Predicting Antimicrobial Peptides Using ESMFold-Predicted Structures and ESM-2-Based Amino Acid Features with Graph Deep Learning.

Currently, antimicrobial resistance constitutes a serious threat to human health. Drugs based on antimicrobial peptides (AMPs) constitute one of the alternatives to address it. Shallow and deep learning (DL)-based models have mainly been built from amino acid sequences to predict AMPs. Recent advances in tertiary (3D) structure prediction have opened new opportunities in this field. In this sense, models based on graphs derived from predicted peptide structures have recently been proposed. However, these models are not in correspondence with state-of-the-art approaches to codify evolutionary information, and, in addition, they are memory- and time-consuming because depend on multiple sequence alignment. Herein, we presented a framework to create alignment-free models based on graph representations generated from ESMFold-predicted peptide structures, whose nodes are characterized with amino acid-level evolutionary information derived from the Evolutionary Scale Modeling (ESM-2) models. A graph attention network (GAT) was implemented to assess the usefulness of the framework in the AMP classification. To this end, a set comprised of 67,058 peptides was used. It was demonstrated that the proposed methodology allowed to build GAT models with generalization abilities consistently better than 20 state-of-the-art non-DL-based and DL-based models. The best GAT models were developed using evolutionary information derived from the 36- and 33-layer ESM-2 models. Similarity studies showed that the best-built GAT models codified different chemical spaces, and thus they were fused to significantly improve the classification. In general, the results suggest that esm-AxP-GDL is a promissory tool to develop good, structure-dependent, and alignment-free models that can be successfully applied in the screening of large data sets. This framework should not only be useful to classify AMPs but also for modeling other peptide and protein activities.

Examining evolutionary scale modeling-derived different-dimensional embeddings in the antimicrobial peptide classification through a KNIME workflow.

Molecular features play an important role in different bio-chem-informatics tasks, such as the Quantitative Structure-Activity Relationships (QSAR) modeling. Several pre-trained models have been recently created to be used in downstream tasks, either by fine-tuning a specific model or by extracting features to feed traditional classifiers. In this regard, a new family of Evolutionary Scale Modeling models (termed as ESM-2 models) was recently introduced, demonstrating outstanding results in protein structure prediction benchmarks. Herein, we studied the usefulness of the different-dimensional embeddings derived from the ESM-2 models to classify antimicrobial peptides (AMPs). To this end, we built a KNIME workflow to use the same modeling methodology across experiments in order to guarantee fair analyses. As a result, the 640- and 1280-dimensional embeddings derived from the 30- and 33-layer ESM-2 models, respectively, are the most valuable  since statistically better performances were achieved by the QSAR models built from them. We also fused features of the different ESM-2 models, and it was concluded that the fusion contributes to getting better QSAR models than using features of a single ESM-2 model. Frequency studies revealed that only a portion of the ESM-2 embeddings is valuable for modeling tasks since between 43% and 66% of the features were never used. Comparisons regarding state-of-the-art deep learning (DL) models confirm that when performing methodologically principled studies in the prediction of AMPs, non-DL based QSAR models yield comparable-to-superior performances to DL-based QSAR models. The developed KNIME workflow is available-freely at https://github.com/cicese-biocom/classification-QSAR-bioKom. This workflow can be valuable to avoid unfair comparisons regarding new computational methods, as well as to propose new non-DL based QSAR models.

StarPep Toolbox: an open-source software to assist chemical space analysis of bioactive peptides and their functions using complex networks.

MOTIVATION: Antimicrobial peptides (AMPs) are promising molecules to treat infectious diseases caused by multi-drug resistance pathogens, some types of cancer, and other conditions. Computer-aided strategies are efficient tools for the high-throughput screening of AMPs. RESULTS: This report highlights StarPep Toolbox, an open-source and user-friendly software to study the bioactive chemical space of AMPs using complex network-based representations, clustering, and similarity-searching models. The novelty of this research lies in the combination of network science and similarity-searching techniques, distinguishing it from conventional methods based on machine learning and other computational approaches. The network-based representation of the AMP chemical space presents promising opportunities for peptide drug repurposing, development, and optimization. This approach could serve as a baseline for the discovery of a new generation of therapeutics peptides. AVAILABILITY AND IMPLEMENTATION: All underlying code and installation files are accessible through GitHub (https://github.com/Grupo-Medicina-Molecular-y-Traslacional/StarPep) under the Apache 2.0 license.

