Universal Approach for Structural Interpretation of QSAR/QSPR Models.

In this paper we offer a novel approach for the structural interpretation of QSAR models. The major advantage of our developed methodology is its universality, i.e., it can be applied to any QSAR/QSPR model irrespective of chemical descriptors and machine learning methods applied. This universality was achieved by using only the information obtained from substructures of the compounds of interest to interpret model outcomes. Reliability of the offered approach was confirmed by the results of three case studies, including end-points of different types (continuous and binary classification) and nature (solubility, mutagenicity, and inhibition of Transglutaminase 2), various fragment and whole-molecule descriptors (Simplex and Dragon), and multiple modeling techniques (partial least squares, random forest, and support vector machines). We compared the global contributions of molecular fragments obtained using our methodology with known SAR rules derived experimentally. In all cases high concordance between our interpretation and results published by others was observed. Although the proposed interpretation approach could be easily extended to any type of descriptors, we would recommend using Simplex descriptors to achieve a larger variety of investigated molecular fragments. The developed approach is a good tool for interpretation of such "black box" models like random forest, neural networks, etc. Analysis of fragment global contributions and their deviation across a dataset could be useful for the identification of key fragments and structural alerts. This information could be helpful to maximize the positive influence of structural surroundings on the given fragment and to decrease the negative effects.

Existing and Developing Approaches for QSAR Analysis of Mixtures.

This review is devoted to the critical analysis of advantages and disadvantages of existing mixture descriptors and their usage in various QSAR/QSPR tasks. We describe good practices for the QSAR modeling of mixtures, data sources for mixtures, a discussion of various mixture descriptors and their application, recommendations about proper external validation specific for mixture QSAR modeling, and future perspectives of this field. The biggest problem in QSAR of mixtures is the lack of reliable data about the mixtures' properties. Various mixture descriptors are used for the modeling of different endpoints. However, these descriptors have certain disadvantages, such as applicability only to 1 : 1 binary mixtures, and additive nature. The field of QSAR of mixtures is still under development, and existing efforts could be considered as a foundation for future approaches and studies. The usage of non-additive mixture descriptors, which are sensitive to interaction effects, in combination with best practices of QSAR model development (e.g., thorough data collection and curation, rigorous external validation, etc.) will significantly improve the quality of QSAR studies of mixtures.

QSPR Prediction of Lipophilicity for Organic Compounds Using Random Forest Technique on the Basis of Simplex Representation of Molecular Structure.

The relationship between the octanol-water partition coefficient for more than twelve thousand organic compounds and their structures was investigated using a QSPR approach based on Simplex Representation of Molecular Structure (SiRMS). The dataset used in our study included 10973 compounds with experimental values of lipophilicity (LogKow ) for different chemical compounds. Random Forest (RF) method was used for statistical modeling at the 2D level of representation of molecular structure. Developed models are adequate and successfully validated with external test sets. Proposed models have clear interpretation due to the use of simplex representation of molecular structure and predict the LogKow values with the accuracy of the best modern models. Thus QSPR models proposed in this study represent powerful and easy-to use virtual screening tool that can be recommended for prediction of octanol-water partition coefficient.

QSAR analysis of [(biphenyloxy)propyl]isoxazoles: agents against coxsackievirus B3.

BACKGROUND: Antiviral drugs are urgently needed for the treatment of acute and chronic diseases caused by enteroviruses such as coxsackievirus B3 (CVB3). The main goal of this study is quantitative structure-activity relationship (QSAR) analysis of anti-CVB3 activity (clinical CVB3 isolate 97927 [log IC50, µM]) and investigation of the selectivity of 25 ([biphenyloxy]propyl)isoxazoles, followed by computer-aided design and virtual screening of novel active compounds. DISCUSSION: The 2D QSAR obtained models are quite satisfactory (R(2) = 0.84-0.99, Q(2) = 0.76-0.92, R(2)(ext) = 0.62-0.79). Compounds with high antiviral activity and selectivity have to contain 5-trifluoromethyl-[1,2,4]oxadiazole or 2,4-difluorophenyl fragments. Insertion of 2,5-dimethylbenzene, napthyl and especially biphenyl substituents into investigated compounds substantially decreases both their antiviral activity and selectivity. Several compounds were proposed as a result of design and virtual screening. A high level of activity of 2-methoxy-1-phenyl-1H-imidazo[4,5-c]pyridine (sm428) was confirmed experimentally. CONCLUSION: Simplex representation of molecular structure allows successful QSAR analysis of anti-CVB3 activity of ([biphenyloxy]propyl)isoxazole derivatives. Two possible ways of battling CVB3 are considered as a future perspective.

Interpretation of QSAR Models Based on Random Forest Methods.

