Quasi-QSAR for mutagenic potential of multi-walled carbon-nanotubes Andrey A. Toropov ⇑ , Alla P. Toropova IRCCS, Istituto di Ricerche Farmacologiche Mario Negri, Via La Masa 19, 20156 Milano, Italy highlights  Quasi-QSAR for MWCNTs is suggested.  The model of mutagenicity is a mathematical function of conditions.  The statistical quality of the quasi-QSAR is quite good. article info Article history: Received 22 July 2014 Received in revised form 15 October 2014 Accepted 18 October 2014 Available online xxxx Handling Editor: Tamara S. Galloway Keywords: MWCNT Mutagenicity TA100 Monte Carlo method Quasi-QSAR abstract Available on the Internet, the CORAL software (http://www.insilico.eu/coral) has been used to build up quasi-quantitative structure–activity relationships (quasi-QSAR) for prediction of mutagenic potential of multi-walled carbon-nanotubes (MWCNTs). In contrast with the previous models built up by CORAL which were based on representation of the molecular structure by simplified molecular input-line entry system (SMILES) the quasi-QSARs based on the representation of conditions (not on the molecular struc- ture) such as concentration, presence (absence) S9 mix, the using (or without the using) of preincubation were encoded by so-called quasi-SMILES. The statistical characteristics of these models (quasi-QSARs) for three random splits into the visible training set and test set and invisible validation set are the following: (i) split 1: n = 13, r 2 = 0.8037, q 2 = 0.7260, s = 0.033, F = 45 (training set); n = 5, r 2 = 0.9102, s = 0.071 (test set); n = 6, r 2 = 0.7627, s = 0.044 (validation set); (ii) split 2: n = 13, r 2 = 0.6446, q 2 = 0.4733, s = 0.045, F = 20 (training set); n = 5, r 2 = 0.6785, s = 0.054 (test set); n = 6, r 2 = 0.9593, s = 0.032 (validation set); and (iii) n = 14, r 2 = 0.8087, q 2 = 0.6975, s = 0.026, F = 51 (training set); n = 5, r 2 = 0.9453, s = 0.074 (test set); n = 5, r 2 = 0.8951, s = 0.052 (validation set). Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Quantitative structure–property/activity relationships (QSPRs/ QSARs) based on various descriptors (Gutman et al., 2005; Furtula and Gutman, 2011) are a tool of investigation of physico- chemical (Torrens and Castellano, 2012; Nesmerak et al., 2013, 2014; Achary, 2014a), biological (Rallo et al., 2005; Torrens and Castellano, 2014; Achary, 2014b), and therapeutical (Afantitis et al., 2011; Veselinovic ´ et al., 2013a,b; Comelli et al., 2014; Deng et al., 2014a,b) behavior of various substances. There are the considerable number of attempts to carry out the QSPR/QSAR analyses of various nanomaterials (Kar et al., 2014; Toropov et al., 2013; Pathakoti et al., 2014; Singh and Gupta, 2014). However, the main problem of this fresh field of natural sci- ences is deficit of available experimental data on physicochemical parameters and biological activity of these substances (González- Díaz et al., 2013; Winkler et al., 2013). Traditional QSAR approaches were used to build up nano-QSAR in recent work (Ibrahim et al., 2010; Fourches et al., 2010; Shahlaei et al., 2014). It is paradox, but quantum mechanics descriptors often are involved as a tool to build up a model for nanomaterials (Ibrahim et al., 2010; Shahlaei et al., 2014), in spite of large size of their molecules. Finally, the prediction of endpoints related to nanomaterials as a mathematical function of their physicochemical properties can be prepared if these data are available (Sayes and Ivanov, 2010). So-called optimal descriptors calculated with the Monte Carlo technique are an attractive alternative for the above-mentioned approaches, because (i) these descriptors can be calculated from arbitrary eclectic information (Toropova and Toropov, 2013; Toropov and Toropova, 2014); and (ii) these descriptors can be easily modified for fresh experimental data if these will become available (Toropov et al., 2010; Toropova et al., 2010). Analysis of the state-of-art situation with QSAR theory for nanomaterials has shown: large standardized databases on the nanomaterials and their endpoints is absent, but there are small data related sometimes to the same endpoint, such as cytotoxicity http://dx.doi.org/10.1016/j.chemosphere.2014.10.067 0045-6535/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: andrey.toropov@marionegri.it (A.A. Toropov). Chemosphere xxx (2014) xxx–xxx Contents lists available at ScienceDirect Chemosphere journal homepage: www.elsevier.com/locate/chemosphere Please cite this article in press as: Toropov, A.A., Toropova, A.P. Quasi-QSAR for mutagenic potential of multi-walled carbon-nanotubes. Chemosphere (2014), http://dx.doi.org/10.1016/j.chemosphere.2014.10.067