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

Tensor algebra-based geometric methodology to codify central chirality on organic molecules

A novel mathematical procedure to codify chiral features of organic molecules in the QuBiLS-MIDAS framework is introduced. This procedure constitutes a generalization to that commonly used to date, where the values 1 and -1 (correction factor) are employed to weight the molecular vectors when each atom is labelled as R (rectus) or S (sinister) according to the Cahn-Ingold-Prelog rules. Therefore, values in the range [Formula: see text] with steps equal to 0.25 may be accounted for. The atoms labelled R or S can have negative and positive values assigned (e.g. -3 for an R atom and 1 for an S atom, or vice versa), opposed values (e.g. -3 for an R atom and 3 for an S atom, or vice versa), positive values (e.g. 3 for an R atom and 1 for an S atom) or negative values (e.g. -3 for an R atom and -1 for an S atom). These proposed Chiral QuBiLS-MIDAS 3D-MDs are real numbers, non-symmetric and reduced to 'classical' (non-chiral) QuBiLS-MIDAS 3D-MDs when symmetry is not codified (correction factor equal to zero). In this report, only the factors with opposed values were considered with the purpose of demonstrating the feasibility of this proposal. From QSAR modelling carried out on four chemical datasets (Cramer's steroids, fenoterol stereoisomer derivatives, N-alkylated 3-(3-hydroxyphenyl)-piperidines, and perindoprilat stereoisomers), it was demonstrated that the use of several correction factors contributes to the building of models with greater robustness and predictive ability than those reported in the literature, as well as with respect to the models exclusively developed with QuBiLS-MIDAS 3D-MDs based on the factor 1 | -1. In conclusion, it can be stated that this novel strategy constitutes a suitable alternative to computed chirality-based descriptors, contributing to the development of good models to predict properties depending on symmetry.

Simultaneous virtual prediction of anti-Escherichia coli activities and ADMET profiles: A chemoinformatic complementary approach for high-throughput screening

Escherichia coli remains one of the principal pathogens that cause nosocomial infections, medical conditions that are increasingly common in healthcare facilities. E. coli is intrinsically resistant to many antibiotics, and multidrug-resistant strains have emerged recently. Chemoinformatics has been a great ally of experimental methodologies such as high-throughput screening, playing an important role in the discovery of effective antibacterial agents. However, there is no approach that can design safer anti-E. coli agents, because of the multifactorial nature and complexity of bacterial diseases and the lack of desirable ADMET (absorption, distribution, metabolism, elimination, and toxicity) profiles as a major cause of disapproval of drugs. In this work, we introduce the first multitasking model based on quantitative-structure biological effect relationships (mtk-QSBER) for simultaneous virtual prediction of anti-E. coli activities and ADMET properties of drugs and/or chemicals under many experimental conditions. The mtk-QSBER model was developed from a large and heterogeneous data set of more than 37800 cases, exhibiting overall accuracies of >95% in both training and prediction (validation) sets. The utility of our mtk-QSBER model was demonstrated by performing virtual prediction of properties for the investigational drug avarofloxacin (AVX) under 260 different experimental conditions. Results converged with the experimental evidence, confirming the remarkable anti-E. coli activities and safety of AVX. Predictions also showed that our mtk-QSBER model can be a promising computational tool for virtual screening of desirable anti-E. coli agents, and this chemoinformatic approach could be extended to the search for safer drugs with defined pharmacological activities.

BCL::EMAS--enantioselective molecular asymmetry descriptor for 3D-QSAR

Stereochemistry is an important determinant of a molecule’s biological activity. Stereoisomers can have different degrees of efficacy or even opposing effects when interacting with a target protein. Stereochemistry is a molecular property difficult to represent in 2D-QSAR as it is an inherently three-dimensional phenomenon. A major drawback of most proposed descriptors for 3D-QSAR that encode stereochemistry is that they require a heuristic for defining all stereocenters and rank-ordering its substituents. Here we propose a novel 3D-QSAR descriptor termed Enantioselective Molecular ASymmetry (EMAS) that is capable of distinguishing between enantiomers in the absence of such heuristics. The descriptor aims to measure the deviation from an overall symmetric shape of the molecule. A radial-distribution function (RDF) determines a signed volume of tetrahedrons of all triplets of atoms and the molecule center. The descriptor can be enriched with atom-centric properties such as partial charge. This descriptor showed good predictability when tested with a dataset of thirty-one steroids commonly used to benchmark stereochemistry descriptors (r² = 0.89, q² = 0.78). Additionally, EMAS improved enrichment of 4.38 versus 3.94 without EMAS in a simulated virtual high-throughput screening (vHTS) for inhibitors and substrates of cytochrome P450 (PUBCHEM AID891).

