Development of linear, ensemble, and nonlinear models for the prediction and interpretation of the biological activity of a set of PDGFR inhibitors

Prediction of Human Liver Microsome Clearance with Chirality-Focused Graph Neural Networks

In drug candidate design, clearance is one of the most crucial pharmacokinetic parameters to consider. Recent advancements in machine learning techniques coupled with the growing accumulation of drug data have paved the way for the construction of computational models to predict drug clearance. However, concerns persist regarding the reliability of data collected from public sources, and a majority of current in silico quantitative structure-property relationship models tend to neglect the influence of molecular chirality. In this study, we meticulously examined human liver microsome (HLM) data from public databases and constructed two distinct data sets with varying HLM data quantity and quality. Two baseline models (RF and DNN) and three chirality-focused GNNs (DMPNN, TetraDMPNN, and ChIRo) were proposed, and their performance on HLM data was evaluated and compared with each other. The TetraDMPNN model, which leverages chirality from 2D structure, exhibited the best performance with a test R2 of 0.639 and a test root-mean-squared error of 0.429. The applicability domain of the model was also defined by using a molecular similarity-based method. Our research indicates that graph neural networks capable of capturing molecular chirality have significant potential for practical application and can deliver superior performance.

Random kernel k-nearest neighbors regression

The k-nearest neighbors (KNN) regression method, known for its nonparametric nature, is highly valued for its simplicity and its effectiveness in handling complex structured data, particularly in big data contexts. However, this method is susceptible to overfitting and fit discontinuity, which present significant challenges. This paper introduces the random kernel k-nearest neighbors (RK-KNN) regression as a novel approach that is well-suited for big data applications. It integrates kernel smoothing with bootstrap sampling to enhance prediction accuracy and the robustness of the model. This method aggregates multiple predictions using random sampling from the training dataset and selects subsets of input variables for kernel KNN (K-KNN). A comprehensive evaluation of RK-KNN on 15 diverse datasets, employing various kernel functions including Gaussian and Epanechnikov, demonstrates its superior performance. When compared to standard KNN and the random KNN (R-KNN) models, it significantly reduces the root mean square error (RMSE) and mean absolute error, as well as improving R-squared values. The RK-KNN variant that employs a specific kernel function yielding the lowest RMSE will be benchmarked against state-of-the-art methods, including support vector regression, artificial neural networks, and random forests.

Comparison and improvement of the predictability and interpretability with ensemble learning models in QSPR applications

Ensemble learning helps improve machine learning results by combining several models and allows the production of better predictive performance compared to a single model. It also benefits and accelerates the researches in quantitative structure–activity relationship (QSAR) and quantitative structure–property relationship (QSPR). With the growing number of ensemble learning models such as random forest, the effectiveness of QSAR/QSPR will be limited by the machine’s inability to interpret the predictions to researchers. In fact, many implementations of ensemble learning models are able to quantify the overall magnitude of each feature. For example, feature importance allows us to assess the relative importance of features and to interpret the predictions. However, different ensemble learning methods or implementations may lead to different feature selections for interpretation. In this paper, we compared the predictability and interpretability of four typical well-established ensemble learning models (Random forest, extreme randomized trees, adaptive boosting and gradient boosting) for regression and binary classification modeling tasks. Then, the blending methods were built by summarizing four different ensemble learning methods. The blending method led to better performance and a unification interpretation by summarizing individual predictions from different learning models. The important features of two case studies which gave us some valuable information to compound properties were discussed in detail in this report. QSPR modeling with interpretable machine learning techniques can move the chemical design forward to work more efficiently, confirm hypothesis and establish knowledge for better results.

A novel hybrid method named electron conformational genetic algorithm as a 4D QSAR investigation to calculate the biological activity of the tetrahydrodibenzazosines

To understand the structure-activity correlation of a group of tetrahydrodibenzazocines as inhibitors of 17β-hydroxysteroid dehydrogenase type 3, we have performed a combined genetic algorithm (GA) and four-dimensional quantitative structure-activity relationship (4D-QSAR) modeling study. The computed electronic and geometry structure descriptors were regulated as a matrix and named as electron-conformational matrix of contiguity (ECMC). A chemical property-based pharmacophore model was developed for series of tetrahydrodibenzazocines by EMRE software package. GA was employed to choose an optimal combination of parameters. A model has been developed for estimating anticancer activity quantitatively. All QSAR models were established with 40 compounds (training set), then they were considered for selective capability with additional nine compounds (test set). A statistically valid 4D-QSAR ( R training 2 = 0.856 , R test 2 = 0.851 and q² = 0.650) with good external set prediction was obtained.

