Short Communication Optimal descriptor as a translator of eclectic data into endpoint prediction: Mutagenicity of fullerene as a mathematical function of conditions Andrey A. Toropov ⇑ , Alla P. Toropova IRCCS – Istituto di Ricerche Farmacologiche Mario Negri, Via La Masa 19, Milano 20156, Italy highlights  Quasi-QSAR for fullerene C60 nanoparticles 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 12 September 2013 Received in revised form 21 October 2013 Accepted 26 October 2013 Available online xxxx Keywords: Fullerene C60 Bacterial reverse mutation test Quasi-QSAR Optimal descriptor abstract The experimental data on the bacterial reverse mutation test on C60 nanoparticles (TA100) is examined as an endpoint. By means of the optimal descriptors calculated with the Monte Carlo method a mathematical model of the endpoint has been built up. The model is the mathematical function of (i) dose (g/plate); (ii) metabolic activation (i.e. with S9 mix or without S9 mix); and (iii) illumination (i.e. dark or irradiation). The statistical quality of the model is the following: n = 10, r 2 = 0.7549, q 2 = 0.5709, s = 7.67, F = 25 (Training set); n = 5, r 2 = 0.8987, s = 18.4 (Calibration set); and n = 5, r 2 = 0.6968, s = 10.9 (Validation set). Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction The development of the systematical representation for various nanomaterials is complex task since the molecular architecture of these substances is very untypical in comparison with architecture of organic (Toropova et al., 2011a), inorganic, organometallic (Toropova et al., 2011b) substances which can be represented by the molecular graph (Toropov and Toropova 2002; Toropov and Toropova 2003; Toropov and Roy 2004; Castillo-Garit et al., 2007; Fourches et al., 2010; Afantitis et al., 2011; Furtula and Gutman, 2011), simplified molecular input-line entry systems (García et al., 2011; Garro Martinez et al., 2011; Mullen et al., 2011; Toropov et al., 2011; Ibezim et al., 2012) (SMILES) or International Chemical Identifier (InChI) (Toropov et al., 2009; Toropov et al., 2010). Even in the case of majority of polymers their molecular structure can be systematized via the architecture of monomers (Toropov et al., 1999). Quantitative structure–property/activity relationships (QSPRs/QSARs) give the possibility to define preferable substances to solve various practical tasks (Puzyn et al., 2009; Leszczynski, 2010). This definition is based on the mathematical comparison of variety of molecular structures characterized by the measure of their ability to solve the given practical task. These measures are obtained from the relevant experiment. In fact the selection of molecular structure is the selection of the substance with the most appropriate above-mentioned measure. ‘‘Classic’’ QSPR/QSAR analyses for nanomaterials are limited by the absence of standardized databases on their structure together with physicochemical and biomedical endpoints. However, in the case of the nanomaterials various technological conditions as well as conditions of exposure can influence an effect of these substances upon biological objects. Under such circumstances the quasi-QSAR where instead of the representation of a substance by molecular structure the representation of this by the above- mentioned available eclectic information becomes attractive alter- native of ‘‘classic’’ QSAR (Toropov et al., 2007; Toropova et al., 2013). Optimal descriptors calculated with so-called correlation weights of various attributes of nanomaterials may be a tool to build up the quasi-QSAR. The aim of the present work is the esti- mation of the optimal descriptors as possible approach to build 0045-6535/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.chemosphere.2013.10.079 ⇑ Corresponding author. Tel.: +39 02 39014595; fax: +39 02 39014735. E-mail address: andrey.toropov@marionegri.it (A.A. Toropov). Chemosphere xxx (2013) 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. Optimal descriptor as a translator of eclectic data into endpoint prediction: Mutagenicity of fullerene as a mathematical function of conditions. Chemosphere (2013), http://dx.doi.org/10.1016/j.chemosphere.2013.10.079