Atom, atom-type and total molecular linear indices as a promising approach for bioorganic and medicinal chemistry: theoretical and experimental assessment of a novel method for virtual screening and rational design of new lead anthelmintic

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.

Enantiomeric separation and determination of absolute stereochemistry of asymmetric molecules in drug discovery—Building chiral technology toolboxes

The application of Chiral Technology, or the (extensive) use of techniques or tools for the determination of absolute stereochemistry and the enantiomeric or chiral separation of racemic small molecule potential lead compounds, has been critical to successfully discovering and developing chiral drugs in the pharmaceutical industry. This has been due to the rapid increase over the past 10-15 years in potential drug candidates containing one or more asymmetric centers. Based on the experiences of one pharmaceutical company, a summary of the establishment of a Chiral Technology toolbox, including the implementation of known tools as well as the design, development, and implementation of new Chiral Technology tools, is provided.

Unified QSAR approach to antimicrobials. Part 2: Predicting activity against more than 90 different species in order to halt antibacterial resistance

There are many different kinds of pathogenic bacteria species with very different susceptibility profiles to different antibacterial drugs. One limitation of QSAR models is that they consider the biological activity of drugs against only one species of bacteria. In a previous paper, we developed a unified Markov model to describe the biological activity of different drugs tested in the literature against some antimicrobial species. Consequently, predicting the probability with which a drug is active against different species of bacteria with a single unified model is a goal of major importance. The work described here develops the unified Markov model to describe the biological activity of more than 70 drugs from the literature tested against 96 species of bacteria. We applied linear discriminant analysis (LDA) to classify drugs as active or inactive against the different tested bacterial species. The model correctly classified 199 out of 237 active compounds (83.9%) and 168 out of 200 inactive compounds (84%). Overall training predictability was 84% (367 out of 437 cases). Validation of the model was carried out using an external predicting series, with the model classifying 202 out of 243 (i.e., 83.13%) of the compounds. In order to show how the model functions in practice, a virtual screening was carried out and the model recognized as active 84.5% (480 out of 568) antibacterial compounds not used in the training or predicting series. The current study is an attempt to calculate within a unified framework the probabilities of antibacterial action of drugs against many different species.

Unify QSAR approach to antimicrobials. Part 1: Predicting antifungal activity against different species

Most of up-to-date reported molecular descriptors encode only information about the molecular structure. In previous papers, we have extended stochastic descriptors to encode additional information such as target site, partition system, or biological species [Bioorg. Med. Chem. Lett.2005, 15, 551; Bioorg. Med. Chem. 2005, 13, 1119]. This work develops an unify Markov model to describe with a single linear equation the biological activity of 74 drugs tested in the literature against some of the fungi species selected from a list of 87 species (491 cases in total). The data were processed by linear discriminant analysis (LDA) classifying drugs as active or non-active against the different tested fungi species. The model correctly classifies 338 out of 368 active compounds (91.85%) and 89 out of 123 non-active compounds (72.36%). Overall training predictability was 86.97% (427 out of 491 compounds). Validation of the model was carried out by means of leave-species-out (LSO) procedure. After elimination step-by-step of all drugs tested against one specific species, we record the percentage of good classification of leave-out compounds (LSO-predictability). In addition, robustness of the model to the elimination of the compounds (LSO-robustness) was considered. This aspect was considered as the variation of the percentage of good classification of the modified model (Delta) in LSO with respect to the original one. Average LSO-predictability was 86.41+/-0.95% (average+/-SD) and Delta = -0.55%, being 6 the average number of drugs tested against each fungi species. Results for some of the 87 studied species were Candida albicans: 43 tested compounds, 100% of LSO-predictability, Delta = -3.49%; Candida parapsilosis 23, 100%, Delta = -0.86%; Aspergillus fumigatus 21, 95.20%, Delta = 0.05%; Microsporum canis 12, 91.60%, Delta = -2.84%; Trichophyton mentagrophytes 11, 100%, Delta = -0.51%; Cryptococcus neoformans 10, 90%, Delta = -0.90%. The present one is the first reported unify model that allows one predicting antifungal activity of any organic compound against a very large diversity of fungi pathogens.

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.

