Alignment of molecules by the Monte Carlo optimization of molecular similarity indices

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.

Examining the predictive accuracy of the novel 3D N-linear algebraic molecular codifications on benchmark datasets

BACKGROUND

Recently, novel 3D alignment-free molecular descriptors (also known as QuBiLS-MIDAS) based on two-linear, three-linear and four-linear algebraic forms have been introduced. These descriptors codify chemical information for relations between two, three and four atoms by using several (dis-)similarity metrics and multi-metrics. Several studies aimed at assessing the quality of these novel descriptors have been performed. However, a deeper analysis of their performance is necessary. Therefore, in the present manuscript an assessment and statistical validation of the performance of these novel descriptors in QSAR studies is performed.

RESULTS

To this end, eight molecular datasets (angiotensin converting enzyme, acetylcholinesterase inhibitors, benzodiazepine receptor, cyclooxygenase-2 inhibitors, dihydrofolate reductase inhibitors, glycogen phosphorylase b, thermolysin inhibitors, thrombin inhibitors) widely used as benchmarks in the evaluation of several procedures are utilized. Three to nine variable QSAR models based on Multiple Linear Regression are built for each chemical dataset according to the original division into training/test sets. Comparisons with respect to leave-one-out cross-validation correlation coefficients[Formula: see text] reveal that the models based on QuBiLS-MIDAS indices possess superior predictive ability in 7 of the 8 datasets analyzed, outperforming methodologies based on similar or more complex techniques such as: Partial Least Square, Neural Networks, Support Vector Machine and others. On the other hand, superior external correlation coefficients[Formula: see text] are attained in 6 of the 8 test sets considered, confirming the good predictive power of the obtained models. For the [Formula: see text] values non-parametric statistic tests were performed, which demonstrated that the models based on QuBiLS-MIDAS indices have the best global performance and yield significantly better predictions in 11 of the 12 QSAR procedures used in the comparison. Lastly, a study concerning to the performance of the indices according to several conformer generation methods was performed. This demonstrated that the quality of predictions of the QSAR models based on QuBiLS-MIDAS indices depend on 3D structure generation method considered, although in this preliminary study the results achieved do not present significant statistical differences among them.

CONCLUSIONS

As conclusions it can be stated that the QuBiLS-MIDAS indices are suitable for extracting structural information of the molecules and thus, constitute a promissory alternative to build models that contribute to the prediction of pharmacokinetic, pharmacodynamics and toxicological properties on novel compounds.Graphical abstractComparative graphical representation of the performance of the novel QuBiLS-MIDAS 3D-MDs with respect to other methodologies in QSAR modeling of eight chemical datasets.

Three-dimensional compound comparison methods and their application in drug discovery

Virtual screening has been widely used in the drug discovery process. Ligand-based virtual screening (LBVS) methods compare a library of compounds with a known active ligand. Two notable advantages of LBVS methods are that they do not require structural information of a target receptor and that they are faster than structure-based methods. LBVS methods can be classified based on the complexity of ligand structure information utilized: one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D). Unlike 1D and 2D methods, 3D methods can have enhanced performance since they treat the conformational flexibility of compounds. In this paper, a number of 3D methods will be reviewed. In addition, four representative 3D methods were benchmarked to understand their performance in virtual screening. Specifically, we tested overall performance in key aspects including the ability to find dissimilar active compounds, and computational speed.

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.

BRUTUS: Optimization of a grid-based similarity function for rigid-body molecular superposition. II. Description and characterization

Finding novel lead molecules is one of the primary goals in early phases of drug discovery projects. However, structurally dissimilar compounds may exhibit similar biological activity, and finding new and structurally diverse lead compounds is difficult for computer algorithms. Molecular energy fields are appropriate for finding structurally novel molecules, but they are demanding to calculate and this limits their usefulness in virtual screening of large chemical databases. In our approach, energy fields are computed only once per superposition and a simple interpolation scheme is devised to allow coarse energy field lattices having fewer grid points to be used without any significant loss of accuracy. The resulting processing speed of about 0.25 s per conformation on a 2.4 GHz Intel Pentium processor allows the method to be used for virtual screening on commonly available desktop machines. Moreover, the results indicate that grid-based superposition methods could be efficiently used for the virtual screening of compound libraries.

