Short Communication Optimal descriptor as a translator of eclectic information into the prediction of membrane damage by means of various TiO 2 nanoparticles Alla P. Toropova, Andrey A. Toropov ⇑ IRCCS, Istituto di Ricerche Farmacologiche Mario Negri, 20156, Via La Masa 19, Milano, Italy highlights  Nanoparticles are represented by codes of physicochemical feature.  Optimal descriptors were used to build up predictive model for membrane damage.  Statistical quality of the model is quite good. article info Article history: Received 24 June 2013 Received in revised form 20 August 2013 Accepted 20 September 2013 Available online 22 October 2013 Keywords: QSAR Monte Carlo method TiO 2 nanoparticle Membrane damage abstract The increasing use of nanomaterials incorporated into consumer products leads to the need for develop- ing approaches to establish ‘‘quantitative structure–activity relationships’’ (QSARs) for various nanoma- terials. However, the molecular structure as rule is not available for nanomaterials at least in its classic meaning. An possible alternative of classic QSAR (based on the molecular structure) is the using of data on physicochemical features of TiO 2 nanoparticles. The damage to cellular membranes (units L 1 ) by means of various TiO 2 nanoparticles is examined as the endpoint. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction The establishing of quantitative structure – property/activity relationships (QSPR/QSAR) is one of the well known tasks of mod- ern natural sciences (Afantitis et al., 2011; Furtula and Gutman 2011; García et al., 2011; Garro Martinez et al., 2011; Mullen et al., 2011; Ibezim et al., 2012). The main aim of QSPR/QSAR anal- yses is design of predictive models which give possibility to esti- mate various endpoints from analysis of their molecular structure. In the case of ‘‘classic’’ QSPR/QSAR analysis the paradigm is the following: endpoint is a mathematical function of molecular structure. However, in the case of nanomaterials (Puzyn et al., 2009; Fourches et al., 2010; Petrova et al., 2011; Toropov et al., 2012, 2013a,b), this paradigm meets a problem: the molecular structure of nanomaterials is not only complex, but sometimes is unclear at all. Under such circumstances, classic descriptors cannot be a tool to design of predictive models for endpoints related to various nanomaterials which are widely involved in the modern everyday life (food packaging, forestry and paper, cosmetics, plastics and paints, and electronics). Optimal descriptors (Toropov and Toropova 2002, 2003; Toropov et al., 2008, 2011, 2013b; Toropova et al., 2011a,b) are an approach that gives an alternative of QSPR/QSAR analyses based on the molecular structure. This alternative is the involving to de- sign of predictive models of all available eclectic information re- lated to genesis and various features of nanomaterials. The aim of the present study is the estimation of optimal descriptors calcu- lated with the Monte Carlo method as a tool to predict influence of TiO 2 nanoparticles with various physicochemical features upon the membrane damage. 2. Method 2.1. Data Experimental data on the physicochemical features of TiO 2 nanoparticles and their influence on the membrane damage are taken in the literature (Sayes and Ivanov, 2010). These are (i) engi- 0045-6535/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.chemosphere.2013.09.089 ⇑ Corresponding author. E-mail address: andrey.toropov@marionegri.it (A.A. Toropov). Chemosphere 93 (2013) 2650–2655 Contents lists available at ScienceDirect Chemosphere journal homepage: www.elsevier.com/locate/chemosphere