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Fast determination of the optimal rotational matrix for macromolecular superpositions.

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 x 3 or 4 x 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.

SUBMITTER: Liu P

PROVIDER: S-EPMC2958452 | biostudies-literature | 2010 May

REPOSITORIES: biostudies-literature

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Fast determination of the optimal rotational matrix for macromolecular superpositions.

Liu Pu P Agrafiotis Dimitris K DK Theobald Douglas L DL

Journal of computational chemistry 20100501 7

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 x 3 or 4 x 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 ...[more]

PMID: 20017124

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