A Bayesian molecular interaction library

We describe a library of molecular fragments designed to model and predict non-bonded interactions between atoms. We apply the Bayesian approach, whereby prior knowledge and uncertainty of the mathematical model are incorporated into the estimated model and its parameters. The molecular interaction data are strengthened by narrowing the atom classification to 14 atom types, focusing on independent molecular contacts that lie within a short cutoff distance, and symmetrizing the interaction data for the molecular fragments. Furthermore, the location of atoms in contact with a molecular fragment are modeled by Gaussian mixture densities whose maximum a posteriori estimates are obtained by applying a version of the expectation-maximization algorithm that incorporates hyperparameters for the components of the Gaussian mixtures. A routine is introduced providing the hyperparameters and the initial values of the parameters of the Gaussian mixture densities. A model selection criterion, based on the concept of a `minimum message length' is used to automatically select the optimal complexity of a mixture model and the most suitable orientation of a reference frame for a fragment in a coordinate system. The type of atom interacting with a molecular fragment is predicted by values of the posterior probability function and the accuracy of these predictions is evaluated by comparing the predicted atom type with the actual atom type seen in crystal structures. The fact that an atom will simultaneously interact with several molecular fragments forming a cohesive network of interactions is exploited by introducing two strategies that combine the predictions of atom types given by multiple fragments. The accuracy of these combined predictions is compared with those based on an individual fragment. Exhaustive validation analyses and qualitative examples (e.g., the ligand-binding domain of glutamate receptors) demonstrate that these improvements lead to effective modeling and prediction of molecular interactions.