Bilinear Indices Research Articles

Evaluating the Predictive Accuracy of Corn Phenological Durations in Iowa and Illinois

Core IdeasThis paper evaluates the predictive accuracy of thermal heat sum indices. The data used is extensive both spatially (district level data for Iowa and Illinois) and temporally (period 1996–2016). This data is used to evaluate the predictive accuracy of several types of thermal heat sum indices (e.g., bilinear and non‐linear) for granular growth intervals. The evaluation is executed by a novel technique using out‐of‐sample contemporaneous forecasts. ABSTRACTThermal heat sum indices are used to predict the duration of corn (Zea mays L.) growth intervals. Surprisingly, there exists very few studies in agronomic literature that assess predictive accuracy of these indices. This paper contributes to this topic in several ways using USDA‐NASS corn growth data for Iowa (IA) and Illinois (IL) which together cover about 30% of corn production in the United States. First, the dataset spans from 1996 to 2016 and covers all the districts in both Iowa and Illinois. Second, the data are used to evaluate the predictive accuracy of several types of thermal heat sum indices (bilinear and nonlinear) for granular growth intervals. Third, the evaluation is executed using out‐of‐sample contemporaneous forecasts. The results show that nonlinear thermal heat sum indices (HSIs) have superior predictive accuracy to bilinear indices, whereas linear HSIs turn out to be inferior. Overall, the predicted durations using nonlinear thermal HSIs for the Iowa and Illinois combined districts are reasonably accurate. There is little bias across most of the growth intervals despite including the 2009 and 2012 growing seasons with extreme weather conditions. The mean absolute percentage error (MAPE) of the predicted durations relative to actual is well within 10% for almost all growth intervals across combined districts in IA and IL with a low MAPE of 5% for the full growing season duration using the nonlinear thermal heat sum indices. In comparison with other growth intervals, the vegetative growth interval has the lowest MAPE for both IA and IL combined districts.

Fishing Anti-Inflammatories from Known Drugs: In Silico Repurposing, Design, Synthesis and Biological Evaluation of Bisacodyl Analogues.

Herein is described in silico repositioning, design, synthesis, biological evaluation and structure-activity relationship (SAR) of an original class of anti-inflammatory agents based on a polyaromatic pharmacophore structurally related to bisacodyl (BSL) drug used in therapeutic as laxative. We describe the potential of TOMOCOMD-CARDD methods to find out new anti-inflammatory drug-like agents from a diverse series of compounds using the total and local atom based bilinear indices as molecular descriptors. The models obtained were validated by biological studies, identifying BSL as the first anti-inflammatory lead-like using in silico repurposing from commercially available drugs. Several biological in vitro and in vivo assays were performed in order to understand its mechanism of action. A set of analogues of BSL was prepared using low-cost synthetic procedures and further biologically investigated in zebrafish models. Compound 5c and 7e exhibited the best antiinflammatory activities and represent new promising anti-inflammatory agents for further preclinical development.

Dry selection and wet evaluation for the rational discovery of new anthelmintics

ABSTRACTHelminths infections remain a major problem in medical and public health. In this report, atom-based 2D bilinear indices, a TOMOCOMD-CARDD (QuBiLs-MAS module) molecular descriptor family and linear discriminant analysis (LDA) were used to find models that differentiate among anthelmintic and non-anthelmintic compounds. Two classification models obtained by using non-stochastic and stochastic 2D bilinear indices, classified correctly 86.64% and 84.66%, respectively, in the training set. Equation 1(2) correctly classified 141(135) out of 165 [85.45%(81.82%)] compounds in external validation set. Another LDA models were performed in order to get the most likely mechanism of action of anthelmintics. The model shows an accuracy of 86.84% in the training set and 94.44% in the external prediction set. Finally, we carry out an experiment to predict the biological profile of our ‘in-house’ collections of indole, indazole, quinoxaline and cinnoline derivatives (∼200 compounds). Subsequently, we selected a group of nine of the theoretically most active structures. Then, these chemicals were tested in an in vitro assay and one good candidate (VA5-5c) as fasciolicide compound (100% of reduction at concentrations of 50 and 10 mg/L) was discovered.

