Quadratic indices of the ‘molecular pseudograph’s atom adjacency matrix’ and their stochastic forms: a novel approach for virtual screening and in silico discovery of new lead paramphistomicide drugs-like compounds Yovani Marrero-Ponce a, * , Alma Huesca-Guille ´n b , Froyla ´n Ibarra-Velarde b a Department of Pharmacy, Faculty of Chemical-Pharmacy and Department of Drug Design, Chemical Bioactive Center, Central University of Las Villas, Santa Clara, 54830 Villa Clara, Cuba b Department of Parasitology, Faculty of Veterinary Medicine and Zootechny, UNAM, Mexico D.F. 04510, Mexico Received 23 July 2004; accepted 4 November 2004 Available online 8 January 2005 Abstract Quadratic indices of the ‘molecular pseudograph’s atom adjacency matrix’ have been generalized to codify chemical structure information. In this sense; stochastic quadratic indices have been introduced for the description of the molecular structure. These stochastic indices are based on a simple model for the intramolecular movement of all valence-bond electrons. In this paper, we extend our earlier work by applying non-stochastic and stochastic quadratic indices to the discrimination of paramphistomicide compounds from inactive ones. Two linear discriminant analysis models were obtained. The first one was performed considering non-stochastic descriptors and classifies correctly 95.00% of active compounds and 86.67% of non-active one for a global good classification of 91.437%. The last model classified correctly 90.00% of the active and 86.67% of the inactive compounds in a training set, result that represent a total of 88.57% accuracy in classification. Similar predictive behavior was observed in a leave-one-out cross-validation procedure for both equations. Canonical regression analysis corroborated the statistical quality of these models (R can Z0.75) and was also used to compute biology activity canonical scores for each compound. A few anthelmintics compounds and other drugs from the Merk Index, Negwer handbook, and Goodman and Gilman were selected/identified by the models as possible paramphistomicide, one of them was found in the recent literature as possessing this activity. The results demonstrate the usefulness of our topological approach for drug discovery of new lead compounds active against Paramphistomum sp. q 2004 Elsevier B.V. All rights reserved. Keywords: TOMOCOMD-CARDD software; Quadratic indices; Stochastic quadratic indices; QSAR; Paramphistomicide compound 1. Introduction Helminthiasis is one of the most important groups of parasitic diseases in several continents. Among these infections, stomach and liver flukes (such as Paramphisto- mum spp. or Calicophoron spp. and Fasciola spp., respectively) play a significant role [1–3]. The loss not only results in the death of livestock but also causes great economic loss in the form of decreased productivity and fertility, decreased drought power, etc. Paramphistomosis caused by a number of species of paramphistomes is responsible for sporadic epizootics of acute parasitic enteritis accompanied with persistent fetid diarrhea in Ruminants [4]. Adult flukes in the rumen (first stomach or paunch) or reticulum (second stomach or honeycomb) for instance, are not known to cause clinical disease. However, heavy infections with immature flukes in the upper small intestine can cause serious ill-health and death. 0166-1280/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2004.11.027 Journal of Molecular Structure: THEOCHEM 717 (2005) 67–79 www.elsevier.com/locate/theochem * Corresponding author. Tel.: C53 42 281192/473; fax: C53 42 281130/455. E-mail addresses: yovanimp@qf.uclv.edu.cu (Y. Marrero-Ponce), ymarrero77@yahoo.es (Y. Marrero-Ponce).