Three-dimensional quantitative structure-activity relationships from tuned molecular quantum similarity measures: prediction of the corticosteroid-binding globulin binding affinity for a steroid family

Higher-Order and Mixed Discrete Derivatives such as a Novel Graph- Theoretical Invariant for Generating New Molecular Descriptors

BACKGROUND

Recently, some authors have defined new molecular descriptors (MDs) based on the use of the Graph Discrete Derivative, known as Graph Derivative Indices (GDI). This new approach about discrete derivatives over various elements from a graph takes as outset the formation of subgraphs. Previously, these definitions were extended into the chemical context (N-tuples) and interpreted in structural/physicalchemical terms as well as applied into the description of several endpoints, with good results.

OBJECTIVE

A generalization of GDIs using the definitions of Higher Order and Mixed Derivative for molecular graphs is proposed as a generalization of the previous works, allowing the generation of a new family of MDs.

METHODS

An extension of the previously defined GDIs is presented, and for this purpose, the concept of Higher Order Derivatives and Mixed Derivatives is introduced. These novel approaches to obtaining MDs based on the concepts of discrete derivatives (finite difference) of the molecular graphs use the elements of the hypermatrices conceived from 12 different ways (12 events) of fragmenting the molecular structures. The result of applying the higher order and mixed GDIs over any molecular structure allows finding Local Vertex Invariants (LOVIs) for atom-pairs, for atoms-pairs-pairs and so on. All new families of GDIs are implemented in a computational software denominated DIVATI (acronym for Discrete DeriVAtive Type Indices), a module of KeysFinder Framework in TOMOCOMD-CARDD system.

RESULTS

QSAR modeling of the biological activity (Log 1/K) of 31 steroids reveals that the GDIs obtained using the higher order and mixed GDIs approaches yield slightly higher performance compared to previously reported approaches based on the duplex, triplex and quadruplex matrix. In fact, the statistical parameters for models obtained with the higher-order and mixed GDI method are superior to those reported in the literature by using other 0-3D QSAR methods.

CONCLUSION

It can be suggested that the higher-order and mixed GDIs, appear as a promissory tool in QSAR/QSPRs, similarity/dissimilarity analysis and virtual screening studies.

QuBiLS-MAS, open source multi-platform software for atom- and bond-based topological (2D) and chiral (2.5D) algebraic molecular descriptors computations

BACKGROUND

In previous reports, Marrero-Ponce et al. proposed algebraic formalisms for characterizing topological (2D) and chiral (2.5D) molecular features through atom- and bond-based ToMoCoMD-CARDD (acronym for Topological Molecular Computational Design-Computer Aided Rational Drug Design) molecular descriptors. These MDs codify molecular information based on the bilinear, quadratic and linear algebraic forms and the graph-theoretical electronic-density and edge-adjacency matrices in order to consider atom- and bond-based relations, respectively. These MDs have been successfully applied in the screening of chemical compounds of different therapeutic applications ranging from antimalarials, antibacterials, tyrosinase inhibitors and so on. To compute these MDs, a computational program with the same name was initially developed. However, this in house software barely offered the functionalities required in contemporary molecular modeling tasks, in addition to the inherent limitations that made its usability impractical. Therefore, the present manuscript introduces the QuBiLS-MAS (acronym for Quadratic, Bilinear and N-Linear mapS based on graph-theoretic electronic-density Matrices and Atomic weightingS) software designed to compute topological (0-2.5D) molecular descriptors based on bilinear, quadratic and linear algebraic forms for atom- and bond-based relations.