Computational discovery of novel trypanosomicidal drug-like chemicals by using bond-based non-stochastic and stochastic quadratic maps and linear discriminant analysis

Herein we present results of a quantitative structure-activity relationship (QSAR) studies to classify and design, in a rational way, new antitrypanosomal compounds by using non-stochastic and stochastic bond-based quadratic indices. A data set of 440 organic chemicals, 143 with antitrypanosomal activity and 297 having other clinical uses, is used to develop QSAR models based on linear discriminant analysis (LDA). Non-stochastic model correctly classifies more than 93% and 95% of chemicals in both training and external prediction groups, respectively. On the other hand, the stochastic model shows an accuracy of about the 87% for both series. As an experiment of virtual lead generation, the present approach is finally satisfactorily applied to the virtual evaluation of 9 already synthesized in house compounds. The in vitro antitrypanosomal activity of this series against epimastigote forms of Trypanosoma cruzi is assayed. The model is able to predict correctly the behaviour for the majority of these compounds. Four compounds (FER16, FER32, FER33 and FER 132) showed more than 70% of epimastigote inhibition at a concentration of 100 microg/mL (86.74%, 78.12%, 88.85% and 72.10%, respectively) and two of these chemicals, FER16 (78.22% of AE) and FER33 (81.31% of AE), also showed good activity at a concentration of 10 microg/mL. At the same concentration, compound FER16 showed lower value of cytotoxicity (15.44%), and compound FER33 showed very low value of 1.37%. Taking into account all these results, we can say that these three compounds can be optimized in forthcoming works, but we consider that compound FER33 is the best candidate. Even though none of them resulted more active than Nifurtimox, the current results constitute a step forward in the search for efficient ways to discover new lead antitrypanosomals.

Multi-target spectral moment: QSAR for antiviral drugs vs. different viral species

The antiviral QSAR models have an important limitation today. They predict the biological activity of drugs against only one viral species. This is determined by the fact that most of the current reported molecular descriptors encode only information about the molecular structure. As a result, predicting the probability with which a drug is active against different viral species with a single unifying model is a goal of major importance. In this work, we use Markov Chain theory to calculate new multi-target spectral moments to fit a QSAR model for drugs active against 40 viral species. The model is based on 500 drugs (including active and non-active compounds) tested as antiviral agents in the recent literature; not all drugs were predicted against all viruses, but only those with experimental values. The database also contains 207 well-known compounds (not as recent as the previous ones) reported in the Merck Index with other activities that do not include antiviral action against any virus species. We used Linear Discriminant Analysis (LDA) to classify all these drugs into two classes as active or non-active against the different viral species tested, whose data we processed. The model correctly classifies 5129 out of 5594 non-active compounds (91.69%) and 412 out of 422 active compounds (97.63%). Overall training predictability was 92.34%. The validation of the model was carried out by means of external predicting series, the model classifying, thus, 2568 out of 2779 non-active compounds and 224 out of 229 active compounds. Overall training predictability was 92.82%. The present work reports the first attempts to calculate within a unified framework the probabilities of antiviral drugs against different virus species based on a spectral moment analysis.

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 (R2=0.791 and s=0.344) and stochastic (R2=0.799 and s=0.343) linear indices. A leave-one-out (LOO) cross-validation procedure was carried out achieving values of q2=0.781 (scv=0.348) and q2=0.786 (scv=0.350), respectively. In addition, a validation through an external test set was performed, which yields significant values of Rpred2 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.

