These 2 authors contributed equally to this study.
A kinematic view of loop closure
Article first published online: 13 JAN 2004
Copyright © 2004 Wiley Periodicals, Inc.
Journal of Computational Chemistry
Volume 25, Issue 4, pages 510–528, March 2004
How to Cite
Coutsias, E. A., Seok, C., Jacobson, M. P. and Dill, K. A. (2004), A kinematic view of loop closure. J. Comput. Chem., 25: 510–528. doi: 10.1002/jcc.10416
- Issue published online: 13 JAN 2004
- Article first published online: 13 JAN 2004
- Manuscript Accepted: 4 NOV 2003
- Manuscript Received: 26 AUG 2003
- loop closure;
- loop modeling;
- Monte Carlo minimization
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