Stochastic entropy QSAR for the in silico discovery of anticancer compounds: Prediction, synthesis, and in vitro assay of new purine carbanucleosides

A Markov model based QSAR is introduced for the rational selection of anticancer compounds. The model discriminates 90.3% of 226 structurally heterogeneous anticancer/non-anticancer compounds in training series. External validation series were used to validate the model; the 91.8% containing 85 compounds, not considered to fit the model, were correctly classified. The model developed is afterwards used in a simulation of a virtual search for anticancer compounds never considered either in training or in predicting series. The 87.7% of the 213 anticancer compounds used in this simulated search were correctly classified. The model also shows high values for specificity (0.89), sensitivity (0.91), and Mathews correlation coefficient (0.79). In addition, the present model compares better-to-similar with respect to other four models elsewhere reported if one takes into consideration 26 comparison parameters. Finally, we exemplify the use of the model in practice with the design of a new series of carbanucleosides. The compounds evaluated with the model were synthesized and experimentally assayed for their antitumor effects on the proliferation of murine leukemia cells (L1210/0) and human T-lymphocyte cells (CEM/0 and Molt4/C8). The more interesting activity was detected for the compound 5a with a predicted probability of 80.2% and IC(50) = 27.0, 27.2, and 29.4 microM, respectively, against the above-mentioned cellular lines. These values are comparable to those for the control compound Ara-A.

A novel non-stochastic quadratic fingerprints-based approach for the 'in silico' discovery of new antitrypanosomal compounds

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 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 predicted a posteriori. In addition, 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 10 already synthesized compounds. The in vitro antitrypanosomal activity of this series against epimastigotes forms of Trypanosomal cruzi was assayed. The model was able to predict correctly the behaviour of these compounds in 90% of the cases.

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.

Linear indices of the 'macromolecular graph's nucleotides adjacency matrix' as a promising approach for bioinformatics studies. Part 1: prediction of paromomycin's affinity constant with HIV-1 psi-RNA packaging region

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 psi-RNA has been performed as example of this approach. A multiple linear regression model predicted the local binding affinity constants [Log K (10(-4) M(-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 = 0.102 x 10(-4) M(-1)) and leave-one-out press statistics evidenced its predictive ability (q2 = 0.82 and s(cv) = 0.108 x 10(-4) M(-1)). The comparison with other approaches (macromolecular quadratic indices, Markovian Negentropies and 'stochastic' spectral moments) reveals a good behavior of our method.

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.

Protein linear indices of the ‘macromolecular pseudograph α-carbon atom adjacency matrix’ in bioinformatics. Part 1: Prediction of protein stability effects of a complete set of alanine substitutions in Arc repressor

A novel approach to bio-macromolecular design from a linear algebra point of view is introduced. A protein's total (whole protein) and local (one or more amino acid) linear indices are a new set of bio-macromolecular descriptors of relevance to protein QSAR/QSPR studies. These amino-acid level biochemical descriptors are based on the calculation of linear maps on Rn[f k(xmi):Rn-->Rn] in canonical basis. These bio-macromolecular indices are calculated from the kth power of the macromolecular pseudograph alpha-carbon atom adjacency matrix. Total linear indices are linear functional on Rn. That is, the kth total linear indices are linear maps from Rn to the scalar R[f k(xm):Rn-->R]. Thus, the kth total linear indices are calculated by summing the amino-acid linear indices of all amino acids in the protein molecule. A study of the protein stability effects for a complete set of alanine substitutions in the Arc repressor illustrates this approach. A quantitative model that discriminates near wild-type stability alanine mutants from the reduced-stability ones in a training series was obtained. This model permitted the correct classification of 97.56% (40/41) and 91.67% (11/12) of proteins in the training and test set, respectively. It shows a high Matthews correlation coefficient (MCC=0.952) for the training set and an MCC=0.837 for the external prediction set. Additionally, canonical regression analysis corroborated the statistical quality of the classification model (Rcanc=0.824). This analysis was also used to compute biological stability canonical scores for each Arc alanine mutant. On the other hand, the linear piecewise regression model compared favorably with respect to the linear regression one on predicting the melting temperature (tm) of the Arc alanine mutants. The linear model explains almost 81% of the variance of the experimental tm (R=0.90 and s=4.29) and the LOO press statistics evidenced its predictive ability (q2=0.72 and scv=4.79). Moreover, the TOMOCOMD-CAMPS method produced a linear piecewise regression (R=0.97) between protein backbone descriptors and tm values for alanine mutants of the Arc repressor. A break-point value of 51.87 degrees C characterized two mutant clusters and coincided perfectly with the experimental scale. For this reason, we can use the linear discriminant analysis and piecewise models in combination to classify and predict the stability of the mutant Arc homodimers. These models also permitted the interpretation of the driving forces of such folding process, indicating that topologic/topographic protein backbone interactions control the stability profile of wild-type Arc and its alanine mutants.

