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Recently, the retention time of pesticides has been considered an informative indicator of the ecological quality of pesticides. Two new possibilities are proposed for building pesticide retention time models using the CORAL program (http://www.insilico.eu/coral). Firstly, the possibility of being involved in modelling the correlation weights of local symmetry fragments in SMILES. Secondly, using two criteria of predictive potential (correlation ideality index and correlation intensity index) as a vector in Monte Carlo optimization for model building. Building models of the retention time of pesticides using the CORAL software confirms the effectiveness of these innovations. [ABSTRACT FROM AUTHOR]

Models of toxicity to tadpoles have been developed as single parameters based on special descriptors which are sums of correlation weights, molecular features, and experimental conditions. This information is presented by quasi-SMILES. Fragments of local symmetry (FLS) are involved in the development of the model and the use of FLS correlation weights improves their predictive potential. In addition, the index of ideality correlation (IIC) and correlation intensity index (CII) are compared. These two potential predictive criteria were tested in models built through Monte Carlo optimization. The CII was more effective than IIC for the models considered here. [ABSTRACT FROM AUTHOR]

The modified version of quasi-SMILES is studied. Unlike the previous ones, the new version allows building codes of experimental conditions in a user-friendly (easily interpreted) form. The quasi-SMILES can be a convenient basis for discussion between experimentalists and developers of models. The optimal descriptors for regression one-parameter models were calculated with the Monte Carlo method, using the vector of ideality of correlation. The vector of the ideality of correlation has two components: (i) the index of ideality of correlation (IIC) and (ii) the correlation intensity index (CII). Both the indices are components of the stochastic Monte Carlo process. The contribution of these indices is paradoxical: they improve the statistical quality of a model on the external validation set but to the detriment of the statistical quality of the model for the training set. Taking into account IIC and CII values for the Monte Carlo optimization gives an improvement of models of zeta potential of considered nanoparticles. The described approach is convenient for modelling the zeta potential of the considered nanoparticles. No less important is the universality of the use of quasi-SMILES as a means for studying the values of endpoints in the form of mathematical functions of not only the structures of the simulated objects (nanoparticles) but also the experimental conditions. [ABSTRACT FROM AUTHOR]

Data on Henry's law constants make it possible to systematize geochemical conditions affecting atmosphere status and consequently triggering climate changes. The constants of Henry's law are desired for assessing the processes related to atmospheric contaminations caused by pollutants. The most important are those that are capable of long-term movements over long distances. This ability is closely related to the values of Henry's law constants. Chemical changes in gaseous mixtures affect the fate of atmospheric pollutants and ecology, climate, and human health. Since the number of organic compounds present in the atmosphere is extremely large, it is desirable to develop models suitable for predictions for the large pool of organic molecules that may be present in the atmosphere. Here, we report the development of such a model for Henry's law constants predictions of 29,439 compounds using the CORAL software (2023). The statistical quality of the model is characterized by the value of the coefficient of determination for the training and validation sets of about 0.81 (on average). [ABSTRACT FROM AUTHOR]

The minimal inhibitory concentrations (pMIC) are a valuable measure of the biological activity of polypeptides. Numerical data on the pMIC are necessary to systematize knowledge on polypeptides' biochemical behaviour. The model of negative decimal logarithm of pMIC of polypeptides in the form of a mathematical function of a sequence of amino acids is suggested. The suggested model is based on the so-called correlation weights of amino acids together with the correlation weights of fragments of local symmetry (FLS). Three kinds of the FLS are considered: (i) three-symbol fragments '...xyx...', (ii) four-symbol fragments '...xyyx...', and (iii) five-symbol fragments '...xyzyx...'. The models built using the Monte Carlo technique improved by applying the index of ideality of correlation (IIC) and correlation intensity index (CII). [ABSTRACT FROM AUTHOR]

The assessment of cardiotoxicity is a persistent problem in medicinal chemistry. Quantitative structure–activity relationships (QSAR) are one possible way to build up models for cardiotoxicity. Here, we describe the results obtained with the Monte Carlo technique to develop hybrid optimal descriptors correlated with cardiotoxicity. The predictive potential of the cardiotoxicity models (pIC50, Ki in nM) of piperidine derivatives obtained using this approach provided quite good determination coefficients for the external validation set, in the range of 0.90–0.94. The results were best when applying the so-called correlation intensity index, which improves the predictive potential of a model. [ABSTRACT FROM AUTHOR]

Quantitative structure-property/activity relationships (QSPRs/QSARs) are a tool of modern theoretical and computational chemistry. The self-consistent model system is both a method to build up a group of QSPR/QSAR models and an approach to checking the reliability of these models. Here, a group of models of pesticide toxicity toward Daphnia magna for different distributions into training and test sub-sets is compared. This comparison is the basis for formulating the system of self-consistent models. The so-called index of the ideality of correlation (IIC) has been used to improve the above models' predictive potential of pesticide toxicity. The predictive potential of the suggested models should be classified as high since the average value of the determination coefficient for the validation sets is 0.841, and the dispersion is 0.033 (on all five models). The best model (number 4) has an average determination coefficient of 0.89 for the external validation sets (related to all five splits). [ABSTRACT FROM AUTHOR]