RESULTS

The QuBiLS-MAS module was designed as standalone software, in which extensions and generalizations of the former ToMoCoMD-CARDD 2D-algebraic indices are implemented, considering the following aspects: (a) two new matrix normalization approaches based on double-stochastic and mutual probability formalisms; (b) topological constraints (cut-offs) to take into account particular inter-atomic relations; (c) six additional atomic properties to be used as weighting schemes in the calculation of the molecular vectors; (d) four new local-fragments to consider molecular regions of interest; (e) number of lone-pair electrons in chemical structure defined by diagonal coefficients in matrix representations; and (f) several aggregation operators (invariants) applied over atom/bond-level descriptors in order to compute global indices. This software permits the parallel computation of the indices, contains a batch processing module and data curation functionalities. This program was developed in Java v1.7 using the Chemistry Development Kit library (version 1.4.19). The QuBiLS-MAS software consists of two components: a desktop interface (GUI) and an API library allowing for the easy integration of the latter in chemoinformatics applications. The relevance of the novel extensions and generalizations implemented in this software is demonstrated through three studies. Firstly, a comparative Shannon's entropy based variability study for the proposed QuBiLS-MAS and the DRAGON indices demonstrates superior performance for the former. A principal component analysis reveals that the QuBiLS-MAS approach captures chemical information orthogonal to that codified by the DRAGON descriptors. Lastly, a QSAR study for the binding affinity to the corticosteroid-binding globulin using Cramer's steroid dataset is carried out.

CONCLUSIONS

From these analyses, it is revealed that the QuBiLS-MAS approach for atom-pair relations yields similar-to-superior performance with regard to other QSAR methodologies reported in the literature. Therefore, the QuBiLS-MAS approach constitutes a useful tool for the diversity analysis of chemical compound datasets and high-throughput screening of structure-activity data.

Tensor algebra-based geometric methodology to codify central chirality on organic molecules

A novel mathematical procedure to codify chiral features of organic molecules in the QuBiLS-MIDAS framework is introduced. This procedure constitutes a generalization to that commonly used to date, where the values 1 and -1 (correction factor) are employed to weight the molecular vectors when each atom is labelled as R (rectus) or S (sinister) according to the Cahn-Ingold-Prelog rules. Therefore, values in the range [Formula: see text] with steps equal to 0.25 may be accounted for. The atoms labelled R or S can have negative and positive values assigned (e.g. -3 for an R atom and 1 for an S atom, or vice versa), opposed values (e.g. -3 for an R atom and 3 for an S atom, or vice versa), positive values (e.g. 3 for an R atom and 1 for an S atom) or negative values (e.g. -3 for an R atom and -1 for an S atom). These proposed Chiral QuBiLS-MIDAS 3D-MDs are real numbers, non-symmetric and reduced to 'classical' (non-chiral) QuBiLS-MIDAS 3D-MDs when symmetry is not codified (correction factor equal to zero). In this report, only the factors with opposed values were considered with the purpose of demonstrating the feasibility of this proposal. From QSAR modelling carried out on four chemical datasets (Cramer's steroids, fenoterol stereoisomer derivatives, N-alkylated 3-(3-hydroxyphenyl)-piperidines, and perindoprilat stereoisomers), it was demonstrated that the use of several correction factors contributes to the building of models with greater robustness and predictive ability than those reported in the literature, as well as with respect to the models exclusively developed with QuBiLS-MIDAS 3D-MDs based on the factor 1 | -1. In conclusion, it can be stated that this novel strategy constitutes a suitable alternative to computed chirality-based descriptors, contributing to the development of good models to predict properties depending on symmetry.

Analyzing the substitution effect on the CoMFA results within the framework of density functional theory (DFT)

Though QSAR was originally developed in the context of physical organic chemistry, it has been applied very extensively to chemicals (drugs) which act on biological systems, in this idea one of the most important QSAR methods is the 3D QSAR model. However, due to the complexity of understanding the results it is necessary to postulate new methodologies to highlight their physical-chemical meaning. In this sense, this work postulates new insights to understand the CoMFA results using molecular quantum similarity and chemical reactivity descriptors within the framework of density functional theory. To obtain these insights a simple theoretical scheme involving quantum similarity (overlap, coulomb operators, their euclidean distances) and chemical reactivity descriptors such as chemical potential (μ), hardness (ɳ), softness (S), electrophilicity (ω), and the Fukui functions, was used to understand the substitution effect. In this sense, this methodology can be applied to analyze the biological activity and the stabilization process in the non-covalent interactions on a particular molecular set taking a reference compound.

