Monte Carlo Optimization Method Based QSAR Modeling of Placental Barrier Permeability.

PURPOSE: In order to ensure that drug administration is safe during pregnancy, it is crucial to have the possibility to predict the placental permeability of drugs in humans. The experimental method which is most widely used for the said purpose is in vitro human placental perfusion, though the approach is highly expensive and time consuming. Quantitative structure-activity relationship (QSAR) modeling represents a powerful tool for the assessment of the drug placental transfer, and can be successfully employed to be an alternative in in vitro experiments. METHODS: The conformation-independent QSAR models covered in the present study were developed through the use of the SMILES notation descriptors and local molecular graph invariants. What is more, the Monte Carlo optimization method, was used in the test sets and the training sets as the model developer with three independent molecular splits. RESULTS: A range of different statistical parameters was used to validate the developed QSAR model, including the standard error of estimation, mean absolute error, root-mean-square error (RMSE), correlation coefficient, cross-validated correlation coefficient, Fisher ratio, MAE-based metrics and the correlation ideality index. Once the mentioned statistical methods were employed, an excellent predictive potential and robustness of the developed QSAR model was demonstrated. In addition, the molecular fragments, which are derived from the SMILES notation descriptors accounting for the decrease or increase in the investigated activity, were revealed. CONCLUSION: The presented QSAR modeling can be an invaluable tool for the high-throughput screening of the placental permeability of drugs.

The Application of the Combination of Monte Carlo Optimization Method based QSAR Modeling and Molecular Docking in Drug Design and Development.

In recent years, one of the promising approaches in the QSAR modeling Monte Carlo optimization approach as conformation independent method, has emerged. Monte Carlo optimization has proven to be a valuable tool in chemoinformatics, and this review presents its application in drug discovery and design. In this review, the basic principles and important features of these methods are discussed as well as the advantages of conformation independent optimal descriptors developed from the molecular graph and the Simplified Molecular Input Line Entry System (SMILES) notation compared to commonly used descriptors in QSAR modeling. This review presents the summary of obtained results from Monte Carlo optimization-based QSAR modeling with the further addition of molecular docking studies applied for various pharmacologically important endpoints. SMILES notation based optimal descriptors, defined as molecular fragments, identified as main contributors to the increase/ decrease of biological activity, which are used further to design compounds with targeted activity based on computer calculation, are presented. In this mini-review, research papers in which molecular docking was applied as an additional method to design molecules to validate their activity further, are summarized. These papers present a very good correlation among results obtained from Monte Carlo optimization modeling and molecular docking studies.

The study of the index of ideality of correlation as a new criterion of predictive potential of QSPR/QSAR-models.

Acetylcholinesterase (AChE) inhibitors, dihydrofolate reductase inhibitors (DHFR), Toxicity in Tetrahymena pyriformis (TP), Acute Toxicity in fathead minnow (TFat), Water solubility (WS), and Acute Aquatic Toxicity in Daphnia magna (DM) are examined as endpoints to establish quantitative structure - property/activity relationships (QSPRs/QSARs). The Index of Ideality of Correlation (IIC) is a measure of predictive potential. The IIC has been studied in a few recent works. The comparison of models for the six endpoints above confirms that the index can be a useful tool for building up and validation of QSPR/QSAR models. All examined endpoints are important from an ecologic point of view. The diversity of examined endpoints confirms that the IIC is real criterion of the predictive potential of a model.

Development and design of novel cardiovascular therapeutics based on Rho kinase inhibition-In silico approach.

Rho kinases, one of the best-known members of the serine/threonine (Ser/Thr) protein kinase family, can be used as target enzymes for the treatment of many diseases such as cancer or multiple sclerosis, and especially for the treatment of cardiovascular diseases. This study presents QSAR modeling for a series of 41 chemical compounds as Rho kinase inhibitors based on the Monte Carlo method. QSAR models were developed for three random splits into the training and test set. Molecular descriptors used for QSAR modeling were based on the SMILES notation and local invariants of the molecular graph. The statistical quality of the developed model, including robustness and predictability, was tested with different statistical approaches and satisfying results were obtained. The best calculated QSAR model had the following statistical parameters: r2 = 0.8825 and q2 = 0.8626 for the training set and r2 = 0.9377 and q2 = 0.9124 for the test set. Novel statistical metric entitled as the index of ideality of correlation was used for the final model assessment, and the obtained results were 0.6631 for the training and 0.9683 for the test set. Molecular fragments responsible for the increases and decreases of the studied activity were defined and they were further used for the computer-aided design of new compounds as potential Rho kinase inhibitors. The final assessment of the developed QSAR model and designed inhibitors was achieved with the application of molecular docking. An excellent correlation between the results from QSAR and molecular docking studies was obtained.

