Robust QSAR Models from Novel Descriptors and Bayesian Regularised Neural Networks

Abstract The QSAR method, using multivariate statistics, was developed by Hansch and Fujita, and it has been successfully applied to many drug and agrochemical design problems. As well as speed and simplicity QSAR has advantages of being capable of accounting for some transport and metabolic processes which occur once the compound is administered. Until recently QSAR analyses have used relatively simple molecular descriptors based on substituent constants (e.g., Hammett constants, π, or molar refractivities), physicochemical properties (e.g., partition coefficients), topological indices (e.g., Randic and Weiner indices). Recently several new representations have been devised: atomistic; molecular eigenvalues and BCUT indices derived therefrom; E-state fields; topological autocorrelation vectors; various molecular fragment-based hash codes. These representations have advantages in speed of computation, in more accurately representing molecular properties most relevant to activity, or in being more generally applicable to diverse chemical classes acting at a common receptor, than traditional representations. Historically, linear regression methods such as MLR (multiple linear regression) and PLS (partial least squares) have been used to develop QSAR models. Regression is an “ill-posed” problem in statistics, which sometimes results in QSAR models exhibiting instability when trained with noisy data. In addition traditional regression techniques often require subjective decisions to be made on the part of the investigator as to the likely non-linear relationship between structure and activity, and whether there are cross-terms. Regression methods based on neural networks offer some advantages over MLR methods as they can account for non-linear SARs, and can deal with linear dependencies which sometimes appear in real SAR problems. However, some problems still exist in the development of SAR models using conventional backpropagation neural networks. We have used a specific type of neural network, the Bayesian Regularized Artificial Neural Network (BRANN), in the development of SAR models. The advantage of BRANN is that the models are robust and the validation process, which scales as O(N2) in normal regression methods, is unnecessary. These networks have the potential to solve a number of problems which arise in QSAR modelling such as: choice of model; robustness of model; choice of validation set; size of validation effort; and optimization of network architecture. The application of the methods to QSAR of compounds active at the benzodiazepine and muscarinic receptors will be illustrated.