The coefficient of conformism of a correlative prediction (CCCP): Building up reliable nano-QSPRs/QSARs for endpoints of nanoparticles in different experimental conditions encoded via quasi-SMILES.

Simulation of the physicochemical and biochemical behavior of nanomaterials has its own specifics. However, the main goal of modeling for both traditional substances and nanomaterials is the same. This is an ecologic risk assessment. The universal indicator of toxicity is the n-octanol/water partition coefficient. Mutagenicity indicates the possibility of future undesirable environmental effects, possibly greater than toxicity. Models have been proposed for the octanol/water distribution coefficient of gold nanoparticles and the mutagenicity of silver nanoparticles. Unlike the previous studies, here the models are built using an updated scheme, which includes two improvements. Firstly, the computing involves a new criterion for prediction potential, the so-called coefficient of conformism of a correlative prediction (CCCP); secondly, the Las Vegas algorithm is used to select the potentially most promising models from a group of models obtained by the Monte Carlo algorithm. Apparently, CCCP is a measure of the predictive potential (not only correlation). This can give an advantage in developing a model in comparison to using the classic determination coefficient. Likely, CCCP can be more informative than the classical determination coefficient. The Las Vegas algorithm is able to improve the model obtained by the Monte Carlo method.

Using the Correlation Intensity Index to Build a Model of Cardiotoxicity of Piperidine Derivatives.

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.

Using the local symmetry in amino acids sequences of polypeptides to improve the predictive potential of models of their inhibitor activity.

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).

The system of self-consistent models for pesticide toxicity to Daphnia magna.

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).

In Silico Simulation of Impacts of Metal Nano-Oxides on Cell Viability in THP-1 Cells Based on the Correlation Weights of the Fragments of Molecular Structures and Codes of Experimental Conditions Represented by Means of Quasi-SMILES.

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.

Quasi-SMILES as a basis to build up models of endpoints for nanomaterials.

Simplified molecular input-line entry system (SMILES) is a format for representing of the molecular structure. Quasi-SMILES is an extended format for representing molecular structure data and some eclectic data, which in principle could be applied to improve a model's predictive potential. Nano-quantitative structure-property relationships (nano-QSPRs) for energy gap (Eg, eV) of the metals oxide nanoparticles based on the quasi-SMILES give a predictive model for Eg, characterized by the following statistical quality for external validation set n = 22, R2 = 0.83, RMSE = 0.267.

Monte Carlo Models for Sub-Chronic Repeated-Dose Toxicity: Systemic and Organ-Specific Toxicity.

The risk-characterization of chemicals requires the determination of repeated-dose toxicity (RDT). This depends on two main outcomes: the no-observed-adverse-effect level (NOAEL) and the lowest-observed-adverse-effect level (LOAEL). These endpoints are fundamental requirements in several regulatory frameworks, such as the Registration, Evaluation, Authorization and Restriction of Chemicals (REACH) and the European Regulation of 1223/2009 on cosmetics. The RDT results for the safety evaluation of chemicals are undeniably important; however, the in vivo tests are time-consuming and very expensive. The in silico models can provide useful input to investigate sub-chronic RDT. Considering the complexity of these endpoints, involving variable experimental designs, this non-testing approach is challenging and attractive. Here, we built eight in silico models for the NOAEL and LOAEL predictions, focusing on systemic and organ-specific toxicity, looking into the effects on the liver, kidney and brain. Starting with the NOAEL and LOAEL data for oral sub-chronic toxicity in rats, retrieved from public databases, we developed and validated eight quantitative structure-activity relationship (QSAR) models based on the optimal descriptors calculated by the Monte Carlo method, using the CORAL software. The results obtained with these models represent a good achievement, to exploit them in a safety assessment, considering the importance of organ-related toxicity.

The searching for agents for Alzheimer's disease treatment via the system of self-consistent models.

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 (http://www.insilico.eu/coral) 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.

A regression-based QSAR-model to predict acute toxicity of aromatic chemicals in tadpoles of the Japanese brown frog (Rana japonica): Calibration, validation, and future developments to support risk assessment of chemicals in amphibians.

