Discrete derivatives for atom-pairs as a novel graph-theoretical invariant for generating new molecular descriptors: Orthogonality, interpretation and QSARs/QSPRs on benchmark databases

Oscar Martínez-Santiago, Reisel Millán-Cabrera, Yovani Marrero-Ponce, Stephen J. Barigye, Yoan Martínez-Lõpez, Francisco Torrens, Facundo Pérez-Giménez

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

16 Citas (Scopus)

Resumen

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)=(f i-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 17O 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.

Idioma originalInglés
Páginas (desde-hasta)343-368
Número de páginas26
PublicaciónMolecular Informatics
Volumen33
N.º5
DOI
EstadoPublicada - may. 2014
Publicado de forma externa

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