Cheminfomatic-based Drug Discovery of Human Tyrosine Kinase Inhibitors

Receptor Tyrosine Kinases (RTKs) are essential components for regulating cell-cell signaling and communication events in cell growth, proliferation, differentiation, survival and metabolism. Deregulation of RTKs and their associated signaling pathways can lead to a wide variety of human diseases such as immunodeficiency, diabetes, arterosclerosis, psoriasis and cancer. Thus RTKs have become one of the most important drug targets families in recent decade. Pharmaceutical companies have dedicated their research efforts towards the discovery of small-molecule inhibitors of RTKs, many of which had been approved by the U.S. Food and Drug Administration (US FDA) or are currently in clinical trials. The great successes in the development of small-molecule inhibitors of RTKs are largely attributed to the use of modern cheminformatic approaches to identifying lead scaffolds. Those include the quantitative structure-activity relationship (QSAR) modeling, as well as the structure-, and ligand-based pharmacophore modeling techniques in this case. Herein we inspected the literature thoroughly in an effort to conduct a comparative analysis of major findings regarding the essential structure-activity relationships (SARs)/pharmacophore features of known active RTK inhibitors, most of which were collected from cheminformatic modeling approaches.

Estimation of biliary excretion of foreign compounds using properties of molecular structure

Biliary excretion is one of the main elimination pathways for drugs and/or their metabolites. Therefore, an insight into the structural profile of cholephilic compounds through accurate modelling of the biliary excretion is important for the estimation of clinical pharmacokinetics in early stages of drug discovery. The aim of this study was to develop quantitative structure-activity relationships as computational tools for the estimation of biliary excretion and identification of the molecular properties controlling this process. The study used percentage of dose excreted intact into bile measured in vivo in rat for a diverse dataset of 217 compounds. Statistical techniques were multiple linear regression analysis, regression trees, random forest and boosted trees. A simple regression tree model generated using the CART algorithm was the most accurate in the estimation of the percentage of bile excretion of compounds, and this outperformed the more sophisticated boosted trees and random forest techniques. Analysis of the outliers indicated that the models perform best when lipophilicity is not too extreme (log P < 5.35) and for compounds with molecular weight above 280 Da. Molecular descriptors selected by all these models including the top ten incorporated in boosted trees and random forest indicated a higher biliary excretion for relatively hydrophilic compounds especially if they are anionic or cationic, and have a large molecular size. A statistically validated molecular weight threshold for potentially significant biliary excretion was above 348 Da.

Classification models for safe drug molecules

Frequent failure of drug candidates during development stages remains the major deterrent for an early introduction of new drug molecules. The drug toxicity is the major cause of expensive late-stage development failures. An early identification/optimization of the most favorable molecule will naturally save considerable cost, time, human efforts and minimize animal sacrifice. (Quantitative) Structure Activity Relationships [(Q)SARs] represent statistically derived predictive models correlating biological activity (including desirable therapeutic effect and undesirable side effects) of chemicals (drugs/toxicants/environmental pollutants) with molecular descriptors and/or properties. (Q)SAR models which categorize the available data into two or more groups/classes are known as classification models. Numerous techniques of diverse nature are being presently employed for development of classification models. Though there is an increasing use of classification models for prediction of either biological activity or toxicity, the future trend will naturally be towards the development of classification models capable of simultaneous prediction of biological activity, toxicity, and pharmacokinetic parameters so as to accelerate development of bioavailable safe drug molecules.

Machine learning methods for property prediction in chemoinformatics: Quo Vadis?