Amphibian populations are undergoing a global decline worldwide. Such decline has been attributed to their unique physiology, ecology, and exposure to multiple stressors including chemicals, temperature, and biological hazards such as fungi of the Batrachochytrium genus, viruses such as Ranavirus, and habitat reduction. There are limited toxicity data for chemicals available for amphibians and few quantitative structure-activity relationship (QSAR) models have been developed and are publicly available. Such QSARs provide important tools to assess the toxicity of chemicals particularly in a data poor context. QSARs provide important tools to assess the toxicity of chemicals particularly when no toxicological data are available. This manuscript provides a description and validation of a regression-based QSAR model to predict, in a quantitative manner, acute lethal toxicity of aromatic chemicals in tadpoles of the Japanese brown frog (Rana japonica). QSAR models for acute median lethal molar concentrations (LC50-12 h) of waterborne chemicals using the Monte Carlo method were developed. The statistical characteristics of the QSARs were described as average values obtained from five random distributions into training and validation sets. Predictions from the model gave satisfactory results for the overall training set (R2 = 0.72 and RMSE = 0.33) and were even more robust for the validation set (R2 = 0.96 and RMSE = 0.11). Further development of QSAR models in amphibians, particularly for other life stages and species, are discussed.

Nanomaterials: Quasi-SMILES as a flexible basis for regulation and environmental risk assessment.

Basic principles and problems of the systematization of data on nanomaterials are discussed. The eclectic character of nanomaterials is defined as the key difference between nanomaterials and traditional substances. The quasi-SMILES technique is described and discussed. The possible role of the approach is bridging between experimentalists and developers of models for endpoints related to nanomaterials. The use of models on the possible impact of nanomaterials on the environment and human health has been collected and compared. The new criteria of the predictive potential for the above models are discussed. The advantage of the statistical criteria sensitive simultaneously to both the correlation coefficient and the root mean square error noted. The rejection of the border between the effect of the biochemical reality of substances at a molecular level and the effect of experiment conditions at the macro level gives the possibility to develop models that are epistemologically more reliable in the comparison with traditional models based exclusively on the molecular structure-biological activity interdependence (without taking into account experimental conditions). Models of the physicochemical and biochemical behaviour of nanomaterials are necessary in order to develop and apply new industrial achievements, everyday comfort species, medicine, cosmetics, and foods without negative effects on ecology and human health. The CORAL (abbreviation CORrelation And Logic) software provides the user with the possibility to build up nano-QSAR models as a mathematical function of so-called correlation weights of fragments of quasi-SMILES. These models are built up via the Monte Carlo method. Apparently, the quasi-SMILES is a universal representation of nano-reality since there is no limitation to choose the list of eclectic data able to have an impact on nano-phenomena. This paradigm is a convenient language to the conversation of experimentalists and developers of models for nano-phenomena.

Paradox of 'ideal correlations': improved model for air half-life of persistent organic pollutants.

The persistence of organic pollutants is an important environmental property due to the extended possibility to have an impact of corresponding substances. In many cases, the experimental values of the thousands of contaminants are missing. The object of the study is novel computational modelling for air pollutions. Quantitative structure-property relationship (QSPR) for air half-life has been built using the Monte Carlo method with applying the index of ideality of correlation (IIC). The basis of the predictive model of air half-life is the representation of the molecular structure by simplifying molecular input-line entry system (SMILES) and numerical data on the above endpoint (expressed by hours) converted to a decimal logarithm. The statistical quality of the model has been checked up with different validation metrics and is quite good. Paradoxically, the improvement of the statistical quality via the IIC for the validation set is done in detriment to the training set. The new model has performed better than those obtained previously on the same set of compounds, for the prediction of new compounds in the validation set. Some semi-quantitative indicators for the mechanistic interpretation of the model are suggested.

Application of quasi-SMILES to the model of gold-nanoparticles uptake in A549 cells.