Overproduce and select, or determine optimal molecular descriptor subset via configuration space optimization? Application to the prediction of ecotoxicological endpoints.

Predicting the likely biological activity (or property) of compounds is a fundamental and challenging task in the drug discovery process. Current computational methodologies aim to improve their predictive accuracies by using deep learning (DL) approaches. However, non-DL based approaches for small- and medium-sized chemical datasets have demonstrated to be most suitable for. In this approach, an initial universe of molecular descriptors (MDs) is first calculated, then different feature selection algorithms are applied, and finally, one or several predictive models are built. Herein we demonstrate that this traditional approach may miss relevant information by assuming that the initial universe of MDs codifies all relevant aspects for the respective learning task. We argue that this limitation is mainly because of the constrained intervals of the parameters used in the algorithms that compute MDs, parameters that define the Descriptor Configuration Space (DCS). We propose to relax these constraints in an open CDS approach, so that a larger universe of MDs can be initially considered. We model the generation of MDs as a multicriteria optimization problem and tackle it with a variant of the standard genetic algorithm. As a novel component, the fitness function is computed by aggregating four criteria via the Choquet integral. Experimental results show that the proposed approach generates a meaningful DCS by improving state-of-the-art approaches in most of the benchmarking chemical datasets accounted for.

Fuzzy spherical truncation-based multi-linear protein descriptors: From their definition to application in structural-related predictions.

This study introduces a set of fuzzy spherically truncated three-dimensional (3D) multi-linear descriptors for proteins. These indices codify geometric structural information from kth spherically truncated spatial-(dis)similarity two-tuple and three-tuple tensors. The coefficients of these truncated tensors are calculated by applying a smoothing value to the 3D structural encoding based on the relationships between two and three amino acids of a protein embedded into a sphere. At considering, the geometrical center of the protein matches with center of the sphere, the distance between each amino acid involved in any specific interaction and the geometrical center of the protein can be computed. Then, the fuzzy membership degree of each amino acid from an spherical region of interest is computed by fuzzy membership functions (FMFs). The truncation value is finally a combination of the membership degrees from interacting amino acids, by applying the arithmetic mean as fusion rule. Several fuzzy membership functions with diverse biases on the calculation of amino acids memberships (e.g., Z-shaped (close to the center), PI-shaped (middle region), and A-Gaussian (far from the center)) were considered as well as traditional truncation functions (e.g., Switching). Such truncation functions were comparatively evaluated by exploring: 1) the frequency of membership degrees, 2) the variability and orthogonality analyses among them based on the Shannon Entropy's and Principal Component's methods, respectively, and 3) the prediction performance of alignment-free prediction of protein folding rates and structural classes. These analyses unraveled the singularity of the proposed fuzzy spherically truncated MDs with respect to the classical (non-truncated) ones and respect to the MDs truncated with traditional functions. They also showed an improved prediction power by attaining an external correlation coefficient of 95.82% in the folding rate modelling and an accuracy of 100% in distinguishing structural protein classes. These outcomes are better than the ones attained by existing approaches, justifying the theoretical contribution of this report. Thus, the fuzzy spherically truncated-based protein descriptors from MuLiMs-MCoMPAs (http://tomocomd.com/mulims-mcompas) are promising alignment-free predictors for modeling protein functions and properties.

Handcrafted versus non-handcrafted (self-supervised) features for the classification of antimicrobial peptides: complementary or redundant?

Antimicrobial peptides (AMPs) have received a great deal of attention given their potential to become a plausible option to fight multi-drug resistant bacteria as well as other pathogens. Quantitative sequence-activity models (QSAMs) have been helpful to discover new AMPs because they allow to explore a large universe of peptide sequences and help reduce the number of wet lab experiments. A main aspect in the building of QSAMs based on shallow learning is to determine an optimal set of protein descriptors (features) required to discriminate between sequences with different antimicrobial activities. These features are generally handcrafted from peptide sequence datasets that are labeled with specific antimicrobial activities. However, recent developments have shown that unsupervised approaches can be used to determine features that outperform human-engineered (handcrafted) features. Thus, knowing which of these two approaches contribute to a better classification of AMPs, it is a fundamental question in order to design more accurate models. Here, we present a systematic and rigorous study to compare both types of features. Experimental outcomes show that non-handcrafted features lead to achieve better performances than handcrafted features. However, the experiments also prove that an improvement in performance is achieved when both types of features are merged. A relevance analysis reveals that non-handcrafted features have higher information content than handcrafted features, while an interaction-based importance analysis reveals that handcrafted features are more important. These findings suggest that there is complementarity between both types of features. Comparisons regarding state-of-the-art deep models show that shallow models yield better performances both when fed with non-handcrafted features alone and when fed with non-handcrafted and handcrafted features together.