Background: The system of self-consistent models is an attempt to develop a tool to assess the predictive potential of various approaches by considering a group of random distributions of available data into training and validation sets. Considering many different splits is more informative than considering a single model. Methods: Models studied here build up for solubility of fullerenes C60 and C70 in different organic solvents using so-called quasi-SMILES, which contain traditional simplified molecular input-line entry systems (SMILES) incorporated with codes that reflect the presence of C60 and C70. In addition, the fragments of local symmetry (FLS) in quasi-SMILES are applied to improve the solubility's predictive potential (expressed via mole fraction at 298'K) models. Results: Several versions of the Monte Carlo procedure are studied. The use of the fragments of local symmetry along with a special vector of the ideality of correlation improves the predictive potential of the models. The average value of the determination coefficient on the validation sets is equal to 0.9255 ± 0.0163. Conclusions: The comparison of different manners of the Monte Carlo optimization of the correlation weights has shown that the best predictive potential was observed for models where both fragments of local symmetry and the vector of the ideality of correlation were applied. [ABSTRACT FROM AUTHOR]

The octanol–water partition coefficient (logP) of platinum (IV) complexes is an essential indicator of the biological activity of coordination compounds in the aspect of potential application for drug design. The additive scheme of the logP simulation using a Simplified Molecular Input-Line Entry System (SMILES) was tested in a previous study. Here, it is proposed to take into account fragments of local symmetry (FLS) in SMILES. FLS are recognized as groups "xyx," "xyyx," and "xyzyx." The CORAL software (www.insilico.eu/coral) generates optimal descriptors. The optimal descriptor is calculated using the so-called correlation weights for different SMILES fragments. Expanding the list of SMILES fragments by adding the aforementioned local symmetry markedly improves the predictive potential of models for the n-octanol–water partition coefficient of platinum (IV) coordination compounds (without FLS, the average determination coefficient for validation set is 0.87 ± 0.04, using FLS, the average becomes 0.91 ± 0.05). Thus, the involving fragments of local symmetry can improve the predictive potential of logP-models. [ABSTRACT FROM AUTHOR]

Context: To apply the quantitative relationships "structure-endpoint" approach, the reliability of prediction is necessary but sometimes challenging to achieve. In this work, an attempt is made to accomplish the reliability of forecasts by creating a set of random partitions of data into training and validation sets, followed by constructing random models. A system of random models for a helpful approach should be self-consistent, giving a similar or at least comparable statistical quality of the predictions for models obtained using different splits of available data into training and validation sets. Method: The carried out computer experiments aimed at obtaining blood–brain barrier permeation models showed that, in principle, can be used such an approach (the Monte Carlo optimization of the correlation weights for different molecular features) for the above purpose taking advantage of specific algorithms to optimize the modelling steps with applying of new statistical criteria such as the index of ideality of correlation (IIC) and the correlation intensity index (CII). The results so obtained are good and better than what was reported previously. The suggested approach to validation of models is non-identic to traditionally applied manners of the checking up models. The concept of validation can be used for arbitrary models (not only for models of the blood–brain barrier). [ABSTRACT FROM AUTHOR]

Algorithms of the simulation of the anticancer activity of nanoparticles under different experimental conditions toward cell lines A549 (lung cancer), THP-1 (leukemia), MCF-7 (breast cancer), Caco2 (cervical cancer), and hepG2 (hepatoma) have been developed using the quasi-SMILES approach. This approach is suggested as an efficient tool for the quantitative structure–property–activity relationships (QSPRs/QSARs) analysis of the above nanoparticles. The studied model is built up using the so-called vector of ideality of correlation. The components of this vector include the index of ideality of correlation (IIC) and the correlation intensity index (CII). The epistemological component of this study is the development of methods of registration, storage, and effective use of experimental situations that are comfortable for the researcher-experimentalist in order to be able to control the physicochemical and biochemical consequences of using nanomaterials. The proposed approach differs from the traditional models based on QSPR/QSAR in the following respects: (i) not molecules but experimental situations available in a database are considered; in other words, an answer is offered to the question of how to change the plot of the experiment in order to achieve the desired values of the endpoint being studied; and (ii) the user has the ability to select a list of controlled conditions available in the database that can affect the endpoint and evaluate how significant the influence of the selected controlled experimental conditions is. [ABSTRACT FROM AUTHOR]

A simulation of the effect of metal nano-oxides at various concentrations (25, 50, 100, and 200 milligrams per millilitre) on cell viability in THP-1 cells (%) based on data on the molecular structure of the oxide and its concentration is proposed. We used a simplified molecular input-line entry system (SMILES) to represent the molecular structure. So-called quasi-SMILES extends usual SMILES with special codes for experimental conditions (concentration). The approach based on building up models using quasi-SMILES is self-consistent, i.e., the predictive potential of the model group obtained by random splits into training and validation sets is stable. The Monte Carlo method was used as a basis for building up the above groups of models. The CORAL software was applied to building the Monte Carlo calculations. The average determination coefficient for the five different validation sets was R2 = 0.806 ± 0.061. [ABSTRACT FROM AUTHOR]

Binding to acetylcholinesterase (AChE k1) may cause toxic effects in humans. Organophosphates simultaneously are both dangerous and useful substances. Dangerous since they are employed in chemical warfare and useful when they are applied as pesticides. Here, we suggest the models for organophosphates binding to AChE k1 developed via representing the molecular structure by a simplified molecular input-line entry system using so-called optimal descriptors calculated with the Monte Carlo technique using the Correlation and Logic (CORAL) free software available on the Internet (). Quantitative structure-activity relationships (QSARs) serve to develop predictive models for organophosphates. The predictive potential of these models is quite good: the determination coefficient for the validation set ranged from 0.87 to 0.90. These models were built up according to the principle 'QSARs is a random event', that is, predictive potential of an approach should be checked up with several splits of available data into the training and test sets. The special scheme of mechanistic interpretation definition is represented. The mechanistic interpretation is based on probabilities of molecular features to be in the sub-group of promoters of increase for endpoint or in sub-group of promoters of it is decrease. [ABSTRACT FROM AUTHOR]