Cell death is critical to human health and is associated with a variety of medical conditions. Therefore, new controllers of cell death are needed for the treatment of diverse diseases. In particular, nanoparticles (NP) are now regularly used in various applications, including a variety of products and medicines. Gold nanoparticles (GNPs) are widely used in the medical field against A549 lung carcinoma cells. The present study is devoted to developing computational models of the cellular uptake potentials by A549 cells of gold nanoparticles (GNPs) under various conditions. Simplified molecular input-line entry system (SMILES) is an efficient tool to represent the molecular structure by a sequence of symbols. Quasi-SMILES represents an extended version of SMILES where symbols to denote physicochemical and/or biochemical conditions are added. In other words, the quasi-SMILES represents a biochemical (medical) phenomenon related to the whole matter (not only molecular structure). We developed models for the cellular utpake potential of gold nanoparticles (GNPs) in A549 [10-11 g Au/Cell] under various conditions based on quasi-SMILES using the Monte Carlo method. The statistical quality of these models is quite good.

The system of self-consistent models for the uptake of nanoparticles in PaCa2 cancer cells.

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).

The index of ideality of correlation improves the predictive potential of models of the antioxidant activity of tripeptides from frog skin (Litoria rubella).

It is usually held that good-quality models for the biological activity of peptides must take into account their 3D architecture and descriptors of quantum mechanics. However, the present study shows that it is possible to build up models without these complex calculations. The structure of tripeptides represented by sequences of one-symbol abbreviations of the corresponding amino acids serves to build up quantitative structure-activity relationships for the antioxidant activity of tripeptides from frog skin. The statistical quality of the best model for the validation set is n = 27, r2 = 0.93, RMSE = 0.15.

Can the Monte Carlo method predict the toxicity of binary mixtures?

Risk assessment of toxicants mainly is a result of experiments with single substances. However, toxicity in natural ecosystems typically does not result from single toxicant exposure but is rather a result of exposure to mixtures of toxicants. It is not surprising a mixture of toxicity is a subject of eco-toxicological interest for several decades. A quantitative structure-activity relationships (QSAR)-based approach is an attractive approach to assessing the joint effects in the binary mixtures. The validity of the proposed approach was demonstrated by comparing the predicted values against the experimentally determined values. Simplified molecular input-line entry system (SMILES) is used for the representation of the molecular structures of components of two-component mixtures to build up QSAR. The SMILES-based models are improving if the Monte Carlo optimization aimed to define 2D-optimal descriptors apply the so-called index of ideality of correlation (IIC), which is a mathematical function of both the correlation coefficient and mean absolute error calculated for the positive and negative difference between observed and calculated values of toxicity. The average statistical quality of these models (for the validation set) is n=25, R2=0.95, and RMSE=0.375.

Quasi-SMILES as a basis for the development of models for the toxicity of ZnO nanoparticles.

The application of nanomaterials is expanding. Therefore, it is necessary to investigate the relationship between the structure and toxicity of different nanomaterials. Quasi-SMILES is a line of symbols which are codes of corresponding conditions of experiments aimed to estimate the toxicity of ZnO nanoparticles towards the rat via intraperitoneal injections. By means of the Monte Carlo method, the so-called correlation weights for fragments of quasi-SMILES can be calculated. Having the numerical data on the correlation weights one can build up a one-variable model for the toxicity. The checking up of the approach with five random splits of all available data on results of thirty-six experiments into a sub-system of training and sub-system of validation has confirmed the significance of the statistical quality of models obtained with the above approach. The average determination coefficient equal to 0.957 (dispersion 0.010) and average root mean square error equal to 7.25 [mg/kg] (dispersion 0.59 [mg/kg]).

Interpretable SMILES-based QSAR Model of Inhibitory Activity of Sirtuins 1 and 2.