Do deep learning models make a difference in the identification of antimicrobial peptides?

In the last few decades, antimicrobial peptides (AMPs) have been explored as an alternative to classical antibiotics, which in turn motivated the development of machine learning models to predict antimicrobial activities in peptides. The first generation of these predictors was filled with what is now known as shallow learning-based models. These models require the computation and selection of molecular descriptors to characterize each peptide sequence and train the models. The second generation, known as deep learning-based models, which no longer requires the explicit computation and selection of those descriptors, started to be used in the prediction task of AMPs just four years ago. The superior performance claimed by deep models regarding shallow models has created a prevalent inertia to using deep learning to identify AMPs. However, methodological flaws and/or modeling biases in the building of deep models do not support such superiority. Here, we analyze the main pitfalls that led to establish biased conclusions on the leading performance of deep models. Also, we analyze whether deep models truly contribute to achieve better predictions than shallow models by performing fair studies on different state-of-the-art benchmarking datasets. The experiments reveal that deep models do not outperform shallow models in the classification of AMPs, and that both types of models codify similar chemical information since their predictions are highly similar. Thus, according to the currently available datasets, we conclude that the use of deep learning could not be the most suitable approach to develop models to identify AMPs, mainly because shallow models achieve comparable-to-superior performances and are simpler (Ockham's razor principle). Even so, we suggest the use of deep learning only when its capabilities lead to obtaining significantly better performance gains worth the additional computational cost.

Alignment-Free Antimicrobial Peptide Predictors: Improving Performance by a Thorough Analysis of the Largest Available Data Set.

In the last two decades, a large number of machine-learning-based predictors for the activities of antimicrobial peptides (AMPs) have been proposed. These predictors differ from one another in the learning method and in the training and testing data sets used. Unfortunately, the training data sets present several drawbacks, such as a low representativeness regarding the experimentally validated AMP space, and duplicated peptide sequences between negative and positive data sets. These limitations give a low confidence to most of the approaches to be used in prospective studies. To address these weaknesses, we propose novel modeling and assessing data sets from the largest experimentally validated nonredundant peptide data set reported to date. From these novel data sets, alignment-free quantitative sequence-activity models (AF-QSAMs) based on Random Forest are created to identify general AMPs and their antibacterial, antifungal, antiparasitic, and antiviral functional types. An applicability domain analysis is carried out to determine the reliability of the predictions obtained, which, to the best of our knowledge, is performed for the first time for AMP recognition. A benchmarking is undertaken between the models proposed and several models from the literature that are freely available in 13 programs (ClassAMP, iAMP-2L, ADAM, MLAMP, AMPScanner v2.0, AntiFP, AMPfun, PEPred-suite, AxPEP, CAMPR3, iAMPpred, APIN, and Meta-iAVP). The models proposed are those with the best performance in all of the endpoints modeled, while most of the methods from the literature have weak-to-random predictive agreements. The models proposed are also assessed through Y-scrambling and repeated k-fold cross-validation tests, demonstrating that the outcomes obtained by them are not given by chance. Three chemometric analyses also confirmed the relevance of the peptides descriptors used in the modeling. Therefore, it can be concluded that the models built by fixing the drawbacks existing in the literature contribute to identifying antibacterial, antifungal, antiparasitic, and antiviral peptides with high effectivity and reliability. Models are freely available via the AMPDiscover tool at https://biocom-ampdiscover.cicese.mx/.

Automatic construction of molecular similarity networks for visual graph mining in chemical space of bioactive peptides: an unsupervised learning approach.

