QSAR as a random event: criteria of predictive potential for a chance model

In silico aquatic toxicity prediction of chemicals toward Daphnia magna and fathead minnow using Monte Carlo approaches

The fast-increasing use of chemicals led to large numbers of chemical compounds entering the aquatic environment, raising concerns about their potential effects on ecosystems. Therefore, assessment of the ecotoxicological features of organic compounds on aquatic organisms is very important. Daphnia magna and Fathead minnow are two aquatic species that are commonly tested as standard test organisms for aquatic risk assessment and are typically chosen as the biological model for the ecotoxicology investigations of chemical pollutants. Herein, global quantitative structure-toxicity relationship (QSTR) models have been developed to predict the toxicity (pEC(LC)50) of a large dataset comprising 2106 chemicals toward Daphnia magna and Fathead minnow. The optimal descriptor of correlation weights (DCWs) is calculated using the notation of simplified molecular input line entry system (SMILES) and is used to construct QSTR models. Three target functions, TF1, TF2, and TF3 are utilized to generate 12 QSTR models from four splits, and their statistical characteristics are also compared. The designed QSTR models are validated using both internal and external validation criteria and are found to be reliable, robust, and excellently predictive. Among the models, those generated using the TF3 demonstrate the best statistical quality with R2 values ranging from 0.9467 to 0.9607, Q2 values ranging from 0.9462 to 0.9603 and RMSE values ranging from 0.3764 to 0.4413 for the validation set. The applicability domain and the mechanistic interpretations of generated models were also discussed.

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.

A simple and reliable QSPR model for prediction of chromatography retention indices of volatile organic compounds in peppers

Worldwide, various types of pepper are used in food as an additive due to their unique pungency, aroma, taste, and color. This spice is valued for its pungency contributed by the alkaloid piperine and aroma attributed to volatile essential oils. The essential oils are composed of volatile organic compounds (VOCs) in different concentrations and ratios. In chromatography, the identification of compounds is done by comparing obtained peaks with a reference standard. However, there are cases where reference standards are either unavailable or the chemical information of VOCs is not documented in reference libraries. To overcome these limitations, theoretical methodologies are applied to estimate the retention indices (RIs) of new VOCs. The aim of the present work is to develop a reliable QSPR model for the RIs of 273 identified VOCs of different types of pepper. Experimental retention indices were measured using comprehensive two-dimensional gas chromatography coupled to quadrupole mass spectrometry (GC × GC/qMS) using a coupled BPX5 and BP20 column system. The inbuilt Monte Carlo algorithm of CORAL software is used to generate QSPR models using the hybrid optimal descriptor extracted from a combination of SMILES and HFG (hydrogen-filled graph). The whole dataset of 273 VOCs is used to make ten splits, each of which is further divided into four sets: active training, passive training, calibration, and validation. The balance of correlation method with four target functions i.e. TF0 (WIIC = WCII = 0), TF1 (WIIC = 0.5 & WCII = 0), TF2 (WIIC = 0 & WCII = 0.3) and TF3 (WIIC = 0.5 & WCII = 0.3) is used. The results of the statistical parameters of each target function are compared with each other. The simultaneous application of the index of ideality of correlation (IIC) and correlation intensity index (CII) improves the predictive potential of the model. The best model is judged on the basis of the numerical value of R2 of the validation set. The statistical result of the best model for the validation set of split 6 computed with TF3 (WIIC = 0.5 & WCII = 0.3) is R2 = 0.9308, CCC = 0.9588, IIC = 0.7704, CII = 0.9549, Q2 = 0.9281 and RMSE = 0.544. The promoters of increase/decrease for RI are also extracted using the best model (split 6). Moreover, the proposed model was used for an external validation set.

The System of Self-Consistent Models: The Case of Henry's Law Constants

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).

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).

The enhancement scheme for the predictive ability of QSAR: A case of mutagenicity

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 value of the determination coefficient for the validation set is 0.8737 ± 0.0312.

CORAL: Model of Ecological Impact of Heavy Metals on Soils via the Study of Modification of Concentration of Biomolecules in Earthworms (Eisenia fetida)

The traditional application for quantitative structure-property/activity relationships (QSPRs/QSARs) in the fields of thermodynamics, toxicology or drug design is predicting the impact of molecular features using data on the measurable characteristics of substances. However, it is often necessary to evaluate the influence of various exposure conditions and environmental factors, besides the molecular structure. Different enzyme-driven processes lead to the accumulation of metal ions by the worms. Heavy metals are sequestered in these organisms without being released back into the soil. In this study, we propose a novel approach for modeling the absorption of heavy metals, such as mercury and cobalt by worms. The models are based on optimal descriptors calculated for the so-called quasi-SMILES, which incorporate strings of codes reflecting experimental conditions. We modeled the impact on the levels of proteins, hydrocarbons, and lipids in an earthworm's body caused by different combinations of concentrations of heavy metals and exposure time observed over two months of exposure with a measurement interval of 15 days.