This paper is focused on modern approaches to machine learning, most of which are as yet used infrequently or not at all in chemoinformatics. Machine learning methods are characterized in terms of the "modes of statistical inference" and "modeling levels" nomenclature and by considering different facets of the modeling with respect to input/ouput matching, data types, models duality, and models inference. Particular attention is paid to new approaches and concepts that may provide efficient solutions of common problems in chemoinformatics: improvement of predictive performance of structure-property (activity) models, generation of structures possessing desirable properties, model applicability domain, modeling of properties with functional endpoints (e.g., phase diagrams and dose-response curves), and accounting for multiple molecular species (e.g., conformers or tautomers).

Using kernel alignment to select features of molecular descriptors in a QSAR study

Quantitative structure-activity relationships (QSARs) correlate biological activities of chemical compounds with their physicochemical descriptors. By modeling the observed relationship seen between molecular descriptors and their corresponding biological activities, we may predict the behavior of other molecules with similar descriptors. In QSAR studies, it has been shown that the quality of the prediction model strongly depends on the selected features within molecular descriptors. Thus, methods capable of automatic selection of relevant features are very desirable. In this paper, we present a new feature selection algorithm for a QSAR study based on kernel alignment which has been used as a measure of similarity between two kernel functions. In our algorithm, we deploy kernel alignment as an evaluation tool, using recursive feature elimination to compute a molecular descriptor containing the most important features needed for a classification application. Empirical results show that the algorithm works well for the computation of descriptors for various applications involving different QSAR data sets. The prediction accuracies are substantially increased and are comparable to those from earlier studies.

Models for antitubercular activity of 5â-O-[(N-Acyl)sulfamoyl]adenosines

The relationship between topological indices and antitubercular activity of 5â-O-[(N-Acyl)sulfamoyl]adenosines has been investigated. A data set consisting of 31 analogues of 5â-O-[(N-Acyl)sulfamoyl]adenosines was selected for the present study. The values of numerous topostructural and topochemical indices for each of 31 differently substituted analogues of the data set were computed using an in-house computer program. Resulting data was analyzed and suitable models were developed through decision tree, random forest and moving average analysis (MAA). The goodness of the models was assessed by calculating overall accuracy of prediction, sensitivity, specificity and Mathews correlation coefficient. Pendentic eccentricity index â a novel highly discriminating, non-correlating pendenticity based topochemical descriptor â was also conceptualized and successfully utilized for the development of a model for antitubercular activity of 5â-O-[(N-Acyl)sulfamoyl]adenosines. The proposed index exhibited not only high sensitivity towards both the presence as well as relative position(s) of pendent/heteroatom(s) but also led to significant reduction in degeneracy. Random forest correctly classified the analogues into active and inactive with an accuracy of 67.74%. A decision tree was also employed for determining the importance of molecular descriptors. The decision tree learned the information from the input data with an accuracy of 100% and correctly predicted the cross-validated (10 fold) data with accuracy up to 77.4%. Statistical significance of proposed models was also investigated using intercorrelation analysis. Accuracy of prediction of proposed MAA models ranged from 90.4 to 91.6%.

Estimation of the applicability domain of kernel-based machine learning models for virtual screening

BACKGROUND

The virtual screening of large compound databases is an important application of structural-activity relationship models. Due to the high structural diversity of these data sets, it is impossible for machine learning based QSAR models, which rely on a specific training set, to give reliable results for all compounds. Thus, it is important to consider the subset of the chemical space in which the model is applicable. The approaches to this problem that have been published so far mostly use vectorial descriptor representations to define this domain of applicability of the model. Unfortunately, these cannot be extended easily to structured kernel-based machine learning models. For this reason, we propose three approaches to estimate the domain of applicability of a kernel-based QSAR model.

RESULTS

We evaluated three kernel-based applicability domain estimations using three different structured kernels on three virtual screening tasks. Each experiment consisted of the training of a kernel-based QSAR model using support vector regression and the ranking of a disjoint screening data set according to the predicted activity. For each prediction, the applicability of the model for the respective compound is quantitatively described using a score obtained by an applicability domain formulation. The suitability of the applicability domain estimation is evaluated by comparing the model performance on the subsets of the screening data sets obtained by different thresholds for the applicability scores. This comparison indicates that it is possible to separate the part of the chemspace, in which the model gives reliable predictions, from the part consisting of structures too dissimilar to the training set to apply the model successfully. A closer inspection reveals that the virtual screening performance of the model is considerably improved if half of the molecules, those with the lowest applicability scores, are omitted from the screening.

