Generating properly weighted ensemble of conformations of proteins from sparse or indirect distance constraints

Inferring three-dimensional structural information of biomacromolecules such as proteins from limited experimental data is an important and challenging task. Nuclear Overhauser effect measurements based on nucleic magnetic resonance, disulfide linking, and electron paramagnetic resonance labeling studies can all provide useful partial distance constraint characteristic of the conformations of proteins. In this study, we describe a general approach for reconstructing conformations of biomolecules that are consistent with given distance constraints. Such constraints can be in the form of upper bounds and lower bounds of distances between residue pairs, contact maps based on specific contact distance cutoff values, or indirect distance constraints such as experimental phi-value measurement. Our approach is based on the framework of sequential Monte Carlo method, a chain growth-based method. We have developed a novel growth potential function to guide the generation of conformations that satisfy given distance constraints. This potential function incorporates not only the distance information of current residue during growth but also the distance information of future residues by introducing global distance upper bounds between residue pairs and the placement of reference points. To obtain protein conformations from indirect distance constraints in the form of experimental phi-values, we first generate properly weighted contact maps satisfying phi-value constraints, we then generate conformations from these contact maps. We show that our approach can faithfully generate conformations that satisfy the given constraints, which approach the native structures when distance constraints for all residue pairs are given.