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Fast determination of the optimal rotational matrix for macromolecular superpositions
Article first published online: 16 DEC 2009
DOI: 10.1002/jcc.21439
Copyright © 2009 Wiley Periodicals, Inc.
1096-987X/asset/cover.gif?v=1&s=4429aac2462ebd499c13b3d7fe983679c5767778 "Journal of Computational Chemistry")
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How to Cite
Liu, P., Agrafiotis, D. K. and Theobald, D. L. (2010), Fast determination of the optimal rotational matrix for macromolecular superpositions. Journal of Computational Chemistry, 31: 1561–1563. doi: 10.1002/jcc.21439
Publication History
- Issue published online: 24 MAR 2010
- Article first published online: 16 DEC 2009
- Manuscript Accepted: 13 SEP 2009
- Manuscript Received: 12 AUG 2009
Funded by
- Camille and Henry Dreyfus Foundation
- Johnson & Johnson Pharmaceutical Research and Development, L.L.C.
- Abstract
- Article
- References
- Cited By
Keywords:
- rotational matrix;
- superposition;
- RMSD;
- quaternion;
- adjoint matrix;
- root mean squared deviation;
- protein structure alignment;
- fragment-assembly;
- conformational sampling
Graphical Abstract
Abstract
Finding the rotational matrix that minimizes the sum of squared deviations between two vectors is an important problem in bioinformatics and crystallography. Traditional algorithms involve the inversion or decomposition of a 3 × 3 or 4 × 4 matrix, which can be computationally expensive and numerically unstable in certain cases. Here, we present a simple and robust algorithm to rapidly determine the optimal rotation using a Newton-Raphson quaternion-based method and an adjoint matrix. Our method is at least an order of magnitude more efficient than conventional inversion/decomposition methods, and it should be particularly useful for high-throughput analyses of molecular conformations. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010