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On the Definition of Artificial Backbones for the Discretizable Molecular Distance Geometry Problem

Finding the conformation of a molecule is one of the major challenges in chemistry and biology. Information obtained by NMR experiments can be used to provide estimates of some of the distances between the atoms forming the molecule. The conformation of the molecule can be found by solving the corresponding distance geometry problem. In this work, we focus our attention on protein conformations. We show how an artificial backbone of atoms can be defined for exploiting data from NMR in order to reformulate the distance geometry problem as combinatorial. We formally prove that this artificial backbone can only contain hydrogen atoms, and we introduce a particular ordering for such hydrogens. Computational experiments on a set of artificially generated instances are presented.