RESEARCH ARTICLE QSAR as a random event: a case of NOAEL Alla P. Toropova & Andrey A. Toropov & Jovana B. Veselinović & Aleksandar M. Veselinović Received: 17 October 2014 /Accepted: 9 December 2014 /Published online: 19 December 2014 # Springer-Verlag Berlin Heidelberg 2014 Abstract Quantitative structure–activity relationships (QSAR) for no observed adverse effect levels (NOAEL, mmol/kg/day, in logarithmic units) are suggested. Simplified molecular input line entry systems (SMILES) were used for molecular structure representation. Monte Carlo method was used for one-variable models building up for three different splits into the “visible” training set and “invisible” validation. The statistical quality of the models for three random splits are the following: split 1 n =180, r 2 =0.718, q 2 =0.712, s =0.403, F =454 (training set); n =17, r 2 =0.544, s =0.367 (calibration set); n =21, r 2 =0.61, s =0.44, r m 2 =0.61 (validation set); split 2 n =169, r 2 =0.711, q 2 =0.705, s =0.409, F =411 (training set); n =27, r 2 =0.512, s =0.461 (calibration set); n =22, r 2 =0.669, s =0.360, r m 2 =0.63 (validation set); split 3 n =172, r 2 =0.679, q 2 =0.672, s =0.420, F =360 (training set); n =19, r 2 =0.617, s =0.582 (calibration set); n =21, r 2 =0.627, s =0.367, r m 2 = 0.54 (validation set). All models are built according to OCED principles. Keywords QSAR . Monte Carlo technique . Optimal descriptor . Chronic toxicity . NOAEL Introduction Humans encounter enormous amount of various chemical com- pounds daily in different exposure manners. In modern civili- zation, there are over five million man-made chemicals current- ly known (of which 70,000 are in use today) and about 100,000 naturally occurring chemicals of known structure (Mazzatorta et al. 2008). The evaluation of their potential influence to human health is very difficult since there are or no toxicological information available for most of compounds. Toxicological studies are used for identification and characterization of the potential toxicity of chemical compounds. In many of them, laboratory animals are used to obtain key toxicology informations like acute or chronic toxicity, establishment of dose-response curves, and the determination of the no observed adverse effect level (NOAEL) and lowest observed adverse effect level (LOAEL). The United States Environmental Protection Agency (US EPA) defines NOAEL as an exposure level at which there are no statistically or biologically signif- icant increases in the frequency or severity of adverse effects between the exposed population and its appro- priate control; some effects may be produced at this level, but they are not considered as adverse, or as precursors to adverse effects. In an experiment with several NOAELs, the regulatory focus is primarily on the highest one, leading to the common usage of the term NOAEL as the highest exposure without adverse effects. [http://www.epa.gov/OCEPAterms/nterms.html]. NOAEL is the important information from point of view of risk assessment of various substances which take place in food industry, cosmetics, and in everyday life in general (Contrera, et al. 2004; Zhu et al. 2009; Rupp et al. 2010; Wang et al. 2011). Also, toxicity testing of new compounds is essential for drug development process (Lewis et al. 2002; Parasuraman Responsible editor: Michael Matthies Electronic supplementary material The online version of this article (doi:10.1007/s11356-014-3977-2) contains supplementary material, which is available to authorized users. A. P. Toropova : A. A. Toropov (*) IRCCS, Istituto di Ricerche Farmacologiche Mario Negri, 20156Via La Masa 19, Milano, Italy e-mail: andrey.toropov@marionegri.it J. B. Veselinović : A. M. Veselinović Department of Chemistry, Faculty of Medicine, University of Niš, Niš, Serbia Environ Sci Pollut Res (2015) 22:8264–8271 DOI 10.1007/s11356-014-3977-2