Linear vs. Non-linear Modelling. Case study: modelling of binding affinity of inhibitors to Trypsin

On the set of 53 trypsin inhibitors the affinity to the covalent bound ligands is modeled using linear (MLR) and non-linear (ANN) methods. Each compound is represented by 343 chemical descriptors. The hypothesis was that linear models are not sufficiently flexible to yield the best model, because in MLR (multiple regression analysis) the number of variables (descriptors) is limited by the number of objects in the training set. On the other hand the CP-ANN (counter-propagation-artificial neural network) is not limited by this restriction and can thus involve larger number of variables than there are compounds in the training set. Both methods are applied on the same division of 53 compounds on the training, test, and validation sets. In a systematic GA (genetic algorithm) search the MLR models containing all possible forms of linear polynomials, i.e., from 3 to 25 variables were scanned and no better model that one obtained by the CP-ANN model was found.