Atom-based non-stochastic and stochastic bilinear indices: Application to QSPR/QSAR studies of organic compounds

Tensor Algebra-based Geometrical (3D) Biomacro-Molecular Descriptors for Protein Research: Theory, Applications and Comparison with other Methods

In this report, a new type of tridimensional (3D) biomacro-molecular descriptors for proteins are proposed. These descriptors make use of multi-linear algebra concepts based on the application of 3-linear forms (i.e., Canonical Trilinear (Tr), Trilinear Cubic (TrC), Trilinear-Quadratic-Bilinear (TrQB) and so on) as a specific case of the N-linear algebraic forms. The definition of the kth 3-tuple similarity-dissimilarity spatial matrices (Tensor's Form) are used for the transformation and for the representation of the existing chemical information available in the relationships between three amino acids of a protein. Several metrics (Minkowski-type, wave-edge, etc) and multi-metrics (Triangle area, Bond-angle, etc) are proposed for the interaction information extraction, as well as probabilistic transformations (e.g., simple stochastic and mutual probability) to achieve matrix normalization. A generalized procedure considering amino acid level-based indices that can be fused together by using aggregator operators for descriptors calculations is proposed. The obtained results demonstrated that the new proposed 3D biomacro-molecular indices perform better than other approaches in the SCOP-based discrimination and the prediction of folding rate of proteins by using simple linear parametrical models. It can be concluded that the proposed method allows the definition of 3D biomacro-molecular descriptors that contain orthogonal information capable of providing better models for applications in protein science.

Enhancing Acute Oral Toxicity Predictions by using Consensus Modeling and Algebraic Form-Based 0D-to-2D Molecular Encodes

Quantitative structure-activity relationships (QSAR) are introduced to predict acute oral toxicity (AOT), by using the QuBiLS-MAS (acronym for quadratic, bilinear and N-Linear maps based on graph-theoretic electronic-density matrices and atomic weightings) framework for the molecular encoding. Three training sets were employed to build the models: EPA training set (5931 compounds), EPA-full training set (7413 compounds), and Zhu training set (10 152 compounds). Additionally, the EPA test set (1482 compounds) was used for the validation of the QSAR models built on the EPA training set, while the ProTox (425 compounds) and T3DB (284 compounds) external sets were employed for the assessment of all the models. The k-nearest neighbor, multilayer perceptron, random forest, and support vector machine procedures were employed to build several base (individual) models. The base models with R_EPA-training ≥ 0.75 ( R = correlation coefficient) and MAE_EPA-training ≤ 0.5 (MAE = mean absolute error) were retained to build consensus models. As a result, two consensus models based on the minimum operator and denoted as M19 and M22, as well as a consensus model based on the weighted average operator and denoted as M24, were selected as the best ones for each training set considered. According to the applicability domain (AD) analysis performed, model M19 (built on the EPA training set) has MAE_test-AD = 0.4044, MAE_ProTox-AD = 0.4067 and MAE_T3DB-AD = 0.2586 on the EPA test set, ProTox external set, and T3DB external set, respectively; whereas model M22 (built on the EPA-full set) and model M24 (built on the Zhu set) present MAE_ProTox-AD = 0.3992 and MAE_T3DB-AD = 0.2286, and MAE_ProTox-AD = 0.3773 and MAE_T3DB-AD = 0.2471 on the two external sets accounted for, respectively. These outcomes were compared and statistically validated with respect to 14 QSAR methods (e.g., admetSAR, ProTox-II) from the literature. As a result, model M22 presents the best overall performance. In addition, a retrospective study on 261 withdrawn drugs due to their toxic/side effects was performed, to assess the usefulness of prospectively using the QSAR models proposed in the labeling of chemicals. A comparison with regard to the methods from the literature was also made. As a result, model M22 has the best ability of labeling a compound as toxic according to the globally harmonized system of classification and labeling of chemicals. Therefore, it can be concluded that the models proposed, especially model M22, constitute prominent tools for studying AOT, at providing the best results among all the methods examined. A freely available software was also developed to be used in virtual screening tasks ( http://tomocomd.com/apps/ptoxra ).

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.