Robust quantitative structure-activity relationships (QSARs) for hBACE-1 inhibitors (pIC50) for a large database (n = 1706) are established. New statistical criteria of the predictive potential of models are suggested and tested. These criteria are the index of ideality of correlation (IIC) and the correlation intensity index (CII). The system of self-consistent models is a new approach to validate the predictive potential of QSAR-models. The statistical quality of models obtained using the CORAL software () for the validation sets is characterized by the average determination coefficient R2v= 0.923, and RMSE = 0.345. Three new promising molecular structures which can become inhibitors hBACE-1 are suggested. [ABSTRACT FROM AUTHOR]

Quantitative structure–property/activity relationships (QSPRs/QSARs) are a component of modern natural science. The system of self-consistent models is a specific approach to build up QSPR/QSAR. A group of models of refractive index for different distributions in training and test sets is compared. This comparison is a basis to formulate the system of self-consistent models. The so-called index of ideality of correlation (IIC) has been used to improve the predictive potential of models of the refractive index of different polymers (n = 255). The predictive potential of the suggested models is high since the average value of the determination coefficient for the validation set is 0.885. In addition, the system of self-consistent models may be applied as a tool to assess the predictive potential of an arbitrary QSPR-approach. The statistical characteristics of the best model are the following: n = 57, R2 = 0.7764, RMSE = 0.039 (active training set) and n = 57, R2 = 0.9028, RMSE = 0.019 (validation set). [ABSTRACT FROM AUTHOR]

The development of antiviral agents against SARS-CoV-2 is necessary. Specific drugs for SARS-CoV-2 are not available. In such circumstances, the computational methods of drug discovery can be an attractive addition to usual experiments for drug discovery. Here, the so-called system of semi-correlations was applied as a tool to build up predictive models for biological activity. The semi-correlation system has one traditional continuous variable and a second variable with two values: 1 for active compounds, and 0 for inactive compounds. Therefore, the semi-correlation system is a tool for building a categorical (active/inactive) model for biological activity. The semi-correlation system used to build models for providing antiviral effects for SARS-CoV-2 inhibitors has demonstrated adherence to statistical norms. For the validation set, the best model has a Matthew correlation coefficient of 0.95. Checking the predictive potential of the models built with random splits confirms that most of them exhibit quite satisfactory statistical quality. [ABSTRACT FROM AUTHOR]

Quantitative structure-property/activity relationships (QSPRs/QSARs) are an important component of modern science. Validation of the QSPR/QSAR is the basis for applying. The system of self-consistent models is a new approach to validate QSPR/QSAR. The principle 'QSAR is a random event' means that an approach may be recognized as robust only if the statistical characteristics of models obtained by this approach for different splits (training/test) are reproduced. The above principle applies to the case of the nano-QSAR, also. Here, the cellular uptake of nanoparticles in pancreatic cancer cells examines as the endpoint. Groups of models for different splits (training/test) are compared. This comparison gives the possibility to formulate the system of self-consistent models as a way to assess the predictive potential for an arbitrary QSPR/QSAR and/or nano-QSPR/QSAR. The correlation intensity index (CII) has been tested as a tool to improve the quality of models for the cellular uptake of nanoparticles in pancreatic cancer cells (PaCa2). It has shown, that the CII can be useful, but only incorporating with the Index of ideality of correlation (IIC). [ABSTRACT FROM AUTHOR]

Atom-pairs proportions are the transparent quality of a molecule: if a molecule has two atoms of oxygen and three atoms of nitrogen, the atom-pair atom1-atom2 can be expressed as a code "atom1-atom2-n1-n2," indicating the different atoms and their numbers. These codes for a group of atoms (nitrogen, oxygen, sulfur, phosphorus, fluorine, chlorine, bromine, as well as double and triple covalent bonds) are applied to build up the so-called optimal molecular descriptor calculated with special coefficients named correlation weights of corresponding pairs. The numerical data on the correlation weights are calculated by the Monte Carlo technique using the CORAL software (http://www.insilico.eu/coral). The one-variable model for melting points of 8653 different organic compounds is characterized by the following statistical quality: n=6483, r2=0.6452, RMSE=61.9°C; n=2170, r2=0.7941, RMSE=39.2°C. [ABSTRACT FROM AUTHOR]

• Quantitative structure - activity relationships (QSAR) is a random event. • QSAR must be checked up in several distributions into training and validation sets. • Models for skin sensitivity built up using the above principles are represented. • New criteria of the predictive potential of QSAR-models are demonstrated. Some new products, which include common personal-care products, drugs, household items, can be hazardous in aspect personal care products/cosmetics and their ingredients (i.e. the above can effect human skin). International organizations (e.g. the Organisation for Economic Co-operation and Development-OECD) recommend evaluating individual ingredients when assessing the safety of personal care or cosmetic products. Thus, checking up that "popular at the market" substances are non-toxic, do not penetrate into or through normal or compromised human skin, and therefore, pose no risk to human health is an essential element of modern toxicology. The development of reliable models of toxicological endpoints is a tool to carry out the above checking up via quantitative structure–activity relationships (QSARs). The reliability of the QSAR is the current task of mathematical statistics. Recently, the index of ideality of correlation (IIC) and correlation intensity index (CII) were suggested as criteria of predictive potential (i.e. reliability) of QSAR-models. Here, the abilities of these criteria were studied for the case of building up models for skin sensitivity (LLNA, local lymph node assay). Computational experiments have confirmed that the IIC demonstrates an obvious ability to improve the predictive potential of models of skin sensitization. The applying of the CII for the case of skin sensitization also improves the quality of the model. However, the best models for skin sensitization were observed if the above-mentioned criteria are applied jointly (n = 268; R2 = 0.60; RMSE = 0.63). [ABSTRACT FROM AUTHOR]

