QSAR comparative study of Wiener descriptors for weighted molecular graphs

Quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies use statistical models to compute physical, chemical, or biological properties of a chemical substance from its molecular structure, encoded in a numerical form with the aid of various descriptors. Structural indices derived from molecular graph matrices represent an important group of descriptors used in QSPR and QSAR models; recently, their utilization was extended to molecular similarity and diversity, in database mining and virtual screening of combinatorial libraries. Initially defined from the distance matrix, the Wiener index W was the source of novel graph descriptors derived from recently proposed molecular matrices and of the Wiener graph operator. In this work we present a comparative study of several Wiener-type descriptors computed for vertex- and edge-weighted molecular graphs, corresponding to organic compounds with heteroatoms and multiple bonds. The acute toxicities toward Tetrahymena pyriformis of 47 nitrobenzenes are modeled with multilinear regression equations, using as structural descriptors the hydrophobicity (corrected for ionization) and various Wiener-type indices, with better results than a comparative molecular field analysis model.