BACKGROUND: Sirtuin 1 (Sirt1) and sirtuin 2 (Sirt2) are NAD+-dependent histone deacetylases which play important functional roles in the removal of the acetyl group of acetyllysine substrates. Considering the dysregulation of Sirt1 and Sirt2 as etiological causes of diseases, Sirt1 and Sirt2 are lucrative target proteins for treatment, thus there has been great interest in the development of Sirt1 and Sirt2 inhibitors. OBJECTIVE: This study compiled the bioactivity data of Sirt1 and Sirt2 for the construction of quantitative structure-activity relationship (QSAR) models in accordance with the OECD principles. METHODS: Simplified molecular-input line-entry system (SMILES)-based molecular descriptors were used to characterize the molecular features of inhibitors while the Monte Carlo method of the CORAL software was employed for multivariate analysis. The dataset was subjected to 3 random splits in which each split separated the data into 4 subsets consisting of training, invisible training, calibration, and external sets. RESULTS: Statistical indices for the evaluation of QSAR models suggested the good statistical quality of models of Sirt1 and Sirt2 inhibitors. Furthermore, mechanistic interpretation of molecular substructures that are responsible for modulating the bioactivity (i.e., promoters of increase or decrease of bioactivity) was extracted via the analysis of correlation weights. It exhibited molecular features involved in Sirt1 and Sirt2 inhibitors. CONCLUSION: It is anticipated that QSAR models presented herein can be useful as guidelines in the rational design of potential Sirt1 and Sirt2 inhibitors for the treatment of Sirtuin-related diseases.

How the CORAL software can be used to select compounds for efficient treatment of neurodegenerative diseases?

Recommendations on the efficient application of CORAL software (http://www.insilico.eu/coral) to establish quantitative structure-property/activity relationships (QSPRs/QSARs) are provided. The predictive potential of the approach has been demonstrated for QSAR models developed for inhibitor concentrations (negative decimal logarithm of IC50) of derivatives of N-methyl-d-aspartate (NMDA) receptor, leucine-rich repeat kinase 2 (LRRK2), and tropomyosin receptor kinase A (TrkA). The above three protein targets are related to various neurodegenerative diseases such as Alzheimer's and Parkinson's. Each model was checked using several splits of the data for the training and the validation sets. The index of ideality of correlation (IIC) represents a tool to improve the predictive potential for an arbitrary model. However, the use of the IIC should be carried out according to rules, described in this work.

Correlation intensity index: mathematical modeling of cytotoxicity of metal oxide nanoparticles.

Metal oxide nanoparticles (MO-NPs) have unique structural characteristics, exceptionally high surface area, strong mechanical stability, catalytic activities, and are biocompatible. Consequently, MO-NPs have recently attracted considerable interest in the field of imaging-guided therapeutic and biosensing applications. This study aims to develop Quantitative Structure-Activity Relationships (QSAR) for the prediction of cell viability of MO-NPs. The QSAR model based on the so-called optimal descriptors which calculated with a simplified molecular input-line entry system (SMILES). The Monte Carlo technique applied to calculate correlation weights for SMILES fragments. Factually, the optimal descriptor for SMILES is the summation of the correlation weights. The model of cytotoxicity is one variable correlation between cytotoxicity and the above optimal descriptor. The Correlation Intensity Index (CII) is a possible criterion of the predictive potential of the model. Applying the CII as a component of the target function in the Monte Carlo optimization routine, employed by the CORAL program, that is designed to find a predictive relationship between the optimal descriptor and cytotoxicity of MO-NPs, improves the statistical quality of the model. The significance of different eclectic features, in terms of whether they increase/decrease cell viability, i.e. decrease or increase cytotoxicity, is also discussed. Numerical data on 83 experimental samples of MO-NPs activity under different conditions taken from the literature are applied for the "nano-QSAR" analysis.

QSAR model for pesticides toxicity to Rainbow Trout based on "ideal correlations".

Pesticides have an impact on the aquatic environment, with ecological effects. The regulation of this impact is of key importance. One of the components of the planning of agricultural and industrial activities is the development of databases and models in order to identify substances that may cause damage. In this study, a quantitative structure-activity relationship (QSAR) approach was established for the prediction of acute toxicity toward rainbow trout of various pesticides. The so-called index of ideality of correlation is the main component of this approach. The validation of this approach has been carried out with three random splits into the training and validation sets. The range of statistical quality of models obtained here for the validation set is R2 = [0.81-0.86] and RMSE = [0.55-0.65].