Bond-based global and local (bond, group and bond-type) quadratic indices and their applications to computer-aided molecular design. 1. QSPR studies of diverse sets of organic chemicals

Abstract

The concept of atom-based quadratic indices is extended to a series of molecular descriptors (MDs) (both total and local) based on adjacency between edges. The kth edge-adjacency matrix (E ( k )) denotes the matrix of bond-based quadratic indices (non-stochastic) with respect to the canonical basis set. The kth "stochastic" edge-adjacency matrix, ES ( k ), is here proposed as a new molecular representation easily calculated from E ( k ). Then, the kth stochastic bond-based quadratic indices are calculated using ES ( k ) as operators of quadratic transformations. The study of six representative physicochemical properties of octane isomers was used to compare the ability of both series of MDs to produce significant quantitative structure-property relationship (QSPR) models. Moreover, the general performance of the new MDs in this QSPR study has been evaluated with respect to other 2D/3D well-known sets of indices and the obtained results shown a quite satisfactory behavior of the present method. The novel bond-level MDs were also used for the description and prediction of the boiling point of 28 alkyl-alcohols and to the modeling of the specific rate constant (log k) of 34 derivatives of 2-furylethylenes. These models were statistically significant and showed very good stability to data variation in leave-one-out (LOO) cross-validation experiment. The comparison with other approaches (edge- and vertices-based connectivity indices, total and local spectral moments, and quantum chemical descriptors as well as E-state/biomolecular encounter parameters) expose a good behavior of our method in this QSPR studies. The approach described in this report appears to be a very promising structural invariant, useful for QSPR/QSAR studies, similarity/diversity analysis, and computer-aided "rational" molecular (drug) design.

Atom- and Bond-Based 2D TOMOCOMD-CARDD Approach and Ligand-Based Virtual Screening for the Drug Discovery of New Tyrosinase Inhibitors

“…Earlier publications outlined the theory of all these 2D TOMOCOMD-CARDD descriptors. 7,[14][15][16][17] …”

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

“…They are distinguished in atom-based [33] and bond-based indices [10] depending on whether they are derived from the atom-based or bond-based matrix, respectively. The main diagonal elements for the atom-based matrix [denominated as non-stochastic (NS) when it doesn’t involve any normalization procedure] describe the presence of loops on graph vertices, which are used to characterize atoms in conjugated systems having more than one canonical structure [31, 34].…”

“…In previous reports, Marrero-Ponce et al proposed algebraic formalisms for characterizing topological (2D) and chiral (2.5D) molecular features through atom- and bond-based ToMoCoMD-CARDD (acronym for Topological Molecular Computational Design-Computer Aided Rational Drug Design) molecular descriptors [10–13]. These MDs codify molecular information based on the bilinear, quadratic and linear algebraic forms and the graph - theoretical electronic - density and edge - adjacency matrices in order to consider atom- and bond-based relations, respectively.…”

Discovery of Novel Trichomonacidals Using LDA‐Driven QSAR Models and Bond‐Based Bilinear Indices as Molecular Descriptors

“…In this section, we will first define the nomenclature to be used in this study, then the atom-based molecular vector (" x) will be redefined for bond characterization, by using the same approach as previously reported [91], and finally, some new definition of bond-based non-stochastic and stochastic bilinear indices, with its peculiar mathematical properties, will be given.…”