CONCLUSION

The proposed applicability domain formulations for kernel-based QSAR models can successfully identify compounds for which no reliable predictions can be expected from the model. The resulting reduction of the search space and the elimination of some of the active compounds should not be considered as a drawback, because the results indicate that, in most cases, these omitted ligands would not be found by the model anyway.

Simultaneous feature selection and parameter optimisation using an artificial ant colony: case study of melting point prediction

BACKGROUND

We present a novel feature selection algorithm, Winnowing Artificial Ant Colony (WAAC), that performs simultaneous feature selection and model parameter optimisation for the development of predictive quantitative structure-property relationship (QSPR) models. The WAAC algorithm is an extension of the modified ant colony algorithm of Shen et al. (J Chem Inf Model 2005, 45: 1024-1029). We test the ability of the algorithm to develop a predictive partial least squares model for the Karthikeyan dataset (J Chem Inf Model 2005, 45: 581-590) of melting point values. We also test its ability to perform feature selection on a support vector machine model for the same dataset.

RESULTS

Starting from an initial set of 203 descriptors, the WAAC algorithm selected a PLS model with 68 descriptors which has an RMSE on an external test set of 46.6 degrees C and R2 of 0.51. The number of components chosen for the model was 49, which was close to optimal for this feature selection. The selected SVM model has 28 descriptors (cost of 5, epsilon of 0.21) and an RMSE of 45.1 degrees C and R2 of 0.54. This model outperforms a kNN model (RMSE of 48.3 degrees C, R2 of 0.47) for the same data and has similar performance to a Random Forest model (RMSE of 44.5 degrees C, R2 of 0.55). However it is much less prone to bias at the extremes of the range of melting points as shown by the slope of the line through the residuals: -0.43 for WAAC/SVM, -0.53 for Random Forest.

CONCLUSION

With a careful choice of objective function, the WAAC algorithm can be used to optimise machine learning and regression models that suffer from overfitting. Where model parameters also need to be tuned, as is the case with support vector machine and partial least squares models, it can optimise these simultaneously. The moving probabilities used by the algorithm are easily interpreted in terms of the best and current models of the ants, and the winnowing procedure promotes the removal of irrelevant descriptors.

Modeling of acetylcholinesterase inhibition by tacrine analogues using Bayesian-regularized Genetic Neural Networks and ensemble averaging

Acetylcholinesterase inhibition was modeled for a set of 136 tacrine analogues using Bayesian-regularized Genetic Neural Networks (BRGNNs). In the BRGNN approach the Bayesian-regularization avoids overtraining/overfitting and the genetic algorithm (GA) allows exploring an ample pool of 3D-descriptors. The predictive capacity of our selected model was evaluated by averaging multiple validation sets generated as members of diverse-training set neural network ensembles (NNEs). The ensemble averaging provides reliable statistics. When 40 members are assembled, the NNE provides a reliable measure of training and test set R values of 0.921 and 0.851 respectively. In other respects, the ability of the nonlinear selected GA space for differentiating the data was evidenced when the total data set was well distributed in a Kohonen Self-Organizing Map (SOM). The location of the inhibitors in the map facilitates the analysis of the connection between compounds and serves as a useful tool for qualitative predictions.

Assessing how well a modeling protocol captures a structure-activity landscape

We introduce the notion of structure-activity landscape index (SALI) curves as a way to assess a model and a modeling protocol, applied to structure-activity relationships. We start from our earlier work [ J. Chem. Inf. Model., 2008, 48, 646-658], where we show how to study a structure-activity relationship pairwise, based on the notion of "activity cliffs"--pairs of molecules that are structurally similar but have large differences in activity. There, we also introduced the SALI parameter, which allows one to identify cliffs easily, and which allows one to represent a structure-activity relationship as a graph. This graph orders every pair of molecules by their activity. Here, we introduce the new idea of a SALI curve, which tallies how many of these orderings a model is able to predict. Empirically, testing these SALI curves against a variety of models, ranging over two-dimensional quantitative structure-activity relationship (2D-QSAR), three-dimensional quantitative structure-activity relationship (3D-QSAR), and structure-based design models, the utility of a model seems to correspond to characteristics of these curves. In particular, the integral of these curves, denoted as SCI and being a number ranging from -1.0 to 1.0, approaches a value of 1.0 for two literature models, which are both known to be prospectively useful.

