Local Graph Invariants Research Articles

In silico development of novel angiotensin-converting-enzyme-I inhibitors by Monte Carlo optimization based QSAR modeling, molecular docking studies and ADMET predictions

Within the realm of pharmacological strategies for cardiovascular diseases (CVD) like hypertension, stroke, and heart failure, targeting the angiotensin-converting enzyme I (ACE-I) stands out as a significant treatment approach. This study employs QSAR modeling using Monte Carlo optimization techniques to investigate a range of compounds known for their ACE-I inhibiting properties. The modeling process involved leveraging local molecular graph invariants and SMILES notation as descriptors to develop conformation-independent QSAR models. The dataset was segmented into distinct sets for training, calibration, and testing to ensure model accuracy. Through the application of various statistical analyses, the efficacy, reliability, and predictive capability of the models were evaluated, showcasing promising outcomes. Additionally, molecular fragments derived from SMILES notation descriptors were identified to elucidate the activity changes observed in the compounds. The validation of the QSAR model and designed inhibitors was carried out via molecular docking, aligning well with the QSAR results. To ascertain the drug-worthiness of the designed molecules, their physicochemical properties were computed, aiding in the prediction of ADME parameters, pharmacokinetic attributes, drug-likeness, and medicinal chemistry compatibility.

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

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

Development of Novel Therapeutics for Schizophrenia Treatment Based on a Selective Positive Allosteric Modulation of α1-Containing GABAARs-In Silico Approach.

For the development of atypical antipsychotics, the selective positive allosteric modulation of the ionotropic GABAA receptor (GABAAR) has emerged as a promising approach. In the presented research, two unrelated methods were used for the development of QSAR models for selective positive allosteric modulation of 1-containing GABAARs with derivatives of imidazo [1,2-a]-pyridine. The development of conformation-independent QSAR models, based on descriptors derived from local molecular graph invariants and SMILES notation, was achieved with the Monte Carlo optimization method. From the vast pool of 0D, 1D, and 2D molecule descriptors, the GA-MLR method developed additional QSAR models. Various statistical methods were utilised for the determination of the developed models’ robustness, predictability, and overall quality, and according to the obtained results, all QSAR models are considered good. The molecular fragments that have a positive or negative impact on the studied activity were obtained from the studied molecules’ SMILES notations, and according to the obtained results, nine novel compounds were designed. The binding affinities to GABAAR of designed compounds were assessed with the application of molecular docking studies and the obtained results showed a high correlation with results obtained from QSAR modeling. To assess all designed molecules’ “drug-likeness”, their physicochemical descriptors were computed and utilised for the prediction of medicinal chemistry friendliness, pharmacokinetic properties, ADME parameters, and druglike nature.

QSAR modelling, molecular docking studies and ADMET predictions of polysubstituted pyridinylimidazoles as dual inhibitors of JNK3 and p38α MAPK

This research paper employs different types of QSAR modeling for the molecules that act as dual inhibitors of JNK3 and p38α MAPK. The SMILES notation and the local molecular graph invariants served as descriptors for QSAR model building, while the Monte Carlo optimization method was assigned the purpose of a model developer. GA-MLR was utilized to obtain a QSAR model from the pool of vast 2D molecule descriptors. To assess the developed models’ quality, robustness, and predictability, several statistical methods were employed, and these yielded favorable results. The molecular fragments which were responsible for the increase/decrease of the examined activity were identified and used for the computer-aided design of new compounds. Molecular docking studies were utilized for the final assessment of the designed inhibitors, highlighting an exceptional correlation with the QSAR modeling results. ADME parameters, pharmacokinetic properties, the drug-like nature, and medicinal chemistry friendliness were predicted by computing physicochemical descriptors to support drug discovery. Based on the obtained results, all the designed molecules possess high drug-likeness.