Combining spatial and chemical information for clustering pharmacophores

BACKGROUND

A pharmacophore model consists of a group of chemical features arranged in three-dimensional space that can be used to represent the biological activities of the described molecules. Clustering of molecular interactions of ligands on the basis of their pharmacophore similarity provides an approach for investigating how diverse ligands can bind to a specific receptor site or different receptor sites with similar or dissimilar binding affinities. However, efficient clustering of pharmacophore models in three-dimensional space is currently a challenge.

RESULTS

We have developed a pharmacophore-assisted Iterative Closest Point (ICP) method that is able to group pharmacophores in a manner relevant to their biochemical properties, such as binding specificity etc. The implementation of the method takes pharmacophore files as input and produces distance matrices. The method integrates both alignment-dependent and alignment-independent concepts.

CONCLUSIONS

We apply our three-dimensional pharmacophore clustering method to two sets of experimental data, including 31 globulin-binding steroids and 4 groups of selected antibody-antigen complexes. Results are translated from distance matrices to Newick format and visualised using dendrograms. For the steroid dataset, the resulting classification of ligands shows good correspondence with existing classifications. For the antigen-antibody datasets, the classification of antigens reflects both antigen type and binding antibody. Overall the method runs quickly and accurately for classifying the data based on their binding affinities or antigens.

Noncontiguous atom matching structural similarity function

Measuring similarity between molecules is a fundamental problem in cheminformatics. Given that similar molecules tend to have similar physical, chemical, and biological properties, the notion of molecular similarity plays an important role in the exploration of molecular data sets, query-retrieval in molecular databases, and in structure-property/activity modeling. Various methods to define structural similarity between molecules are available in the literature, but so far none has been used with consistent and reliable results for all situations. We propose a new similarity method based on atom alignment for the analysis of structural similarity between molecules. This method is based on the comparison of the bonding profiles of atoms on comparable molecules, including features that are seldom found in other structural or graph matching approaches like chirality or double bond stereoisomerism. The similarity measure is then defined on the annotated molecular graph, based on an iterative directed graph similarity procedure and optimal atom alignment between atoms using a pairwise matching algorithm. With the proposed approach the similarities detected are more intuitively understood because similar atoms in the molecules are explicitly shown. This noncontiguous atom matching structural similarity method (NAMS) was tested and compared with one of the most widely used similarity methods (fingerprint-based similarity) using three difficult data sets with different characteristics. Despite having a higher computational cost, the method performed well being able to distinguish either different or very similar hydrocarbons that were indistinguishable using a fingerprint-based approach. NAMS also verified the similarity principle using a data set of structurally similar steroids with differences in the binding affinity to the corticosteroid binding globulin receptor by showing that pairs of steroids with a high degree of similarity (>80%) tend to have smaller differences in the absolute value of binding activity. Using a highly diverse set of compounds with information about the monoamine oxidase inhibition level, the method was also able to recover a significantly higher average fraction of active compounds when the seed is active for different cutoff threshold values of similarity. Particularly, for the cutoff threshold values of 86%, 93%, and 96.5%, NAMS was able to recover a fraction of actives of 0.57, 0.63, and 0.83, respectively, while the fingerprint-based approach was able to recover a fraction of actives of 0.41, 0.40, and 0.39, respectively. NAMS is made available freely for the whole community in a simple Web based tool as well as the Python source code at http://nams.lasige.di.fc.ul.pt/.

BCL::EMAS--enantioselective molecular asymmetry descriptor for 3D-QSAR

Stereochemistry is an important determinant of a molecule’s biological activity. Stereoisomers can have different degrees of efficacy or even opposing effects when interacting with a target protein. Stereochemistry is a molecular property difficult to represent in 2D-QSAR as it is an inherently three-dimensional phenomenon. A major drawback of most proposed descriptors for 3D-QSAR that encode stereochemistry is that they require a heuristic for defining all stereocenters and rank-ordering its substituents. Here we propose a novel 3D-QSAR descriptor termed Enantioselective Molecular ASymmetry (EMAS) that is capable of distinguishing between enantiomers in the absence of such heuristics. The descriptor aims to measure the deviation from an overall symmetric shape of the molecule. A radial-distribution function (RDF) determines a signed volume of tetrahedrons of all triplets of atoms and the molecule center. The descriptor can be enriched with atom-centric properties such as partial charge. This descriptor showed good predictability when tested with a dataset of thirty-one steroids commonly used to benchmark stereochemistry descriptors (r² = 0.89, q² = 0.78). Additionally, EMAS improved enrichment of 4.38 versus 3.94 without EMAS in a simulated virtual high-throughput screening (vHTS) for inhibitors and substrates of cytochrome P450 (PUBCHEM AID891).