Prediction of tyrosinase inhibition activity using atom-based bilinear indices

A set of novel atom-based molecular fingerprints is proposed based on a bilinear map similar to that defined in linear algebra. These molecular descriptors (MDs) are proposed as a new means of molecular parametrization easily calculated from 2D molecular information. The nonstochastic and stochastic molecular indices match molecular structure provided by molecular topology by using the kth nonstochastic and stochastic graph-theoretical electronic-density matrices, M(k) and S(k), respectively. Thus, the kth nonstochastic and stochastic bilinear indices are calculated using M(k) and S(k) as matrix operators of bilinear transformations. Chemical information is coded by using different pair combinations of atomic weightings (mass, polarizability, vdW volume, and electronegativity). The results of QSAR studies of tyrosinase inhibitors using the new MDs and linear discriminant analysis (LDA) demonstrate the ability of the bilinear indices in testing biological properties. A database of 246 structurally diverse tyrosinase inhibitors was assembled. An inactive set of 412 drugs with other clinical uses was used; both active and inactive sets were processed by hierarchical and partitional cluster analyses to design training and predicting sets. Twelve LDA-based QSAR models were obtained, the first six using the nonstochastic total and local bilinear indices and the last six with the stochastic MDs. The discriminant models were applied; globally good classifications of 99.58 and 89.96 % were observed for the best nonstochastic and stochastic bilinear indices models in the training set along with high Matthews correlation coefficients (C) of 0.99 and 0.79, respectively, in the learning set. External prediction sets used to validate the models obtained were correctly classified, with accuracies of 100 and 87.78 %, respectively, yielding C values of 1.00 and 0.73. This subset contains 180 active and inactive compounds not considered to fit the models. A simulated virtual screen demonstrated this approach in searching tyrosinase inhibitors from compounds never considered in either training or predicting series. These fitted models permitted the selection of new cycloartane compounds isolated from herbal plants as new tyrosinase inhibitors. A good correspondence between theoretical and experimental inhibitory effects on tyrosinase was observed; compound CA6 (IC(50)=1.32 microM) showed higher activity than the reference compounds kojic acid (IC(50)=16.67 microM) and L-mimosine (IC(50)=3.68 microM).

Estimation of ADME Properties in Drug Discovery: Predicting Caco-2 Cell Permeability Using Atom-Based Stochastic and Non-stochastic Linear Indices

The in vitro determination of the permeability through cultured Caco-2 cells is the most often-used in vitro model for drug absorption. In this report, we use the largest data set of measured P(Caco-2), consisting of 157 structurally diverse compounds. Linear discriminant analysis (LDA) was used to obtain quantitative models that discriminate higher absorption compounds from those with moderate-poorer absorption. The best LDA model has an accuracy of 90.58% and 84.21% for training and test set. The percentage of good correlation, in the virtual screening of 241 drugs with the reported values of the percentage of human intestinal absorption (HIA), was greater than 81%. In addition, multiple linear regression models were developed to predict Caco-2 permeability with determination coefficients of 0.71 and 0.72. Our method compares favorably with other approaches implemented in the Dragon software, as well as other methods from the international literature. These results suggest that the proposed method is a good tool for studying the oral absorption of drug candidates.

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 sigma-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 sigma-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.

Bond-based 2D TOMOCOMD-CARDD approach for drug discovery: aiding decision-making in 'in silico' selection of new lead tyrosinase inhibitors

In this paper, we present a new set of bond-level TOMOCOMD-CARDD molecular descriptors (MDs), the bond-based bilinear indices, based on a bilinear map similar to those defined in linear algebra. These novel MDs are used here in Quantitative Structure-Activity Relationship (QSAR) studies of tyrosinase inhibitors, for finding functions that discriminate between the tyrosinase inhibitor compounds and inactive ones. In total 14 models were obtained and the best two discriminant functions (Eqs. 32 and 33) shown globally good classification of 91.00% and 90.17%, respectively, in the training set. The test set had accuracies of 93.33% and 88.89% for the models 32 and 33, correspondingly. A simulated virtual screening was also carried out to prove the quality of the determined models. In a final step, the fitted models were used in the biosilico identification of new synthesized tetraketones, where a good agreement could be observed between the theoretical and experimental results. Four compounds of the novel bioactive chemicals discovered as tyrosinase inhibitors: TK10 (IC(50) = 2.09 microM), TK11 (IC(50) = 2.61 microM), TK21 (IC(50) = 2.06 microM), TK23 (IC(50) = 3.19 microM), showed more potent activity than L-mimose (IC(50) = 3.68 microM). Besides, for this study a heterogeneous database of tyrosinase inhibitors was collected, and could be a useful tool for the scientist in the domain of tyrosinase enzyme researches. The current report could help to shed some clues in the identification of new chemicals that inhibits enzyme tyrosinase, for entering in the pipeline of drug discovery development.

QSAR study of anticoccidial activity for diverse chemical compounds: Prediction and experimental assay of trans-2-(2-nitrovinyl)furan

