Generation of Pairwise Potentials Using Multidimensional Data Mining

The rapid development of molecular structural databases provides the chemistry community access to an enormous array of experimental data that can be used to build and validate computational models. Using radial distribution functions collected from experimentally available X-ray and NMR structures, a number of so-called statistical potentials have been developed over the years using the structural data mining strategy. These potentials have been developed within the context of the two-particle Kirkwood equation by extending its original use for isotropic monatomic systems to anisotropic biomolecular systems. However, the accuracy and the unclear physical meaning of statistical potentials have long formed the central arguments against such methods. In this work, we present a new approach to generate molecular energy functions using structural data mining. Instead of employing the Kirkwood equation and introducing the “reference state” approximation, we model the multidimensional probability distributions of the molecular system using graphical models and generate the target pairwise Boltzmann probabilities using the Bayesian field theory. Different from the current statistical potentials that mimic the “knowledge-based” PMF based on the 2-particle Kirkwood equation, the graphical-model-based structure-derived potential developed in this study focuses on the generation of lower-dimensional Boltzmann distributions of atoms through reduction of dimensionality. We have named this new scoring function GARF, and in this work we focus on the mathematical derivation of our novel approach followed by validation studies on its ability to predict protein–ligand interactions.