The unify representation of spectral moments, classic topologic indices, quadratic indices, and stochastic molecular descriptors shown that all these molecular descriptors lie within the same family. Consequently, the same priori probability for a success quantitative-structure-activity-relationship (QSAR) may be expected no matter which indices are selected. Herein, we used stochastic spectral moments as molecular descriptors to seek a QSAR using a database of 221 bioactive compounds previously tested against diverse RNA-viruses and 402 non-active ones. The QSAR model thus obtained correctly classifies 90.9 % of compounds in training. The model also correctly classifies a total of 87.9 % of 207 compounds on additional external predicting series, 73 of them having anti-RNA-virus activity and 134 non-active ones. In addition, all compounds were regrouped into five different subsets for leave-group-out studies: 1) antiinfluenza, 2) anti-picornavirus, 3) anti-paramyxovirus, 4) anti-RSV/anti-influenza, and 5) broad range anti-RNA-virus activity. The model has retained overall accuracies about 90 % on these studies validating model robustness. Finally, we exemplify the practical use of the model with the discovery of compounds 124 and 128. These compounds presented MIC50 values = 3.2 and 8 µg/mL against respiratory syncytial virus (RSV) respectively. Both compounds have also low cytotoxicity expressed by their Minimal Cytotoxic Concetrations > 400 µg/mL for HeLa cells. The present approach represent and effort toward a formalization and application of molecular indices in bioinformatics, bioorganic and medicinal chemistry.

The design of novel anti-HIV compounds has now become a crucial area for scientists around the world. In this paper a new set of macromolecular descriptors (that are calculated from the macromolecular graph’s nucleotide adjacency matrix) of relevance to nucleic acid QSAR/QSPR studies, nucleic acids’ linear indices. A study of the interaction of the antibiotic Paromomycin with the packaging region of the HIV-1 ?-RNA has been performed as example of this approach. A multiple linear regression model predicted the local binding affinity constants [log K (10-4M-1)] between a specific nucleotide and the aforementioned antibiotic. The linear model explains more than 87% of the variance of the experimental log K (R = 0.93 and s = 0.102x10- 4M-1) and leave-one-out press statistics evidenced its predictive ability (q2 = 0.82 and scv = 0.108x10-4M-1). The comparison with other approaches (macromolecular quadratic indices, Markovian Negentropies and ´stochastic´ spectral moments) reveals a good behavior of our method.

Algorithms for classification and taxonomy are proposed based on criteria, e.g. information entropy and its production. The feasibility of replacing a given anaesthetic by similar ones in the composition of a complex drug is studied. Some local anaesthetics currently in use are classified using characteristic chemical properties of different portions of their molecules. Many classification algorithms are based on information entropy. When applying these procedures to sets of moderate size, an excessive number of results appear compatible with data and this number suffers a combinatorial explosion. However, after the equipartition conjecture, one has a selection criterion between different variants resulting from classification between hierarchical trees. According to this conjecture, for a given charge or duty, the best configuration of a flowsheet is the one in which the entropy production is most uniformly distributed. Information entropy analysis of the structural parameters and principal component analysis (PCA) of the anaesthetics permit classifying them and agree. A periodic table of anaesthetics is built. The periodic law has not the rank of the laws of physics: (1) the properties of anaesthetics are not repeated; (2) the order relationships are repeated with exceptions. The proposed statement is: The relationships that any anaesthetic p has with its neighbour p + 1 are approximately repeated for each period.

A Non-Stochastic Quadratic Fingerprints-based approach is introduced to classify and design, in a rational way, new antitrypanosomal compounds. A data set of 153 organic-chemicals; 62 with antitrypanosomal activity and 91 having other clinical uses, was processed by a k-means cluster analysis in order to design training and predicting data sets. Afterwards, a linear classification function was derived allowing the discrimination between active and inactive compounds. The model classifies correctly more than 93% of chemicals in both training and external prediction groups. The predictability of this discriminant function was also assessed by a leave-group-out experiment, in which 10% of the compounds were removed at random at each time and their activity a posteriori predicted. Also a comparison with models generated using four well-known families of 2D molecular descriptors was carried out. As an experiment of virtual lead generation, the present TOMOCOMD approach was finally satisfactorily applied on the virtual evaluation of ten already synthesized compounds. The in vitro antitrypanosomal activity of this series against epimastigotes forms of T. cruzi was assayed. The model was able to predict correctly the behaviour of these compounds in 90% of the cases.