In this work we report a QSAR model that discriminates between chemically heterogeneous classes of anticoccidial and non-anticoccidial compounds. For this purpose we used the Markovian Chemicals in silico Design (MARCH-INSIDE) approach J. Mol. Mod.2002, 8, 237-245; J. Mol. Mod.2003, 9, 395-407]. Linear discriminant analysis allowed us to fit the discriminant function. This function correctly classifies 86.67% of anticoccidial compounds and 96.23% of inactive compounds in the training series. Overall classification is 94.12%. We validated the model by means of an external predicting series, with 86.96% of global predictability. Remarkably, the present model is based on topological as well as configuration-dependent molecular descriptors. Therefore, the model performs timely calculations and allows discrimination between Z/E and chiral isomers. Finally, to exemplify the use of the model in practice we report the prediction and experimental assay of trans-2-(2-nitrovinyl)furan. It is notable that lesion control was 72.86% at mg/kg of body weight with respect to 60% at 125 mg/kg for amprolium (control drug). The back-projection map for this compound predicts a high level of importance for the double bond and for the nitro group in the trans position. We conclude that the MARCH-INSIDE approach enables the accurate fast track identification of anticoccidial hits. Moreover, trans-2-(2-nitrovinyl)furan seems to be a promising drug for the treatment of coccidiosis.

Predicting antitrichomonal activity: A computational screening using atom-based bilinear indices and experimental proofs

Existing Trichomonas vaginalis therapies are out of reach for most trichomoniasis people in developing countries and, where available, they are limited by their toxicity (mainly in pregnant women) and their cost. New antitrichomonal agents are needed to combat emerging metronidazole-resistant trichomoniasis and reduce the side effects associated with currently available drugs. Toward this end, atom-based bilinear indices, a new TOMOCOMD-CARDD molecular descriptor, and linear discriminant analysis (LDA) were used to discover novel, potent, and non-toxic lead trichomonacidal chemicals. Two discriminant functions were obtained with the use of non-stochastic and stochastic atom-type bilinear indices for heteroatoms and H-bonding of heteroatoms. These atomic-level molecular descriptors were calculated using a weighting scheme that includes four atomic labels, namely atomic masses, van der Waals volumes, atomic polarizabilities, and atomic electronegativities in Pauling scale. The obtained LDA-based QSAR models, using non-stochastic and stochastic indices, were able to classify correctly 94.51% (90.63%) and 93.41% (93.75%) of the chemicals in training (test) sets, respectively. They showed large Matthews' correlation coefficients (C); 0.89 (0.79) and 0.87 (0.85), for the training (test) sets, correspondingly. The result of predictions on the 15% full-out cross-validation test also evidenced the robustness and predictive power of the obtained models. In addition, canonical regression analyses corroborated the statistical quality of these models (R(can) of 0.749 and of 0.845, correspondingly); they were also used to compute biological activity canonical scores for each compound. On the other hand, a close inspection of the molecular descriptors included in both equations showed that several of these molecular fingerprints are strongly interrelated with each other. Therefore, these models were orthogonalized using the Randić orthogonalization procedure. These classification functions were then applied to find new lead antitrichomonal agents and six compounds were selected as possible active compounds by computational screening. The designed compounds were synthesized and tested for in vitro activity against T. vaginalis. Out of the six compounds that were designed, and synthesized, three molecules (chemicals VA5-5a, VA5-5c, and VA5-12b) showed high to moderate cytocidal activity at the concentration of 10 microg/ml, other two compounds (VA5-8pre and VA5-8) showed high cytocidal and cytostatic activity at the concentration of 100 microg/ml and 10 microg/ml, correspondingly, and the remaining chemical (compound VA5-5e) was inactive at these assayed concentrations. Nonetheless, these compounds possess structural features not seen in known trichomonacidal compounds and thus can serve as excellent leads for further optimization of antitrichomonal activity. The LDA-based QSAR models presented here can be considered as a computer-assisted system that could potentially significantly reduce the number of synthesized and tested compounds and increase the chance of finding new chemical entities with antitrichomonal activity.

Atom-based 3D-chiral quadratic indices. Part 2: Prediction of the corticosteroid-binding globulinbinding affinity of the 31 benchmark steroids data set

A quantitative structure-activity relationship (QSAR) study to predict the relative affinities of the steroid 'benchmark' data set to the corticosteroid-binding globulin (CBG) is described. It is shown that the 3D-chiral quadratic indices closely correlate with the measured CBG affinity values for the 31 steroids. The calculated descriptors were correlated with biological data through multiple linear regressions. Two statistically significant models were obtained when non-stochastic (R = 0.924 and s = 0.46) as well as stochastic (R = 0.929 and s = 0.46) 3D-chiral quadratic indices were used. A leave-one-out (LOO) approach to model validation is used here; the best results obtained in the cross-validation procedure with non-stochastic (q2 = 0.781) and stochastic (q2 = 0.735) 3D-chiral quadratic indices are better or similar to most of the 3D-QSAR approaches reported so far. These results support the idea that the 3D-chiral quadratic indices may be helpful in prediction of the corticosteroid-binding affinity for new compounds.