The numerical encoding of chemical structure with Topological Indices (TIs) is currently growing in importance in Medicinal Chemistry and Bioinformatics. This approach allows the rapid collection, annotation, retrieval, comparison and mining of chemical structures within large databases. TIs can subsequently be used to seek quantitative structure-activity relationships (QSAR), which are models connecting chemical structure with biological activity. In the early 1990s, there was an explosion in the introduction and definition of new TIs. The Handbook of Molecular Descriptors by Todeschini and Consonni lists more than 1500 of these indices. At the end of the last century, researchers produced a large number of TIs with essentially the same advantages and/or disadvantages. Consequently, many researchers abandoned the definition of TIs for a time. In our opinion, one of the problems associated with TIs is that researchers aimed their efforts only at the codification of chemical connectivity for small-sized drugs. As a consequence, recently it seems that we have arrived at “Fukuyamas End of History in TIs definition”. In the work described here, we review and comment on the “quo vadis” and challenges in the definition of TIs as we enter the new century. Emphasis is placed on new chiral TIs (CTIs), flexible TIs for unifying QSAR models with multiple targets, topographic indices (TPGIs), TIs for DNA and protein sequences, TIs for 2D RNA structures, TPGIs and drug-protein or drug-RNA quantitative structure-binding relationship (QSBR) studies, TIs to encode protein surface information and TIs for protein interaction networks (PINs).

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.