Prediction of Caco-2 Cell Permeability Using Bilinear Indices and Multiple Linear Regression

Prediction of Caco-2 Cell Permeability Using Bilinear Indices and Multiple Linear Regression

Bond-based bilinear indices for computational discovery of novel trypanosomicidal drug-like compounds through virtual screening

Two-dimensional bond-based bilinear indices and linear discriminant analysis are used in this report to perform a quantitative structure–activity relationship study to identify new trypanosomicidal compounds. A data set of 440 organic chemicals, 143 with antitrypanosomal activity and 297 having other clinical uses, is used to develop the theoretical models. Two discriminant models, computed using bond-based bilinear indices, are developed and both show accuracies higher than 86% for training and test sets. The stochastic model correctly indentifies nine out of eleven compounds of a set of organic chemicals obtained from our synthetic collaborators. The in vitro antitrypanosomal activity of this set against epimastigote forms of Trypanosoma cruzi is assayed. Both models show a good agreement between theoretical predictions and experimental results. Three compounds showed IC50 values for epimastigote elimination (AE) lower than 50 μM, while for the benznidazole the IC50 = 54.7 μM which was used as reference compound. The value of IC50 for cytotoxicity of these compounds is at least 5 times greater than their value of IC50 for AE. Finally, we can say that, the present algorithm constitutes a step forward in the search for efficient ways of discovering new antitrypanosomal compounds.

In silicoAntibacterial Activity Modeling Based on the TOMOCOMD-CARDD Approach

In the recent times, the race to cope with the increasing multidrug resistance of pathogenic bacteria has lost much of its momentum and health professionals are grasping for solutions to deal with the unprecedented resistance levels. As a result, there is an urgent need for a concerted effort towards the development of new antimicrobial drugs to stay ahead in the fight against the ever adapting bacteria. In the present report, antibacterial classification functions (models) based on the topological molecular computational design-computer aided ‘‘rational’’ drug design (TOMOCOMD-CARDD) atom-based non-stochastic and stochastic bilinear indices are presented. These models were built using the linear discriminant analysis (LDA) method over a balanced chemical compounds dataset of 2230 molecular structures, with a diverse range of structural and molecular mechanism modes. The results of this study indicated that the non-stochastic and stochastic bilinear indices provided excellent classification of the chemical compounds (with accuracies of 86.31% and 84.92%, respectively, in the training set). These models were further externally validated yielding correct classification percentages of 86.55% and 87.91% for the non-stochastic and stochastic bilinear models, respectively. Additionally, the obtained models were compared with those reported in the literature and demonstrated comparable results, although the latter were built over much smaller datasets and with much higher degrees of freedom. Finally, simulated ligand-based virtual screening of 116 compounds, recently identified as potential antibacterials, was performed yielding 86.21% and 83.62% of correct classification, respectively, and thus demonstrating the utility of the obtained TOMOCOMD-CARDD models in the search of novel compounds with desirable antibacterial activity.

Identification In Silico and In Vitro of Novel Trypanosomicidal Drug‐Like Compounds

Atom-based bilinear indices and linear discriminant analysis are used to discover novel trypanosomicidal compounds. The obtained linear discriminant analysis-based quantitative structure-activity relationship models, using non-stochastic and stochastic indices, provide accuracies of 89.02% (85.11%) and 89.60% (88.30%) of the chemicals in the training (test) sets, respectively. Later, both models were applied to the virtual screening of 18 in-house synthesized compounds to find new pro-lead antitrypanosomal agents. The in vitro antitrypanosomal activity of this set against epimastigote forms of Trypanosoma cruzi is assayed. Predictions agree with experimental results to a great extent (16/18) of the chemicals. Sixteen compounds show more than 70% of epimastigote inhibition at a concentration 100 μg/mL. In addition, three compounds (CRIS 112, CRIS 140 and CRIS 147) present more than 70% of epimastigote inhibition at a concentration of 10 μg/mL (79.95%, 73.97% and 78.13%, respectively) with low values of cytotoxicity (19.7%, 7.44% and 20.63%, correspondingly).Taking into account all these results, we could say that these three compounds could be optimized in forthcoming works. 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.