Communications on quantum similarity, part 3: a geometric-quantum similarity molecular superposition algorithm

This work describes a new procedure to obtain optimal molecular superposition based on quantum similarity (QS): the geometric-quantum similarity molecular superposition (GQSMS) algorithm. It has been inspired by the QS Aufbau principle, already described in a previous work, to build up coherently quantum similarity matrices (QSMs). The cornerstone of the present superposition technique relies upon the fact that quantum similarity integrals (QSIs), defined using a GTO basis set, depend on the squared intermolecular atomic distances. The resulting QSM structure, constructed under the GQSMS algorithm, becomes not only optimal in terms of its QSI elements but can also be arranged to produce a positive definite matrix global structure. Kruskal minimum spanning trees are also discussed as a device to order molecular sets described in turn by means of QSM. Besides the main subject of this work, focused on MS and QS, other practical considerations are also included in this study: essentially the use of elementary Jacobi rotations as QSM refinement tools and inward functions as QSM scaling methods.

Communications on quantum similarity (2): A geometric discussion on holographic electron density theorem and confined quantum similarity measures

The so-called holographic electron density theorem (HEDT) is analyzed from an algebraic perspective, and a brief analytical point of view is also given. The connection of the HEDT with quantum similarity measures (QSM) over electronic density functions (DF) is studied using GTO functions, atomic ASA DF, and promolecular ASA DF. Restricted integration of QSM over a box of finite side length is discussed for all this DF. This work emphasizes the geometric aspects of HEDT, but for the sake of completeness, some analytical insight based on a general Taylor series expansion is also given at the end.

Atom-based stochastic and non-stochastic 3D-chiral bilinear indices and their applications to central chirality codification

Non-stochastic and stochastic 2D bilinear indices have been generalized to codify chemical structure information for chiral drugs, making use of a trigonometric 3D-chirality correction factor. In order to evaluate the effectiveness of this novel approach in drug design we have modeled the angiotensin-converting enzyme inhibitory activity of perindoprilate's sigma-stereoisomers combinatorial library. Two linear discriminant analysis models, using non-stochastic and stochastic linear indices, were obtained. The models had shown an accuracy of 95.65% for the training set and 100% for the external prediction set. Next the prediction of the sigma-receptor antagonists of chiral 3-(3-hydroxyphenyl)piperidines by multiple linear regression analysis was carried out. Two statistically significant QSAR models were obtained when non-stochastic (R(2)=0.953 and s=0.238) and stochastic (R(2)=0.961 and s=0.219) 3D-chiral bilinear indices were used. These models showed adequate predictive power (assessed by the leave-one-out cross-validation experiment) yielding values of q(2)=0.935 (s(cv)=0.259) and q(2)=0.946 (s(cv)=0.235), respectively. Finally, the prediction of the corticosteroid-binding globulin binding affinity of steroids set was performed. The obtained results are rather similar to most of the 3D-QSAR approaches reported so far. The validation of this method was achieved by comparison with previous reports applied to the same data set. The non-stochastic and stochastic 3D-chiral linear indices appear to provide a very interesting alternative to other more common 3D-QSAR descriptors.

Toward an alternative hardness kernel matrix structure in the Electronegativity Equalization Method (EEM)

This study presents an alternative of the Electronegativity Equalization Method (EEM), where the usual Coulomb kernel has been transformed into a smooth function. The new framework, as the classical EEM, permits fast calculations of atomic charges in a given molecule for a small computational cost. The original EEM procedure needs to previously calibrate the different implied atomic hardness and electronegativity, using a chosen set of molecules. In the new EEM algorithm half the number of parameters needs to be calibrated, since a relationship between electronegativities and hardnesses has been found.

