Fast Determination of the Optimal Rotational Matrix for Macromolecular Superpositions
Fast Determination of the Optimal Rotational Matrix for Macromolecular Superpositions
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DOI：
10.1002/jcc.21439
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发表时间：
2010-05-01
影响因子：
3
通讯作者：
Theobald, Douglas L.
中科院分区：
文献类型：
--
作者：
Liu, Pu;Agrafiotis, Dimitris K.;Theobald, Douglas L.
在生物信息学和晶体学中，寻找使两个向量的偏差平方和最小的旋转矩阵是一个重要的问题。传统的算法涉及3 × 3或4 × 4矩阵的求逆或分解，这在某些情况下可能是计算昂贵的并且在数值上不稳定。在这里，我们提出了一个简单而强大的算法来快速确定最佳的旋转使用牛顿-拉夫森四元数为基础的方法和伴随矩阵。我们的方法是至少一个数量级比传统的反演/分解方法更有效，它应该是特别有用的高通量分析的分子构象。(C)2009 Wiley Periodicals，Inc. J Comput Chem 31：1561-1563，2010
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. (C) 2009 Wiley Periodicals, Inc. J Comput Chem 31: 1561-1563, 2010