An artificial backbone of hydrogens for finding the conformation of protein molecules

NMR experiments can provide distances between pairs of hydrogens of a protein molecule. The problem of identifying the coordinates of such hydrogens by exploiting the information on the distances is a molecular distance geometry problem (MDGP). In a previous work, we defined an artificial backbone of hydrogens related to the protein backbones, where a particular ordering was given to the hydrogens. This ordering allows to formulate the MDGP as a combinatorial optimization problem, to which we refer as the discretizable MDGP (DMDGP) and that we efficiently solve by an exact algorithm, the branch and prune (BP) algorithm. Once the coordinates of the hydrogens have been found, the problem of finding the remaining backbone atoms (N, C and C) is another MDGP. In this short paper, we propose a simple method for solving the MDGP related to the backbone atoms N, C and C of a protein, where the coordinates of the hydrogens previously found by the BP algorithm are exploited.