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Fast determination of the optimal rotational matrix for macromolecular superpositions

✍ Scribed by Pu Liu; Dimitris K. Agrafiotis; Douglas L. Theobald

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
65 KB
Volume
31
Category
Article
ISSN
0192-8651

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✦ Synopsis

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

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Comment on “Fast determination of the op
Comment on “Fast determination of the optimal rotational matrix for macromolecular superpositions” [J. Comp. Chem. 31, 1561 (2010)]
✍ Gerald R. Kneller 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 54 KB

## Abstract Recently Liu et al. published a fast algorithm to solve the eigenvector problem arising in the quaternion‐based method for the rotational superposition of molecular structures (J Comput Chem 2010, 31, 1561.). In this Comment, it is shown that the construction of the 4 × 4 matrix to be d