A kinematic view of loop closure

By E. Coutsias, Chaok Seok, Matthew P. Jacobson, Ken A. Dill. Journal of Computational Chemistry, 2004

306 citations recorded by the source corpus.

We consider the problem of loop closure, i.e., of finding the ensemble of possible backbone structures of a chain segment of a protein molecule that is geometrically consistent with preceding and following parts of the chain whose structures are given. We reduce this problem of determining the loop conformations of six torsions to finding the real roots of a 16th degree polynomial in one variable, based on the robotics literature on the kinematics of the equivalent rotator linkage in the most general case of oblique rotators. We provide a simple intuitive view and derivation of the polynomial for the case in which each of the three pair of torsional axes has a common point. Our method generalizes previous work on analytical loop closure in that the torsion angles need not be consecutive, and any rigid intervening segments are allowed between the free torsions. Our approach also allows for a small degree of flexibility in the bond angles and the peptide torsion angles; this substantially enlarges the space of solvable configurations as is demonstrated by an application of the method to the modeling of cyclic pentapeptides. We give further applications to two important problems. First, we show that this analytical loop closure algorithm can be efficiently combined with an existing loop‐construction algorithm to sample loops longer than three residues. Second, we show that Monte Carlo minimization is made severalfold more efficient by employing the local moves generated by the loop closure algorithm, when applied to the global minimization of an eight‐residue loop. Our loop closure algorithm is freely available at http://dillgroup. ucsf.edu/loop_closure/. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 510–528, 2004

Subfields: Computational Mechanics, Control and Systems Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/2e2ea3990cc02b7d069c48c58627f511ea037961

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Citations in the corpus

Modeling and docking antibody structures with Rosetta (2017, methodology): “We suggest using Rosetta’s relax (unconstrained) 30,31 and KIC 19–21 protocols to generate docking ensembles for antigens.”
GalaxyWEB server for protein structure prediction and refinement (2012, methodology): “During CSA optimization, the triaxial loop closure algorithm (18) is extensively used to generate geometrically proper backbone structures for loops (19).”
Protein Loop Modeling Using a New Hybrid Energy Function and Its Application to Modeling in Inaccurate Structural Environments (2014, methodology): “The initial bank is generated by the fragment assembly with loop closure (FALC) loop sampling procedure [50, 51], and the triaxial loop closure algorithm [52] is used to maintain the structural integrity of the loop after mixing the conformations.”
GalaxyRefine2: simultaneous refinement of inaccurate local regions and overall protein structure (2019, background): “‘Fragment assembly’ re-builds regions with higher estimated errors through fragment assembly and triaxial loop closure (26,27).”
Backbone flexibility in computational protein design. (2009, methodology): “The ‘kinematic closure’ method of Coutsias and colleagues [44] analytically determines conformations for peptide chains of any length by varying 6 torsions and keeping the remaining torsions, bond lengths, and bond angles fixed.”
Refinement of unreliable local regions in template‐based protein models (2012, methodology): “The loop sampling efficiency is enhanced by generating proper closed-loop conformations with the triaxial loop closure (TLC) algo-rithm 11 during global optimization by conformational space annealing (CSA).12 The CSA was previously applied successfully to protein structure prediction13,14 and…”
Rosetta3: An Object-Oriented Software Suite for the Simulation and Design of Macromolecules (2011, unknown): “The second type uses an algorithm called kinematic closure (KIC; Coutsias et al. , 2004; Mandell et al. , 2009).”
Practically Useful: What the Rosetta Protein Modeling Suite Can Do for You (2010, methodology): “Consequently, R OSETTA starts with the template structure and builds in missing loops using fragment insertion or randomization of φ and ψ angles followed by one of the loop closure algorithms such as cyclic coordinate descent or kinematic closure ( 23 - 25 ).”
A Web Resource for Standardized Benchmark Datasets, Metrics, and Rosetta Protocols for Macromolecular Modeling and Design (2015, background): “These remaining three pairs of φ/ψ torsion angles are then solved analytically through kinematic closure to close the chain break [51].”
Fast Protein Loop Sampling and Structure Prediction Using Distance-Guided Sequential Chain-Growth Monte Carlo Method (2014, unknown): “When the growing end is three residues away from the C-terminal anchor atom of the loop, Cl , we apply the CSJD analytical closure method to generate coordinates of the remaining backbone atoms [12].”
RosettaAntibody: antibody variable region homology modeling server (2009, background): “kinematic loop closure (44) or hierarchical local optimization (45,46)] become available.”
All-atom ab initio folding of a diverse set of proteins. (2006, background): “A local move has an effect on four successive residues within a window, with atoms outside this window unchanged (Coutsias et al., 2004).”
Resultants and Loop Closure (2006, methodology): “1 Coefficients of the polynomials Requiring that the bonds Ni–Cαi and Cαi–Ci maintain a given angle θi leads to the relation [8], cos θi + cos ηi cos ξi−1 cosαi = sinαi(sin ξi−1 cos ηi cos σi−1 + cos ξi−1 sin ηi cos τi) 8”