Atom-based 3D-chiral quadratic indices. Part 2: Prediction of the corticosteroid-binding globulinbinding affinity of the 31 benchmark steroids data set

A quantitative structure-activity relationship (QSAR) study to predict the relative affinities of the steroid 'benchmark' data set to the corticosteroid-binding globulin (CBG) is described. It is shown that the 3D-chiral quadratic indices closely correlate with the measured CBG affinity values for the 31 steroids. The calculated descriptors were correlated with biological data through multiple linear regressions. Two statistically significant models were obtained when non-stochastic (R = 0.924 and s = 0.46) as well as stochastic (R = 0.929 and s = 0.46) 3D-chiral quadratic indices were used. A leave-one-out (LOO) approach to model validation is used here; the best results obtained in the cross-validation procedure with non-stochastic (q2 = 0.781) and stochastic (q2 = 0.735) 3D-chiral quadratic indices are better or similar to most of the 3D-QSAR approaches reported so far. These results support the idea that the 3D-chiral quadratic indices may be helpful in prediction of the corticosteroid-binding affinity for new compounds.

Molecular Quantum Similarity Measures from Fermi Hole Densities: Modeling Hammett Sigma Constants

A new approach, based on the use of fragment Quantum Self-Similarity Measures (MQS-SM) as descriptors of electronic substituent effect in aromatic series, was proposed. The novelty of this approach consists of the fact that the corresponding MQS-SM are not derived, as usual, from ordinary density functions (DF) but from the so-called domain averaged Fermi holes. This approach was applied to the study of substituent effects on the acidobasic dissociation constants in 6 series of para-substituted aromatic carboxylic acids. It has been shown that MQS-SM calculated for each particular set of acids correlate with the Hammett substituent constants. As a consequence, the corresponding similarity measures can be used as new efficient descriptors of the substituent effect, which hopefully could replace empirical sigma constants in QSAR models.

Improving the performance of SOMFA by use of standard multivariate methods

Self-Organizing Molecular Field Analysis (SOMFA) comes with a built-in regression methodology, the Self-Organizing Regression (SOR), instead of relying on external methods such as PLS. In this article we present a proof of the equivalence between SOR and SIMPLS with one principal component. Thus, the modest performance of SOMFA on complex datasets can be primarily attributed to the low performance of the SOMFA regression methodology. A multi-component extension of the original SOR methodology (MCSOR) is introduced, and the performances of SOR, MCSOR and SIMPLS are compared using several datasets. The results indicate that in general the performance of SOMFA models is greatly improved if SOR is replaced with a more sophisticated regression method. The results obtained for the Cramer (CBG) dataset further underline the fact that it is a very poor benchmark dataset and should not be used to evaluate the performance of QSAR techniques.

Comparing the Performance of FLUFF-BALL to SEAL-CoMFA with a Large Diverse Estrogen Data Set: From Relevant Superpositions to Solid Predictions

In this work a template-based molecular mechanistic superposition algorithm FLUFF (Flexible Ligand Unified Force Field) and an accompanying local coordinate QSAR method BALL (Boundless Adaptive Localized Ligand) are validated against the benchmark techniques SEAL (Steric and Electrostatic Alignment) and CoMFA (Comparative Molecular Field Analysis) using a large diverse set of 245 xenoestrogens extracted from the EDKB (Endocrine Disruptor Knowledge Base) maintained by NCTR (National Centre for Toxicological Research). The results indicate that FLUFF is capable of generating relevant superpositions not only for BALL but also for CoMFA, as both techniques give predictive QSAR models. When the BALL and CoMFA methods are compared, it is clear that the BALL algorithm met or even exceeded the results of the standard 3D-QSAR method CoMFA using alignments either from the tailor-made superposition technique FLUFF or the reference method SEAL. The FLUFF-BALL method can be easily automated, and it is computationally light, providing thus a good computational "sieve" capable of fast screening of large molecule libraries.

