Tripeptide loop closure: A detailed study of reconstructions based on Ramachandran distributions

Tripeptide loop closure (TLC) is a standard procedure to reconstruct protein backbone conformations, by solving a zero-dimensional polynomial system yielding up to 16 solutions. In this work, we first show that multiprecision is required in a TLC solver to guarantee the existence and the accuracy of solutions. We then compare solutions yielded by the TLC solver against tripeptides from the Protein Data Bank. We show that these solutions are geometrically diverse (up to $$ Root mean square deviation with respect to the data) and sound in terms of potential energy. Finally, we compare Ramachandran distributions of data and reconstructions for the three amino acids. The distribution of reconstructions in the second angular space $$ stands out, with a rather uniform distribution leaving a central void. We anticipate that these insights, coupled to our robust implementation in the Structural Bioinformatics Library ( https://sbl.inria.fr/doc/Tripeptide_loop_closure-user-manual.html), will help understanding the properties of TLC reconstructions, with potential applications to the generation of conformations of flexible loops in particular.