Asymmetric bagging and feature selection for activities prediction of drug molecules

Background

Activities of drug molecules can be predicted by QSAR (quantitative structure activity relationship) models, which overcomes the disadvantages of high cost and long cycle by employing the traditional experimental method. With the fact that the number of drug molecules with positive activity is rather fewer than that of negatives, it is important to predict molecular activities considering such an unbalanced situation.

Results

Here, asymmetric bagging and feature selection are introduced into the problem and asymmetric bagging of support vector machines (asBagging) is proposed on predicting drug activities to treat the unbalanced problem. At the same time, the features extracted from the structures of drug molecules affect prediction accuracy of QSAR models. Therefore, a novel algorithm named PRIFEAB is proposed, which applies an embedded feature selection method to remove redundant and irrelevant features for asBagging. Numerical experimental results on a data set of molecular activities show that asBagging improve the AUC and sensitivity values of molecular activities and PRIFEAB with feature selection further helps to improve the prediction ability.

Conclusion

Asymmetric bagging can help to improve prediction accuracy of activities of drug molecules, which can be furthermore improved by performing feature selection to select relevant features from the drug molecules data sets.

Protein radial distribution function (P-RDF) and Bayesian-Regularized Genetic Neural Networks for modeling protein conformational stability: Chymotrypsin inhibitor 2 mutants

Development of novel computational approaches for modeling protein properties is a main goal in applied Proteomics. In this work, we reported the extension of the radial distribution function (RDF) scores formalism to proteins for encoding 3D structural information with modeling purposes. Protein-RDF (P-RDF) scores measure spherical distributions on protein 3D structure of 48 amino acids/residues properties selected from the AAindex data base. P-RDF scores were tested for building predictive models of the change of thermal unfolding Gibbs free energy change (DeltaDeltaG) of chymotrypsin inhibitor 2 upon mutations. In this sense, an ensemble of Bayesian-Regularized Genetic Neural Networks (BRGNNs) yielded an optimum nonlinear model for the conformational stability. The ensemble predictor described about 84% and 70% variance of the data in training and test sets, respectively.

2D Autocorrelation, CoMFA, and CoMSIA modeling of protein tyrosine kinases' inhibition by substituted pyrido[2,3-d]pyrimidine derivatives

2D Autocorrelation, comparative molecular field analysis (CoMFA), and comparative molecular similarity indices analysis (CoMSIA) were undertaken for a series of substituted pyrido[2,3-d]pyrimidine derivatives to correlate platelet-derived growth factor receptor (PDGFR), fibroblast growth factor receptor (FGFR), and c-Src tyrosine kinases' inhibition with 2D and 3D structural properties of 22 known compounds. QSAR models with considerable internal as well as external predictive ability were obtained. The relevant 2D autocorrelation descriptors for modeling each protein tyrosine kinase (PTK) inhibitory activity were selected by genetic algorithm (GA) and multiple linear regression (MLR) approach. The 2D autocorrelation space brings different descriptors for each PTK inhibition and suggests the atomic properties relevant for the inhibitors to interact with each PTK active site. CoMFA and CoMSIA were developed with a focus on interpretative ability using coefficient contour maps. CoMSIA produced significantly better results for all correlations. The results indicate a strong correlation between the inhibitory activity of the modeled compounds and the hydrophobic and H-bond donor fields around them.

