1. Introduction Coumarins are found in nature in a great variety of plants where they have an important effect on plant biochemistry and physiology. They are involved in many metabolic processes [1]. Their antioxidant [2], anti-infammatory [3] and antiviral activities [4] have been studied previously. The hydroxycoumarins are some of the most active compounds from the coumarin family, previously being used as chelators and radical scavengers [5]. Some hydroxycoumarins perform single-electron reduction of free radicals, in which the phenoxyl radical can be stabilized by bulky or electron-withdrawing groups on the ring system or by the reduction caused by another hydroxy group to generate and stabilize the quinone-like product [6]. This mechanism is common in most vitamin E-like antioxidants, although not all coumarins tested for antiradical activity follow such mechanism [7]. The production of free radicals in mammals is promoted by environmental chemicals, stress or even metabolic processes capable of oxidizing biomolecules, resulting in infammation, coronary heart disease and cancer [8]. For this reason the development of new antioxidant compounds are of much interest in medicinal chemistry. The production of reactive oxygen species (ROS) is associated with some redox enzymatic processes, Central European Journal of Chemistry QSAR study of the DPPH• radical scavenging activity of coumarin derivatives and xanthine oxidase inhibition by molecular docking * E-mail: zgomez@ucol.mx Received 11 September 2013; Accepted 25 January 2014 Abstract: © Versita Sp. z o.o. Keywords: QSAR • DPPH• • Coumarins • Xanthine Oxidase • Docking 1 Faculty of Chemical Sciences, University of Colima, Mexico, C.P. 28400, Mexico 2 Association of Retired at the University of Guanajuato, Guanajuato, Gto., Mexico, C.P. 36000, Mexico 3 Secretary of Research and Graduate Studies, Autonomous University of Nayarit, City of Culture “Amado Nervo”, Tepic, Nayarit CP 63190, Mexico Rodrigo S. Razo-Hernández 1 , Kayim Pineda-Urbina 1 , Marlene A. Velazco-Medel 1 , Manuel Villanueva-García 2 , M. Teresa Sumaya-Martínez 3 , Francisco J. Martínez-Martínez 1 , Zeferino Gómez-Sandoval 1 Research Article A Quantitative Structure-Activity Relationship (QSAR) of coumarins by genetic algorithms employing physicochemical, topological, lipophilic and electronic descriptors was performed. We have used experimental antioxidant activities of specifc coumarin derivatives against the DPPH• radical molecule. Molecular descriptors such as Randic Path/Walk, hydrophilic factor and chemical hardness were selected to propose a mathematical model. We obtained a linear correlation with R 2 = 96.65 and 2 LOO Q = 93.14 values. The evaluation of the predictive ability of the model was performed by applying the 2 ASYM Q , ˆ and 2 m r ∆ methods. Fukui functions were calculated here for coumarin derivatives in order to delve into the mechanics by which they work as primary antioxidants. We also investigated xanthine oxidase inhibition with these coumarins by molecular docking. Our results show that hydrophobic, electrostatic and hydrogen bond interactions are crucial in the inhibition of xanthine oxidase by coumarins. Cent. Eur. J. Chem. • 12(10) • 2014 • 1067-1080 DOI: 10.2478/s11532-014-0555-x 1067