Nowadays, the interest in the search for new nanomaterials with improved electrical, optical, catalytic and biological properties has increased. Despite the potential benefits that can be gathered from the use of nanoparticles, only little attention has been paid to their possible toxic effects that may affect human health. In this context, several assays have been carried out to evaluate the cytotoxicity of nanoparticles in mammalian cells. Owing to the cost in both resources and time involved in such toxicological assays, there has been a considerable increase in the interest towards alternative computational methods, like the application of quantitative structure–activity/toxicity relationship (QSAR/QSTR) models for risk assessment of nanoparticles. However, most QSAR/QSTR models developed so far have predicted cytotoxicity against only one cell line, and they did not provide information regarding the influence of important factors rather than composition or size. This work reports a QSTR-perturbation model aiming at simultaneously predicting the cytotoxicity of different nanoparticles against several mammalian cell lines, and also considering different times of exposure of the cell lines, as well as the chemical composition of nanoparticles, size, conditions under which the size was measured, and shape. The derived QSTR-perturbation model, using a dataset of 1681 cases (nanoparticle–nanoparticle pairs), exhibited an accuracy higher than 93% for both training and prediction sets. In order to demonstrate the practical applicability of our model, the cytotoxicity of different silica (SiO₂), nickel (Ni), and nickel(II) oxide (NiO) nanoparticles were predicted and found to be in very good agreement with experimental reports. To the best of our knowledge, this is the first attempt to simultaneously predict the cytotoxicity of nanoparticles under multiple experimental conditions by applying a single unique QSTR model.

Nanotechnology has brought great advances to many fields of modern science. A manifold of applications of nanoparticles have been found due to their interesting optical, electrical, and biological/chemical properties. However, the potential toxic effects of nanoparticles to different ecosystems are of special concern nowadays. Despite the efforts of the scientific community, the mechanisms of toxicity of nanoparticles are still poorly understood. Quantitative-structure activity/toxicity relationships (QSAR/QSTR) models have just started being useful computational tools for the assessment of toxic effects of nanomaterials. But most QSAR/QSTR models have been applied so far to predict ecotoxicity against only one organism/bio-indicator such as Daphnia magna. This prevents having a deeper knowledge about the real ecotoxic effects of nanoparticles, and consequently, there is no possibility to establish an efficient risk assessment of nanomaterials in the environment. In this work, a perturbation model for nano-QSAR problems is introduced with the aim of simultaneously predicting the ecotoxicity of different nanoparticles against several assay organisms (bio-indicators), by considering also multiple measures of ecotoxicity, as well as the chemical compositions, sizes, conditions under which the sizes were measured, shapes, and the time during which the diverse assay organisms were exposed to nanoparticles. The QSAR-perturbation model was derived from a database containing 5520 cases (nanoparticle-nanoparticle pairs), and it was shown to exhibit accuracies of ca. 99% in both training and prediction sets. In order to demonstrate the practical applicability of our model, three different nickel-based nanoparticles (Ni) with experimental values reported in the literature were predicted. The predictions were found to be in very good agreement with the experimental evidences, confirming that Ni-nanoparticles are not ecotoxic when compared with other nanoparticles. The results of this study thus provide a single valuable tool toward an efficient prediction of the ecotoxicity of nanoparticles under multiple experimental conditions.

In general perturbation methods starts with a known exact solution of a problem and add “small” variation terms in order to approach to a solution for a related problem without known exact solution. Perturbation theory has been widely used in almost all areas of science. Bhor’s quantum model, Heisenberg’s matrix mechanincs, Feyman diagrams, and Poincare’s chaos model or “butterfly effect” in complex systems are examples of perturbation theories. On the other hand, the study of Quantitative Structure-Property Relationships (QSPR) in molecular complex systems is an ideal area for the application of perturbation theory. There are several problems with exact experimental solutions (new chemical reactions, physicochemical properties, drug activity and distribution, metabolic networks, etc.) in public databases like CHEMBL. However, in all these cases, we have an even larger list of related problems without known solutions. We need to know the change in all these properties after a perturbation of initial boundary conditions. It means, when we test large sets of similar, but different, compounds and/or chemical reactions under the slightly different conditions (temperature, time, solvents, enzymes, assays, protein targets, tissues, partition systems, organisms, etc.). However, to the best of our knowledge, there is no QSPR general-purpose perturbation theory to solve this problem. In this work, firstly we review general aspects and applications of both perturbation theory and QSPR models. Secondly, we formulate a general-purpose perturbation theory for multiple-boundary QSPR problems. Last, we develop three new QSPR-Perturbation theory models. The first model classify correctly >100,000 pairs of intra-molecular carbolithiations with 75-95% of Accuracy (Ac), Sensitivity (Sn), and Specificity (Sp). The model predicts probabilities of variations in the yield and enantiomeric excess of reactions due to at least one perturbation in boundary conditions (solvent, temperature, temperature of addition, or time of reaction). The model also account for changes in chemical structure (connectivity structure and/or chirality paterns in substrate, product, electrophile agent, organolithium, and ligand of the asymmetric catalyst). The second model classifies more than 150,000 cases with 85-100% of Ac, Sn, and Sp. The data contains experimental shifts in up to 18 different pharmacological parameters determined in >3000 assays of ADMET (Absorption, Distribution, Metabolism, Elimination, and Toxicity) properties and/or interactions between 31723 drugs and 100 targets (metabolizing enzymes, drug transporters, or organisms). The third model classifies more than 260,000 cases of perturbations in the self-aggregation of drugs and surfactants to form micelles with Ac, Sn, and Sp of 94-95%. The model predicts changes in 8 physicochemical and/or thermodynamics output parameters (critic micelle concentration, aggregation number, degree of ionization, surface area, enthalpy, free energy, entropy, heat capacity) of self-aggregation due to perturbations. The perturbations refers to changes in initial temperature, solvent, salt, salt concentration, solvent, and/or structure of the anion or cation of more than 150 different drugs and surfactants. QSPR-Perturbation Theory models may be useful for multi-objective optimization of organic synthesis, physicochemical properties, biological activity, metabolism, and distribution profiles towards the design of new drugs, surfactants, asymmetric ligands for catalysts, and other materials.