3D-chiral Atom, Atom-type, and Total Non-stochastic and Stochastic Molecular Linear Indices and their Applications to Central Chirality Codification

Non-stochastic and stochastic 2D linear indices have been generalized to codify chemical structure information for chiral drugs, making use of a trigonometric 3D-chirality correction factor. These descriptors circumvent the inability of conventional 2D non-stochastic [Y. Marrero-Ponce. J. Chem. Inf. Comp., Sci. l 44 (2004) 2010] and stochastic [Y. Marrero-Ponce, et al. Bioorg. Med. Chem., 13 (2005) 1293] linear indices to distinguish sigma-stereoisomers. In order to test the potential of this novel approach in drug design we have modelled the angiotensin-converting enzyme inhibitory activity of perindoprilate's sigma-stereoisomers combinatorial library. Two linear discriminant analysis models, using non-stochastic and stochastic linear indices, were obtained. The models showed an accuracy of 100% and 96.65% for the training set; and 88.88% and 100% in the external test set, respectively. Canonical regression analysis corroborated the statistical quality of these models (R(can) of 0.78 and of 0.77) and was also used to compute biology activity canonical scores for each compound. After that, the prediction of the sigma-receptor antagonists of chiral 3-(3-hydroxyphenyl)piperidines by linear multiple regression analysis was carried out. Two statistically significant QSAR models were obtained when non-stochastic (R2 = 0.982 and s = 0.157) and stochastic (R2 = 0.941 and s = 0.267) 3D-chiral linear indices were used. The predictive power was assessed by the leave-one-out cross-validation experiment, yielding values of q2 = 0.982 (s(cv) = 0.186) and q2 = 0.90 (s(cv) = 0.319), respectively. Finally, the prediction of the corticosteroid-binding globulin binding affinity of steroids set was performed. The best results obtained in the cross-validation procedure with non-stochastic (q2 = 0.904) and stochastic (q2 = 0.88) 3D-chiral linear indices are rather similar to most of the 3D-QSAR approaches reported so far. The validation of this method was achieved by comparison with previous reports applied to the same data set. The non-stochastic and stochastic 3D-chiral linear indices appear to provide an interesting alternative to other more common 3D-QSAR descriptors.

Ligand intramolecular motions in ligand-protein interaction: ALPHA, a novel dynamic descriptor and a QSAR study with extended steroid benchmark dataset

The role of intramolecular motions in ligand-macromolecule interactions has been explored by developing and validating ALPHA, a novel QSAR (quantitative structure-activity relationship) descriptor. It is based on the spectral exponents (alpha), which measure the degree of 1/f alpha noise of coordinate fluctuations in molecular dynamics (MD) simulations. ALPHA is the first truly 'dynamic' QSAR descriptor, i.e., it can be derived directly from an MD trajectory. The performance of ALPHA was tested in detail employing the CBG (corticosteroid binding globulin) affinity of 31 benchmark steroids, supplemented with 11 steroids as an external test set. The only fair (42-50%) correlations of ALPHA with static 3D and electronic descriptors mean that ALPHA forms an independent molecular property. Furthermore, inclusion of ALPHA in the SOMFA/ESP model improves the correlation coefficient from 0.86 to 0.91, and /delta/ave from 0.46 to 0.36 for the benchmark dataset. The predictive ability of ALPHA can be interpreted as indirect evidence of the dynamic contribution to ligand-macromolecule interactions. The physical background of ALPHA is discussed and the importance of molecular motions for biological activity is anticipated.

Quantitative structure-activity relationships from optimised ab initio bond lengths: steroid binding affinity and antibacterial activity of nitrofuran derivatives

The present day abundance of cheap computing power enables the use of quantum chemical ab initio data in Quantitative Structure-Activity Relationships (QSARs). Optimised bond lengths are a new such class of descriptors, which we have successfully used previously in representing electronic effects in medicinal and ecological QSARs (enzyme inhibitory activity, hydrolysis rate constants and pKas). Here we use AM1 and HF/3-21G* bond lengths in conjunction with Partial Least Squares (PLS) and a Genetic Algorithm (GA) to predict the Corticosteroid-Binding Globulin (CBG) binding activity of the classic steroid data set, and the antibacterial activity of nitrofuran derivatives. The current procedure, which does not require molecular alignment, produces good r2 and q2 values. Moreover, it highlights regions in the common steroid skeleton deemed relevant to the active regions of the steroids and nitrofuran derivatives.

