Exploring proteasome inhibition using atomic weighted vector indices and machine learning approaches.

Ubiquitin-proteasome system (UPS) is a highly regulated mechanism of intracellular protein degradation and turnover. The UPS is involved in different biological activities, such as the regulation of gene transcription and cell cycle. Several researchers have applied cheminformatics and artificial intelligence methods to study the inhibition of proteasomes, including the prediction of UPP inhibitors. Following this idea, we applied a new tool for obtaining molecular descriptors (MDs) for modeling proteasome Inhibition in terms of EC50 (µmol/L), in which a set of new MDs called atomic weighted vectors (AWV) and several prediction algorithms were used in cheminformatics studies. In the manuscript, a set of descriptors based on AWV are presented as datasets for training different machine learning techniques, such as linear regression, multiple linear regression (MLR), random forest (RF), K-nearest neighbors (IBK), multi-layer perceptron, best-first search, and genetic algorithm. The results suggest that these atomic descriptors allow adequate modeling of proteasome inhibitors despite artificial intelligence techniques, as a variant to build efficient models for the prediction of inhibitory activity.

When global and local molecular descriptors are more than the sum of its parts: Simple, But Not Simpler?

In this report, we introduce a set of aggregation operators (AOs) to calculate global and local (group and atom type) molecular descriptors (MDs) as a generalization of the classical approach of molecular encoding using the sum of the atomic (or fragment) contributions. These AOs are implemented in a new and free software denominated MD-LOVIs ( http://tomocomd.com/md-lovis ), which allows for the calculation of MDs from atomic weights vector and LOVIs (local vertex invariants). This software was developed in Java programming language and employed the Chemical Development Kit (CDK) library for handling chemical structures and the calculation of atomic weights. An analysis of the complexities of the algorithms presented herein demonstrates that these aspects were efficiently implemented. The calculation speed experiments show that the MD-LOVIs software has satisfactory behavior when compared to software such as Padel, CDKDescriptor, DRAGON and Bluecal software. Shannon's entropy (SE)-based variability studies demonstrate that MD-LOVIs yields indices with greater information content when compared to those of popular academic and commercial software. A principal component analysis reveals that our approach captures chemical information orthogonal to that codified by the DRAGON, Padel and Mold2 software, as a result of the several generalizations in MD-LOVIs not used in other programs. Lastly, three QSARs were built using multiple linear regression with genetic algorithms, and the statistical parameters of these models demonstrate that the MD-LOVIs indices obtained with AOs yield better performance than those obtained when the summation operator is used exclusively. Moreover, it is also revealed that the MD-LOVIs indices yield models with comparable to superior performance when compared to other QSAR methodologies reported in the literature, despite their simplicity. The studies performed herein collectively demonstrated that MD-LOVIs software generates indices as simple as possible, but not simpler and that use of AOs enhances the diversity of the chemical information codified, which consequently improves the performance of traditional MDs.

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.

Prediction of aquatic toxicity of benzene derivatives using molecular descriptor from atomic weighted vectors.

Several descriptors from atom weighted vectors are used in the prediction of aquatic toxicity of set of organic compounds of 392 benzene derivatives to the protozoo ciliate Tetrahymena pyriformis (log(IGC50)-1). These descriptors are calculated using the MD-LOVIs software and various Aggregation Operators are examined with the aim comparing their performances in predicting aquatic toxicity. Variability analysis is used to quantify the information content of these molecular descriptors by means of an information theory-based algorithm. Multiple Linear Regression with Genetic Algorithms is used to obtain models of the structure-toxicity relationships; the best model shows values of Q2=0.830 and R2=0.837 using six variables. Our models compare favorably with other previously published models that use the same data set. The obtained results suggest that these descriptors provide an effective alternative for determining aquatic toxicity of benzene derivatives.

State of the Art Review and Report of New Tool for Drug Discovery.

BACKGROUND: There are a great number of tools that can be used in QSAR/QSPR studies; they are implemented in several programs that are reviewed in this report. The usefulness of new tools can be proved through comparison, with previously published approaches. In order to perform the comparison, the most usual is the use of several benchmark datasets such as DRAGON and Sutherland's datasets. METHODS: Here, an exploratory study of Atomic Weighted Vectors (AWVs), a new tool useful for drug discovery using different datasets, is presented. In order to evaluate the performance of the new tool, several statistics and QSAR/QSPR experiments are performed. Variability analyses are used to quantify the information content of the AWVs obtained from the tool, by means of an information theory-based algorithm. RESULTS: Principal components analysis is used to analyze the orthogonality of these descriptors, for which the new MDs from AWVs provide different information from those codified by DRAGON descriptors (0-2D). The QSAR models are obtained for every Sutherland's dataset, according to the original division into training/test sets, by means of the multiple linear regression with genetic algorithm (MLR-GA). These models have been validated and compared favorably to several previously published approaches, using the same benchmark datasets. CONCLUSION: The obtained results show that this tool should be a useful strategy for the QSAR/QSPR studies, despite its simplicity.

