N-Linear Algebraic Maps for Chemical Structure Codification: A Suitable Generalization for Atom-pair Approaches?

Abstract

The present manuscript introduces, for the first time, a novel 3D-QSAR alignment free method (QuBiLS-MIDAS) based on tensor concepts through the use of the three-linear and four-linear algebraic forms as specific cases of n-linear maps. To this end, the k(th) three-tuple and four-tuple spatial-(dis)similarity matrices are defined, as tensors of order 3 and 4, respectively, to represent 3Dinformation among "three and four" atoms of the molecular structures. Several measures (multi-metrics) to establish (dis)-similarity relations among "three and four" atoms are discussed, as well as, normalization schemes proposed for the n-tuple spatial-(dis)similarity matrices based on the simple-stochastic and mutual probability algebraic transformations. To consider specific interactions among atoms, both for the global and local indices, n-tuple path and length cut-off constraints are introduced. This algebraic scaffold can also be seen as a generalization of the vector-matrix-vector multiplication procedure (which is a matrix representation of the traditional linear, quadratic and bilinear forms) for the calculation of molecular descriptors and is thus a new theoretical approach with a methodological contribution. A variability analysis based on Shannon's entropy reveals that the best distributions are achieved with the ternary and quaternary measures corresponding to the bond and dihedral angles. In addition, the proposed indices have superior entropy behavior than the descriptors calculated by other programs used in chemo-informatics studies, such as, DRAGON, PADEL, Mold2, and so on. A principal component analysis shows that the novel 3D n-tuple indices codify the same information captured by the DRAGON 3D-indices, as well as, information not codified by the latter. A QSAR study to obtain deeper criteria on the contribution of the novel molecular parameters was performed for the binding affinity to the corticosteroid-binding globulin, using Cramer's steroid database. The achieved results reveal superior statistical parameters for the Bond Angle and Dihedral Angle approaches, consistent with the results obtained in variability analysis. Finally, the obtained QuBiLS-MIDAS models yield superior performances than all 3D-QSAR methods reported in the literature using the 31 steroids as training set, and for the popular division of Cramer's database in training (1-21) and test (22-31) sets, comparable to superior results in the prediction of the activity of the steroids are obtained. From the results achieved, it can be suggested that the proposed QuBiLS-MIDAS N-tuples indices are a useful tool to be considered in chemo-informatics studies.

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

“…The QuBiLS‐MIDAS framework is one of the novel strategies introduced for the MDs computation based on atoms (LOVIs) –. This framework enables to determine geometric molecular descriptors (3D‐MDs) based on multi‐linear algebraic maps.…”

QuBiLS-MAS, open source multi-platform software for atom- and bond-based topological (2D) and chiral (2.5D) algebraic molecular descriptors computations

“…Additionally, other operators (see Additional file 1: Table SI2) applicable to the vector of LOVEIs were applied with the aim of generalizing the use of the linear combination to obtain global indices. It has been demonstrated in several reports [24–28] that better correlations for bioactivities may be attained when operators other than the sum are employed.…”

“…The use of several aggregation operators is based on the idea that the most suitable global definition of a system may not necessarily be additive. In fact, it is reported in the literature that operators other than the sum could yield better correlations with determined chemical properties [24–28]. In this sense, in the present report strategies are defined to generalize the procedure of obtaining global or local QuBiLS-MAS (acronym for Quadratic, Bilinear and N-Linear mapS based on graph-theoretic electronic-density Matrices and Atomic weightingS) indices using the so-called aggregation operators.…”

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

“…Molecular structural codification research has continued to attract the attention of several scholars in the present times, evidenced with the ever increasing amount of molecular descriptors (MDs) proposed (Barigye et al, 2013;García-Jacas et al, 2014;Todeschini and Consonni, 2009). These MDs can accordingly be employed to develop models that link the chemical structure with some activity/property (QSAR/QSPR) of interest and select candidate structures for new drugs using several statistical or machine learning techniques.…”

“…These MDs can accordingly be employed to develop models that link the chemical structure with some activity/property (QSAR/QSPR) of interest and select candidate structures for new drugs using several statistical or machine learning techniques. A lot of efforts have been placed on the characterization of small-to-medium-sized molecules, and large number of MDs have been proposed in the literature (Barigye et al, 2013;García-Jacas et al, 2014;Todeschini and Consonni, 2009). However, the same cannot be claimed for macromolecules (e.g.…”