Exploring the QSAR's predictive truthfulness of the novel N-tuple discrete derivative indices on benchmark datasets

Graph derivative indices (GDIs) have recently been defined over N-atoms (N = 2, 3 and 4) simultaneously, which are based on the concept of derivatives in discrete mathematics (finite difference), metaphorical to the derivative concept in classical mathematical analysis. These molecular descriptors (MDs) codify topo-chemical and topo-structural information based on the concept of the derivative of a molecular graph with respect to a given event (S) over duplex, triplex and quadruplex relations of atoms (vertices). These GDIs have been successfully applied in the description of physicochemical properties like reactivity, solubility and chemical shift, among others, and in several comparative quantitative structure activity/property relationship (QSAR/QSPR) studies. Although satisfactory results have been obtained in previous modelling studies with the aforementioned indices, it is necessary to develop new, more rigorous analysis to assess the true predictive performance of the novel structure codification. So, in the present paper, an assessment and statistical validation of the performance of these novel approaches in QSAR studies are executed, as well as a comparison with those of other QSAR procedures reported in the literature. To achieve the main aim of this research, QSARs were developed on eight chemical datasets widely used as benchmarks in the evaluation/validation of several QSAR methods and/or many different MDs (fundamentally 3D MDs). Three to seven variable QSAR models were built for each chemical dataset, according to the original dissection into training/test sets. The models were developed by using multiple linear regression (MLR) coupled with a genetic algorithm as the feature wrapper selection technique in the MobyDigs software. Each family of GDIs (for duplex, triplex and quadruplex) behaves similarly in all modelling, although there were some exceptions. However, when all families were used in combination, the results achieved were quantitatively higher than those reported by other authors in similar experiments. Comparisons with respect to external correlation coefficients (q²_ext) revealed that the models based on GDIs possess superior predictive ability in seven of the eight datasets analysed, outperforming methodologies based on similar or more complex techniques and confirming the good predictive power of the obtained models. For the q²_ext values, the non-parametric comparison revealed significantly different results to those reported so far, which demonstrated that the models based on DIVATI's indices presented the best global performance and yielded significantly better predictions than the 12 0-3D QSAR procedures used in the comparison. Therefore, GDIs are suitable for structure codification of the molecules and constitute a good alternative to build QSARs for the prediction of physicochemical, biological and environmental endpoints.

Bond-based bilinear indices for computational discovery of novel trypanosomicidal drug-like compounds through virtual screening

Two-dimensional bond-based bilinear indices and linear discriminant analysis are used in this report to perform a quantitative structure-activity relationship study to identify new trypanosomicidal compounds. A data set of 440 organic chemicals, 143 with antitrypanosomal activity and 297 having other clinical uses, is used to develop the theoretical models. Two discriminant models, computed using bond-based bilinear indices, are developed and both show accuracies higher than 86% for training and test sets. The stochastic model correctly indentifies nine out of eleven compounds of a set of organic chemicals obtained from our synthetic collaborators. The in vitro antitrypanosomal activity of this set against epimastigote forms of Trypanosoma cruzi is assayed. Both models show a good agreement between theoretical predictions and experimental results. Three compounds showed IC50 values for epimastigote elimination (AE) lower than 50 μM, while for the benznidazole the IC50 = 54.7 μM which was used as reference compound. The value of IC50 for cytotoxicity of these compounds is at least 5 times greater than their value of IC50 for AE. Finally, we can say that, the present algorithm constitutes a step forward in the search for efficient ways of discovering new antitrypanosomal compounds.

QuBiLS-MIDAS: a parallel free-software for molecular descriptors computation based on multilinear algebraic maps

The present report introduces the QuBiLS-MIDAS software belonging to the ToMoCoMD-CARDD suite for the calculation of three-dimensional molecular descriptors (MDs) based on the two-linear (bilinear), three-linear, and four-linear (multilinear or N-linear) algebraic forms. Thus, it is unique software that computes these tensor-based indices. These descriptors, establish relations for two, three, and four atoms by using several (dis-)similarity metrics or multimetrics, matrix transformations, cutoffs, local calculations and aggregation operators. The theoretical background of these N-linear indices is also presented. The QuBiLS-MIDAS software was developed in the Java programming language and employs the Chemical Development Kit library for the manipulation of the chemical structures and the calculation of the atomic properties. This software is composed by a desktop user-friendly interface and an Abstract Programming Interface library. The former was created to simplify the configuration of the different options of the MDs, whereas the library was designed to allow its easy integration to other software for chemoinformatics applications. This program provides functionalities for data cleaning tasks and for batch processing of the molecular indices. In addition, it offers parallel calculation of the MDs through the use of all available processors in current computers. The studies of complexity of the main algorithms demonstrate that these were efficiently implemented with respect to their trivial implementation. Lastly, the performance tests reveal that this software has a suitable behavior when the amount of processors is increased. Therefore, the QuBiLS-MIDAS software constitutes a useful application for the computation of the molecular indices based on N-linear algebraic maps and it can be used freely to perform chemoinformatics studies.

