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We present a method to measure the relative importance of the descriptors present in a QSAR model developed with a computational neural network (CNN). The approach is based on a sensitivity analysis of the descriptors. We tested the method on three published data sets for which linear and CNN models were previously built. The original work reported interpretations for the linear models, and we compare the results of the new method to the importance of descriptors in the linear models as described by a PLS technique. The results indicate that the proposed method is able to rank descriptors such that important descriptors in the CNN model correspond to the important descriptors in the linear model.

Quinolone and quinoline are known to be liver carcinogens in rodents, and a number of their derivatives have been shown to exhibit mutagenicity in the Ames test, using Salmonella typhimurium strain TA 100 in the presence of S9. Both the carcinogenicity and the mutagenicity of quinolone and quinoline derivatives, as determined by SAS, can be attributed to their genotoxicity potential. This potential, which is measured by genotoxicity tests, is a good indication of carcinogenicity and mutagenicity because compounds that are positive in these tests have the potential to be human carcinogens and/or mutagens. In this study, a collection of quinolone and quinoline derivatives' carcinogenicity is determined by qualitatively predicting their genotoxicity potential with predictive PNN (probabilistic neural network) classification models. In addition, a multiple classifier system is also developed to improve the predictability of genotoxicity. Superior results are seen with the multiple classifier system over the individual PNN classification models. With the multiple classifier system, 89.4% of the quinolone derivatives were predicted correctly, and higher predictability is seen with the quinoline derivatives at 92.2% correct. The multiple classifier system not only is able to accurately predict the genotoxicity but also provides an insight about the main determinants of genotoxicity of the quinolone and quinoline derivatives. Thus, the PNN multiple classifier system generated in this study is a beneficial contributor toward predictive toxicology in the design of less carcinogenic bioactive compounds.

The determination of the validity of a QSAR model when applied to new compounds is an important concern in the field of QSAR and QSPR modeling. Various scoring techniques can be applied to specific types of models. We present a technique with which we can state whether a new compound will be well predicted by a previously built QSAR model. In this study we focus on linear regression models only, though the technique is general and could also be applied to other types of quantitative models. Our technique is based on a classification method that divides regression residuals from a previously generated model into a good class and bad class and then builds a classifier based on this division. The trained classifier is then used to determine the class of the residual for a new compound. We investigated the performance of a variety of classifiers, both linear and nonlinear. The technique was tested on two data sets from the literature and a hand built data set. The data sets selected covered both physical and biological properties and also presented the methodology with quantitative regression models of varying quality. The results indicate that this technique can determine whether a new compound will be well or poorly predicted with weighted success rates ranging from 73% to 94% for the best classifier.

Classification models were developed to provide accurate prediction of genotoxicity of 277 polycyclic aromatic compounds (PACs) directly from their molecular structures. Numerical descriptors encoding the topological, geometric, electronic, and polar surface area properties of the compounds were calculated to represent the structural information. Each compound's genotoxicity was represented with IMAX (maximal SOS induction factor) values measured by the SOS Chromotest in the presence and absence of S9 rat liver homogenate. The compounds' class identity was determined by a cutoff IMAX value of 1.25&sbd;compounds with IMAX > 1.25 in either test were classified as genotoxic, and the ones with IMAX ≤ 1.25 were nongenotoxic. Several binary classification models were generated to predict genotoxicity:  k-nearest neighbor (k-NN), linear discriminant analysis, and probabilistic neural network. The study showed k-NN to provide the highest predictive ability among the three classifiers with a training set classification rate of 93.5%. A consensus model was also developed that incorporated the three classifiers and correctly predicted 81.2% of the 277 compounds. It also provided a higher prediction rate on the genotoxic class than any other single model.

We report several binary classification models that directly link the genetic toxicity of a series of 140 thiophene derivatives with information derived from the compounds' molecular structure. Genetic toxicity was measured using an SOS Chromotest. IMAX (maximal SOS induction factor) values were recorded for each of the 140 compounds both in the presence and in the absence of S9 rat liver homogenate. Compounds were classified as genotoxic if IMAX ≥ 1.5 in either test or nongenotoxic if IMAX < 1.5 for both tests. The molecular structures were represented by numerical descriptors that encoded the topological, geometric, electronic, and polar surface area properties of the thiophene derivatives. The classification models used were linear discriminant analysis (LDA), k-nearest neighbor classification (k-NN), and the probabilistic neural network (PNN). These were used in conjunction with either a genetic algorithm or a generalized simulated annealing to find optimal subsets of descriptors for each classifier. The quality of the resulting models was determined by the number of misclassified compounds, with preference given to models that produced fewer false negative classifications. Model sizes ranged from seven descriptors for LDA to three descriptors for k-NN and PNN. Very good classification results were obtained with all three classifiers. Classification rates for the LDA, k-NN, and PNN models were 80, 85, and 85%, respectively, for the prediction set compounds. Additionally, a consensus model was generated that incorporated all three of the basic model types. This consensus model correctly predicted the genotoxicity of 95% of the prediction set compounds.

