Protein Loop Modeling via the Discretizable Distance Geometry Problem with Hydrogen-Based NMR Constraints

Protein loop modeling remains a fundamental challenge in computational biology due to the inherent flexibility of loops and their critical role in biological functions. In this work, we employ a discrete distance geometry formulation, efficiently solved using the Branch-and-Prune algorithm, with a key innovation being the incorporation of hydrogen atoms into the model. Hydrogen atoms bonded to N and C _α in the protein backbone introduce additional geometric constraints, and their inclusion is particularly justified in the context of nuclear magnetic resonance (NMR) experiments, where short-range hydrogen-hydrogen distances can be detected and provide valuable structural information. By integrating these experimentally accessible constraints into the modeling process, we refine the representation of protein conformations. Computational experiments demonstrate that incorporating hydrogen atoms reduces the conformational space, leading to a more constrained and biologically realistic model. Comparisons with hydrogen-free formulations confirm that our approach improves agreement with known protein structures, further highlighting the relevance of distance geometry methods in structural refinement.