Semi-correlations combined with the index of ideality of correlation: a tool to build up model of mutagenic potential.

Mutagenicity is the ability of a substance to induce mutations. This hazardous ability of a substance is decisive from point of view of ecotoxicology. The number of substances, which are used for practical needs, grows every year. Consequently, methods for at least preliminary estimation of mutagenic potential of new substances are necessary. Semi-correlations are a special case of traditional correlations. These correlations can be named as "correlations along two parallel lines." This kind of correlation has been tested as a tool to predict selected endpoints, which are represented by only two values: "inactive/active" (0/1). Here this approach is used to build up predictive models for mutagenicity of large dataset (n = 3979). The so-called index of ideality of correlation (IIC) has been tested as a statistical criterion to estimate the semi-correlation. Three random splits of experimental data into the training, invisible-training, calibration, and validation sets were analyzed. Two models were built up for each split: the first model based on optimization without the IIC and the second model based on optimization where IIC is involved in the Monte Carlo optimization. The statistical characteristics of the best model (calculated with taking into account the IIC) n = 969; sensitivity = 0.8050; specificity = 0.9069; accuracy = 0.8648; Matthews's correlation coefficient = 0.7196 (using IIC). Thus, the use of IIC improves the statistical quality of the binary classification models of mutagenic potentials (Ames test) of organic compounds.

In silico studies and the design of novel agents for the treatment of systemic tuberculosis.

Tuberculosis (TB) is an ancient infectious disease, which re-emerged with the appearance of multidrug-resistant strains and acquired immune deficiency syndrome. Enoyl-acyl-carrier protein reductase (InhA) has emerged as a promising target for the development of anti-tuberculosis therapeutics. This study aims to develop quantitative structure-activity relationship (QSAR) models for a series of arylcarboxamides as InhA inhibitors. The QSAR models were calculated on the basis of optimal molecular descriptors based on the simplified molecular-input line-entry system (SMILES) notation with the Monte Carlo method as a model developer. The molecular docking study was used for the final assessment of the developed QSAR model and designed novel inhibitors. Methods used for the validation indicated that the predictability of the developed model was good. Structural indicators defined as molecular fragments responsible for increases and decreases of the studied activity were defined. The computer-aided design of new compounds as potential InhA inhibitors was presented. The Monte Carlo optimization was capable of being an efficient in silico tool for developing a model of good statistical quality. The predictive potential of the applied approach was tested and the robustness of the model was proven using different methods. The results obtained from molecular docking studies were in excellent correlation with the results from QSAR studies. This study can be useful in the search for novel anti-tuberculosis therapeutics based on InhA inhibition. Communicated by Ramaswamy H. Sarma.

The anesthetic action of some polyhalogenated ethers-Monte Carlo method based QSAR study.

Up to this date, there has been an ongoing debate about the mode of action of general anesthetics, which have postulated many biological sites as targets for their action. However, postoperative nausea and vomiting are common problems in which inhalational agents may have a role in their development. When a mode of action is unknown, QSAR modelling is essential in drug development. To investigate the aspects of their anesthetic, QSAR models based on the Monte Carlo method were developed for a set of polyhalogenated ethers. Until now, their anesthetic action has not been completely defined, although some hypotheses have been suggested. Therefore, a QSAR model should be developed on molecular fragments that contribute to anesthetic action. QSAR models were built on the basis of optimal molecular descriptors based on the SMILES notation and local graph invariants, whereas the Monte Carlo optimization method with three random splits into the training and test set was applied for model development. Different methods, including novel Index of ideality correlation, were applied for the determination of the robustness of the model and its predictive potential. The Monte Carlo optimization process was capable of being an efficient in silico tool for building up a robust model of good statistical quality. Molecular fragments which have both positive and negative influence on anesthetic action were determined. The presented study can be useful in the search for novel anesthetics.