Comparative Molecular Active Site Analysis (CoMASA). 1. An Approach to Rapid Evaluation of 3D QSAR

We have developed a rapid evaluation method, comparative molecular active site analysis (CoMASA), for obtaining 3D QSAR. CoMASA has three major advantages: (1) the CoMASA results would easily transform to pharmacophore and/or queries required for 3D database searches, (2) the CoMASA method is not required to consider orientation and translation of molecules against a lattice, and (3) standard PCs can be used to perform the analysis. The potential of these improvements and possible further enhancements are discussed.

FLUFF-BALL, A Template-Based Grid-Independent Superposition and QSAR Technique: Validation Using a Benchmark Steroid Data Set

The Flexible Ligand Unified Force Field (FLUFF) is a molecular mechanistic superposition algorithm utilizing a template structure, on top of which the ligand(s) are superimposed. FLUFF enables a flexible semiautomatic superimposition in which the ligand and the template are allowed to seek the best common conformation, which can then be used to predict the biological activity by Boundless Adaptive Localized Ligand (BALL). In BALL, the similarity of the electrostatic and van der Waals volumes of the template and ligand is evaluated using the template-based coordinate system which makes the FLUFF-BALL invariant as to the rotations and translations of the global coordinate system. When tested using the CBG (corticosteroid binding globulin) affinities of 31 benchmark steroids, the FLUFF-BALL technique produced results comparable to standard 3D-QSAR methods. Supplementary test calculations were performed with five additional data sets. Due to its high level of automation and high throughput, the FLUFF-BALL is highly suitable for use in drug design and in scanning of large molecular libraries.

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 analysis of estrogenic activity

The main objective of this study was to evaluate the capability of 120 aromatic chemicals to bind to the human alpha estrogen receptor (hER alpha) by the use of quantum similarity methods. The experimental data were segregated into two categories, i.e., those compounds with and without estrogenicity activity (active and inactive). To identify potential ligands, semiquantitative structure-activity relationships were developed for the complete set correlating the presence or lack of binding affinity to the estrogen receptor with structural features of the molecules. The structure-activity relationships were based upon molecular similarity indices, which implicitly contain information related to changes in the electron distributions of the molecules, along with indicator variables, accounting for several structural features. In addition, the whole set was split into several chemical classes for modeling purposes. Models were validated by dividing the complete set into several training and test sets to allow for external predictions to be made.

Quantum similarity superposition algorithm (QSSA): a consistent scheme for molecular alignment and molecular similarity based on quantum chemistry

The use of the molecular quantum similarity overlap measure for molecular alignment is investigated. A new algorithm is presented, the quantum similarity superposition algorithm (QSSA), expressing the relative positions of two molecules in terms of mutual translation in three Cartesian directions and three Euler angles. The quantum similarity overlap is then used to optimize the mutual positions of the molecules. A comparison is made with TGSA, a topogeometrical approach, and the influence of differences on molecular clustering is discussed.

Molecular quantum similarity matrix based clustering of molecules using dendrograms

A new scheme for general classification of quantum objects is presented. Based on molecular quantum similarity matrices (MQSM), different algorithms are presented for generating Molecular Quantum Similarity Dendrograms (MQSD). An application of MQSD is presented 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 (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.

Molecular quantum similarity and the fundamentals of QSAR

A general overview on quantum similarity and applications to QSAR is presented. The concepts regarding quantum similarity from its theoretical foundation and consecutive development, involving mathematical formulation and similarity measures, are presented and complemented with application examples. The practical part, based on the well-known Crammer 31 steroids set, covers approximate quantum similarity calculations, molecular superposition, and statistics. In this way, the reader will find both basic general information and applicability of quantum similarity.