Quantitative structure activity relationship studies of androgen receptor binding affinity of endocrine disruptor chemicals with index of ideality of correlation, their molecular docking, molecular dynamics and ADME studies

Endocrine disrupter chemicals (EDCs) are both natural and man-made chemicals that mimic, block or interfere with human hormonal system. In the present manuscript, QSAR modeling was performed for the androgen disruptors that interfere with biosynthesis, metabolism or action of androgens that causes adverse effects on male reproductive system. A set of 96 EDCs that exhibited affinity towards androgen receptors (Log RBA) in rats were employed for carrying out QSAR studies using Hybrid descriptors (combination of HFG and SMILES) through Monte Carlo Optimization. Using index of ideality of correlation (TF2), five splits were formed and predictability of five models resulting from these splits was assessed by various validation parameters. Models resulted from first split was the top most one with R2validation = 0.7878. Structural attributes responsible for change in endpoint were studied by employing correlation weights of structural attributes. In order to further validate the model, new EDCs were designed using these attributes. In silico molecular modelling studies were performed to assess the detailed interactions with the receptor. The binding energies of all the designed compounds were observed to be better than lead and are in the range of -10.46 to -14.80. Molecular dynamics simulation of 100 ns was performed for ED01 and NED05. The results revealed that the protein-ligand complex bearing NED05 was more stable than lead ED01 exhibiting better interactions with the receptor. Further, in an attempt to assess their metabolism, ADME studies were evaluated using SwissADME. The developed model enables to predict the characteristics of designed compounds in an authentic way.Communicated by Ramaswamy H. Sarma.

Exploring the Gallic and Cinnamic Acids Chimeric Derivatives as Anticancer Agents over HeLa Cell Line: An in silico and in vitro Study

Cervical cancer is one of the most aggressive and important cancer types in the female population, due to its low survival rate. Actually, the search for new bioactive compounds, like gallic and cinnamic acid, is one of the most employed options to finding a treatment. In the present study, 134 phenolic compounds with cytotoxic activity over HeLa cell line were used to generate a descriptive ( R 2 ${{R}^{2}}$ =0.76) and predictive ( Q 2 ${{Q}^{2}}$ =0.69 and Q e x t 2 ${{Q}_{{\rm e}{\rm x}{\rm t}}^{2}}$ =0.62) QSAR model. Structural, electronic, steric, and hydrophobic features are represented as different molecular descriptors in our QSAR model. From this model, nine gallate-cinnamate ester derivatives (N1-N9) were designed and synthesized. Furthermore, in vitro cytotoxic activity was evaluated against HeLa and non-tumorigenic cells. Derivatives N6, N5, N1, and N9 were the most active molecules with IC_50ExpHeLa values from 7.26 to 11.95 μM. Finally, the binding of the synthesized compounds to the colchicine binding site on tubulin was evaluated by molecular docking as a possible action mechanism. N1, N5 and N6 can be considered as templates for the design of new cervical anticancer compounds.

Identifications of good and bad structural fragments of hydrazone/2,5-disubstituted-1,3,4-oxadiazole hybrids with correlation intensity index and consensus modelling using Monte Carlo based QSAR studies, their molecular docking and ADME analysis

The application of QSAR along with other in silico tools like molecular docking, and molecular dynamics provide a lot of promise for finding new treatments for life-threatening diseases like Type 2 diabetes mellitus (T2DM). The present study is an attempt to develop Monte Carlo algorithm-based QSAR models using freely available CORAL software. The experimental data on the α-amylase inhibition by a series of benzothiazole-linked hydrazone/2,5-disubstituted-1,3,4-oxadiazole hybrids were selected as endpoint for the model generation. Initially, a total of eight QSAR models were built using correlation intensity index (CII) as a criterion of predictive potential. The model developed from split 6 using CII was the most reliable because of the highest numerical value of the determination coefficient of the validation set (r²_VAL = 0.8739). The important structural fragments responsible for altering the endpoint were also extracted from the best-built model. With the goal of improved prediction quality and lower prediction errors, the validated models were used to build consensus models. Molecular docking was used to know the binding mode and pose of the selected derivatives. Further, to get insight into their metabolism by living beings, ADME studies were investigated using internet freeware, SwissADME.

Semi-correlations as a tool to model for skin sensitization

Semi-correlation specifically assesses the correlation between a binary variable and a continuous variable. Semi-correlations were applied to develop binary models for various endpoints. We applied the semi-correlation to develop models of two kinds of skin sensitization one related to animals (local lymph node assay LLNA) and one to human beings (direct peptide reactivity assay DPRA and/or human cell line activation test h-CLAT). The models refer to binary classification for a two-level strategy: the first level (analysis of all compounds) is used in the format "sensitizer or non-sensitizer", and the second level (only sensitizers) is a further classification in the format "strong or weak sensitizer". The ranges of statistical characteristics of the models depend on the endpoint, LLNA or DPRA/h-CLAT: for the first level, sensitivity: 0.69-0.88, specificity: 0.75-0.89, accuracy: 0.77-0.87, Matthew's correlation coefficient (MCC): 0.54-0.57 and for the second level, sensitivity: 0.70-1.0, specificity: 0.78-0.83, accuracy: 0.77-0.87, MCC: 0.54-0.76. Thus, the described approach can be applied to building up models of the skin sensitization potency.