Bond-extended stochastic and nonstochastic bilinear indices. I. QSPR/QSAR applications to the description of properties/activities of small-medium size organic compounds

Bond-extended stochastic and nonstochastic bilinear indices are introduced in this article as novel bond-level molecular descriptors (MDs). These novel totals (whole-molecule) MDs are based on bilinear maps (forms) similar to use defined in linear algebra. The proposed nonstochastic indices try to match molecular structure provided by the molecular topology by using the kth Edge(Bond)-Adjacency Matrix (Ek, designed here as a nonstochastic E matrix). The stochastic parameters are computed by using the kth stochastic edge-adjacency matrix, ESk, as matrix operators of bilinear transformations. This new edge (bond)-adjacency relationship can be obtained directly from Ek and can be considered like a new matrix-transformation strategic to obtain new relations for a molecular graph. In both set of MDs, chemical information is codified by using different pair combinations of atomic weightings (in this case four atomic-labels: atomic mass, polarizability, van der Waals volume, and electronegativity). In addition, a local-fragment (bond-type) formalism was also developed. The kth bond-type bilinear indices are calculated by summing the kth bond bilinear indices of all bonds of the same bond type in the molecules. The new set of MDs can be easily and quickly calculated in our in house software TOMOCOMD-CARDD (topological molecular computational design computer-aided-rational-drug design). The reported application and utilization of these MDs for predictive capability correlations of structure with physicochemical and pharmacological properties are reviewed. Three benchmark datasets have been used to evaluate the QSPR/QSAR behavior of the new bond-level TOMOCOMD-CARDD MDs. We developed the QSPR models to describe several physicochemical properties of octane isomers (First Case) and, to analyze of the boiling point of 28 alkyl-alcohols (Second Case) and to examine of the specific rate constant (log k), the partition coefficient (log P), as well as the antibacterial activity of 34 derivatives of 2-furylethylenes (Third Case). For these three rounds, the quantitative models found are significant from a statistical point of view and permit a clear interpretation of the studied properties in terms of the structural features of molecules. A leave-one-out cross-validation procedure revealed that the regression models had a good predictability. The comparison with other approaches reveals good performance of the method proposed. Therefore, it is clearly demonstrated that this suitability is higher than that shown by other 2D/3D well-known sets of MDs. The approach described here appears to be a very promising structural invariant, useful for QSPR/QSAR studies and shown to provide an excellent alternative or guides for discovery and optimization of new lead compounds, reducing the time and cost of the traditional procedure. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Ligand-Based Computer-Aided Discovery of Tyrosinase Inhibitors. Applications of the TOMOCOMD-CARDD Method to the Elucidation of New Compounds

In this review an overview of the application of computational approaches is given. Specifically, the uses of Quantitative Structure-Activity Relationship (QSAR) methods for in silico identification of new families of compounds as novel tyrosinase inhibitors are revised. Assembling, validation of models through prediction series, and virtual screening of external data sets are also shown, to prove the accuracy of the QSAR models obtained with the TOMOCOMD-CARDD (TOpological MOlecular COMputational Design-Computer-Aided Rational Drug Design) software and Linear Discriminant Analysis (LDA) as statistical technique. Together with this, a database is collected for these QSAR studies, and could be considered a useful tool in future QSAR modeling of tyrosinase activity and for scientists that work in the field of this enzyme and its inhibitors. Finally, a translation to real world applications is shown by the use of QSAR models in the identification and posterior in-vitro evaluation of different families of compounds. Several different classes of compounds from various sources (natural and synthetic) were identified. Between them, we can find tetraketones, cycloartanes, ethylsteroids, lignans, dicoumarins and vanilloid derivatives. Finally, some considerations are discussed in order to improve the identification of novel drug-like compounds based on the use of QSAR-Ligand-Based Virtual Screening (LBVS).

Tomocomd-camps and protein bilinear indices - novel bio-macromolecular descriptors for protein research: I. Predicting protein stability effects of a complete set of alanine substitutions in the Arc repressor

Descriptors calculated from a specific representation scheme encode only one part of the chemical information. For this reason, there is a need to construct novel graphical representations of proteins and novel protein descriptors that can provide new information about the structure of proteins. Here, a new set of protein descriptors based on computation of bilinear maps is presented. This novel approach to biomacromolecular design is relevant for QSPR studies on proteins. Protein bilinear indices are calculated from the kth power of nonstochastic and stochastic graph-theoretic electronic-contact matrices, M(m)(k) and (s)M(m)(k), respectively. That is to say, the kth nonstochastic and stochastic protein bilinear indices are calculated using M(m)(k) and (s)M(m)(k) as matrix operators of bilinear transformations. Moreover, biochemical information is codified by using different pair combinations of amino acid properties as weightings. Classification models based on a protein bilinear descriptor that discriminate between Arc mutants of stability similar or inferior to the wild-type form were developed. These equations permitted the correct classification of more than 90% of the mutants in training and test sets, respectively. To predict t(m) and Delta DeltaG(f)(o) values for Arc mutants, multiple linear regression and piecewise linear regression models were developed. The multiple linear regression models obtained accounted for 83% of the variance of the experimental t(m). Statistics calculated from internal and external validation procedures demonstrated robustness, stability and suitable power ability for all models. The results achieved demonstrate the ability of protein bilinear indices to encode biochemical information related to those structural changes significantly influencing the Arc repressor stability when punctual mutations are induced.