Fullerenes are materials which have many applications as in the field of chemical technology as well as in the field of biochemistry and medicine. Solubility of fullerenes in different solvents has been studied many times in the field of computational chemistry. However, analysis of different approaches which able help to solve the task of prediction of solubility fullerenes remains attractive and very important direction of scientific activity. The correlation intensity index (CII) is a new criterion of the predictive potential of models. The applying of CII together with Index of Ideality Correlation (IIC) in modeling of fullerenes solubility in various solvents by the Monte Carlo method using the CORAL software () indicates that applying of the CII improves the predictive potential of these models. These models can be applied for systematization of ecological, biochemical, and medicinal knowledge related to applying of fullerenes. This systematization gradually becomes a factor of key importance, since the applying of the fullerenes expanded day by day. [ABSTRACT FROM AUTHOR]

Predictive models for toxicity to Tetrahymena pyriformis are an important component of natural sciences. The present study aims to build up a predictive model for the endpoint using the so-called index of ideality of correlation (IIC). Besides, the comparison of the predictive potential of these models with the predictive potential of models suggested in the literature is the task of the present study. The Monte Carlo technique is a tool to build up the predictive model applied in this study. The molecular structure is represented via a simplified molecular input-line entry system (SMILES). The IIC is a statistical characteristic sensitive to both the correlation coefficient and mean absolute error. Applying of the IIC to build up quantitative structure–activity relationships (QSARs) for the toxicity to Tetrahymena pyriformis improves the predictive potential of those models for random splits into the training set and the validation set. The calculation was carried out with CORAL software (). The statistical quality of the suggested models is incredibly good for the external validation set, but the statistical quality of the models for the training set is modest. This is the paradox of ideal correlation, which is obtained with applying the IIC. The Monte Carlo technique is a convenient and reliable way to build up a predictive model for toxicity to Tetrahymena pyriformis. The IIC is a useful statistical criterion for building up predictive models as well as for the assessment of their statistical quality. [ABSTRACT FROM AUTHOR]

Optimal descriptors calculated with SMILES represented a structure of monomer units applied to build up a model of glass transition temperatures of diverse polymers. Quantitative structure-property relationships (QSPRs) were established for the above dataset. The statistical quality of the model of glass transition temperatures is quite good. The simplified molecular input-line entry system (SMILES) has been used to represent the molecular structure of corresponding monomers. The hybrid optimal descriptors calculated with the so-called correlation weights of molecular features extracted from SMILES and molecular hydrogen-suppressed graph (HSG) were used as the basis of the one-variable model. The index of ideality of correlation (IIC) is a new criterion of the predictive potential of the QSPR model. Here, the applicability of the IIC as a tool to improve the predictive potential of the model for glass transition temperatures is confirmed. [ABSTRACT FROM AUTHOR]

Computational prediction of HIV-1 protease inhibitor via quantitative structure–activity relationships (QSARs) is a popular study in the field of computational chemistry. The aim of the present study was building up of QSAR models for anti-HIV activity by means of the CORAL software (http://www.insilico.eu/coral). Applying of correlation weights for five and six-member molecular rings as components of the target function in the Monte Carlo optimization that is aimed to build up correlation between activity of HIV-1 protease inhibitors expressed as pIC50 = lg[1/(IC50 × 109)] and optimal descriptor improves the predictive potential. Simplified molecular input-line entry system (SMILES) is used as the representation of the molecular structure of HIV-1 protease inhibitors for the QSAR analysis. New criterion of predictive potential so-called index of ideality of correlation (IIC) has been appllied to improve the model for HIV-1 protease inhibitors activity. High correlation coefficients were observed between the experimental and predicted anti-HIV activity. Applying of special ring code as component of the Monte Carlo calculation significantly improves the statistical quality of the model. Furthermore, applying of the IIC as component of the Monte Carlo optimization improves the predictive potential of the CORAL models. The presence of the rings and the quality of these are very important molecular features which are able to improve statistical quality of model for anti-HIV activity. In addition, the ability of IIC to improve predictive potential of a model has been confirmed. [ABSTRACT FROM AUTHOR]

Reliable information related to the flash point of ternary mixtures assists in the rational classification of different ternary mixtures of liquids. Hence, dependable computational models for the predictions of the abovementioned endpoint can be useful. A simplified molecular input-line entry system (SMILES) is the representation of the molecular structure. Quasi-SMILES is the expansion of traditional SMILES by means of additional symbols that reflect ''eclectic'', which are able to influence the physicochemical behaviour of substances. The application of quasi-SMILES to build up a model for the flammability of ternary liquid mixtures has indicated that the approach provides a very good model for the flash points of the ternary mixtures of organic substances. The index of ideality of correlation (IIC) is a criterion of the predictive potential of the QSPR/QSAR models. The attempts of applying IIC to improve models for the flammability of ternary liquid mixtures confirm the applicability of this criterion to improve the predictive potential of the above-mentioned models. [ABSTRACT FROM AUTHOR]