QSPR in forensic analysis - The prediction of retention time of pesticide residues based on the Monte Carlo method.

A method for the prediction of retention indices of pesticides using the Monte Carlo method and with optimal molecular descriptors based on local graph invariants and the SMILES notation of studied compounds has been presented. Quite satisfactory results were obtained with the proposed method, since a robust model with good statistical quality was developed. The predictive potential of the applied approach was tested and the robustness of the model was proven with different methods. The best calculated QSPR model had following statistical parameters: r2 = 0.9182 for the training set and r2 = 0.8939 for the test set. Structural indicators defined as molecular fragments responsible for the increases and decreases of gas chromatographic retention indices activity were calculated.

Prediction of gas chromatographic retention indices based on Monte Carlo method.

A new method for the prediction of retention indices using Monte Carlo method and based on local graph invariants and SMILES notation of studied compounds has been presented. Very satisfactory results were obtained with the proposed method, since robust model with good statistical quality was developed. The predictive potential of the applied approach was tested and the robustness of the model was proven with different methods. The best calculated QSPR model had following statistical parameters: r2=0.8097 for the training set and r2=0.9372 for the test set. Structural indicators defined responsible for the increases and decreases of gas chromatographic retention indices activity have been calculated.

Monte Carlo-based quantitative structure-activity relationship models for toxicity of organic chemicals to Daphnia magna.

Quantitative structure-activity relationships (QSARs) for toxicity of a large set of 758 organic compounds to Daphnia magna were built up. The simplified molecular input-line entry system (SMILES) was used to represent the molecular structure. The Correlation and Logic (CORAL) software was utilized as a tool to develop the QSAR models. These models are built up using the Monte Carlo method and according to the principle "QSAR is a random event" if one checks a group of random distributions in the visible training set and the invisible validation set. Three distributions of the data into the visible training, calibration, and invisible validation sets are examined. The predictive potentials (i.e., statistical characteristics for the invisible validation set of the best model) are as follows: n = 87, r2 = 0.8377, root mean square error = 0.564. The mechanistic interpretations and the domain of applicability of built models are suggested and discussed. Environ Toxicol Chem 2016;35:2691-2697. © 2016 SETAC.

The Monte Carlo technique as a tool to predict LOAEL.

Quantitative structure - activity relationships (QSARs) for the Lowest Observed Adverse Effect Level (LOAEL) for a large set of organic compounds (n = 341) are suggested. The molecular structures of these compounds are represented by Simplified Molecular Input-Line Entry Systems (SMILES). A criteria for the estimation quality of split into the "visible" training set (used for developing a model) and "invisible" external validation set is suggested. The correlation between the above criterion and the predictive potential of developed QSAR model (root-mean-square error for "invisible" validation set) has been detected. One-variable models are built up for several different splits into the "visible" training set and "invisible" validation set. The statistical quality of these models is quite good. Mechanistic interpretation and the domain of applicability for these models are defined according to probabilistic point of view. The methodology for defining applicability domain in QSAR modeling with SMILES notation based optimal descriptors is presented.

Nano-QSAR: Model of mutagenicity of fullerene as a mathematical function of different conditions.

The experimental data on the bacterial reverse mutation test (under various conditions) on C60 nanoparticles for the cases (i) TA100, and (ii) WP2uvrA/pkM101 are examined as endpoints. By means of the optimal descriptors calculated with the Monte Carlo method a mathematical model of these endpoints has been built up. The models are a mathematical function of eclectic data such as (i) dose (g/plate); (ii) metabolic activation (i.e. with mix S9 or without mix S9); and (iii) illumination (i.e. darkness or irradiation). The eclectic data on different conditions were represented by so-called quasi-SMILES. In contrast to the traditional SMILES which are representation of molecular structure, the quasi-SMILES are representation of conditions by sequence of symbols. The calculations were carried out with the CORAL software, available on the Internet at http://www.insilico.eu/coral. The main idea of the suggested descriptors is the accumulation of all available eclectic information in the role of logical and digital basis for building up a model. The computational experiments have shown that the described approach can be a tool to build up models of mutagenicity of fullerene under different conditions.

