Rethinking the applicability domain analysis in QSAR models.

Notwithstanding the wide adoption of the OECD principles (or best practices) for QSAR modeling, disparities between in silico predictions and experimental results are frequent, suggesting that model predictions are often too optimistic. Of these OECD principles, the applicability domain (AD) estimation has been recognized in several reports in the literature to be one of the most challenging, implying that the actual reliability measures of model predictions are often unreliable. Applying tree-based error analysis workflows on 5 QSAR models reported in the literature and available in the QsarDB repository, i.e., androgen receptor bioactivity (agonists, antagonists, and binders, respectively) and membrane permeability (highest membrane permeability and the intrinsic permeability), we demonstrate that predictions erroneously tagged as reliable (AD prediction errors) overwhelmingly correspond to instances in subspaces (cohorts) with the highest prediction error rates, highlighting the inhomogeneity of the AD space. In this sense, we call for more stringent AD analysis guidelines which require the incorporation of model error analysis schemes, to provide critical insight on the reliability of underlying AD algorithms. Additionally, any selected AD method should be rigorously validated to demonstrate its suitability for the model space over which it is applied. These steps will ultimately contribute to more accurate estimations of the reliability of model predictions. Finally, error analysis may also be useful in "rational" model refinement in that data expansion efforts and model retraining are focused on cohorts with the highest error rates.

Complex Networks Analyses of Antibiofilm Peptides: An Emerging Tool for Next-Generation Antimicrobials' Discovery.

Microbial biofilms cause several environmental and industrial issues, even affecting human health. Although they have long represented a threat due to their resistance to antibiotics, there are currently no approved antibiofilm agents for clinical treatments. The multi-functionality of antimicrobial peptides (AMPs), including their antibiofilm activity and their potential to target multiple microbes, has motivated the synthesis of AMPs and their relatives for developing antibiofilm agents for clinical purposes. Antibiofilm peptides (ABFPs) have been organized in databases that have allowed the building of prediction tools which have assisted in the discovery/design of new antibiofilm agents. However, the complex network approach has not yet been explored as an assistant tool for this aim. Herein, a kind of similarity network called the half-space proximal network (HSPN) is applied to represent/analyze the chemical space of ABFPs, aiming to identify privileged scaffolds for the development of next-generation antimicrobials that are able to target both planktonic and biofilm microbial forms. Such analyses also considered the metadata associated with the ABFPs, such as origin, other activities, targets, etc., in which the relationships were projected by multilayer networks called metadata networks (METNs). From the complex networks' mining, a reduced but informative set of 66 ABFPs was extracted, representing the original antibiofilm space. This subset contained the most central to atypical ABFPs, some of them having the desired properties for developing next-generation antimicrobials. Therefore, this subset is advisable for assisting the search for/design of both new antibiofilms and antimicrobial agents. The provided ABFP motifs list, discovered within the HSPN communities, is also useful for the same purpose.

Searching glycolate oxidase inhibitors based on QSAR, molecular docking, and molecular dynamic simulation approaches.

Primary hyperoxaluria type 1 (PHT1) treatment is mainly focused on inhibiting the enzyme glycolate oxidase, which plays a pivotal role in the production of glyoxylate, which undergoes oxidation to produce oxalate. When the renal secretion capacity exceeds, calcium oxalate forms stones that accumulate in the kidneys. In this respect, detailed QSAR analysis, molecular docking, and dynamics simulations of a series of inhibitors containing glycolic, glyoxylic, and salicylic acid groups have been performed employing different regression machine learning techniques. Three robust models with less than 9 descriptors-based on a tenfold cross (Q2 CV) and external (Q2 EXT) validation-were found i.e., MLR1 (Q2 CV = 0.893, Q2 EXT = 0.897), RF1 (Q2 CV = 0.889, Q2 EXT = 0.907), and IBK1 (Q2 CV = 0.891, Q2 EXT = 0.907). An ensemble model was built by averaging the predicted pIC50 of the three models, obtaining a Q2 EXT = 0.933. Physicochemical properties such as charge, electronegativity, hardness, softness, van der Waals volume, and polarizability were considered as attributes to build the models. To get more insight into the potential biological activity of the compouds studied herein, docking and dynamic analysis were carried out, finding the hydrophobic and polar residues show important interactions with the ligands. A screening of the DrugBank database V.5.1.7 was performed, leading to the proposal of seven commercial drugs within the applicability domain of the models, that can be suggested as possible PHT1 treatment.

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.

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.

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.

Predicting structural classes of proteins by incorporating their global and local physicochemical and conformational properties into general Chou's PseAAC.

In this study, I introduce novel global and local 0D-protein descriptors based on a statistical quantity named Total Sum of Squares (TSS). This quantity represents the sum of the squares differences of amino acid properties from the arithmetic mean property. As an extension, the amino acid-types and amino acid-groups formalisms are used for describing zones of interest in proteins. To assess the effectiveness of the proposed descriptors, a Nearest Neighbor model for predicting the major four protein structural classes was built. This model has a success rate of 98.53% on the jackknife cross-validation test; this performance being superior to other reported methods despite the simplicity of the predictor. Additionally, this predictor has an average success rate of 98.35% in different cross-validation tests performed. A value of 0.98 for the Kappa statistic clearly discriminates this model from a random predictor. The results obtained by the Nearest Neighbor model demonstrated the ability of the proposed descriptors not only to reflect relevant biochemical information related to the structural classes of proteins but also to allow appropriate interpretability. It can thus be expected that the current method may play a supplementary role to other existing approaches for protein structural class prediction and other protein attributes.

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.

Novel 3D bio-macromolecular bilinear descriptors for protein science: Predicting protein structural classes.

In the present study, we introduce novel 3D protein descriptors based on the bilinear algebraic form in the ℝ(n) space on the coulombic matrix. For the calculation of these descriptors, macromolecular vectors belonging to ℝ(n) space, whose components represent certain amino acid side-chain properties, were used as weighting schemes. Generalization approaches for the calculation of inter-amino acidic residue spatial distances based on Minkowski metrics are proposed. The simple- and double-stochastic schemes were defined as approaches to normalize the coulombic matrix. The local-fragment indices for both amino acid-types and amino acid-groups are presented in order to permit characterizing fragments of interest in proteins. On the other hand, with the objective of taking into account specific interactions among amino acids in global or local indices, geometric and topological cut-offs are defined. To assess the utility of global and local indices a classification model for the prediction of the major four protein structural classes, was built with the Linear Discriminant Analysis (LDA) technique. The developed LDA-model correctly classifies the 92.6% and 92.7% of the proteins on the training and test sets, respectively. The obtained model showed high values of the generalized square correlation coefficient (GC(2)) on both the training and test series. The statistical parameters derived from the internal and external validation procedures demonstrate the robustness, stability and the high predictive power of the proposed model. The performance of the LDA-model demonstrates the capability of the proposed indices not only to codify relevant biochemical information related to the structural classes of proteins, but also to yield suitable interpretability. It is anticipated that the current method will benefit the prediction of other protein attributes or functions.

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.