Development of non-peptide ACE inhibitors as novel and potent cardiovascular therapeutics: An in silico modelling approach

ABSTRACTAngiotensin-converting enzyme (ACE) inhibitors have been acknowledged as first-line agents for the treatment of hypertension and a variety of cardiovascular disorders. In this context, quantitative structure–activity relationship (QSAR) models for a series of non-peptide compounds as ACE inhibitors are developed based on Simplified Molecular Input-Line Entry System (SMILES) notation and local graph invariants. Three random splits into the training and test sets are used. The Monte Carlo method is applied for model development. Molecular docking studies are used for the final assessment of the developed QSAR model and the design of novel inhibitors. The statistical quality of the developed model is good. Molecular fragments responsible for the increase/decrease of the studied activity are calculated. The computer-aided design of new compounds, as potential ACE inhibitors, is presented. The predictive potential of the applied approach is tested, and the robustness of the model is proven using different methods. The results obtained from molecular docking studies are in excellent correlation with the results from QSAR studies. The presented study may be useful in the search for novel cardiovascular therapeutics based on ACE inhibition.

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

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

QSAR study of 2,4-dihydro-3H-1,2,4-triazol-3-ones derivatives as angiotensin II AT1 receptor antagonists based on the Monte Carlo method

The Monte Carlo method was used for QSAR modelling 2,4-dihydro-3H-1,2,4-triazol-3-ones derivatives as angiotensin II AT1 receptor antagonists. QSAR models were calculated with the representation of the molecular structure by the simplified molecular input-line entry system (SMILES) and with optimal molecular descriptors based on the SMILES notation and local graph invariants. One random split into the training and the test set was used. The statistical quality of the developed model was good. The best calculated QSAR model had the following statistical parameters: r 2 = 0.8701 for the training set and r 2 = 0.8430 for the test set. Novel statistical metric entitled as the index of ideality of correlation was used for final model assessment, and the obtained results were good. Structural indicators defined as molecular fragments responsible for increases and decreases of the studied activity were calculated. The computer-aided design of new compounds as potential angiotensin II AT1 receptor antagonists with the application of defined structural alerts was presented.

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

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

Prediction of gas chromatographic retention indices based on Monte Carlo method

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

QSAR study of dihydrofolate reductase inhibitors activities based on optimization of correlation weights of local graph invariants

The aim of this work is modeling the activities of 67 E. coli dihydrofolate reductase (DHFR) inhibitors 2,4-diamino-5-(substituted benzyl) pyramidines by optimization of correlation weights of local graph invariants (cwlgis), assisting genetic algorithm (GA). The relationship between the descriptors and molecular activities was modeled using radial basis function partial least squares (rbfPLS). Proper relation between activities and the optimized molecular descriptors were shown, R training = 0.92 and r test = 0.85. The results indicate promising potential for the optimization of a correlation weights scheme. It is the first application of GA in optimization of cwlgis. The study also shows the ability of rbfPLS, combined with GA, in a factor-based nonlinear QSAR modeling using simple flexible descriptors.

Improved QSAR modeling of anti-HIV-1 acivities by means of the optimized correlation weights of local graph invariants

AbstractWe report the results derived from the use of molecular descriptors calculated with the correlation weights (CWs) of local graph invariants for modeling of anti-HIV-1 potencies of two groups of reverse transcriptase inhibitors. The presence of different chemical elements in the molecular structure of the inhibitors and the Morgan extended connectivity values of zeroth-, first-, and second order have been examined as local graph invariants in the labeled hydrogen-filled graphs. We have computed via Monte Carlo optimization procedure the values of CWs which produce the largest possible correlation coefficient between the numerical data on the anti-HIV-1 potencies and those values of the descriptors on the training set. The model of the anti-HIV-1 activity obtained with compounds of training set by means of optimization of correlation weights of chemical elements present together with Morgan extended connectivity of first order makes up a sensible model for a satisfactory prediction of the endpoints of the compounds belonging to the test set.

