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 3normalÅ 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 (),ϕ2ψ2 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.

Designing movesets providing high quality protein conformations remains a hard problem, especially when it comes to deforming a long protein backbone segment, and a key building block to do so is the so-called tripeptide loop closure (TLC). Consider a tripeptide whose first and last segments (N1Cα;1 and Cα;3C3) are fixed, and so are all internal coordinates except the six {(ϕ, ψ)i=1,2,3 dihedral angles associated to the three Cα carbons. Under these conditions, the TLC algorithm provides all possible values for these six dihedral angles--there exist at most 16 solutions. TLC moves atoms up to ~ 5Å in one step and retains low energy conformations, whence it pivotal role to design move sets sampling protein loop conformations. In this work, we relax the previous constraints, allowing the last segment (Cα;3C3) to freely move in 3D space--or equivalently in a 5D configuration space. We exhibit necessary geometric constraints in this 5D space for TLC to admit solutions. Our analysis provides key insights on the geometry of solutions for TLC. Most importantly, when using TLC to sample loop conformations based on m consecutive tripeptides along a protein backbone, we obtain an exponential gain in the volume of the 5m-dimensional configuration space to be explored.

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 3 Angstroms RMSD 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 (φ2 , ψ2) 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 boost the interest of TLC for structural modeling in general, and the generation of conformations of flexible loops in particular.

Flexible loops are paramount to protein functions, with action modes ranging from localized dynamics contributing to the free energy of the system, to large amplitude conformational changes accounting for the repositioning whole SSE or protein domains. However, generating diverse and low energy loops remains a difficult problem.This work introduces a novel paradigm to sample loop conformations, in the spirit of the Hit-and-Run (HAR) Markov chain Monte Carlo technique. The algorithm uses a decomposition of the loop into tripeptides, and a novel characterization of necessary conditions for Tripeptide Loop Closure to admit solutions. Denoting m the number of tripeptides, the algorithm works in an angular space of dimension 12m. In this space, the hyper-surfaces associated with the aforementioned necessary conditions are used to run a HAR-like sampling technique.On classical loop cases up to 15 amino acids, our parameter free method compares favorably to previous work, generating more diverse conformational ensembles. We also report experiments on a 30 amino acids long loop, a size not processed in any previous work.

Flexible loops are paramount to protein functions, with action modes ranging from localized dynamics contributing to the free energy of the system, to large amplitude conformational changes accounting for the repositioning whole secondary structure elements or protein domains. However, generating diverse and low energy loops remains a difficult problem. This work introduces a novel paradigm to sample loop conformations, in the spirit of the hit‐and‐run (HAR) Markov chain Monte Carlo technique. The algorithm uses a decomposition of the loop into tripeptides, and a novel characterization of necessary conditions for Tripeptide Loop Closure to admit solutions. Denoting m the number of tripeptides, the algorithm works in an angular space of dimension 12 m. In this space, the hyper‐surfaces associated with the aforementioned necessary conditions are used to run a HAR‐like sampling technique. On classical loop cases up to 15 amino acids, our parameter free method compares favorably to previous work, generating more diverse conformational ensembles. We also report experiments on a 30 amino acids long loop, a size not processed in any previous work.