• A model for the physicochemical behaviour of peptides is suggested. • Sequences of amino acids applying as the quasi-SMILES. • The model is based on optimal descriptors calculated with quasi-SMILES. • Measures of symmetry and chaos improve building up the model. • The approach is checking up with several random splits. Most of the protein interactions rely on small domains binding to short peptides. However, neither the number of potential interactions mediated by each domain nor the degree of affinity at a whole proteome level has been studied. Peptide segments involved in 14–3–3 domain-medicated cellular signalling networks were collected from sequence-based datasets of domain-peptide interaction affinities. The affinities peptides measured represented by the Boehringer light units (logBLU) considered as the endpoint for the development of peptide quantitative structure-property/activity relationships (p-QSPR/QSARs). The sequences of amino acids are examined as the structure of the peptide. This approach allows the rational simulate interaction of proteomic systems via amino acid configurations in proteins. Adding the contributions of local symmetry and chaos extracted from the amino acid sequences described here increases the value of the average (over seven different splits into training and control) determination coefficient for the external validation set and reduces its dispersion. [Display omitted] [ABSTRACT FROM AUTHOR]

Correlations of criteria of predictive potential of models for solubility of fullerenes C[60] and C[70] observed for the calibration (visible) set with the determination coefficient of corresponding models for validation sets (external, invisible). The Index of Ideality of Correlation (IIC) gave the best correlation with the determination coefficient for the validation set. The IIC was involved in the Monte Carlo optimization used to build up one-variable quantitative structure-property relationships (QSPR) to predict the solubility of fullerenes C[60] and C[70]. This considerably improved the predictive potential of models for this solubility. According to principle "QSPR is a random event", corresponding computational experiments, which are aimed to build up model, were carried out for group of ten random splits into the training and validation sets. These calculations are source of usual data related to assessment of predictive models, such as the statistical quality for the training and validation sets and mechanistic interpretation of models in terms of structural alerts which are promoter of increase (or decrease) for an endpoint. [ABSTRACT FROM AUTHOR]

The CORAL software (http://www.insilico.eu/coral) was suggested as a tool to build up quantitative structure–property/activity relationships (QSPRs/QSARs). This software is based on conception "a QSPR/QSAR model should be interpreted as a random event." This is reflection of fact: different distributions into the training set (substances involved in modeling process) and the validation set (substances, which are not known at the moment of the modeling process) give models with significant dispersion in the statistical quality of the QSPR/QSAR. Results of experiments with the software and possible ways of further improvement of this software are discussed. The most attractive new ways to estimate predictive potential of the CORAL model seem to be the following ones: (i) index of ideality of correlation and (ii) correlation contradiction index. These can be also proposed as criteria of predictive potential for arbitrary QSPR/QSAR. [ABSTRACT FROM AUTHOR]

The interpretation of the mutagenic potential of silver nanoparticles as a mathematical function of (i) dose; (ii) coating; and (iii) type of mutagenicity (TA98 and TA100) gives quantitative models with good statistical quality. So-called quasi-SMILES are used to represent examined objects (silver nanoparticles under different conditions) for building up models. Simplified molecular input-line entry systems (SMILES) is a well-known sequence of symbols for representation of the molecular structure. Quasi-SMILES is a similar sequence of symbols for representation of experimental conditions. The Correlation Contradiction Index (CCI) calculated with data on the calibration set gives possibility to predict quality of correlation of "experimental vs. calculated values of endpoint" for external validation set. Unlabelled Image • The number of colonies per plate (N cp) examined as measure of the mutagenicity. • Quasi-SMILES technique is applied to build up model for N cp. • Index of Ideality of Correlation is tested as a criterion of predictive potential. • Correlation Contradiction Index tested as a criterion of predictive potential. [ABSTRACT FROM AUTHOR]

• Predictive models for activity of peptides are suggested. • These models are a mathematical function of amino acids of peptide. • The Index of ideality of correlation (IIC) is a criterion of predictive potential. • Applying of IIC improves statistical quality for validation set. Sequences of one-symbol abbreviations of amino acids are applied as the basis to build up predictive model of Angiotensin converting enzyme (ACE) inhibitory activity of dipeptides and antibacterial activity of group of polypeptides. The developed models are one-variable correlations between biological activity and descriptors calculated with so-called correlation weights of amino acids. The numerical data on the correlation weights are obtained by the Monte Carlo method. The Index of Ideality of Correlation (IIC) is a mathematical function of (i) the determination coefficient; and (ii) sums of positive and negative values of "observed minus predicted" endpoints values. The obtained results confirm that IIC can be applied to improve predictive potential of models for ACE inhibitor activity of dipeptides and antibacterial activity of polypeptides. [ABSTRACT FROM AUTHOR]

The interpretation of mode of action for GABAA receptor modulator activity is an important task of medicinal chemistry. The computational elucidation of the modulator activity is one of the ways to solve the above task. So-called semi-correlation is a tool for prediction of GABAA receptor modulator activity. The semi-correlation is based on the Monte Carlo method. This approach is to build up categorical classification models into two classes: (i) active and (ii) inactive. The CORAL software (http://www.insilico.eu/coral) can be used to build up the semi-correlations. The statistical quality of models (for external validation sets) based on semi-correlation has the range of Matthews correlation coefficient (MCC) is 0.72–1.00 for 30 random splits of all available data (n = 210) into the training and validation sets. In contrast to existing approaches, the predictive CORAL models give prediction using solely data on molecular architecture (represented by simplified molecular input-line entry system = SMILES) and available experimental data on endpoints. Suggested models for prediction of GABAA receptor modulator activity are built up according to the OECD principles. Thus, the approach based on the semi-correlation can be a useful tool for studying of the GABAA receptor modulators activity. [ABSTRACT FROM AUTHOR]