Correlation weighting of valence shells in QSAR analysis of toxicity

In the rainbow trout ( Oncorhynchus mykiss), we studied the acute toxicity LC 50-96h of 274 organic pesticides with a wide variety of molecular structures. Optimization of correlation weights of local and global graph invariants (OCWLGI) gave quantitative structure–activity relationships (QSARs) for predicting toxicity. We used a labeled hydrogen-filled graph (LHFG) to elucidate the molecular structure. We also used the extended connectivity of zero ( 0EC k ), first ( 1EC k ), and second ( 2EC k ) order, numbers of path lengths 2 (P2 k ) and 3 (P3 k ) starting from a given vertex in the LHFG, and valence shells of second order (S2 k ). S2 k is the sum of the degree of vertices at distance 2 from a given vertex k. The presence of three-, five-, and six-member cycles and hydrogen bond indices suggested they might be used as global LHFG invariants. We applied this method to a broad set of pesticides, to predict toxicity for the trout. The best model used weighted S2 k and global LHFG invariants. Statistical characteristics of this model are as follows: n = 233, r 2 = 0.7689, r 2(pred) = 0.7688, s = 0.75, F = 769 (training set); n = 41, r 2 = 0.6421, r 2(pred) = 0.4241, s = 1.14, F = 70 (test set).

QSAR models for Daphnia toxicity of pesticides based on combinations of topological parameters of molecular structures

A topological parameter is defined as an integer value of a given local or global invariant of a molecular graph. We examined three types of local graph invariants, the vertex degrees ( 0EC), the extended connectivity of first order ( 1EC), and the numbers of paths of length two (P2), as elementary invariants for construction of quantitative structure–activity relationships (QSAR). We also examined combined invariants, obtained by multiplying one of these three elementary types with another (i.e., [ 0EC · 1EC], [ 0EC · P2], and [ 1EC · P2]), as graph invariants. Finally, global invariants were used in the QSAR analyses, codifying the presence and nature of cycles in the molecular structures under consideration. We used the correlation weights of these invariants to obtain optimal descriptors. These descriptors have been used in one-variable models to predict toxicity toward Daphnia magna for a set of pesticides. Statistical characteristics of the best model, based on the correlation weight of local topological parameters (the [ 0EC · P2]) together with the global topological parameters, are the following: n = 220, r 2 = 0.7822, s = 0.849, F = 783 (training set); n = 42, r 2 = 0.7388, s = 0.941, F = 113 (test set). The role of these topological parameters is discussed.

QSPR modeling of the water solubility of diverse functional aliphatic compounds by optimization of correlation weights of local graph invariants

The optimization of correlation weights scheme was used to model the water solubility (ln S) of diverse functional aliphatic compounds (n = 193). The optimized descriptor formulated based on the data of a training set (n = 96) generated statistically acceptable relations for the training set (r2 = 0.987), test set (n = 97; r2 = 0.986) and combined set (r2 = 0.987). When the relation of ln S values with the optimized molecular descriptor formulated based on the data of the training set was used for the calculation of ln S values of the training set, r(pred)2 value was found to be satisfactory (0.988), which is indicative of the predictive potential of the scheme. The results indicate the promising potential of the optimization of correlation weights scheme in modeling studies.

Nearest neighboring code and hydrogen bond index in labeled hydrogen-filled graph and graph of atomic orbitals: application to model of normal boiling points of haloalkanes

Nearest Neighboring Code (NNC) of given vertex in molecular graph is a topological and chemical invariant. Numerical value of the NNC k of given kth vertex is mathematical function of both number and composition of vertices which are neighbors of the kth vertex in molecular graph. Hydrogen Bond Index (HBI) is global invariant of a molecular graph. Descriptors calculated with optimal correlation weights of the NNC and HBI have been studied. The optimal correlation weights have been obtained by Monte Carlo method. This approach is named as Optimization of Correlation Weights of Local and Global graph Invariants (OCWLI). Two categories of molecular graph have been used. First category is a Labeled Hydrogen-Filled Graphs (LHFGs). Second category is a Graph of atomic orbitals (GAO). Types of vertices in the LHFG are chemical elements (i.e. H, C, F, and Cl). Types of vertices in the GAO are atomic orbitals (i.e. 1s 1, 1s 2, 2s 2, 2p 2, 2p 5, 2p 6, 3s 2, and 3p 5). Comparison of series of models based on extended connectivity, NNC, and HBI in the LHFG and GAO has shown, that best OCWLI model is one based on optimized correlation weights NNC and HBI in the GAO. Statistical characteristics of this model are the following: n=138; r 2=0.9897; s=7.87 (°C); F=13094 (Training Set), n=138; r 2=0.9871; s=6.94 (°C); F=10374 (Test Set), n=276; r 2=0.9886; s=7.41 (°C); F=23863 (all compounds)