Atom, atom-type, and total nonstochastic and stochastic quadratic fingerprints: a promising approach for modeling of antibacterial activity

The TOpological MOlecular COMputer Design (TOMOCOMD-CARDD) approach has been introduced for the classification and design of antimicrobial agents using computer-aided molecular design. For this propose, atom, atom-type, and total quadratic indices have been generalized to codify chemical structure information. In this sense, stochastic quadratic indices have been introduced for the description of the molecular structure. These stochastic fingerprints are based on a simple model for the intramolecular movement of all valence-bond electrons. In this work, a complete data set containing 1006 antimicrobial agents is collected and presented. Two structure-based antibacterial activity classification models have been generated. The models (including nonstochastic and stochastic indices) classify correctly more than 90% of 1525 compounds in training sets. These models permit the correct classification of 92.28% and 89.31% of 505 compounds in an external test sets. The TOMOCOMD-CARDD approach, also, satisfactorily compares with respect to nine of the most useful models for antimicrobial selection reported to date. Finally, a virtual screening of 87 new compounds reported in the antiinfective field with antibacterial activities is developed showing the ability of the TOMOCOMD-CARDD models to identify new leads as antibacterial.

Protein quadratic indices of the "macromolecular pseudograph's alpha-carbon atom adjacency matrix". 1. Prediction of Arc repressor alanine-mutant's stability

This report describes a new set of macromolecular descriptors of relevance to protein QSAR/QSPR studies, protein's quadratic indices. These descriptors are calculated from the macromolecular pseudograph's alpha-carbon atom adjacency matrix. A study of the protein stability effects for a complete set of alanine substitutions in Arc repressor illustrates this approach. Quantitative Structure-Stability Relationship (QSSR) models allow discriminating between near wild-type stability and reduced-stability A-mutants. A linear discriminant function gives rise to excellent discrimination between 85.4% (35/41)and 91.67% (11/12) of near wild-type stability/reduced stability mutants in training and test series, respectively. The model's overall predictability oscillates from 80.49 until 82.93, when n varies from 2 to 10 in leave-n-out cross validation procedures. This value stabilizes around 80.49% when n was > 6. Additionally, canonical regression analysis corroborates the statistical quality of the classification model (Rcanc = 0.72, p-level <0.0001). This analysis was also used to compute biological stability canonical scores for each Arc A-mutant. On the other hand, nonlinear piecewise regression model compares favorably with respect to linear regression one on predicting the melting temperature (tm)of the Arc A-mutants. The linear model explains almost 72% of the variance of the experimental tm (R = 0.85 and s = 5.64) and LOO press statistics evidenced its predictive ability (q2 = 0.55 and scv = 6.24). However, this linear regression model falls to resolve t(m) predictions of Arc A-mutants in external prediction series. Therefore, the use of nonlinear piecewise models was required. The tm values of A-mutants in training (R = 0.94) and test(R = 0.91) sets are calculated by piecewise model with a high degree of precision. A break-point value of 51.32 degrees C characterizes two mutants' clusters and coincides perfectly with the experimental scale. For this reason, we can use the linear discriminant analysis and piecewise models in combination to classify and predict the stability of the mutants' Arc homodimers. These models also permit the interpretation of the driving forces of such a folding process. The models include protein's quadratic indices accounting for hydrophobic (z1), bulk-steric (z2), and electronic (z3) features of the studied molecules. Preponderance of z1 and z3 over z2 indicates the higher importance of the hydrophobic and electronic side chain terms in the folding of the Arc dimer. In this sense, developed equations involve short-reaching (k < or = 3), middle- reaching (3 < k < or = 7) and far-reaching (k= 8 or greater) z1, 2, 3-protein's quadratic indices. This situation points to topologic/topographic protein's backbone interactions control of the stability profile of wild-type Arc and its A-mutants. Consequently, the present approach represents a novel and very promising way to mathematical research in biology sciences.