The increasing interest in bioactive peptides with therapeutic potentials has been reflected in a large variety of biological databases published over the last years. However, the knowledge discovery process from these heterogeneous data sources is a nontrivial task, becoming the essence of our research endeavor. Therefore, we devise a unified data model based on molecular similarity networks for representing a chemical reference space of bioactive peptides, having an implicit knowledge that is currently not explicitly accessed in existing biological databases. Indeed, our main contribution is a novel workflow for the automatic construction of such similarity networks, enabling visual graph mining techniques to uncover new insights from the "ocean" of known bioactive peptides. The workflow presented here relies on the following sequential steps: (i) calculation of molecular descriptors by applying statistical and aggregation operators on amino acid property vectors; (ii) a two-stage unsupervised feature selection method to identify an optimized subset of descriptors using the concepts of entropy and mutual information; (iii) generation of sparse networks where nodes represent bioactive peptides, and edges between two nodes denote their pairwise similarity/distance relationships in the defined descriptor space; and (iv) exploratory analysis using visual inspection in combination with clustering and network science techniques. For practical purposes, the proposed workflow has been implemented in our visual analytics software tool ( http://mobiosd-hub.com/starpep/ ), to assist researchers in extracting useful information from an integrated collection of 45120 bioactive peptides, which is one of the largest and most diverse data in its field. Finally, we illustrate the applicability of the proposed workflow for discovering central nodes in molecular similarity networks that may represent a biologically relevant chemical space known to date.

Ensemble Models Based on QuBiLS-MAS Features and Shallow Learning for the Prediction of Drug-Induced Liver Toxicity: Improving Deep Learning and Traditional Approaches.

Drug-induced liver injury (DILI) is a key safety issue in the drug discovery pipeline and a regulatory concern. Thus, many in silico tools have been proposed to improve the hepatotoxicity prediction of organic-type chemicals. Here, classifiers for the prediction of DILI were developed by using QuBiLS-MAS 0-2.5D molecular descriptors and shallow machine learning techniques, on a training set composed of 1075 molecules. The best ensemble model build, E13, was obtained with good statistical parameters for the learning series, namely, the following: accuracy = 0.840, sensibility = 0.890, specificity = 0.761, Matthew's correlation coefficient = 0.660, and area under the ROC curve = 0.904. The model was also satisfactorily evaluated with Y-scrambling test, and repeated k-fold cross-validation and repeated k-holdout validation. In addition, an exhaustive external validation was also carried out by using two test sets and five external test sets, with an average accuracy value equal to 0.854 (±0.062) and a coverage equal to 98.4% according to its applicability domain. A statistical comparison of the performance of the E13 model, with regard to results and tools (e.g., Padel DDPredictor Software, Deep Learning DILIserver, and Vslead) reported in the literature, was also performed. In general, E13 presented the best global performance in all experiments. The sum of the ranking differences procedure provided a very similar grouping pattern to that of the M-ANOVA statistical analysis, where E13 was identified as the best model for DILI predictions. A noncommercial and fully cross-platform software for the DILI prediction was also developed, which is freely available at http://tomocomd.com/apps/ptoxra. This software was used for the screening of seven data sets, containing natural products, leads, toxic materials, and FDA approved drugs, to assess the usefulness of the QSAR models in the DILI labeling of organic substances; it was found that 50-92% of the evaluated molecules are positive-DILI compounds. All in all, it can be stated that the E13 model is a relevant method for the prediction of DILI risk in humans, as it shows the best results among all of the methods analyzed.

Predicting reactive sites with quantum chemical topology: carbonyl additions in multicomponent reactions.

Quantum Chemical Topology (QCT) is a well established structural theoretical approach, but the development of its reactivity component is still a challenge. The hypothesis of this work is that the reactivity of an atom within a molecule is a function of its electronic population, its delocalization in the rest of the molecule, and the way it polarizes within an atomic domain. In this paper, we present a topological reactivity predictor for cabonyl additions, κ. It is a measure of the polarization of the electron density with the carbonyl functional group. κ is a model obtained from a QSAR procedure, using quantum-topological atomic descriptors and reported hydration equilibrium constants of carbonyl compounds. To validate the predictive capability of κ, we applied it to organic reactions, including a multicomponent reaction. κ was the only property that predicts the reactivity in each reaction step. The shape of κ can be interpreted as the change between two electrophilic states of a functional group, reactive and non-reactive.

