## 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(v_{i},v_{j})=(f _{i}-2f_{ij}+f_{j})/f_{ij}, where f_{i} (or f_{j}) and f_{ij} 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, Δ_{i}, 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 Δ_{i} 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 ^{17}O 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 original | Inglés |
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Páginas (desde-hasta) | 343-368 |

Número de páginas | 26 |

Publicación | Molecular Informatics |

Volumen | 33 |

N.º | 5 |

DOI | |

Estado | Publicada - may. 2014 |

Publicado de forma externa | Sí |