A data set of 348 urea-like compounds that inhibit the soluble epoxide hydrolase enzyme in mice and humans is examined. Compounds having IC50 values ranging from 0.06 to >500 μM (murine) and 0.10 to >500 μM (human) are categorized as active or inactive for classification, while quantitation is performed on smaller compound subsets ranging from 0.07 to 431 μM (murine) and 0.11 to 490 μM (human). Each compound is represented by calculated structural descriptors that encode topological, geometrical, electronic, and polar surface features. Multiple linear regression (MLR) and computational neural networks (CNNs) are employed for quantitative models. Three classification algorithms, k-nearest neighbor (kNN), linear discriminant analysis (LDA), and radial basis function neural networks (RBFNN), are used to categorize compounds as active or inactive based on selected data split points. Quantitative modeling of human enzyme inhibition results in a nonlinear, five-descriptor model with root-mean-square errors (log units of IC50 [μM]) of 0.616 (r² = 0.66), 0.674 (r² = 0.61), and 0.914 (r² = 0.33) for training, cross-validation, and prediction sets, respectively. The best classification results for human and murine enzyme inhibition are found using kNN. Human classification rates using a seven-descriptor model for training and prediction sets are 89.1% and 91.4%, respectively. Murine classification rates using a five-descriptor model for training and prediction sets are 91.5% and 88.6%, respectively.

The Probabilistic Neural Network (PNN) and its close relative, the Generalized Regression Neural Network (GRNN), are presented as simple yet powerful neural network techniques for use in Quantitative Structure−Activity Relationship (QSAR) and Quantitative Structure−Property Relationship (QSPR) studies. The PNN methodology is applicable to classification problems, and the GRNN is applicable to continuous function mapping problems. The basic underlying theory behind these probability-based methods is presented along with two applications of the PNN/GRNN methodology. The PNN model presented identifies molecules as potential soluble epoxide hydrolase inhibitors using a binary classification scheme. The GRNN model presented predicts the aqueous solubility of nitrogen- and oxygen-containing small organic molecules. For each application, the network inputs consist of a small set of descriptors that encode structural features at the molecular level. Each of these studies has also been previously addressed in this research group using more traditional techniques such as k-nearest neighbor classification, multiple linear regression, and multilayer feed-forward neural networks. In each case, the predictive power of the PNN and GRNN models was found to be comparable to that of the more traditional techniques but requiring significantly fewer input descriptors.

Quantitative structure−property relationships (QSPR) are developed to correlate glass transition temperatures and chemical structure. Both monomer and repeat unit structures are used to build several QSPR models for Parts 1 and 2 of this study, respectively. Models are developed using numerical descriptors, which encode important information about chemical structure (topological, electronic, and geometric). Multiple linear regression analysis (MLRA) and computational neural networks (CNNs) are used to generate the models after descriptor generation. Optimization routines (simulated annealing and genetic algorithm) are utilized to find information-rich subsets of descriptors for prediction. A 10-descriptor CNN model was found to be optimal in predicting Tg values using the monomer structure (Part 1) for 165 polymers. A committee of 10 CNNs produced a training set rms error of 10.1K (r² = 0.98) and a prediction set rms error of 21.7K (r² = 0.92). An 11-descriptor CNN model was developed for 251 polymers using the repeat unit structure (Part 2). A committee of CNNs produced a training set rms error of 21.1K (r² = 0.96) and a prediction set rms error of 21.9K (r² = 0.96).

Mathematical models are developed to find quantitative structure−activity relationships that correlate chemical structure and inhibition toward three carbonic anhydrase (CA) isozymes:  CA I, II, and IV. Numerical descriptors are generated to encode important topological, geometric, and electronic features of molecular structure. After descriptor generation, multiple linear regression, and computational neural network (CNN) analyses are performed on various descriptor subsets to find superior models for prediction. Committees of five CNNs were utilized to average final predicted values for the 142-compound data set. For inhibitors of CA I, an 8−5−1 CNN committee produced a training set rms error of 0.105 log Ki (r² = 0.994) and prediction set rms error of 0.208 log Ki (r² = 0.980). Training and prediction set rms errors of 0.140 log Ki (r² = 0.992) and 0.231 log Ki (r² = 0.971), respectively, were produced by a 9−5−1 CNN committee for inhibitors of CA II. For prediction of CA IV inhibitors, an 8−5−1 CNN committee produced training and prediction set rms errors of 0.147 log Ki (r² = 0.992) and 0.211 log Ki (r² = 0.991), respectively. In addition, classification models were built using k-nearest neighbor (kNN) analysis to solve two- and three-class problems for inhibitors of CA IV. A three-descriptor classification model proved superior in labeling compounds as active or inactive inhibitors for the two-class problem. Training and prediction set percent classification rates of 100% and 87.1%, respectively, were obtained. For the three-class (active/moderate/inactive) problem, a five-descriptor model was deemed optimal producing a training set percent classification rate of 98.8% and prediction set rate of 79.0%.

