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 comp…
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 subgrap…
Atom-based non-stochastic and stochastic bilinear indices: Application to QSPR/QSAR studies of organic compounds
The recently introduced bilinear indices are applied to the QSAR/QSPR studies of heteroatomic molecules. These novel atom-based molecular fingerprints are used to predict the boiling point of 28 alkyl-alcohols and partition coefficient, specific rate constant and antibacterial activity of 34 2-furylethylenes derivatives. The obtained models are statistically significant and show rather very good stability in a cross-validation experiment. The comparison with other approaches exposes a good behavior of our method in this QSPR studies. The obtained results suggest that with the present method, it is possible to obtain a good estimation of physical, chemical and physicochemical properties for …
Generalized Molecular Descriptors Derived From Event-Based Discrete Derivative.
In the present study, a generalized approach for molecular structure characterization is introduced, based on the relation frequency matrix (F) representation of the molecular graph and the subsequent calculation of the corresponding discrete derivative (finite difference) over a pair of elements (atoms). In earlier publications (22- 24), an unique event, named connected subgraphs, (based on the Kier-Hall's subgraphs) was systematically employed for the computation of the matrix F. The present report is a generalization of this notion, in which eleven additional events are introduced, classified in three categories, namely, topological (terminal paths, vertex path incidence, quantum subgrap…