On suitable orders for discretizing Molecular Distance Geometry problems related to protein side chains

Proteins are important molecules that are widely studied in biology. Their three-dimensional conformations can give clues about their function, however an optimal methodology for the identification of such conformations has not been found yet. Experiments of Nuclear Magnetic Resonance (NMR) are able to estimate distances between some pairs of atoms forming the protein, and the problem of identifying the possible conformations satisfying the available distance constraints is known in the scientific literature as the Molecular Distance Geometry Problem (MDGP). Since some years, some of us have been working on a suitable discretization for the MDGP and on an efficient Branch & Prune (BP) algorithm which is based on a tree search. In order to perform this discretization, however, some assumptions need to be satisfied. We recently hand-crafted a special order for protein backbone atoms which allows us to discretize all MDGPs concerning backbones. In this paper, we do the same for the side chains of some amino acids. Our computational experiments show that the inclusion of the side chain information allows to improve the performances of the BP algorithm.