Amino acid sequence autocorrelation vectors and bayesian-regularized genetic neural networks for modeling protein conformational stability: Gene V protein mutants

Development of novel computational approaches for modeling protein properties from their primary structure is the main goal in applied proteomics. In this work, we reported the extension of the autocorrelation vector formalism to amino acid sequences for encoding protein structural information with modeling purposes. Amino acid sequence autocorrelation (AASA) vectors were calculated by measuring the autocorrelations at sequence lags ranging from 1 to 15 on the protein primary structure of 48 amino acid/residue properties selected from the AAindex data base. A total of 720 AASA descriptors were tested for building predictive models of the change of thermal unfolding Gibbs free energy change (delta deltaG) of gene V protein upon mutation. In this sense, ensembles of Bayesian-regularized genetic neural networks (BRGNNs) were used for obtaining an optimum nonlinear model for the conformational stability. The ensemble predictor described about 88% and 66% variance of the data in training and test sets respectively. Furthermore, the optimum AASA vector subset not only helped to successfully model unfolding stability but also well distributed wild-type and gene V protein mutants on a stability self-organized map (SOM), when used for unsupervised training of competitive neurons.

Ensembles of Bayesian-regularized genetic neural networks for modeling of acetylcholinesterase inhibition by huprines

Acetylcholinesterase inhibition was modeled for a set of huprines using ensembles of Bayesian-regularized Genetic Neural Networks. In the Bayesian-regularized Genetic Neural Network approach the Bayesian regularization avoids overfitted regressions and the genetic algorithm allows exploring a wide pool of three-dimensional descriptors. The predictive capacity of our selected model was evaluated by averaging multiple validation sets generated as members of neural network ensembles. When 60 members are assembled, the neural network ensemble provides a reliable measure of training and test set R(2)-values of 0.945 and 0.850 respectively. In other respects, the ability of the nonlinear selected genetic algorithm space for differentiate the data were evidenced when total data set was well distributed in a Kohonen self-organizing map. The analysis of the self-organizing map zones allows establishing the main structural features differentiated by our vectorial space.

Bias in random forest variable importance measures: illustrations, sources and a solution

BACKGROUND

Variable importance measures for random forests have been receiving increased attention as a means of variable selection in many classification tasks in bioinformatics and related scientific fields, for instance to select a subset of genetic markers relevant for the prediction of a certain disease. We show that random forest variable importance measures are a sensible means for variable selection in many applications, but are not reliable in situations where potential predictor variables vary in their scale of measurement or their number of categories. This is particularly important in genomics and computational biology, where predictors often include variables of different types, for example when predictors include both sequence data and continuous variables such as folding energy, or when amino acid sequence data show different numbers of categories.

RESULTS

Simulation studies are presented illustrating that, when random forest variable importance measures are used with data of varying types, the results are misleading because suboptimal predictor variables may be artificially preferred in variable selection. The two mechanisms underlying this deficiency are biased variable selection in the individual classification trees used to build the random forest on one hand, and effects induced by bootstrap sampling with replacement on the other hand.

CONCLUSION

We propose to employ an alternative implementation of random forests, that provides unbiased variable selection in the individual classification trees. When this method is applied using subsampling without replacement, the resulting variable importance measures can be used reliably for variable selection even in situations where the potential predictor variables vary in their scale of measurement or their number of categories. The usage of both random forest algorithms and their variable importance measures in the R system for statistical computing is illustrated and documented thoroughly in an application re-analyzing data from a study on RNA editing. Therefore the suggested method can be applied straightforwardly by scientists in bioinformatics research.

Bias in random forest variable importance measures: illustrations, sources and a solution

BACKGROUND

Variable importance measures for random forests have been receiving increased attention as a means of variable selection in many classification tasks in bioinformatics and related scientific fields, for instance to select a subset of genetic markers relevant for the prediction of a certain disease. We show that random forest variable importance measures are a sensible means for variable selection in many applications, but are not reliable in situations where potential predictor variables vary in their scale of measurement or their number of categories. This is particularly important in genomics and computational biology, where predictors often include variables of different types, for example when predictors include both sequence data and continuous variables such as folding energy, or when amino acid sequence data show different numbers of categories.

RESULTS

Simulation studies are presented illustrating that, when random forest variable importance measures are used with data of varying types, the results are misleading because suboptimal predictor variables may be artificially preferred in variable selection. The two mechanisms underlying this deficiency are biased variable selection in the individual classification trees used to build the random forest on one hand, and effects induced by bootstrap sampling with replacement on the other hand.

