Protein Structure Probabilistic Modeling and Simulation

Background: Various forms of the so-called loop closure problem are crucial to protein structure prediction methods. Given an Nand a C-terminal end, the problem consists of finding a suitable segment of a certain length that bridges the ends seamlessly. In homology modelling, the problem arises in predicting loop regions. In de novo protein structure prediction, the problem is encountered when implementing local moves for Markov Chain Monte Carlo simulations. Most loop closure algorithms keep the bond angles fixed or semi-fixed, and only vary the dihedral angles. This is appropriate for a full-atom protein backbone, since the bond angles can be considered as fixed, while the (φ, ψ) dihedral angles are variable. However, many de novo structure prediction methods use protein models that only consist of Cα atoms, or otherwise do not make use of all backbone atoms. These methods require a method that alters both bond and dihedral angles, since the pseudo bond angle between three consecutive Cα atoms also varies considerably. Results: Here we present a method that solves the loop closure problem for Cα only protein models. We developed a variant of Cyclic Coordinate Descent (CCD), an inverse kinematics method from the field of robotics, which was recently applied to the loop closure problem. Since the method alters both bond and dihedral angles, which is equivalent to applying a full rotation matrix, we call our method Full CCD (FCDD). FCCD replaces CCD's vector-based optimization of a rotation around an axis with a singular value decomposition-based optimization of a general rotation matrix. The method is easy to implement and numerically stable. Conclusion: We tested the method's performance on sets of random protein Cα segments between 5 and 30 amino acids long, and a number of loops of length 4, 8 and 12. FCCD is fast, has a high success rate and readily generates conformations close to those of real loops. The presence of constraints on the angles only has a small effect on the performance. A reference implementation of FCCD in Python is available as supplementary information. Background Many protein structure prediction methods require an algorithm that is capable of constructing a new conformation for a short segment of the protein, without affecting Published: 28 June 2005 BMC Bioinformatics 2005, 6:159 doi:10.1186/1471-2105-6-159 Received: 25 April 2005 Accepted: 28 June 2005 This article is available from: http://www.biomedcentral.com/1471-2105/6/159 © 2005 Boomsma and Hamelryck; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 45