Malaria is one of the most significant public health concerns in many tropical and subtropical regions of the world, with 40% of the world population exposed to malaria-causing parasites. Increasing resistance of Plasmodium spp. to existing therapies has heightened alarms about malaria in the international health community. Nowadays there is a pressing need to identify and develop new drug-based antimalarial therapies. In an effort to overcome this problem, the main aim of this study was to develop simple linear discriminant-based QSAR models for the classification and prediction of antimalarial activity using some of the TOMOCOMD-CARDD fingerprints, so as to enable computational screening from virtual combinatorial datasets. In this sense a database of 1562 organic-chemicals having great structural variability; 597 of them antimalarial agents and 965 compounds having other clinical uses, was analyzed and presented as a helpful tool not only for theoretical chemist but also for other researchers in this area. These series of compounds were processed by a k-means cluster analysis in order to design training and predicting sets. Afterward, two linear classification functions were derived toward discrimination between antimalarial and non-antimalarial compounds. The models (including non-stochastic and stochastic indices) classify correctly more than 93% of compounds in both training and external prediction datasets. They showed high Matthews´ correlation coefficients; 0.889 and 0.866 for training and 0.855 and 0.857 for test set. Models predictivity were also assessed and validated by the random removal of 10% of the compounds to form a test set, for which predictions were made from the models. The overall mean of the correct classification for this process (leave-group 10% full-out cross-validation) for obtained equations with non-stochastic and stochastic quadratic fingerprints were 93.93% and 92.77%, correspondingly. The quadratic maps-based TOMOCOMD-CARDD approach implemented in this work was successfully compared with four of the most useful models for antimalarials selection reported to date. The models developed with non-stochastic and stochastic quadratic indices were then used in a simulation of a virtual search for Ras FTase inhibitors with antimalarial activity; 70% and 100% of the 10 inhibitors used in this virtual search were correctly classified, showing the ability of the models to identify new lead antimalarials. Finally, these two QSAR models were used in the identification of previously un-known antimalarials compounds. In this sense, three synthetic intermediaries of quinolinic compounds were evaluated as active/inactive ones using the developed models. The synthesis and biological evaluation of these chemicals against two Malaria strains, using Chloroquine as reference, was performed. An accuracy of 100% with the theoretical predictions was observed. The compound 3 shown antimalarial activity, being the first report of an arylaminomethylenemalonate having such activity. This result opens a door to a virtual study considering a higher variability of the central core already evaluated, as well as other chemicals not included in this family. We conclude that the approach described here seems to be a promising QSAR tool for molecular discovery of novel classes of antimalarial drugs which may meet the dual challenges posed by drug-resistant parasites and the rapid progression of malaria illness.

Novel atom-based molecular descriptors based on a bilinear map similar to use defined in linear algebra are presented. These molecular descriptors, called “local (atom, group and atom-type) and total (global) bilinear indices”, are proposed here as a new molecular parametrization easily calculated from the 2D molecular information. The proposed non-stochastic and stochastic molecular fingerprints try to match molecular structure provided by the molecular topology by using the kth non-stochatic (Marrero-Ponce, Y. J. Chem. Inf. Comput. Sci. 2004, 44, 2010 and Marrero-Ponce, Y. Molecules 2003, 8, 687) and stochastic (Marrero-Ponce, Y., et al. J. Mol. Struc. (Theochem) 2005, 717, 67 and Marrero-Ponce, Y.; Castillo-Garit, J. A. J. Comput.-Aided Mol. Des. DOI: DO00017575) graph–theoretic electronic-density matrices, Mk and Sk, respectively. That is to say, the kth non-stochastic and stochastic bilinear indices are calculated using Mk and Sk as matrix operators of bilinear transformations. Moreover, chemical information is codified by using different pair combinations of atomic weightings (atomic mass, polarizability, van der Waals volume, and electronegativity). The prediction ability in Quantitative Structure-Property Relationships (QSPR) of the new molecular descriptors was tested by analysing regressions of these descriptors for six selected properties of octane isomers. It was clearly demonstrated that prediction ability was higher than those showed by other 2D/3D well-known sets of molecular descriptors. The obtained results suggest that with the present method it is possible to obtain a good estimation of these physicochemical properties for octanes. The approach described in the present report appears to be a prominent method to find quantitative models for description of physicochemical and biological properties.

Novel bond-level molecular descriptors based on linear maps similar to those defined in algebra theory are proposed. The kth edge-adjacency matrix (Ek) denotes the matrix of bond linear indices (non-stochastic) with respect to the canonical basis set. The kth stochastic edge-adjacency matrix, ESk, is here proposed as a new molecular representation easily calculated from Ek. Then, the kth stochastic bond linear indices are calculated using ESk as operators of linear transformations. In both cases, the bond-type formalism was developed. The kth non-stochastic and stochastic bond-type linear indices values are the sum of the kth nonstochastic and stochastic bond linear indices values for bonds of the same bond type, respectively. In the same way, the kth non-stochastic and stochastic total (whole-molecule) linear indices are calculated by summing up the kth non-stochastic and stochastic bond linear indices, correspondingly, of all bonds in the molecule. The new bond-based molecular descriptors were tested for suitability for the quantitative structure-property relationship (QSPR) by analyzing regressions of novel indices for selected physicochemical properties of octane isomers. All the found regression models are very significant from the statistical point of view and showed very good stability to data variation in leave-one-out crossvalidation experiments. General performance of the new descriptors in this QSPR studies has been evaluated with respect to the well-known sets of 2D/3D molecular descriptors. From the analysis, we can conclude that the non-stochastic and stochastic bond-based (total and bond-type) linear indices have an overall good modeling capability proving their usefulness in QSPR studies. The approach described in this work appears to be a very promising structural invariant, useful not alone for QSPR/QSAR studies, but also for similarity/diversity analysis and drug discovery protocols.