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.

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.

BRUTUS: Optimization of a Grid-Based Similarity Function for Rigid-Body Molecular Superposition. 1. Alignment and Virtual Screening Applications

We have developed a fast grid-based algorithm, BRUTUS, for rigid-body molecular superposition and similarity searching. BRUTUS aligns molecules using field information derived from charge distributions and van der Waals shapes of the compounds. Molecules can have similar biological properties if their charge distributions and shapes are similar, even though they have different chemical structures; that is, BRUTUS can identify compounds possessing similar properties, regardless of their structures. In this paper, we present two applications of BRUTUS. First, BRUTUS was used to superimpose five sets of inhibitors. Second, two sets of known inhibitors were searched from a database, and the results were analyzed using self-organizing maps. We demonstrate that BRUTUS is successful in superimposing compounds using molecular fields and, importantly, is fast and accurate enough for virtual screening of chemical databases using a standard personal computer. This fast and efficient molecular-field-based algorithm is applicable for virtual screening of structurally diverse, active molecules.

Assessment of Docking Poses: Interactions-Based Accuracy Classification (IBAC) versus Crystal Structure Deviations

Six docking programs (FlexX, GOLD, ICM, LigandFit, the Northwestern University version of DOCK, and QXP) were evaluated in terms of their ability to reproduce experimentally observed binding modes (poses) of small-molecule ligands to macromolecular targets. The accuracy of a pose was assessed in two ways: First, the RMS deviation of the predicted pose from the crystal structure was calculated. Second, the predicted pose was compared to the experimentally observed one regarding the presence of key interactions with the protein. The latter assessment is referred to as interactions-based accuracy classification (IBAC). In a number of cases significant discrepancies were found between IBAC and RMSD-based classifications. Despite being more subjective, the IBAC proved to be a more meaningful measure of docking accuracy in all these cases.

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.

Field interaction and geometrical overlap: a new simplex and experimental design based computational procedure for superposing small ligand molecules

Alignment of molecules is a crucial and time-consuming step in any 3D-QSAR study. For this reason, the field interaction and geometrical overlap (FIGO) procedure presented in this paper is particularly relevant because it can provide an objective and automatic superposition of ligands through the computation of an appropriate alignment index (AI). Ligand overlay takes place via a simplex optimization of the AI function. Experimental design strategies (full factorial design, D-optimal design) are used to define the starting positions of the superposing molecules. Overlay experiments are carried out to test the performance of the method. Comparison between the results obtained with FIGO and known ligand-receptor X-ray crystallographic data (Protein Data Bank) suggests that FIGO is an effective and reliable computational procedure.

Automatic generation of alignments for 3D QSAR analyses

Many 3D QSAR methods require the alignment of the molecules in a dataset, which can require a fair amount of manual effort in deciding upon a rational basis for the superposition. This paper describes the use of FBSS, a program for field-based similarity searching in chemical databases, for generating such alignments automatically. The CoMFA and CoMSIA experiments with several literature datasets show that the QSAR models resulting from the FBSS alignments are broadly comparable in predictive performance with the models resulting from manual alignments.

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.

Quantum molecular similarity. 3. QTMS descriptors

Building on the ideas of a previous paper [part 1, J. Phys. Chem. A 1999, 103, 2883] we present a new molecular similarity method based on the topology of the electron density. This method is directly applicable to QSARs and is called quantum topological molecular similarity (QTMS). It has been tested for five sets of carboxylic systems including para- and meta-benzoic acid, para-phenylacetic acid, 4-X-bicyclo[2.2.2]octane-1-carboxylic acids, and polysubstituted benzoic acids. In combination with the partial least squares (PLS) procedure QTMS is able to produce excellent and statistically valid regressions. It is shown that QTMS avoids certain challenges of traditional Carbó-like similarity indices. Finally, QTMS is able to suggest a molecular fragment that contains the active center or the part of the molecule that is responsible for the QSAR.