Distributed and multicore QuBiLS-MIDAS software v2.0: Computing chiral, fuzzy, weighted and truncated geometrical molecular descriptors based on tensor algebra.

Advances to the distributed, multi-core and fully cross-platform QuBiLS-MIDAS software v2.0 (http://tomocomd.com/qubils-midas) are reported in this article since the v1.0 release. The QuBiLS-MIDAS software is the only one that computes atom-pair and alignment-free geometrical MDs (3D-MDs) from several distance metrics other than the Euclidean distance, as well as alignment-free 3D-MDs that codify structural information regarding the relations among three and four atoms of a molecule. The most recent features added to the QuBiLS-MIDAS software v2.0 are related (a) to the calculation of atomic weightings from indices based on the vertex-degree invariant (e.g., Alikhanidi index); (b) to consider central chirality during the molecular encoding; (c) to use measures based on clustering methods and statistical functions to codify structural information among more than two atoms; (d) to the use of a novel method based on fuzzy membership functions to spherically truncate inter-atomic relations; and (e) to the use of weighted and fuzzy aggregation operators to compute global 3D-MDs according to the importance and/or interrelation of the atoms of a molecule during the molecular encoding. Moreover, a novel module to compute QuBiLS-MIDAS 3D-MDs from their headings was also developed. This module can be used either by the graphical user interface or by means of the software library. By using the library, both the predictive models built with the QuBiLS-MIDAS 3D-MDs and the QuBiLS-MIDAS 3D-MDs calculation can be embedded in other tools. A set of predefined QuBiLS-MIDAS 3D-MDs with high information content and low redundancy on a set comprised of 20,469 compounds is also provided to be employed in further cheminformatics tasks. This set of predefined 3D-MDs evidenced better performance than all the universe of Dragon (v5.5) and PaDEL 0D-to-3D MDs in variability studies, whereas a linear independence study proved that these QuBiLS-MIDAS 3D-MDs codify chemical information orthogonal to the Dragon 0D-to-3D MDs. This set of predefined 3D-MDs would be periodically updated as long as new results be achieved. In general, this report highlights our continued efforts to provide a better tool for a most suitable characterization of compounds, and in this way, to contribute to obtaining better outcomes in future applications.

LEGO-based generalized set of two linear algebraic 3D bio-macro-molecular descriptors: Theory and validation by QSARs.

Novel 3D protein descriptors based on bilinear, quadratic and linear algebraic maps in Rn are proposed. The latter employs the kth 2-tuple (dis) similarity matrix to codify information related to covalent and non-covalent interactions in these biopolymers. The calculation of the inter-amino acid distances is generalized by using several dis-similarity coefficients, where normalization procedures based on the simple stochastic and mutual probability schemes are applied. A new local-fragment approach based on amino acid-types and amino acid-groups is proposed to characterize regions of interest in proteins. Topological and geometric macromolecular cutoffs are defined using local and total indices to highlight non-covalent interactions existing between the side-chains of each amino acid. Moreover, local and total indices calculations are generalized considering a LEGO approach, by using several aggregation operators. Collinearity and variability analyses are performed to evaluate every generalizing component applied to the definition of these novel indices. These experiments are oriented to reduce the number of MDs obtained for performing prediction models. The predictive power of the proposed indices was evaluated using two benchmark datasets, folding rate and secondary structural classification of proteins. The proposed MDs are modeled using the following strategies: Multiple Linear Regression (MLR) and Support Vector Machine (SVM), respectively. The best regression model developed for the folding rate of proteins yields a cross-validation coefficient of 0.875 (Test Set) and the best model developed for secondary structural classification obtained 98% of instances correctly classified (Test Set). These statistical parameters are superior to the ones obtained with existing MDs reported in the literature. Overall, the new theoretical generalization enhanced the information extraction into the MDs, allowing a better correlation between these two evaluated benchmark datasets and the proposed indices. The optimal theoretical configurations defined for the calculation of these MDs consider low collinearity and less information redundancy among them. These theoretical configurations and the software are available at http://tomocomd.com/mulims-mcompas.

Smoothed Spherical Truncation based on Fuzzy Membership Functions: Application to the Molecular Encoding.

