Physico-Chemical and Structural Interpretation of Discrete Derivative Indices on N-Tuples Atoms

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.

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.

Data Analysis in Chemistry and Bio-Medical Sciences

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