Nucleotide's bilinear indices: Novel bio-macromolecular descriptors for bioinformatics studies of nucleic acids. I. Prediction of paromomycin's affinity constant with HIV-1 Ψ-RNA packaging region

A new set of nucleotide-based bio-macromolecular descriptors are presented. This novel approach to bio-macromolecular design from a linear algebra point of view is relevant to nucleic acids quantitative structure-activity relationship (QSAR) studies. These bio-macromolecular indices are based on the calculus of bilinear maps on ℜ n [ b mk ( x ¯ m , y ¯ m ) : ℜ n × ℜ n → ℜ ] in canonical basis. Nucleic acid's bilinear indices are calculated from kth power of non-stochastic and stochastic nucleotide's graph-theoretic electronic-contact matrices, M m k and s M m k , respectively. That is to say, the kth non-stochastic and stochastic nucleic acid's bilinear indices are calculated using M m k and s M m k as matrix operators of bilinear transformations. Moreover, biochemical information is codified by using different pair combinations of nucleotide-base properties as weightings (experimental molar absorption coefficient ε 260 at 260 nm and pH=7.0, first ( Δ E 1 ) and second ( Δ E 2 ) single excitation energies in eV, and first ( f 1) and second ( f 2) oscillator strength values (of the first singlet excitation energies) of the nucleotide DNA–RNA bases. As example of this approach, an interaction study of the antibiotic paromomycin with the packaging region of the HIV-1 Ψ-RNA have been performed and it have been obtained several linear models in order to predict the interaction strength. The best linear model obtained by using non-stochastic bilinear indices explains about 91% of the variance of the experimental Log K ( R=0.95 and s=0.08×10 −4 M −1) as long as the best stochastic bilinear indices-based equation account for 93% of the Log K variance ( R=0.97 and s=0.07×10 −4 M −1). The leave-one-out (LOO) press statistics, evidenced high predictive ability of both models ( q 2=0.86 and s cv=0.09×10 −4 M −1 for non-stochastic and q 2=0.91 and s cv=0.08×10 −4 M −1 for stochastic bilinear indices). The nucleic acid's bilinear indices-based models compared favorably with other nucleic acid's indices-based approaches reported nowadays. These models also permit the interpretation of the driving forces of the interaction process. In this sense, developed equations involve short-reaching ( k⩽3), middle-reaching (4< k<9), and far-reaching ( k=10 or greater) nucleotide's bilinear indices. This situation points to electronic and topologic nucleotide's backbone interactions control of the stability profile of paromomycin–RNA complexes. Consequently, the present approach represents a novel and rather promising way to theoretical-biology studies.

Discovery of Novel Trichomonacidals Using LDA‐Driven QSAR Models and Bond‐Based Bilinear Indices as Molecular Descriptors

AbstractFew years ago, the World Health Organization estimated the number of adults with trichomoniasis at 170 million worldwide, more than the combined numbers for gonorrhea, syphilis, and chlamydia. To combat this sexually transmitted disease, Metronidazole (MTZ) has emerged, since 1959, as a powerful drug for the systematic treatment of infected patients. However, increasing resistance to MTZ, adverse effects associated to high‐dose MTZ therapies and very expensive conventional technologies related to the development of new trichomonacidals necessitate novel computational methods that shorten the drug discovery pipeline. Therefore, bond‐based bilinear indices, new 2‐D bond‐based TOMOCOMD‐CARDD Molecular Descriptors (MDs), and Linear Discriminant Analysis (LDA) are combined to discover novel antitrichomonal agents. Generated models, using non‐stochastic and stochastic indices, are able to classify correctly the 90.11% (93.75%) and the 87.92% (87.50%) of chemicals in the training (test) sets, respectively. In addition, they show large Matthews' correlation coefficients (C) of 0.80 (0.86) and 0.76 (0.71) for the training (test) sets, respectively. The result of predictions on the 10% full‐out cross‐validation test also evidences the quality of both models. In order to test the models' predictive power, 12 compounds, already proved against Trichomonas vaginalis (Tv), are screened in a simulated virtual screening experiment. As a result, they correctly classified 9 out of 12 (75.00%) and 10 out of 12 (83.33%) of the chemicals, respectively, which were the most important criteria to validate the models. Finally, in order to prove the reach of TOMOCOMD‐CARDD approach and to discover new trichomonacidals, these classification functions were applied to a set of eight chemicals which, in turn, were synthesized and tested toward in vitro activity against Tv. As a result, experimental observations confirm theoretical predictions to a great extent, since it is gained a correct classification of 87.50% (7/8) of chemicals. Biological tests also show several candidates as antitrichomonals, since almost all the compounds [VAM2‐(3–8)] exhibit pronounced cytocidal activities of 100% at the concentration of 100 μg/mL and at 24 h (48 h) but VAM2–2: 99.37% (100%), and it is remarkable that these compounds do not show toxic activity in macrophage assays at this concentration. The Quantitative Structure–Activity Relationship (QSAR) models presented here could significantly reduce the number of synthesized and tested compounds as well as could act as virtual shortcuts to new chemical entities with trichomonacidal activity.