Evaluation of a novel electronic eigenvalue (EEVA) molecular descriptor for QSAR/QSPR studies: validation using a benchmark steroid data set

A novel electronic eigenvalue (EEVA) descriptor of molecular structure for use in the derivation of predictive QSAR/QSPR models is described. Like other spectroscopic QSAR/QSPR descriptors, EEVA is also invariant as to the alignment of the structures concerned. Its performance was tested with respect to the CBG (corticosteroid binding globulin) affinity of 31 benchmark steroids. It appeared that the electronic structure of the steroids, i.e., the "spectra" derived from molecular orbital energies, is directly related to the CBG binding affinities. The predictive ability of EEVA is compared to other QSAR approaches, and its performance is discussed in the context of the Hammett equation. The good performance of EEVA is an indication of the essential quantum mechanical nature of QSAR. The EEVA method is a supplement to conventional 3D QSAR methods, which employ fields or surface properties derived from Coulombic and van der Waals interactions.

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.

Antimalarial activity of synthetic 1,2,4-trioxanes and cyclic peroxy ketals, a quantum similarity study

In this work, the antimalarial activity of two series of 20 and 7 synthetic 1,2,4-trioxanes and a set of 20 cyclic peroxy ketals are tested for correlation search by means of Molecular Quantum Similarity Measures (MQSM). QSAR models, dealing with different biological responses (IC90, IC50 and ED90) of the parasite Plasmodium Falciparum, are constructed using MQSM as molecular descriptors and are satisfactorily correlated. The statistical results of the 20 1,2,4-trioxanes are deeply analyzed to elucidate the relevant structural features in the biological activity, revealing the importance of phenyl substitutions.

One-dimensional molecular representations and similarity calculations: methodology and validation

Drug discovery research is increasingly dedicated to biological screening on a massive scale, which seems to imply a basic rejection of many computer-assisted techniques originally designed to add rationality to the early stages of discovery. While ever-faster and more clever 3D methodologies continue to be developed and rejected as alternatives to indiscriminant screening, simpler tools based on 2D structure have carved a stable niche in the high-throughput paradigm of drug discovery. Their staying power is due in no small part to simplicity, ease of use, and demonstrated ability to explain structure-activity data. This observation led us to wonder whether an even simpler view of structure might offer an advantage over existing 2D and 3D methods. Accordingly, we introduce 1D representations of chemical structure, which are generated by collapsing a 3D molecular model or a 2D chemical graph onto a single coordinate of atomic positions. Atoms along this coordinate are differentiated according to elemental type, hybridization, and connectivity. By aligning 1D representations to match up identical atom types, a measure of overall structural similarity is afforded. In extensive structure-activity validation tests, 1D similarities consistently outperform both Daylight 2D fingerprints and Cerius(2) pharmacophore fingerprints, suggesting that this new, simple means of representing and comparing structures may offer a significant advantage over existing tried-and-true methods.

Identification of active molecular sites using quantum-self-similarity measures

A novel approach to construct theoretical QSAR models is proposed. This technique, based on the systematic use of quantum similarity measures as theoretical molecular descriptors, opens the possibility to localize and to identify the position of the bioactive part of drug molecules in situations, where the nature of the pharmacophore is not known. To test the reliability of this new approach, the method has been applied to the study of steroids binding to corticosteroid-binding human globulin. The studied molecules involved the set of 31 Cramer's steroids, often used as a benchmark set in QSAR studies. It has been shown that theoretical QSAR models based on the present procedure are superior to those derived from alternative existing approaches. In addition, a new method to measure the statistical significance of multiparameter QSAR models is also proposed.

Modeling antimalarial activity: application of Kinetic Energy Density Quantum Similarity Measures as descriptors in QSAR

In this work, is studied the application, within a quantum similarity framework, of the recently described Kinetic Energy Density Function in the evaluation of the antimalarial activity. First, this new type of Density Function is briefly presented from its theoretical foundations, and its inclusion in the molecular quantum similarity is discussed afterward. The application of Kinetic Energy-based Quantum Similarity Measures to QSAR is tested with 2 molecular sets composed of artemisinin derivatives, in which the 50% inhibition of synthesis and reduction of hidrofolate (IC50) in different Plasmodium falciparum clones are analyzed. Satisfactory correlations are obtained for all antimalarial activities in all studied molecular sets. Molecular Quantum Similarity analysis provides a consistent, unbiased, and homogeneous set of molecular descriptors and is a feasible alternative to the use of classical physicochemical descriptors.