QSAR modeling of the antimicrobial activity of peptides as a mathematical function of a sequence of amino acids.

Antimicrobial peptides have emerged as new therapeutic agents for fighting multi-drug-resistant bacteria. However, the process of optimizing peptide antimicrobial activity and specificity using large peptide libraries is both tedious and expensive. Therefore, computational techniques had to be applied for process optimization. In this work, the representation of the molecular structure of peptides (mastoparan analogs) by a sequence of amino acids has been used to establish quantitative structure-activity relationships (QSARs) for their antibacterial activity. The data for the studied peptides were split three times into the training, calibration and test sets. The Monte Carlo method was used as a computational technique for QSAR models calculation. The statistical quality of QSAR for the antibacterial activity of peptides for the external validation set was: n=7, r(2)=0.8067, s=0.248 (split 1); n=6, r(2)=0.8319, s=0.169 (split 2); and n=6, r(2)=0.6996, s=0.297 (split 3). The stated statistical parameters favor the presented QSAR models in comparison to 2D and 3D descriptor based ones. The Monte Carlo method gave a reasonably good prediction for the antibacterial activity of peptides. The statistical quality of the prediction is different for three random splits. However, the predictive potential is reasonably well for all cases. The presented QSAR modeling approach can be an attractive alternative of 3D QSAR at least for the described peptides.

In silico prediction of the ß-cyclodextrin complexation based on Monte Carlo method.

In this study QSPR models were developed to predict the complexation of structurally diverse compounds with ß-cyclodextrin based on SMILES notation optimal descriptors using Monte Carlo method. The predictive potential of the applied approach was tested with three random splits into the sub-training, calibration, test and validation sets and with different statistical methods. Obtained results demonstrate that Monte Carlo method based modeling is a very promising computational method in the QSPR studies for predicting the complexation of structurally diverse compounds with ß-cyclodextrin. The SMILES attributes (structural features both local and global), defined as molecular fragments, which are promoters of the increase/decrease of molecular binding constants were identified. These structural features were correlated to the complexation process and their identification helped to improve the understanding for the complexation mechanisms of the host molecules.

Monte Carlo method based QSAR modeling of maleimide derivatives as glycogen synthase kinase-3ß inhibitors.

The Monte Carlo method was used for QSAR modeling of maleimide derivatives as glycogen synthase kinase-3ß inhibitors. The first QSAR model was developed for a series of 74 3-anilino-4-arylmaleimide derivatives. The second QSAR model was developed for a series of 177 maleimide derivatives. QSAR models were calculated with the representation of the molecular structure by the simplified molecular input-line entry system. Two splits have been examined: one split into the training and test set for the first QSAR model, and one split into the training, test and validation set for the second. The statistical quality of the developed model is very good. The calculated model for 3-anilino-4-arylmaleimide derivatives had following statistical parameters: r(2)=0.8617 for the training set; r(2)=0.8659, and r(m)(2)=0.7361 for the test set. The calculated model for maleimide derivatives had following statistical parameters: r(2)=0.9435, for the training, r(2)=0.9262 and r(m)(2)=0.8199 for the test and r(2)=0.8418, r(av)(m)(2)=0.7469 and ∆r(m)(2)=0.1476 for the validation set. Structural indicators considered as molecular fragments responsible for the increase and decrease in the inhibition activity have been defined. The computer-aided design of new potential glycogen synthase kinase-3ß inhibitors has been presented by using defined structural alerts.

Application of SMILES Notation Based Optimal Descriptors in Drug Discovery and Design.

SMILES notation based optimal descriptors as a universal tool for the QSAR analysis with further application in drug discovery and design is presented. The basis of this QSAR modeling is Monte Carlo method which has important advantages over other methods, like the possibility of analysis of a QSAR as a random event, is discussed. The advantages of SMILES notation based optimal descriptors in comparison to commonly used descriptors are defined. The published results of QSAR modeling with SMILES notation based optimal descriptors applied for various pharmacologically important endpoints are listed. The presented QSAR modeling approach obeys OECD principles and has mechanistic interpretation with possibility to identify molecular fragments that contribute in positive and negative way to studied biological activity, what is of big importance in computer aided drug design of new compounds with desired activity.

The Monte Carlo method based on eclectic data as an efficient tool for predictions of endpoints for nanomaterials - two examples of application.

