Stochastic Linear Indices Research Articles

A novel approach to predict aquatic toxicity from molecular structure

The main aim of the study was to develop quantitative structure–activity relationship (QSAR) models for the prediction of aquatic toxicity using atom-based non-stochastic and stochastic linear indices. The used dataset consist of 392 benzene derivatives, separated into training and test sets, for which toxicity data to the ciliate Tetrahymena pyriformis were available. Using multiple linear regression, two statistically significant QSAR models were obtained with non-stochastic ( R 2 = 0.791 and s = 0.344) and stochastic ( R 2 = 0.799 and s = 0.343) linear indices. A leave-one-out (LOO) cross-validation procedure was carried out achieving values of q 2 = 0.781 ( s cv = 0.348) and q 2 = 0.786 ( s cv = 0.350), respectively. In addition, a validation through an external test set was performed, which yields significant values of R pred 2 of 0.762 and 0.797. A brief study of the influence of the statistical outliers in QSAR’s model development was also carried out. Finally, our method was compared with other approaches implemented in the Dragon software achieving better results. The non-stochastic and stochastic linear indices appear to provide an interesting alternative to costly and time-consuming experiments for determining toxicity.

Atom-based stochastic and non-stochastic 3D-chiral bilinear indices and their applications to central chirality codification

Non-stochastic and stochastic 2D bilinear indices have been generalized to codify chemical structure information for chiral drugs, making use of a trigonometric 3D-chirality correction factor. In order to evaluate the effectiveness of this novel approach in drug design we have modeled the angiotensin-converting enzyme inhibitory activity of perindoprilate's σ-stereoisomers combinatorial library. Two linear discriminant analysis models, using non-stochastic and stochastic linear indices, were obtained. The models had shown an accuracy of 95.65% for the training set and 100% for the external prediction set. Next the prediction of the σ-receptor antagonists of chiral 3-(3-hydroxyphenyl)piperidines by multiple linear regression analysis was carried out. Two statistically significant QSAR models were obtained when non-stochastic ( R 2 = 0.953 and s = 0.238) and stochastic ( R 2 = 0.961 and s = 0.219) 3D-chiral bilinear indices were used. These models showed adequate predictive power (assessed by the leave-one-out cross-validation experiment) yielding values of q 2 = 0.935 ( s cv = 0.259) and q 2 = 0.946 ( s cv = 0.235), respectively. Finally, the prediction of the corticosteroid-binding globulin binding affinity of steroids set was performed. The obtained results are rather similar to most of the 3D-QSAR approaches reported so far. The validation of this method was achieved by comparison with previous reports applied to the same data set. The non-stochastic and stochastic 3D-chiral linear indices appear to provide a very interesting alternative to other more common 3D-QSAR descriptors.

Non-stochastic and stochastic linear indices of the molecular pseudograph’s atom-adjacency matrix: a novel approach for computational in silico screening and “rational” selection of new lead antibacterial agents

A novel approach (TOMOCOMD-CARDD) to computer-aided "rational" drug design is illustrated. This approach is based on the calculation of the non-stochastic and stochastic linear indices of the molecular pseudograph's atom-adjacency matrix representing molecular structures. These TOMOCOMD-CARDD descriptors are introduced for the computational (virtual) screening and "rational" selection of new lead antibacterial agents using linear discrimination analysis. The two structure-based antibacterial-activity classification models, including non-stochastic and stochastic indices, classify correctly 91.61% and 90.75%, respectively, of 1525 chemicals in training sets. These models show high Matthews correlation coefficients (MCC=0.84 and 0.82). An external validation process was carried out to assess the robustness and predictive power of the model obtained. These QSAR models permit the correct classification of 91.49% and 89.31% of 505 compounds in an external test set, yielding MCCs of 0.84 and 0.79, respectively. The TOMOCOMD-CARDD approach compares satisfactorily with respect to nine of the most useful models for antimicrobial selection reported to date. Finally, an in silico screening of 87 new chemicals reported in the anti-infective field with antibacterial activities is developed showing the ability of the TOMOCOMD-CARDD models to identify new lead antibacterial compounds.