Abstract 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. Graphical abstract Unlabelled Image Highlights • The index of Ideality of Correlation (IIC) is a criterion of predictive potential. • The IIC was used to build up models for endpoints related to human health. • The IIC was used to build up models for endpoints related to environmental risk. • The use of the IIC improves the statistical quality of the models. [ABSTRACT FROM AUTHOR]

The CORAL software is a tool to build up quantitative structure-property/activity relationships (QSPRs/QSARs). The project of updated version of the CORAL software is discussed in terms of practical applications for building up various models. The updating is the possibility to improve the predictive potential of models using the so-called Index of Ideality of Correlation (IIC) as a criterion of the predictive potential for QSPR/QSAR models. Efficacy of the IIC is examined with three examples of building up QSARs: (i) models for anticancer activity; (ii) models for mutagenicity; and (iii) models for toxicity of psychotropic drugs. The validation of these models has been carried out with several splits into the training, invisible training, calibration, and validation sets. The ability of IIC to be an indicator of predictive potential of QSAR models is confirmed. The updated version of the CORAL software (CORALSEA-2017, http://www.insilico.eu/coral) is available on the Internet. [ABSTRACT FROM AUTHOR]

Most quantitative structure-property/activity relationships (QSPRs/QSARs) techniques involve using different programs separately for generating molecular descriptors and separately for building models based on available descriptors. Here, the capabilities of the CORAL program are evaluated. A user of the program should apply as the basis for models the representation of the molecular structure by means of the simplified molecular input-line entry system (SMILES) as well as experimental data on the endpoint of interest. The local symmetry of SMILES is a novel composition of symmetrically represented symbols, which are three ' xyx ', four ' xyyx ', or five symbols ' xyzyx '. We updated our CORAL software using this optimal, new flexible descriptor, sensitive to the symmetric composition of a specific part of the molecule. Computational experiments have shown that taking account of these attributes of SMILES can improve the predictive potential of models for the mutagenicity of nitroaromatic compounds. In addition, the above computational experiments have confirmed the advantage of using the index of ideality of correlation (IIC) and the correlation intensity index (CII) for Monte Carlo optimization of the correlation weights for various attributes of SMILES, including the local symmetry. The average value of the coefficient of determination for the validation set (five different models) without fragments of local symmetry is 0.8589 ± 0.025, whereas using fragments of local symmetry improves this criterion of the predictive potential up to 0.9055 ± 0.010. • Local symmetry fragments (LSF) are suggested as an additional base for optimal descriptor. • Optimal descriptors updated by LSF provide improved predictive potential. • The new approach checked with a group of random splits into training and validation sets. [ABSTRACT FROM AUTHOR]

Mutagenicity is one of the most dangerous properties from the point of view of medicine and ecology. Experimental determination of mutagenicity remains a costly process, which makes it attractive to identify new hazardous compounds based on available experimental data through in silico methods or quantitative structure-activity relationships (QSAR). A system for constructing groups of random models is proposed for comparing various molecular features extracted from SMILES and graphs. For mutagenicity (mutagenicity values were expressed by the logarithm of the number of revertants per nanomole assayed by Salmonella typhimurium TA98-S9 microsomal preparation) models, the Morgan connectivity values are more informative than the comparison of quality for different rings in molecules. The resulting models were tested with the previously proposed model self-consistency system. The average determination coefficient for the validation set is 0.8737 ± 0.0312. [Display omitted] • QSAR model for mutagenicity (decimal logarithm revertant/nanomole) suggested. • The model is based on optimal descriptors calculated with SMILES. • The optimization of the descriptors is carried out by the Monte Carlo method. • Improving the model can be reached by considering topological connectivity in a graph. • The approach is checked up with several random splits in training and validation sets. [ABSTRACT FROM AUTHOR]

• Removal rates of pharmaceuticals are examined as an endpoint. • Predictive models for this endpoint are built up. • Molecular structure and physicochemical conditions are used to build up these models. • The statistical quality of these models is good. • These models are built up in accordance to OECD principles. Removal rates for pharmaceuticals and dyes have been modelled using so-called quasi-SMILES, which are representations of the above processes. Quasi-SMILES is an extend of the simplified molecular input-line entry system (SMILES) where, in addition to information on the molecular structure, the codes of physicochemical conditions are included. In addition, these codes can be a representation for various eclectic circumstances, such as presence or absence of light, impact of x-Rays beems, as well seasons (e.g. summer—winter). Analysis of quasi-SMILES of pharmaceuticals by Monte Carlo technique, applied via the CORAL software, shows it is possible to build predictive models using a one-variable correlation between optimal (flexible) descriptors and the removal rates. Removal rates used to build the model were obtained from recent publications including seasonal differences. The statistical characteristics of the best models for removal rates of pharmaceuticals and dyes are quite good for external validation set. [ABSTRACT FROM AUTHOR]

Removal rates for pharmaceuticals and dyes have been modelled using so-called quasi-SMILES, which are representations of the above processes. Quasi-SMILES is an extend of the simplified molecular input-line entry system (SMILES) where, in addition to information on the molecular structure, the codes of physicochemical conditions are included. In addition, these codes can be a representation for various eclectic circumstances, such as presence or absence of light, impact of x-Rays beems, as well seasons (e.g. summer-winter). Analysis of quasi-SMILES of pharmaceuticals by Monte Carlo technique, applied via the CORAL software, shows it is possible to build predictive models using a one-variable correlation between optimal (flexible) descriptors and the removal rates. Removal rates used to build the model were obtained from recent publications including seasonal differences. The statistical characteristics of the best models for removal rates of pharmaceuticals and dyes are quite good for external validation set. [ABSTRACT FROM AUTHOR]

