2,6-dichlorophenol (DCP) was also tested for gene expression induction. However, no induction could be observed. In a second part, DBP and other molecules were modelled in the auxin-binding pocket of the plant auxin receptor TIR1 to evaluate theoretical binding energies. Both DBP and its chlorinated homologue DCP are not strong ligands compared to other known auxins such as IAA. The importance of a carboxylated side chain for optimal binding (and probably auxin activity) was demonstrated.

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.

Bond‐based 3D‐chiral linear indices: Theory and QSAR applications to central chirality codification

The recently introduced non-stochastic and stochastic bond-based linear indices are been generalized to codify chemical structure information for chiral drugs, making use of a trigonometric 3D-chirality correction factor. These improved modified descriptors are applied to several well-known data sets to validate each one of them. Particularly, Cramer's steroid data set has become a benchmark for the assessment of novel quantitative structure activity relationship methods. This data set has been used by several researchers using 3D-QSAR approaches such as Comparative Molecular Field Analysis, Molecular Quantum Similarity Measures, Comparative Molecular Moment Analysis, E-state, Mapping Property Distributions of Molecular Surfaces, and so on. For that reason, it is selected by us for the sake of comparability. In addition, to evaluate the effectiveness of this novel approach in drug design we model the angiotensin-converting enzyme inhibitory activity of perindoprilate's sigma-stereoisomers combinatorial library, as well as codify information related to a pharmacological property highly dependent on the molecular symmetry of a set of seven pairs of chiral N-alkylated 3-(3-hydroxyphenyl)-piperidines that bind sigma-receptors. The validation of this method is achieved by comparison with earlier publications applied to the same data sets. The non-stochastic and stochastic bond-based 3D-chiral linear indices appear to provide a very interesting alternative to other more common 3D-QSAR descriptors.

A quantum similarity matrix (QSM) Aufbau procedure

An Aufbau recursive algorithm, leading to the construction of molecular Quantum similarity matrices (QSM) with positive definite structure is described. As a consequence, Molecular Quantum Similarity measures optimization has to be restricted by a recursive constraint, related to the Euclidian norm of the QSM column elements in Quantum Object density tag reciprocal space.

Unrevealed structural requirements for auxin-like molecules by theoretical and experimental evidences

An computational-biostatistical approach, supported by ab initio optimizations of auxin-like molecules, was used to find biologically meaningful relationships between quantum chemical variables and fresh bioassay’s data. It is proven that the auxin-like recognition requires different molecular assembling states. We suggest that the carboxyl group is not the determining factor in explaining the biological auxin-like conduct. The biological effects depends essentially on the chemical condition of the ring system. The aim to find active molecules (quantum objects) via statistical grouping-analysis of molecular quantum similarity measures was verified by bioactivity assays. Next, this approach led to the discovery of a non-carboxylated active auxin-like molecule (2,6-dibromo-phenol). This is the first publication on structure activity relationship of auxin-like molecules, which relies on highly standardized bioassays of different auxins screened in parallel as well as analysed by multi-dimensional scaling.

Modelling Toxicity using Molecular Quantum Similarity Measures

AbstractIn this work, a general procedure for the application of Molecular Quantum Similarity Measures (MQSM) into the Quantitative Structure‐Toxicity Relationships (QSTR) field is presented. The methodology is presented from its theoretical background, beginning with the formulation of MQSM and the role of density functions. Other topics, like molecular modelling, electronic density fitting, similarity scaling and molecular superposition are also analysed. The theoretical part is complemented with three different application examples dealing with acute aquatic toxicity related to different fish species. The molecular sets are constituted by different kinds of benzene derivatives. Acceptable correlations are obtained for the aquatic toxicity using quantum similarity derived descriptors, allowing a fairly confident classification of the studied compounds according to their toxicity level.

Coulomb and Overlap Self-Similarities: A Comparative Selectivity Analysis of Structure−Function Relationships for Auxin−like Molecules

Auxins are defined mainly by a set of physiological actions, but the structure-effect relationship still is based on chemical intuition. Currently a well-defined auxin molecular structure is not available. The existence of different auxin binding proteins and mechanisms of auxin action, the wide diversity of the auxin molecules, and the pleiotropic effects of auxin imply a completely different mechanism as described for the animal hormone concept. Here, we present a computational approach dealing with semiempirical optimizations of the auxin molecules themselves, which represent a number of about 250 different chemical structures. Our approach uses molecular quantum similarity measures and additional quantum variables for the analysis of auxin-like molecules. The finding of similarities in molecules by focusing basically on their electron structure results in new insights in the relationship of the different auxin groups. Additional statistical analysis allows the identification of relationships between similarity groups and their biological activity, respectively. It is postulated that the auxin-like molecular recognition depends more on specific molecular assembling states than on a specific ring system or side chain.

Descriptors and Probability Distributions in MO Theory: Weighted Mulliken Matrices and Molecular Quantum Similarity Measures

Starting from the original Mulliken study on population analysis, it is shown how these initial ideas not only are expressible as expectation values of a projector, but also how they can be extended and generalized into the domain of non-singular Hermitian operators using the same technique. Some examples of this possibility are given. The formalism is studied in deep, proving that the Mulliken populations are a zero-th order approach to the description of condensed density functions and their connection with quantum similarity measures is analyzed. Employing positive definite operators as natural weights to compute atomic condensed density terms, lead to produce elements of vector semispaces. Such vectors can be subject to Minkowski normalization becoming discrete probability distributions, which can be gathered using several weight operators into stochastic arrays as molecular fingerprint descriptors.