Experimental IC50 data for 314 selective cyclooxygenase-2 (COX-2) inhibitors are used to develop quantitation and classification models as a potential screening mechanism for larger libraries of target compounds. Experimental log(IC50) values ranged from 0.23 to ≥ 5.00. Numerical descriptors encoding solely topological information are calculated for all structures and are used as inputs for linear regression, computational neural network, and classification analysis routines. Evolutionary optimization algorithms are then used to search the descriptor space for information-rich subsets which minimize the rms error of a diverse training set of compounds. An eight-descriptor model was identified as a robust predictor of experimental log(IC50) values, producing a root-mean-square error of 0.625 log units for an external prediction set of inhibitors which took no part in model development. A k-nearest neighbor classification study of the data set discriminating between active and inactive members produced a nine-descriptor model able to accurately classify 83.3% of the prediction set compounds correctly.

Quantitative structure−activity relationships (QSARs) are developed to describe the ability of 6-azasteroids to inhibit human type 1 5α-reductase. Models are generated using a set of 93 compounds with known binding affinities (Ki) to 5α-reductase and 3β-hydroxy-Δ⁵-steroid dehydrogenase/3-keto-Δ⁵-steroid isomerase (3-BHSD). QSARs are generated to predict Ki values for inhibitors of 5α-reductase and to predict selectivity (Si) of compound binding to 3-BHSD relative to 5α-reductase. Log(Ki) values range from −0.70 log units to 4.69 log units, and log(Si) values range from −3.00 log units to 3.84 log units. Topological, geometric, electronic, and polar surface descriptors are used to encode molecular structure. Information-rich subsets of descriptors are identified using evolutionary optimization procedures. Predictive models are generated using linear regression, computational neural networks (CNNs), principal components regression, and partial least squares. Compounds in an external prediction set are used for model validation. A 10−3−1 CNN is developed for prediction of binding affinity to 5α-reductase that produces root-mean-square error (RMSE) of 0.293 log units (R² = 0.97) for compounds in the external prediction set. Additionally, an 8−3−1 CNN is generated for prediction of inhibitor selectivity that produces RMSE = 0.513 log units (R² = 0.89) for the external prediction set. Models are further validated through Monte Carlo experiments in which models are generated after dependent variable values have been scrambled.

The use of quantitative structure−property relationships (QSPRs) to predict aqueous solubilities (log S) of heteroatom-containing organic compounds from their molecular structure is presented. Three data sets are examined. Data set 1 contains 176 compounds having one or more nitrogen atoms with some oxygen (log S[mol/L] range is −7.41 to 0.96). Data set 2 contains 223 compounds having one or more oxygen atoms, with no nitrogen (log S[mol/L] range is −8.77 to 1.57). Data set 3 contains all 399 compounds from sets 1 and 2 (log S/mol/L] range is −8.77 to 1.57). After descriptor generation and feature selection, multiple linear regression (MLR) and computational neural network (CNN) models are developed for aqueous solubility prediction. The best results were obtained with nonlinear CNN models. Root-mean-square (rms) errors for training with the three data sets ranged from 0.3 to 0.6 log units. All models were validated with external prediction sets, with the rms errors ranging from 0.6 log units to 1.5 log units.

Models predicting fullerene solubility in 96 solvents at 298 K were developed using multiple linear regression and feed-forward computational neural networks (CNN). The data set consisted of a diverse set of solvents with solubilities ranging from −3.00 to 2.12 log (solubility) where solubility = (1 × 10⁴)(mole fraction of C60 in saturated solution). Each solvent was represented by calculated molecular structure descriptors. A pool of the best linear models, as determined by rms error, was developed, and a CNN model was developed for each of the linear models. The best CNN model was chosen based on the lowest value of a specified cost function and had an architecture of 9−3−1. The 76-compound training set for this model had a root-mean-square error of 0.255 log solubility units, while the 10-compound cross-validation set had an rms error of 0.253. The 10-compound external prediction set had an rms error of 0.346 log solubility units.