The basic task of the drug discovery is the establishing of molecular structure of new pharmaceutical agents. To define the molecular structure is only half of the way to new drug. The transport of active molecules to appropriate targets in an organism should be elucidated in details. The selection of polymeric structures playing the role of basis for transport of therapeutic agents into the body is one of the ways to solve the task. Drug loading capacity (DLC) and critical micelle concentration (CMC) are measures of ability of “polymer-micelle” systems to be suitable for the process of the transport of therapeutic agents into an organism. Polymeric micelles are a type of complex multi-phase and multicomponent chemical process and can be used to transport drug into an organism. Prediction of ability of “micelle-polymer” systems to be a tool for transport of therapeutic agents to targets in organism is an important task. Models, which are a mathematical function of available eclectic information about architecture of micelles and polymers, are suggested. The eclectic data are represented via the so-called quasi-simplified molecular input-line entry system (SMILES), which are analogy of traditional SMILES. The quasi-SMILES contain some additional information besides the molecular architecture (physicochemical and biochemical conditions). Predictive potential of these models is good. [ABSTRACT FROM AUTHOR]

The purpose of this study was the estimation of ability of the so-called optimal descriptors calculated to be a tool to predict the antimicrobial activity of large pool of peptides. Traditional simplified molecular input-line entry system (SMILES) is an efficient tool to represent the molecular structure of different compounds. Quasi-SMILES represents an extension of traditional SMILES. This approach provides the possibility to involve different eclectic conditions related to analyzed endpoint in the modelling process. In addition, the quasi-SMILES can be used to represent structure of peptides via abbreviations of corresponding amino acids. In this study, quasi-SMILES represents sequences of amino acids in peptides that were tested as the basis to predict antimicrobial activity of 1581 peptides. Predictive potential of binary classification for antimicrobial activity for different splits is quite good when it comes to the training, invisible training, calibration, and validation sets. For the external validation sets, the statistical criteria are ranged: (i) sensitivity 0.82–097; (ii) specificity 0.88–0.99; (iii) accuracy 0.87–0.98; and (iv) Matthews correlation coefficient 0.73–0.97. The suggested optimal descriptors calculated with data on composition of amino acids in peptides can be a tool to predict antimicrobial activity of peptides. [ABSTRACT FROM AUTHOR]

Current clinical therapeutics for the treatment of drug-resistant bacteria are mostly restricted to β-lactam antibiotics in combination with β-lactamase inhibitors. However, with the occurrence of novel pathogens, this strategy has proven to be insufficient; therefore, novel approaches for the treatment of infections must be applied. Filamentous temperature-sensitive protein Z (FtsZ) is one of the appealing targets for the design of antimicrobial therapeutics. The present study aims to develop QSAR models for a series of 3-substituted benzamide derivatives as FtsZ inhibitors. The QSAR models were calculated on the basis of optimal molecular descriptors based on the SMILES notation with the Monte Carlo method as a model developer. The statistical quality of the developed model, including robustness and predictability, was good, and it was tested with different methods. Molecular fragments responsible for the increases and decreases of the studied activity were defined. The computer-aided design of new compounds as potential FtsZ inhibitors was presented. The molecular docking study was used for the final assessment of the developed QSAR model and designed novel inhibitors, and the obtained results were in excellent correlation with the results from QSAR studies. The presented study can be useful in the search for novel antibacterial agents based on FtsZ inhibition. [ABSTRACT FROM AUTHOR]

The CORAL software has been applied to the development of classification models for pesticides relative to two pharmacokinetic properties in humans: (i) gastro-intestinal absorption; and (ii) blood-brain barrier permeation. These models were built up using categorical data on pesticide absorption and brain permeation split into training, invisible training, calibration and external validation sets using Monte Carlo simulations. The models were assessed using several random splits into the training and validation sets. Optimal SMILES-based descriptors sensitive to the presence of different chemical elements and types of covalent bonds have been used to build up models. The range of Matthews correlation coefficient for suggested models is 0.64–0.75. The perspectives of studied approach as a tool to build up models for pharmacokinetic properties of chemicals is discussed. The models are built up according to OECD principles. [ABSTRACT FROM AUTHOR]

The aim of the present work is an attempt to define computable measure of similarity between different endpoints. The similarity of structural alerts of different biochemical endpoints can be used to solve tasks of medicinal chemistry. Optimal descriptors are a tool to build up models for different endpoints. The optimal descriptor is calculated with simplified molecular input-line entry system (SMILES). A group of elements (single symbol or pair of symbols) can represent any SMILES. Each element of SMILES can be represented by so-called correlation weight i.e. coefficient that should be used to calculate descriptor. Numerical data on the correlation weights are calculated by the Monte Carlo method, i.e. by optimization procedure, which gives maximal correlation coefficient between the optimal descriptor and endpoint for the training set. Statistically stable correlation weights observed in several runs of the optimization can be examined as structural alerts, which are promoters of the increase or the decrease of a biochemical activity of a substance. Having data on several runs of the optimization correlation weights, one can extract list of promoters of increase and list of promoters of decrease for an endpoint. The study of similarity and dissimilarity of the above lists has been carried out for the following pairs of endpoints: (i) mutagenicity and anticancer activity; (ii) mutagenicity and blood brain barrier; and (iii) blood brain barrier and anticancer activity. The computational experiment confirms that similarity and dissimilarity for pairs of endpoints can be measured. [ABSTRACT FROM AUTHOR]