Generation of Molecular Fields, Quantum Similarity Measures and Related Questions

A straightforward discussion on how to generate molecular fields is developed within the postulates of quantum mechanics. The theoretical formalism points towards the generalization and extension of the well-known molecular field forms, associated to density function and electrostatic molecular potential (EMP), including another category of fields associated to quantum molecular similarity measures. The results show that the new formalism can be easily applied to obtain an unlimited number of new information about molecular behavior.

Estimation of infinite dilution activity coefficients of organic compounds in water with neural classifiers

AbstractA new approach is presented for the development of quantitative structure–property relations (QSPR) based on the extraction of relevant molecular features with self‐organizing maps and the use of a modified fuzzy‐ARTMAP classifier for variable prediction. The present methodology is demonstrated for the development of a QSPR for the aqueous‐phase infinite dilution activity coefficient γ∞, based on a data set of 325 diverse organic compounds. The QSPR was developed using a set of 11 molecular descriptors (four connectivities vχ1–4, Coulomb self‐similarity measure, electron–nuclear attraction, dipole moment, sum of atomic numbers, number of filled levels, average polarizability, and nuclear–nuclear repulsion). The final set of molecular descriptors was selected from an initial pool of 23 topological and quantum chemical descriptors, including six molecular quantum similarity measures, by means of a topological analysis of self‐organization of the data set. Additional interpolated information to enhance the training of the neural system was obtained from the self‐organization analysis. The resulting fuzzy‐ARTMAP–based QSPRs performed with errors that were on the average seven times smaller compared to previous published models. The use of only four molecular quantum similarity measures proved to be sufficient for building a lnγ∞ fuzzy‐ARTMAP–based QSPR with reasonable accuracy. © 2004 American Institute of Chemical Engineers AIChE J, 50:1315–1343, 2004

Quality of Approximate Electron Densities and Internal Consistency of Molecular Alignment Algorithms in Molecular Quantum Similarity.

The calculation of molecular quantum similarity measures using the molecular electron density requires the electron density and molecular alignment between two molecules. To obtain meaningful quantum similarity matrices, the electron density should be calculated efficiently and accurately and the alignment should be internally consistent. The internal consistency of the alignment for a series of molecules is investigated through distance geometry concepts. The calculation of the quantum similarity matrix requires the calculation of a quadratic number of similarity integrals, and a scheme to obtain these efficiently is developed. Both the alignment procedure and the ASA method for approximate molecular electron densities are tested for a set of steroid molecules.

Quality of approximate electron densities and internal consistency of molecular alignment algorithms in molecular quantum similarity.

The calculation of molecular quantum similarity measures using the molecular electron density requires the electron density and molecular alignment between two molecules. To obtain meaningful quantum similarity matrices, the electron density should be calculated efficiently and accurately and the alignment should be internally consistent. The internal consistency of the alignment for a series of molecules is investigated through distance geometry concepts. The calculation of the quantum similarity matrix requires the calculation of a quadratic number of similarity integrals, and a scheme to obtain these efficiently is developed. Both the alignment procedure and the ASA method for approximate molecular electron densities are tested for a set of steroid molecules.

Molecular Quantum Similarity‐Based QSARs for Binding Affinities of Several Steroid Sets.

The application of Molecular Quantum Similarity Measures (MQSM) to correlate biological activities for three different sets of steroids is reported. A general protocol for the generation of descriptors is detailed, thus covering molecular superposition, electronic density fitting, and quantum similarity calculation issues. Satisfactory Quantitative Structure−Activity Relationship (QSAR) models (r2 ∈ [0.69,0.94] and q2 ∈ [0.59,0.73]), comparable to previous studies, are obtained in all cases, where steroid binding affinities to different enzymes are studied. In this work, MQSM, properly scaled using Carbo Index, are related to activity using a Partial Least Squares routine.

Classification of reaction pathways via momentum–space and quantum molecular similarity measures

For four rearrangement reactions, we evaluate (i) values of the moments of momentum 〈 p n 〉(−2⩽ n⩽+1) for reactants, products and transition states (ii) position–space similarity indices between reactants, products and transition states using wavefunctions generated from both Hartree–Fock and density-functional theory (B3LYP). Both the momentum–space expectation values and the similarity measures can be used to distinguish Hammond and anti-Hammond behaviour. In position–space, two new parameters, δ and φ, are introduced to quantify the position and character of the transition state relative to the reactants and products.

Molecular quantum similarity-based QSARs for binding affinities of several steroid sets.

The application of Molecular Quantum Similarity Measures (MQSM) to correlate biological activities for three different sets of steroids is reported. A general protocol for the generation of descriptors is detailed, thus covering molecular superposition, electronic density fitting, and quantum similarity calculation issues. Satisfactory Quantitative Structure-Activity Relationship (QSAR) models (r(2) in [0.69,0.94] and q(2) in [0.59,0.73]), comparable to previous studies, are obtained in all cases, where steroid binding affinities to different enzymes are studied. In this work, MQSM, properly scaled using Carbó Index, are related to activity using a Partial Least Squares routine.

Using molecular quantum similarity measures under stochastic transformation to describe physical properties of molecular systems.

The application of molecular quantum similarity measures (MQSM) to correlate physicochemical properties is reported. Satisfactory quantitative structure-property relationship (QSPR) models are obtained for three molecular sets, where boiling points and chromatographic retention times and indices are studied. In this work, MQSM are scaled using a stochastic transformation and related to molecular properties using the partial least-squares technique.

Molecular Quantum Similarity Measures as Descriptors for Quantum QSAR

Molecular quantum similarity establishes quantitative similarity measures between molecular structures by means of the comparison of their electronic distributions. From this theoretical framework, different molecular descriptors can be derived and used as QSAR parameters. In particular, molecular quantum similarity matrices and the electron-electron interaction energy are examined. A brief exposition of the methodology and the QSAR protocol is given, and a summary of the results obtained using these descriptors is presented.