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

Predictive models based on tuned molecular quantum similarity measures and their application to obtain quantitative structure-activity relationships (QSAR) are described. In the present paper, the corticosteroid-binding globulin binding affinity of a 31 steroid family is studied by means of a multilinear regression using molecular descriptors derived from mixed steric-electrostatic quantum similarity matrixes as parameters, obtaining satisfactory predictions. A systematic procedure to treat outliers by using triple-density quantum similarity measures is also presented. This method depicts an alternative to the grid-based QSAR techniques, providing a consistent approach that avoids problematic result dependency on the grid parameters.

Self-organizing molecular field analysis: a tool for structure-activity studies

Self-organizing molecular field analysis (SOMFA) is a novel technique for three-dimensional quantitative structure-activity relations (3D-QSAR). It is simple and intuitive in concept and avoids the complex statistical tools and variable selection procedures favored by other methods. Our calculations show the method to be as predictive as the best 3D-QSAR methods available. Importantly, steric and electrostatic maps can be produced to aid the molecular design process by highlighting important molecular features. The simplicity of the technique leaves scope for further development, particularly with regard to handling molecular alignment and conformation selection. Here, the method has been used to predict the corticosteroid-binding globulin binding affinity of the "benchmark" steroids, expanded from the usual 31 compounds to 43 compounds. Test predictions have also been performed on a set of sulfonamide endothelin inhibitors.

FLEXS: a method for fast flexible ligand superposition

If no structural information about a particular target protein is available, methods of rational drug design try to superimpose putative ligands with a given reference, e.g., an endogenous ligand. The goal of such structural alignments is, on the one hand, to approximate the binding geometry and, on the other hand, to provide a relative ranking of the ligands with respect to their similarity. An accurate superposition is the prerequisite of subsequent exploitation of ligand data by either 3D QSAR analyses, pharmacophore hypotheses, or receptor modeling. We present the automatic method FLEXS for structurally superimposing pairs of ligands, approximating their putative binding site geometry. One of the ligands is treated as flexible, while the other one, used as a reference, is kept rigid. FLEXS is an incremental construction procedure. The molecules to be superimposed are partitioned into fragments. Starting with placements of a selected anchor fragment, computed by two alternative approaches, the remaining fragments are added iteratively. At each step, flexibility is considered by allowing the respective added fragment to adopt a discrete set of conformations. The mean computing time per test case is about 1:30 min on a common-day workstation. FLEXS is fast enough to be used as a tool for virtual ligand screening. A database of typical drug molecules has been screened for potential fibrinogen receptor antagonists. FLEXS is capable of retrieving all ligands assigned to platelet aggregation properties among the first 20 hits. Furthermore, the program suggests additional interesting candidates, likely to be active at the same receptor. FLEXS proves to be superior to commonly used retrieval techniques based on 2D fingerprint similarities. The accuracy of computed superpositions determines the relevance of subsequently performed ligand analyses. In order to validate the quality of FLEXS alignments, we attempted to reproduce a set of 284 mutual superpositions derived from experimental data on 76 protein-ligand complexes of 14 proteins. The ligands considered cover the whole range of drug-size molecules from 18 to 158 atoms (PDB codes: 3ptb, 2er7). The performance of the algorithm critically depends on the sizes of the molecules to be superimposed. The limitations are clearly demonstrated with large peptidic inhibitors in the HIV and the endothiapepsin data set. Problems also occur in the presence of multiple binding modes (e.g., elastase and human rhinovirus). The most convincing results are achieved with small- and medium-sized molecules (as, e.g., the ligands of trypsin, thrombin, and dihydrofolate reductase). In more than half of the entire test set, we achieve rms deviations between computed and observed alignment of below 1.5 A. This underlines the reliability of FLEXS-generated alignments.