A new algorithm for the interpretation of Random Forest models has been developed. It allows to calculate the contribution of each descriptor to the calculated property value. In case of the simplex representation of a molecular structure, contributions of individual atoms can be calculated, and thus it becomes possible to estimate the influence of separate molecular fragments on the investigated property. Such information can be used for the design of new compounds with a predefined property value. The proposed measure of descriptor contributions is not an alternative to the importance of Breiman's variable, but it characterizes the contribution of a particular explanatory variable to the calculated response value.

New QSPR equations for prediction of aqueous solubility for military compounds.

The development of a new quantitative structure-property relationship (QSPR) model to predict aqueous solubility (S(w)) accurately for compounds of military interest is presented. The ability of the new model to predict solubility is assessed and compared to available experimental data. A large set of structurally diverse organic compounds was used in this analysis. SiRMS methodology was employed to develop PLS models based on 135 training compounds and predictive accuracy was tested for 155 compounds selected for that purpose. The use of descriptors calculated only from the 2D level of representation of molecular structure produces a well-fitted and robust QSPR model (R(2)=0.90; Q(2)=0.87). Predictive ability for the model produced in this study on external test set (R(test)(2)=0.81) is comparable to the predictive ability of EPI Suite 4.0. Consensus solubility predictions using SiRMS and EPI models for 25 compounds of military interest (not included into the training set) have been completed.

Per aspera ad astra: application of Simplex QSAR approach in antiviral research.

This review explores the application of the Simplex representation of molecular structure (SiRMS) QSAR approach in antiviral research. We provide an introduction to and description of SiRMS, its application in antiviral research and future directions of development of the Simplex approach and the whole QSAR field. In the Simplex approach every molecule is represented as a system of different simplexes (tetratomic fragments with fixed composition, structure, chirality and symmetry). The main advantages of SiRMS are consideration of the different physical-chemical properties of atoms, high adequacy and good interpretability of models obtained and clear procedures for molecular design. The reliability of developed QSAR models as predictive virtual screening tools and their ability to serve as the basis of directed drug design was validated by subsequent synthetic and biological experiments. The SiRMS approach is realized as the complex of the computer program 'HiT QSAR', which is available on request.

Application of Random Forest and Multiple Linear Regression Techniques to QSPR Prediction of an Aqueous Solubility for Military Compounds.

The relationship between the aqueous solubility of more than two thousand eight hundred organic compounds and their structures was investigated using a QSPR approach based on Simplex Representation of Molecular Structure (SiRMS). The dataset consists of 2537 diverse organic compounds. Multiple Linear Regression (MLR) and Random Forest (RF) methods were used for statistical modeling at the 2D level of representation of molecular structure. Statistical characteristics of the best models are quite good (MLR method: R(2) =0.85, Q(2) =0.83; RF method: R(2) =0.99, R(2) oob =0.88). The external validation set of 301 compounds (including 47 nitro-, nitroso- and nitrogen-rich compounds of military interest) which were not included in the training set and modeling process, was used for evaluation of the models predictivity. Thus, well-fitted and robust (R(2) test (MLR)=0.76 and R(2) test (RF)=0.82) models were obtained for both statistical techniques using descriptors based on the topological structural information only. The predicted solubility values for military compounds are in good agreement with experimental ones. Developed QSPR models represent powerful and easy-to-use virtual screening tool that can be recommended for prediction of aqueous solubility.

Application of quantum chemical approximations to environmental problems: prediction of water solubility for nitro compounds.

Water solubility values for 27 nitro compounds with experimentally measured values were computed using the conductor-like screening model for real solvent (COSMO-RS) based on the density functional theory and COSMO technique. We have found that the accuracy of the COSMO-RS approach for prediction of water solubility of liquid nitro compounds is impressively high (the errors are lower than 0.1 LU). However, for some solid nitro compounds, especially nitramines, there is sufficient disagreement between calculated and experimental values. In order to increase the accuracy of predictions the quantitative structure-property relationship (QSPR) part of the COSMO-RS approach has been modified. The solubility values calculated by the modified COSMO-RS method have shown much better agreement with the experimental values (the mean absolute errors are lower than 0.5 LU). Furthermore, this technique has been used for prediction of water solubility for an expanded set of 23 nitro compounds including nitroaromatic, nitramines, nitroanisoles, nitrogen rich compounds, and some their nitroso and amino derivatives with unknown experimental values. The solubility values predicted using the proposed computational technique could be useful for the determination of the environmental fate of military and industrial wastes and the development of remediation strategies for contaminated soils and waters. This predictive capability is especially important for unstable compounds and for compounds that have yet to be synthesized.

Application of random forest approach to QSAR prediction of aquatic toxicity.