Atom-based non-stochastic and stochastic bilinear indices: Application to QSPR/QSAR studies of organic compounds

The recently introduced bilinear indices are applied to the QSAR/QSPR studies of heteroatomic molecules. These novel atom-based molecular fingerprints are used to predict the boiling point of 28 alkyl-alcohols and partition coefficient, specific rate constant and antibacterial activity of 34 2-furylethylenes derivatives. The obtained models are statistically significant and show rather very good stability in a cross-validation experiment. The comparison with other approaches exposes a good behavior of our method in this QSPR studies. The obtained results suggest that with the present method, it is possible to obtain a good estimation of physical, chemical and physicochemical properties for organic compounds.

Novel 2D TOMOCOMD-CARDD molecular descriptors: atom-based stochastic and non-stochastic bilinear indices and their QSPR applications

Novel atom-based molecular descriptors (MDs) based on a bilinear map similar to use defined in linear algebra are presented. These MDs, 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, J Chem Inf Comput Sci 44, 2010, 2004; Marrero-Ponce, Molecules 8, 687, 2003) and stochastic (Marrero-Ponce, et al. J Mol Struc (Theochem) 717, 67, 2005; Marrero-Ponce, Castillo-Garit, J Comput-Aided Mol Design 19, 369, 2005) 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 MDs was tested by analysing regressions of these MDs 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 MDs. 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.

3D-chiral (2.5) atom-based TOMOCOMD-CARDD descriptors: theory and QSAR applications to central chirality codification

The history of the use of chiral descriptors in Quantitative structure–activity relationships (QSAR) studies is described, with a particular emphasis on several series of novel chirality descriptors that have been introduced in this field. Specifically, chiral topological indices that circumvent the inability of conventional (chiral insensitive) topological molecular descriptors are reviewed. These modified descriptors were applied to several well-know data sets in order to validate each one of them. Particularly, Cramer’s steroid data set has become a benchmark for the assessment of novel QSAR methods. This data set has been used by several researches using 3D-QSAR approaches such as Comparative Molecular Field Analysis (CoMFA), Comparative Molecular Similarity Indices Analysis (CoMSIA), Molecular Quantum Similarity Measures (MQSM), 3D-chiral (2.5) TOMOCOMD-CARDD descriptors, Topological Quantum Similarity Indices (TQSI), similarity matrixes, Comparative Molecular Moment Analysis (CoMMA), E-state, Mapping Property Distributions of Molecular Surfaces (MAP), EVA and so on. For that reason, it was selected for the shake of comparability by us. An extensive comparison between all these approaches was updated. In addition, to evaluate the effectiveness of this novel approach in drug design we have modelled the angiotensin-converting enzyme inhibitory activity of perindoprilate’s σ-stereoisomers combinatorial library as well as to codify information related to pharmacological property highly dependent on molecular symmetry of a set of seven pairs of chiral N-alkylated 3-(3-hydroxyphenyl)-piperidines that bind σ-receptors. The validation of this method was achieved by comparison with previous reports applied to the same data sets. The non-stochastic and stochastic 3D-chiral (2.5) bilinear indices appear to provide a very interesting alternative to other more common 3D-QSAR descriptors.

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).

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.

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.

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 (Rcan 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 10μg/ml, other two compounds (VA5-8pre and VA5-8) showed high cytocidal and cytostatic activity at the concentration of 100μg/ml and 10μg/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.