CONCLUSION

We propose to employ an alternative implementation of random forests, that provides unbiased variable selection in the individual classification trees. When this method is applied using subsampling without replacement, the resulting variable importance measures can be used reliably for variable selection even in situations where the potential predictor variables vary in their scale of measurement or their number of categories. The usage of both random forest algorithms and their variable importance measures in the R system for statistical computing is illustrated and documented thoroughly in an application re-analyzing data from a study on RNA editing. Therefore the suggested method can be applied straightforwardly by scientists in bioinformatics research.

QSAR studies on 1-phenylbenzimidazoles as inhibitors of the platelet-derived growth factor

This work is devoted to the development of quantitative structure-activity relationship (QSAR) models of the biological activity of 123 1-phenylbenzimidazoles as inhibitors of the PDGF receptor. The molecular features are represented by chemical descriptors that have been calculated on geometrical, topological, quantum mechanical, and electronic basis by using CODESSA PRO. The obtained models, linear (multilinear regression) and nonlinear (artificial neural network), are aimed to link the structures to their reported activity log 1/IC50. The former model can be used for physico-chemical interpretation, while the latter possesses a superior predictive ability.

Evaluation of a neural networks QSAR method based on ligand representation using substituent descriptors. Application to HIV-1 protease inhibitors

We present here a neural networks method designed to predict biological activity based on a local representation of the ligand. The compounds of the series are represented by a vector mapping for each of four substituent properties: volume, log P, dipole moment and a simple 'steric' parameter relating to its shape. This ligand representation was tested using neural networks on a set of 42 cyclic-urea derivatives, inhibiting HIV-1 protease. The leave-one-out cross-validation using all descriptors in the input gave a correlation factor between prediction and experiment of 0.76 for the overall set and 0.88 when three outliers were left out. To rank the significance of the four descriptors, we further tested all combinations of two and three parameters for each substituent, using two disjunctive testing sets of five inhibitors. In these sets, vectors with extreme descriptor values were used either in the training or the testing set (sets A and B, respectively). The method is a very good interpolator (set A, 95+/-2% accuracy) but a less effective extrapolator (set B, 85+/-2% accuracy). Generally, the combinations including the 'steric' parameter predict better than average, while those containing the volume are less effective. The best prediction, 98.8+/-1.2%, was obtained when log P, the dipole and the steric parameter were used on set A. At the opposite end, the lowest ranked descriptor set was obtained when replacing log P with the volume, giving 92.3+/-6.7% accuracy over the set A.

Probing the Structural and Electronic Factors Affecting the Adsorption and Reactivity of Alkenes in Acidic Zeolites Using DFT Calculations and Multivariate Statistical Methods

Quantum mechanical (QM) cluster calculations have been performed on a model of ZSM-5 at DFT and MP2 levels. We investigated how the adsorption energies and the energetics of alkoxide intermediate formation of six different alkene substrates, ethene, propene, 1-butene, cis/trans butene, and isobutene, vary in this zeolite model. An analysis of the DFT geometric, electronic, and energetic parameters of the zeolite-substrate complexes, transition states, and alkoxide intermediates is performed using principal components analysis (PCA) and partial least squares (PLS). These deliver an insight into the correlated changes that occur between molecular structure and energy along the reaction coordinate between the physisorbed and chemisorbed species within the zeolite. To the best of our knowledge, this is the first occasion multivariate techniques such as PCA or PLS have been employed to profile the changes in electronics, distances, and angles in QM calculations of catalytic systems such as zeolites. We find the calculated adsorption and the alkoxide intermediate energies correlate strongly with the absolute charge on the substrate and the length of the substrate double bond. The transition states' energies are not affected by the zeolite framework as modeled, which explains why they correlate strongly with the gas-phase substrate protonation energy. Our cluster results show that for ethene, propene, 1-butene, and isobutene, the relative energetics associated with the formation of the alkoxide intermediate in ZSM-5 follow the same trends as calculations where the effects of the framework are included.