A novel spherical truncation method, based on fuzzy membership functions, is introduced to truncate interatomic (or interaminoacid) relations according to smoothing values computed from fuzzy membership degrees. In this method, the molecules are circumscribed into a sphere, so that the geometric centers of the molecules are the centers of the spheres. The fuzzy membership degree of each atom (or aminoacid) is computed from its distance with respect to the geometric center of the molecule, by using a fuzzy membership function. So, the smoothing value to be applied in the truncation of a relation (or interaction) is computed by averaging the fuzzy membership degrees of the atoms (or aminoacids) involved in the relation. This truncation method is rather different from the existing ones, at considering the geometric center for the whole molecule and not only for atom-groups, as well as for using fuzzy membership functions to compute the smoothing values. A variability study on a set comprised of 20,469 compounds (15,050 drug-like compounds, 2994 drugs approved, 880 natural products from African sources, and 1545 plant-derived natural compounds exhibiting anti-cancerous activity) demonstrated that the truncation method proposed allows to determine molecular encodings with better ability for discriminating among structurally different molecules than the encodings obtained without applying truncation or applying non-fuzzy truncation functions. Moreover, a principal component analysis revealed that orthogonal chemical information of the molecules is encoded by using the method proposed. Lastly, a modeling study proved that the truncation method improves the modeling ability of existing geometric molecular descriptors, at allowing to develop more robust models than the ones built only using non-truncated descriptors. In this sense, a comparison and statistical assessment were performed on eight chemical datasets. As a result, the models based on the truncated molecular encodings yielded statistically better results than 12 procedures considered from the literature. It can thus be stated that the proposed truncation method is a relevant strategy for obtaining better molecular encodings, which will be ultimately useful in enhancing the modeling ability of existing encodings both on small-to-medium size molecules and biomacromolecules. © 2019 Wiley Periodicals, Inc.

MuLiMs-MCoMPAs: A Novel Multiplatform Framework to Compute Tensor Algebra-Based Three-Dimensional Protein Descriptors.

This report introduces the MuLiMs-MCoMPAs software (acronym for Multi-Linear Maps based on N-Metric and Contact Matrices of 3D Protein and Amino-acid weightings), designed to compute tensor-based 3D protein structural descriptors by applying two- and three-linear algebraic forms. Moreover, these descriptors contemplate generalizing components such as novel 3D protein structural representations, (dis)similarity metrics, and multimetrics to extract geometrical related information between two and three amino acids, weighting schemes based on amino acid properties, matrix normalization procedures that consider simple-stochastic and mutual probability transformations, topological and geometrical cutoffs, amino acid, and group-based MD calculations, and aggregation operators for merging amino acidic and group MDs. The MuLiMs-MCoMPAs software, which belongs to the ToMoCoMD-CAMPS suite, was developed in Java (version 1.8) using the Chemistry Development Kit (CDK) (version 1.4.19) and the Jmol libraries. This software implemented a divide-and-conquer strategy to parallelize the computation of the indices as well as modules for data preprocessing and batch computing functionalities. Furthermore, it consists of two components: (i) a desktop-graphical user interface (GUI) and (ii) an API library. The relevance of this novel approach is demonstrated through two analyses that considered Shannon's entropy-based variability and a principal component analysis. These studies showed that the MuLiMs-MCoMPAs' three-linear descriptor family contains higher informational entropy than several other descriptors generated with available computation tools. Moreover, the MuLiMs-MCoMPAs indices capture additional orthogonal information to the one codified by the available calculation approaches. As a result, two sets of suggested theoretical configurations that contain 13648 two-linear indices and 20263 three-linear indices are available for download at tomocomd.com . Furthermore, as a demonstration of the applicability and easy integration of the MuLiMs library into a QSAR-based expert system, a software application (ProStAF) was generated to predict SCOP protein structural classes and folding rate. It can thus be anticipated that the MuLiMs-MCoMPAs framework will turn into a valuable contribution to the chem- and bioinformatics research fields.

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 REPA-training ≥ 0.75 ( R = correlation coefficient) and MAEEPA-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 MAEtest-AD = 0.4044, MAEProTox-AD = 0.4067 and MAET3DB-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 MAEProTox-AD = 0.3992 and MAET3DB-AD = 0.2286, and MAEProTox-AD = 0.3773 and MAET3DB-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 ).

Choquet integral-based fuzzy molecular characterizations: when global definitions are computed from the dependency among atom/bond contributions (LOVIs/LOEIs).