In silico development of potential therapeutic for the pain treatment by inhibiting voltage-gated sodium channel 1.7

The voltage-gated sodium channel Nav1.7 can be considered as a promising target for the treatment of pain. This research presents conformational-independent and 3D field-based QSAR modeling for a series of aryl sulfonamide acting as Nav1.7 inhibitors. As descriptors used for building conformation-independent QSAR models, SMILES notation and local invariants of the molecular graph were used with the Monte Carlo optimization method as a model developer. Different statistical methods, including the index of ideality of correlation, were used to test the quality of the developed models, robustness and predictability and obtained results were good. Obtained results indicate that there is a very good correlation between 3D QSAR and conformation-independent models. Molecular fragments that account for the increase/decrease of a studied activity were defined and used for the computer-aided design of new compounds as potential analgesics. The final evaluation of the developed QSAR models and designed inhibitors were carried out using molecular docking studies, bringing to light an excellent correlation with the QSAR modeling results.

The unreliability of the reliability criteria in the estimation of QSAR for skin sensitivity: A pun or a reliable law?

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).

Ecosystem ecology: Models for acute toxicity of pesticides towards Daphnia magna

Quantitative structure - activity relationships (QSARs) which are obtained with a representation of the molecular architecture via simplified molecular input-line entry system (SMILES) are applied to build up predictive models of acute toxicity of pesticides towards Daphnia magna. The acute toxicity towards Daphnia magna is an adequate measure of the ecological impact of various substances. The Monte Carlo technique is the basis to build up the above QSAR models. The statistical quality of suggested models is good: the best model is characterized by n = 103, R² = 0.76, RMSE = 0.91 (training set); n = 53, R² = 0.82, RMSE = 0.87 (validation set). The approach provides the mechanistic interpretation (e.g. aromaticity and branching of carbon skeleton are promoters of increase for toxicity towards Daphnia magna in the case of the examined set of pesticides). The approach is attractive to build up predictive models since instead of a large number of different molecular descriptors the corresponding model is based on solely one optimal descriptor calculated with SMILES and all necessary calculations can be done using the CORAL software available on the Internet (http://ww.insilico.eu/coral).

The using of the Index of Ideality of Correlation (IIC) to improve predictive potential of models of water solubility for pesticides

Models for water solubility of pesticides suggested in this manuscript are important data from point of view of ecologic engineering. The Index of Ideality of Correlation (IIC) of groups of quantitative structure-property relationships (QSPRs) for water solubility of pesticides related to the calibration sets was used to identify good in silico models. This comparison confirmed the high IIC set provides better statistical quality of the model for the validation set. Though there are large databases on solubility, the reliable prediction of the endpoint for new substances which are potential pesticides is an important ecologic task. Unfortunately, predictive models for various endpoints suffer overtraining, and the IIC serves to avoid or at least reduce this. Thus, the approach suggested has both theoretical and economic effects for ecology.

QSPR/QSAR: State-of-Art, Weirdness, the Future

Ability of quantitative structure-property/activity relationships (QSPRs/QSARs) to serve for epistemological processes in natural sciences is discussed. Some weirdness of QSPR/QSAR state-of-art is listed. There are some contradictions in the research results in this area. Sometimes, these should be classified as paradoxes or weirdness. These points are often ignored. Here, these are listed and briefly commented. In addition, hypotheses on the future evolution of the QSPR/QSAR theory and practice are suggested. In particular, the possibility of extending of the QSPR/QSAR problematic by searching for the "statistical similarity" of different endpoints is suggested and illustrated by an example for relatively "distanced each from other" endpoints, namely (i) mutagenicity, (ii) anticancer activity, and (iii) blood-brain barrier.

The index of ideality of correlation: models of the flash points of ternary mixtures

Reliable information related to the flash point of ternary mixtures assists in the rational classification of different ternary mixtures of liquids.

Whether the Validation of the Predictive Potential of Toxicity Models is a Solved Task?

Different kinds of biological activities are defined by complex biochemical interactions, which are termed as a "mathematical function" not only of the molecular structure but also for some additional circumstances, such as physicochemical conditions, interactions via energy and information effects between a substance and organisms, organs, cells. These circumstances lead to the great complexity of prediction for biochemical endpoints, since all "details" of corresponding phenomena are practically unavailable for the accurate registration and analysis. Researchers have not a possibility to carry out and analyse all possible ways of the biochemical interactions, which define toxicological or therapeutically attractive effects via direct experiment. Consequently, a compromise, i.e. the development of predictive models of the above phenomena, becomes necessary. However, the estimation of the predictive potential of these models remains a task that is solved only partially. This mini-review presents a collection of attempts to be used for the above-mentioned task, two special statistical indices are proposed, which may be a measure of the predictive potential of models. These indices are (i) Index of Ideality of Correlation; and (ii) Correlation Contradiction Index.