Discrete Derivatives for Atom-Pairs as a Novel Graph-Theoretical Invariant for Generating New Molecular Descriptors: Orthogonality, Interpretation and QSARs/QSPRs on Benchmark Databases.

This report presents a new mathematical method based on the concept of the derivative of a molecular graph (G) with respect to a given event (S) to codify chemical structure information. The derivate over each pair of atoms in the molecule is defined as ∂G/∂S(vi , vj )=(fi -2fij +fj )/fij , where fi (or fj ) and fij are the individual frequency of atom i (or j) and the reciprocal frequency of the atoms i and j, respectively. These frequencies characterize the participation intensity of atom pairs in S. Here, the event space is composed of molecular sub-graphs which participate in the formation of the G skeleton that could be complete (representing all possible connected sub-graphs) or comprised of sub-graphs of certain orders or types or combinations of these. The atom level graph derivative index, Δi , is expressed as a linear combination of all atom pair derivatives that include the atomic nuclei i. Global [total or local (group or atom-type)] indices are obtained by applying the so called invariants over a vector of Δi values. The novel MDs are validated using a data set of 28 alkyl-alcohols and other benchmark data sets proposed by the International Academy of Mathematical Chemistry. Also, the boiling point for the alcohols, the adrenergic blocking activity of N,N-dimethyl-2-halo-phenethylamines and physicochemical properties of polychlorinated biphenyls and octanes are modeled. These models exhibit satisfactory predictive power compared with other 0-3D indices implemented successfully by other researchers. In addition, tendencies of the proposed indices are investigated using examples of various types of molecular structures, including chain-lengthening, branching, heteroatoms-content, and multiple bonds. On the other hand, the relation of atom-based derivative indices with (17) O NMR of a series of ethers and carbonyls reflects that the new MDs encode electronic, topological and steric information. Linear independence between the graph derivative indices and other 0-3D MDs is demonstrated by using principal component analysis on a dataset of 41 heterogeneous molecules. It is concluded that the graph derivative indices are independent indices containing important structural information to be used in QSPR/QSAR and drug design studies, and permit obtaining easier, more interpretable and robust mathematical models than the majority of those reported in the literature.

Relations frequency hypermatrices in mutual, conditional and joint entropy-based information indices.

Graph-theoretic matrix representations constitute the most popular and significant source of topological molecular descriptors (MDs). Recently, we have introduced a novel matrix representation, named the duplex relations frequency matrix, F, derived from the generalization of an incidence matrix whose row entries are connected subgraphs of a given molecular graph G. Using this matrix, a series of information indices (IFIs) were proposed. In this report, an extension of F is presented, introducing for the first time the concept of a hypermatrix in graph-theoretic chemistry. The hypermatrix representation explores the n-tuple participation frequencies of vertices in a set of connected subgraphs of G. In this study we, however, focus on triple and quadruple participation frequencies, generating triple and quadruple relations frequency matrices, respectively. The introduction of hypermatrices allows us to redefine the recently proposed MDs, that is, the mutual, conditional, and joint entropy-based IFIs, in a generalized way. These IFIs are implemented in GT-STAF (acronym for Graph Theoretical Thermodynamic STAte Functions), a new module of the TOMOCOMD-CARDD program. Information theoretic-based variability analysis of the proposed IFIs suggests that the use of hypermatrices enhances the entropy and, hence, the variability of the previously proposed IFIs, especially the conditional and mutual entropy based IFIs. The predictive capacity of the proposed IFIs was evaluated by the analysis of the regression models, obtained for physico-chemical properties the partition coefficient (Log P) and the specific rate constant (Log K) of 34 derivatives of 2-furylethylene. The statistical parameters, for the best models obtained for these properties, were compared to those reported in the literature depicting better performance. This result suggests that the use of the hypermatrix-based approach, in the redefinition of the previously proposed IFIs, avails yet other valuable tools beneficial in QSPR studies and diversity analysis.