New tyrosinase inhibitors selected by atomic linear indices-based classification models

In the present report, the use of the atom-based linear indices for finding functions that discriminate between the tyrosinase inhibitor compounds and inactive ones is presented. In this sense, discriminant models were applied and globally good classifications of 93.51% and 92.46% were observed for non-stochastic and stochastic linear indices best models, respectively, in the training set. The external prediction sets had accuracies of 91.67% and 89.44%. In addition, these fitted models were used in the screening of new cycloartane compounds isolated from herbal plants. A good behavior is shown between the theoretical and experimental results. These results provide a tool that can be used in the identification of new tyrosinase inhibitor compounds.

3D-chiral Atom, Atom-type, and Total Non-stochastic and Stochastic Molecular Linear Indices and their Applications to Central Chirality Codification

Non-stochastic and stochastic 2D linear indices have been generalized to codify chemical structure information for chiral drugs, making use of a trigonometric 3D-chirality correction factor. These descriptors circumvent the inability of conventional 2D non-stochastic [Y. Marrero-Ponce. J. Chem. Inf. Comp., Sci. l 44 (2004) 2010] and stochastic [Y. Marrero-Ponce, et al. Bioorg. Med. Chem., 13 (2005) 1293] linear indices to distinguish sigma-stereoisomers. In order to test the potential of this novel approach in drug design we have modelled the angiotensin-converting enzyme inhibitory activity of perindoprilate's sigma-stereoisomers combinatorial library. Two linear discriminant analysis models, using non-stochastic and stochastic linear indices, were obtained. The models showed an accuracy of 100% and 96.65% for the training set; and 88.88% and 100% in the external test set, respectively. Canonical regression analysis corroborated the statistical quality of these models (R(can) of 0.78 and of 0.77) and was also used to compute biology activity canonical scores for each compound. After that, the prediction of the sigma-receptor antagonists of chiral 3-(3-hydroxyphenyl)piperidines by linear multiple regression analysis was carried out. Two statistically significant QSAR models were obtained when non-stochastic (R2 = 0.982 and s = 0.157) and stochastic (R2 = 0.941 and s = 0.267) 3D-chiral linear indices were used. The predictive power was assessed by the leave-one-out cross-validation experiment, yielding values of q2 = 0.982 (s(cv) = 0.186) and q2 = 0.90 (s(cv) = 0.319), respectively. Finally, the prediction of the corticosteroid-binding globulin binding affinity of steroids set was performed. The best results obtained in the cross-validation procedure with non-stochastic (q2 = 0.904) and stochastic (q2 = 0.88) 3D-chiral linear indices are rather similar to most of the 3D-QSAR approaches reported so far. The validation of this method was achieved by comparison with previous reports applied to the same data set. The non-stochastic and stochastic 3D-chiral linear indices appear to provide an interesting alternative to other more common 3D-QSAR descriptors.

Non-stochastic and stochastic linear indices of the ‘molecular pseudograph’s atom adjacency matrix’: application to ‘in silico’ studies for the rational discovery of new antimalarial compounds

Malaria is one of the most deadly diseases, affecting million of people especially in developing countries. Because of the rapidly increasing threat worldwide of malaria epidemics multidrugs resistant to therapies, there is an urgent global need to discover new classes of antimalarial compounds. In an effort to overcome this problem, we have investigated the use of structure-based classification models for the ‘rational’ selection/identification or design/optimization of new lead antimalarials from virtual combinatorial data sets. In this sense, TOpological MOlecular COMputer Design strategy ( TOMOCOMD approach) has been introduced in order to obtain two quantitative models for the discrimination of antimalarials. A collected data set containing 597 antimalarial compounds is presented as a helpful tool not only for theoretical chemist but for other researchers in this area. The validated models (including non-stochastic and stochastic indices) classify correctly more than 90% of compounds in both training and external prediction data sets. They showed high Matthews’ correlation coefficients; 0.87 and 0.82 for training and 0.86 and 0.79 for test set. The TOMOCOMD– CARDD approach implemented in this work was successfully compared with two of the most useful models for antimalarials selection reported so far. Thus we expect that these two QSAR models can be used in the identification of previously un-known antimalarials compounds.