• Open Access

Fast determination of the optimal rotational matrix for macromolecular superpositions

Authors

  • Pu Liu,

    Corresponding author
    1. Johnson & Johnson Pharmaceutical Research and Development, L.L.C., 665 Stockton Drive, Exton, Pennsylvania 19341
    • Johnson & Johnson Pharmaceutical Research and Development, L.L.C., 665 Stockton Drive, Exton, Pennsylvania 19341
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  • Dimitris K. Agrafiotis,

    1. Johnson & Johnson Pharmaceutical Research and Development, L.L.C., 665 Stockton Drive, Exton, Pennsylvania 19341
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  • Douglas L. Theobald

    1. Department of Biochemistry, Brandeis University, 415 South Street, Waltham, Massachusetts 02454-9110
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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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