Kinematic Reconstruction of Cyclic Peptides and Protein Backbones from Partial Data.

We present an algorithm, QBKR (Quaternary Backbone Kinematic Reconstruction), a fast analytical method for an all-atom backbone reconstruction of proteins and linear or cyclic peptide chains from coordinate traces. Unlike previous analytical methods for deriving all-atom representations from coarse-grained models that rely on canonical geometry with in the conformation, our kinematic model incorporates noncanonical, -, geometry naturally. Perturbations to this geometry can be effected with ease in our formulation, for example, to account for a continuous change from to geometry. A simple optimization of a spring-based objective function is employed for - distance variations that extend beyond the - limit. The kinematic construction produces a linked chain of peptide units, ---, hinged at the atoms spanning all possible planar and nonplanar peptide conformations. We have combined our method with a ring closure algorithm for the case of ring peptides and missing loops in a protein structure. Here, the reconstruction proceeding from both the and termini of the protein backbone (or in both directions from a starting position for rings) requires freedom in the position of one atom (a capstone) to achieve a successful loop or ring closure. A salient feature of our reconstruction method is the ability to enrich conformational ensembles to produce alternative feasible conformations in which H-bond forming C-O or N-H pairs in the backbone can reverse orientations, thus addressing a well-known shortcoming in -based RMSD structure comparison, wherein very close structures may lead to significantly different overall H-bond behavior. We apply the fixed -based design to the reverse reconstruction from noisy Cryo-EM data, a posteriori to the optimization. Our method can be applied to speed up the process of an all-atom description from voluminous experimental data or subpar electron density maps.