The theoretical predictions of endpoints related to nanomaterials are attractive and more efficient alternatives for their experimental determinations. Such type of calculations for the "usual" substances (i.e. non nanomaterials) can be carried out with molecular graphs. However, in the case of nanomaterials, descriptors traditionally used for the quantitative structure--property/activity relationships (QSPRs/QSARs) do not provide reliable results since the molecular structure of nanomaterials, as a rule, cannot be expressed by the molecular graph. Innovative principles of computational prediction of endpoints related to nanomaterials extracted from available eclectic data (technological attributes, conditions of the synthesis, etc.) are suggested, applied to two different sets of data, and discussed in this work.

Monte carlo method-based QSAR modeling of penicillins binding to human serum proteins.

The binding of penicillins to human serum proteins was modeled with optimal descriptors based on the Simplified Molecular Input-Line Entry System (SMILES). The concentrations of protein-bound drug for 87 penicillins expressed as percentage of the total plasma concentration were used as experimental data. The Monte Carlo method was used as a computational tool to build up the quantitative structure-activity relationship (QSAR) model for penicillins binding to plasma proteins. One random data split into training, test and validation set was examined. The calculated QSAR model had the following statistical parameters: r(2) = 0.8760, q(2) = 0.8665, s = 8.94 for the training set and r(2) = 0.9812, q(2) = 0.9753, s = 7.31 for the test set. For the validation set, the statistical parameters were r(2) = 0.727 and s = 12.52, but after removing the three worst outliers, the statistical parameters improved to r(2) = 0.921 and s = 7.18. SMILES-based molecular fragments (structural indicators) responsible for the increase and decrease of penicillins binding to plasma proteins were identified. The possibility of using these results for the computer-aided design of new penicillins with desired binding properties is presented.

QSAR as a random event: a case of NOAEL.

Quantitative structure-activity relationships (QSAR) for no observed adverse effect levels (NOAEL, mmol/kg/day, in logarithmic units) are suggested. Simplified molecular input line entry systems (SMILES) were used for molecular structure representation. Monte Carlo method was used for one-variable models building up for three different splits into the "visible" training set and "invisible" validation. The statistical quality of the models for three random splits are the following: split 1 n = 180, r (2) = 0.718, q (2) = 0.712, s = 0.403, F = 454 (training set); n = 17, r (2) = 0.544, s = 0.367 (calibration set); n = 21, r (2) = 0.61, s = 0.44, r m (2) = 0.61 (validation set); split 2 n = 169, r (2) = 0.711, q (2) = 0.705, s = 0.409, F = 411 (training set); n = 27, r (2) = 0.512, s = 0.461 (calibration set); n = 22, r (2) = 0.669, s = 0.360, r m (2) = 0.63 (validation set); split 3 n = 172, r (2) = 0.679, q (2) = 0.672, s = 0.420, F = 360 (training set); n = 19, r (2) = 0.617, s = 0.582 (calibration set); n = 21, r (2) = 0.627, s = 0.367, r m (2) = 0.54 (validation set). All models are built according to OCED principles.

QSAR Models for the Reactivation of Sarin Inhibited AChE by Quaternary Pyridinium Oximes Based on Monte Carlo Method.

For three random splits, one-variable models of oximes reactivation of sarin inhibited acetylcholinesterase (logarithm of the AChE reactivation percentage by oximes with concentration of 0.001 M) have been calculated with CORAL software. The total number of considered oximes was 42. Simplified molecular input line entry system (SMILES) and hydrogen-suppressed graph (HSG) are used to represent the molecular structure. Using CORAL software by means of the calculation with Monte Carlo optimization of the so called correlation weights for the molecular fragments, optimal SMILES-based descriptors were defined, which are correlated with an endpoint for the training set. The predictability of these descriptors for an external test are estimated. In this study hybrid representation HSG together with SMILES was used. The "classic" scheme (i.e. split data into the training set and test set) of building up quantitative structure-activity relationships was employed. Computational experiments indicated that this approach can satisfactorily predict the desired endpoint. Best model had following statistical characteristics n=32, r2= 0.6012, s= 0.279, F= 45 for training and n=10, r2= 0.9301, s= 0.076, Rm2=0.9206 for test set.