Predictive model of logP for Pt(II) and Pt(IV) complexes built up with the Monte Carlo method using the CORAL software has been validated with six different splits into the training and validation sets. The improving of the predictive potential of models for six different splits has been obtained using so-called index of ideality of correlation. The suggested models give possibility to extract molecular features, which cause the increase or vice versa decrease of the logP. [ABSTRACT FROM AUTHOR]

Continuous QSAR models have been developed and validated for the prediction of no-observed-adverse-effect (NOAEL) in rats, using training and test sets from the Fraunhofer RepDose® database and EFSA’s Chemical Hazards Database: OpenFoodTox. This paper demonstrates that the HARD index, as an integrated attribute of SMILES, improves the prediction power of NOAEL values using the continuous QSAR models and Monte Carlo simulations. The HARD-index is a line of eleven symbols, which represents the presence, or absence of eight chemical elements (nitrogen, oxygen, sulfur, phosphorus, fluorine, chlorine, bromine, and iodine) and different kinds of chemical bonds (double bond, triple bond, and stereo chemical bond). Optimal molecular descriptors calculated with the Monte Carlo technique (maximization of correlation coefficient between the descriptor and endpoint) give satisfactory predictive models for NOAEL. Optimal molecular descriptors calculated in this way with the Monte Carlo technique (maximization of correlation coefficient between the descriptor and endpoint) give amongst the best results available in the literature. The models are built up in accordance with OECD principles. [ABSTRACT FROM AUTHOR]

New criterion of the predictive potential of quantitative structure - property/activity relations (QSPRs/QSARs) named Index of Ideality of Correlation ( IIC) is suggested. This criterion is calculated using the correlation coefficient between experimental and calculated values of an endpoint for the calibration set, taking into account positive and negative differences between experimental and calculated values of the endpoint. Using this criterion improves the predictive potential of QSAR models of toxicity towards fathead minnow ( Pimephales promelas). Comparison of IIC with other metrics of predictive potential shows that (i) the IIC is not identic to other metrics; and (ii) the IIC seems more reliable criterion at least for examined data on toxicity towards fathead minnow. [ABSTRACT FROM AUTHOR]

Quantitative structure - activity relationships (QSARs) for carcinogenicity (rats , TD 50 ) have been built up using the CORAL software. Different molecular features, which are extracted from simplified molecular input-line entry system (SMILES) serve as the basis for building up a model. Correlation weights for the molecular features are calculated by means of the Monte Carlo optimization. Using the numerical data on the correlation weights, one can calculate a model of carcinogenicity as a mathematical function of descriptors, which are sum of the corresponding correlation weights. In other words, the correlation weights provide the maximal correlation coefficient between the descriptor and carcinogenicity, for the training set. This correlation was assessed via external validation set. Finally, lists of molecular alerts in aspects of carcinogenicity for male rats and for female rats were compared and their differences were discussed. [ABSTRACT FROM AUTHOR]

Background and objective Predicting blood-brain barrier permeability for novel compounds is an important goal for neurotherapeutics-focused drug discovery. It is impossible to determine experimentally the blood-brain barrier partitioning of all possible candidates. Consequently, alternative evaluation methods based on computational models are desirable or even necessary. The CORAL software ( http://www.insilico.eu/coral ) has been checked up as a tool to build up quantitative structure – activity relationships for blood-brain barrier permeation. Methods The Monte Carlo technique gives possibility to build up predictive model of an endpoint by means of selection of so-called correlation weights of various molecular features. Descriptors calculated with these weights are basis for correlations “structure − endpoint”. Results The approach gives good models for three random splits into the training and validation sets. The best model characterized by the following statistics for the external validation set: the number of compounds is 41, determination coefficient is equal to 0.896, root mean squared error is equal to 0.175. Conclusions The suggested approach can be applied as a tool for prediction of blood-brain barrier permeation. [ABSTRACT FROM AUTHOR]

Quantitative structure–activity relationship models for bee toxicity have been built up using CORAL software (http://www.insilico.eu/coral). The approach is based on the Monte Carlo technique. The molecular structure for the quantitative structure–activity relationship analysis has been presented by the simplified molecular input-line entry system. The so-called balance of correlations and the traditional scheme of building up quantitative structure–activity relationship models are compared in this work. The traditional scheme is based on three basic sets of compounds: training, calibration, and validation, whereas, the balance of correlations is based on four sets: active training, invisible training, calibration, and validation. As rule, the balance of correlations gives better models in comparison with the traditional scheme. The statistical characteristics of the models are quite good. Possible mechanistic interpretations and indications for the domain of applicability of these models are suggested. [ABSTRACT FROM PUBLISHER]

The index of ideality of correlation (IIC) is a new criterion of the predictive potential of quantitative structure–property/activity relationships (QSPRs/QSARs). This IIC is calculated with using of the correlation coefficient between experimental and calculated values of endpoint for the calibration set, with taking into account the positive and negative dispersions between experimental and calculated values. The mutagenicity is well-known important characteristic of substances from ecological point of view. Consequently, the estimation of the IIC for mutagenicity is well motivated. It is confirmed that the utilization of this criterion significantly improves the predictive potential of QSAR models of mutagenicity. The new criterion can be used for other endpoints. [ABSTRACT FROM AUTHOR]