QSPR modeling aqueous solubility of polychlorinated biphenyls by optimization of correlation weights of local and global graph invariants

AbstractAqueous solubilities of polychlorinated biphenyls have been correlated with topological molecular descriptors which are functions of local and global invariants of labeled hydrogen filled graphs. Morgan extended connectivity and nearest neighboring codes have been used as local graph invariants. The number of chlorine atoms in biphenyls has been employed as a global graph invariant. Present results show that taking into account correlation weights of global invariants gives quite reasonable improvement of statistical characteristics for the prediction of aqueous solubilities of polychlorinated biphenyls.

QSAR Modeling ANTI-HIV-1 Activities by Optimization of Correlation Weights of Local Graph Invariants

Results of using descriptors calculated with the correlation weights (CWs) of local graph invariants for modeling of anti-HIV-1 potencies of two groups of reverse transcriptase (RT) inhibitors are reported. Presence of different chemical elements in molecular structure of the inhibitors and the presence of Morgan extended connectivity values of zeroth-, first- and second order have been examined as local graph invariants in the labeled hydrogen-filled graphs. By Monte Carlo method optimization procedure, values of the CWs which produce as large values as possible of correlation coefficient between the numerical data on the anti-HIV-1 potencies and values of the descriptors on the training set have been computed. The model of the anti-HIV-1 activity obtained with compounds of training set by means of optimization of correlation weights of presence of chemical elements together with the presence of Morgan extended connectivity of first order is reasonable well model for the prediction of endpoints under consideration for compounds of the test set.

QSPR Modeling of Lipid‐Water Partition Coefficient by Optimization of Correlation Weights of Local Graph Invariants.

The optimization of correlation weights scheme was applied to model lipid-water partition coefficient (log P) of two sets of diverse functional aliphatic and aromatic compounds. In both cases, the optimized descriptors formulated based on the data of training sets generated statistically acceptable relations for the corresponding training sets, test sets, and combined sets. When the relations of log P values with the optimized molecular descriptors formulated based on the data of the training sets were used for calculation of log P values of the corresponding training sets, rpred2 values were found to be satisfactory (above 0.99) in both cases, which is indicative of the predictive potential of the scheme. The results indicate promising potential of the optimization of a correlation weights scheme in modeling studies.

QSPR modeling the aqueous solubility of alcohols by optimization of correlation weights of local graph invariants

Optimization of correlation weights of local graph invariants is an approach to model molecular properties and/or activities of chemical or/and biological interest. The essence of the approach may be described by means of three main steps: first, a descriptor which is a function of the weights of local graph invariants must be defined by the suitable choice among the different possibilities from the pool of molecular descriptors; second, correlation weights values which produce as large as possible correlation coefficient value between the selected property values and the descriptor data under consideration are calculated by Monte Carlo optimization procedure (the correlation coefficient is used as the quality objective function); third, a relationship such as property = C0 + C1 descriptor has to be calculated and validated with structures of some training set resorting to the standard least square method. We obtain quite satisfactory results using this calculation procedure to model the aqueous solubility of alcohols whose statistical characteristics are: n = 30, r = 0.9843, s = 0.176, F = 870 (Training Set); n = 33, r = 0.9965, s = 0.0902, F = 4456 (Test Set); n = 63, r = 0.9931, s = 0.121, F = 4379 (complete set of alcohol molecules).

QSPR modeling of lipid-water partition coefficient by optimization of correlation weights of local graph invariants.

The optimization of correlation weights scheme was applied to model lipid-water partition coefficient (log P) of two sets of diverse functional aliphatic and aromatic compounds. In both cases, the optimized descriptors formulated based on the data of training sets generated statistically acceptable relations for the corresponding training sets, test sets, and combined sets. When the relations of log P values with the optimized molecular descriptors formulated based on the data of the training sets were used for calculation of log P values of the corresponding training sets, rpred2 values were found to be satisfactory (above 0.99) in both cases, which is indicative of the predictive potential of the scheme. The results indicate promising potential of the optimization of a correlation weights scheme in modeling studies.