This work is devoted to the application of the random forest approach to QSAR analysis of aquatic toxicity of chemical compounds tested on Tetrahymena pyriformis. The simplex representation of the molecular structure approach implemented in HiT QSAR Software was used for descriptors generation on a two-dimensional level. Adequate models based on simplex descriptors and the RF statistical approach were obtained on a modeling set of 644 compounds. Model predictivity was validated on two external test sets of 339 and 110 compounds. The high impact of lipophilicity and polarizability of investigated compounds on toxicity was determined. It was shown that RF models were tolerant for insertion of irrelevant descriptors as well as for randomization of some part of toxicity values that were representing a "noise". The fast procedure of optimization of the number of trees in the random forest has been proposed. The discussed RF model had comparable or better statistical characteristics than the corresponding PLS or KNN models.

The effects of characteristics of substituents on toxicity of the nitroaromatics: HiT QSAR study.

The present study applies the Hierarchical Technology for Quantitative Structure-Activity Relationships (HiT QSAR) for (i) evaluation of the influence of the characteristics of 28 nitroaromatic compounds (some of which belong to a widely known class of explosives) as to their toxicity; (ii) prediction of toxicity for new nitroaromatic derivatives; (iii) analysis of the effects of substituents in nitroaromatic compounds on their toxicity in vivo. The 50% lethal dose concentration for rats (LD50) was used to develop the QSAR models based on simplex representation of molecular structure. The preliminary 1D QSAR results show that even the information on the composition of molecules reveals the main tendencies of changes in toxicity. The statistic characteristics for partial least squares 2D QSAR models are quite satisfactory (R2 = 0.96-0.98; Q2 = 0.91-0.93; R2 (test) = 0.89-0.92), which allows us to carry out the prediction of activity for 41 novel compounds designed by the application of new combinations of substituents represented in the training set. The comprehensive analysis of toxicity changes as a function of substituent position and nature was carried out. Molecular fragments that promote and interfere with toxicity were defined on the basis of the obtained models. It was shown that the mutual influence of substituents in the benzene ring plays a crucial role regarding toxicity. The influence of different substituents on toxicity can be mediated via different C-H fragments of the aromatic ring.

Quantitative structure-activity relationship studies of [(biphenyloxy)propyl]isoxazole derivatives. Inhibitors of human rhinovirus 2 replication.

The 50% cytotoxic concentration (CC50) in HeLa cells, the 50% inhibitory concentration (IC50) against human rhinovirus 2 (HRV-2), and the selectivity index (SI = CC50/IC50) of [(biphenyloxy)propyl]isoxazole derivatives were used to develop quantitative structure-activity relationships (QSAR) based on simplex representation of molecular structure. Statistic characteristics for partial least-squares models are quite satisfactory (R2 = 0.838 - 0.918; Q2 = 0.695 - 0.87) for prediction of CC50, IC50, and SI values and permit the virtual screening and molecular design of new compounds with strong anti-HRV-2 activity. The quality of prognosis for designed compounds was additionally estimated by analysis of domain applicability for each QSAR model. A hypothesis to the effect that terminal benzene substituents must have negative electrostatic potential and definite length (approximately 5.5-5.6 A) to possess strong antiviral activity has been suggested. The quality of developed analysis, i.e., high level of antiviral action of three new designed compounds, has been confirmed experimentally.

Hierarchic system of QSAR models (1D-4D) on the base of simplex representation of molecular structure.

In this work, a hierarchic system of QSAR models from 1D to 4D is considered on the basis of the simplex representation of molecular structure (SiRMS). The essence of this system is that the QSAR problem is solved sequentially in a series of the improved models of the description of molecular structure. Thus, at each subsequent stage of a hierarchic system, the QSAR problem is not solved ab ovo, but rather the information obtained from the previous step is used. Actually, we deal with a system of solutions defined more exactly. In the SiRMS approach, a molecule is represented as a system of different simplex descriptors (tetratomic fragments with fixed composition, structure, chirality and symmetry). The level of simplex-descriptor detail increases consecutively from 1D to 4D representations of molecular structure. It enables us to determine the fragments of structure that promote or interfere with the given biological activity easily. Molecular design of compounds with a given level of activity is possible on the basis of SiRMS. The efficiency of the method is demonstrated for the example of the analysis of substituted piperazines affinity for the 5-HT1A receptor.

The analysis of structure-anticancer and antiviral activity relationships for macrocyclic pyridinophanes and their analogues on the basis of 4D QSAR models (simplex representation of molecular structure).

A new 4D-QSAR approach has been considered. For all investigated molecules the 3D structural models have been created and the set of conformers (fourth dimension) have been used. Each conformer is represented as a system of different simplexes (tetratomic fragments of fixed structure, chirality and symmetry). The investigation of influence of molecular structure of macrocyclic pyridinophanes, their analogues and certain other compounds on anticancer and antiviral (anti-influenza, antiherpes and antiadenovirus) activity has been carried out by means of the 4D-QSAR. Statistic characteristics for QSAR of PLS (partial least squares) models are satisfactory (R = 0.92-0.97; CVR = 0.63-0.83). Molecular fragments increasing and decreasing biological activity were defined. This information may be useful for design, and direct synthesis of novel anticancer and antiviral agents.