A Euclidean distance matrix model for protein molecular conformation

Protein molecular conformation is an important and challenging problem in biophysics. It is to recover the structure of proteins based on limited information such as noised distances, lower and upper bounds on some distances between atoms. In this paper, based on the recent progress in numerical algorithms for Euclidean distance matrix (EDM) optimization problems, we propose a EDM model for protein molecular conformation. We reformulate the problem as a rank-constrained least squares problem with linear equality constraints, box constraints, as well as a cone constraint. Due to the nonconvexity of the problem, we develop a majorized penalty approach to solve the problem. We apply the accelerated block coordinate descent algorithm proposed in Sun et al. (SIAM J Optim 26(2):1072-1100, 2016) to solve the resulting subproblem. Extensive numerical results demonstrate the efficiency of the proposed model.