BACKGROUND: Several topological (2D) and geometric (3D) molecular descriptors (MDs) are calculated from local vertex/edge invariants (LOVIs/LOEIs) by performing an aggregation process. To this end, norm-, mean- and statistic-based (non-fuzzy) operators are used, under the assumption that LOVIs/LOEIs are independent (orthogonal) values of one another. These operators are based on additive and/or linear measures and, consequently, they cannot be used to encode information from interrelated criteria. Thus, as LOVIs/LOEIs are not orthogonal values, then non-additive (fuzzy) measures can be used to encode the interrelation among them. RESULTS: General approaches to compute fuzzy 2D/3D-MDs from the contribution of each atom (LOVIs) or covalent bond (LOEIs) within a molecule are proposed, by using the Choquet integral as fuzzy aggregation operator. The Choquet integral-based operator is rather different from the other operators often used for the 2D/3D-MDs calculation. It performs a reordering step to fuse the LOVIs/LOEIs according to their magnitudes and, in addition, it considers the interrelation among them through a fuzzy measure. With this operator, fuzzy definitions can be derived from traditional or recent MDs; for instance, fuzzy Randic-like connectivity indices, fuzzy Balaban-like indices, fuzzy Kier-Hall connectivity indices, among others. To demonstrate the feasibility of using this operator, the QuBiLS-MIDAS 3D-MDs were used as study case and, as a result, a module was built into the corresponding software to compute them ( http://tomocomd.com/qubils-midas ). Thus, it is the only software reported in the literature that can be employed to determine Choquet integral-based fuzzy MDs. Moreover, regression models were created on eight chemical datasets. In this way, a comparison between the results achieved by the models based on the non-fuzzy QuBiLS-MIDAS 3D-MDs with regard to the ones achieved by the models based on the fuzzy QuBiLS-MIDAS 3D-MDs was made. As a result, the models built with the fuzzy QuBiLS-MIDAS 3D-MDs achieved the best performance, which was statistically corroborated through the Wilcoxon signed-rank test. CONCLUSIONS: All in all, it can be concluded that the Choquet integral constitutes a prominent alternative to compute fuzzy 2D/3D-MDs from LOVIs/LOEIs. In this way, better characterizations of the compounds can be obtained, which will be ultimately useful in enhancing the modelling ability of existing traditional 2D/3D-MDs.

GOWAWA Aggregation Operator-based Global Molecular Characterizations: Weighting Atom/bond Contributions (LOVIs/LOEIs) According to their Influence in the Molecular Encoding.

A different perspective to compute global weighted definitions of molecular descriptors from the contributions of each atom (LOVIs) or covalent bond (LOEIs) within a molecule is presented, using the generalized ordered weighted averaging - weighted averaging (GOWAWA) aggregation operator. This operator is rather different from the other norm-, mean- and statistic-based operators used up to date for the descriptors calculation from LOVIs/LOEIs. GOWAWA unifies the generalized ordered weighted averaging (GOWA) and the weighted generalized mean (WGM) functions and, in addition, it uses a smoothing parameter to assign different importance values to both functions depending on the problem under study. With the GOWAWA operator, diversity of novel global aggregations of molecular descriptors can be determined, where the influence that each atom (or covalent bond) has on the molecular characterization is taken into account. Therefore, this approach is completely different from the ones reported in the literature, where the values of LOVIs/LOEIs are considered equally important. To demonstrate the feasibility of using this operator, the QuBiLS-MIDAS descriptors (http://tomocomd.com/qubils-midas) were used and, as a result, a module was built into the corresponding software to compute them, being thus the only software reported in the literature that can be employed to determine weighted descriptors. Moreover, several modeling studies were performed on eight chemical datasets, which demonstrated that, with the GOWAWA aggregation operator, weighted QuBiLS-MIDAS descriptors that contribute to develop models with greater predictive power can be computed, if compared to the models based on the non-weighted descriptors calculated from the other operators used up to date. A non-parametric statistical assessment confirmed that the GOWAWA-based predictions are significantly superior to the others obtained. Therefore, all in all, it can be concluded that, from the results achieved, the GOWAWA operator constitutes a prominent alternative to codify relevant chemical information of the molecules, ultimately useful in improving the modeling ability of several old and recent descriptors whose definition is based on the LOVIs/LOEIs calculation.