Comparative study to predict toxic modes of action of phenols from molecular structures

Quantitative structure-activity relationship models for the prediction of mode of toxic action (MOA) of 221 phenols to the ciliated protozoan Tetrahymena pyriformis using atom-based quadratic indices are reported. The phenols represent a variety of MOAs including polar narcotics, weak acid respiratory uncouplers, pro-electrophiles and soft electrophiles. Linear discriminant analysis (LDA), and four machine learning techniques (ML), namely k-nearest neighbours (k-NN), support vector machine (SVM), classification trees (CTs) and artificial neural networks (ANNs), have been used to develop several models with higher accuracies and predictive capabilities for distinguishing between four MOAs. Most of them showed global accuracy of over 90%, and false alarm rate values were below 2.9% for the training set. Cross-validation, complementary subsets and external test set were performed, with good behaviour in all cases. Our models compare favourably with other previously published models, and in general the models obtained with ML techniques show better results than those developed with linear techniques. We developed unsupervised and supervised consensus, and these results were better than our ML models, the results of rule-based approach and other ensemble models previously published. This investigation highlights the merits of ML-based techniques as an alternative to other more traditional methods for modelling MOA.

SMILES-based optimal descriptors: QSAR analysis of fullerene-based HIV-1 PR inhibitors by means of balance of correlations

Quantitative structure-activity relationships (QSAR) for prediction of binding affinities (pEC50, i.e., minus decimal logarithm of the 50% effective concentration) of 20 fullerene derivatives inhibitors of the HIV-1 PR (human immunodeficiency virus type 1 protease) have been developed by application of the optimal descriptors approach calculated with SMILES (simplified molecular input line entry system). The applied models were constructed by the balance of correlations. Three various splits of the experimental data into subtraining set, calibration set, and test set were examined. Comparison of classic scheme (training-test system) and the balance of correlations (subtraining-calibration-test system) show that the balance of correlations gives more robust predictions than the classic scheme for the pEC50 of the fullerene derivatives.

QSPR modeling of enthalpies of formation for organometallic compounds by SMART-based optimal descriptors

A quantitative structure-property relationship (QSPR) model for the prediction of gas-phase enthalpy of formation has been developed, using as chemical information descriptors based on the SMART notation, which is an alternative to SMILES. The model is one-variable equation. The SMART-based descriptors are calculated with correlation weights of SMART attributes which are obtained by the Monte Carlo method. The model addressed organometallic compounds. Statistical characteristics of the model are the following: n = 104, r2 = 0.9944, s = 19.6 (kJ/mol), F = 18,269 (training set) and n = 28, r2 = 0.9909, s = 28.8 (kJ/mol), F = 2832 (test set).

Computational discovery of novel trypanosomicidal drug-like chemicals by using bond-based non-stochastic and stochastic quadratic maps and linear discriminant analysis

Herein we present results of a quantitative structure-activity relationship (QSAR) studies to classify and design, in a rational way, new antitrypanosomal compounds by using non-stochastic and stochastic bond-based quadratic indices. A data set of 440 organic chemicals, 143 with antitrypanosomal activity and 297 having other clinical uses, is used to develop QSAR models based on linear discriminant analysis (LDA). Non-stochastic model correctly classifies more than 93% and 95% of chemicals in both training and external prediction groups, respectively. On the other hand, the stochastic model shows an accuracy of about the 87% for both series. As an experiment of virtual lead generation, the present approach is finally satisfactorily applied to the virtual evaluation of 9 already synthesized in house compounds. The in vitro antitrypanosomal activity of this series against epimastigote forms of Trypanosoma cruzi is assayed. The model is able to predict correctly the behaviour for the majority of these compounds. Four compounds (FER16, FER32, FER33 and FER 132) showed more than 70% of epimastigote inhibition at a concentration of 100 microg/mL (86.74%, 78.12%, 88.85% and 72.10%, respectively) and two of these chemicals, FER16 (78.22% of AE) and FER33 (81.31% of AE), also showed good activity at a concentration of 10 microg/mL. At the same concentration, compound FER16 showed lower value of cytotoxicity (15.44%), and compound FER33 showed very low value of 1.37%. Taking into account all these results, we can say that these three compounds can be optimized in forthcoming works, but we consider that compound FER33 is the best candidate. Even though none of them resulted more active than Nifurtimox, the current results constitute a step forward in the search for efficient ways to discover new lead antitrypanosomals.