用于刚体和多维旋转相关性的非均匀傅里叶变换
NONUNIFORM FOURIER TRANSFORMS FOR RIGID-BODY AND MULTI-DIMENSIONAL ROTATIONAL CORRELATIONS.
作者信息
Bajaj Chandrajit, Bauer Benedikt, Bettadapura Radhakrishna, Vollrath Antje
机构信息
Computational Visualization Center, Department of Computer Sciences and The Institute of Computational Engineering and Sciences, The University of Texas at Austin, 1 University Station C0200, Austin, Texas 78712, USA.
Max Planck Institute for Evolutionary Biology. Plön, Germany.
出版信息
SIAM J Sci Comput. 2013 Jul 1;35(4). doi: 10.1137/120892386.
The task of evaluating correlations is central to computational structural biology. The rigid-body correlation problem seeks the rigid-body transformation (, ), ∈ SO(3), ∈ ℝ that maximizes the correlation between a pair of input scalar-valued functions representing molecular structures. Exhaustive solutions to the rigid-body correlation problem take advantage of the fast Fourier transform to achieve a speedup either with respect to the sought translation or rotation. We present PF, a new exhaustive solution, based on the non-equispaced SO(3) Fourier transform, to the rigid-body correlation problem; unlike previous solutions, ours achieves a combination of translational and rotational speedups without requiring equispaced grids. PF can be straightforwardly applied to a variety of problems in protein structure prediction and refinement that involve correlations under rigid-body motions of the protein. Additionally, we show how it applies, along with an appropriate flexibility model, to analogs of the above problems in which the flexibility of the protein is relevant.
评估相关性的任务是计算结构生物学的核心。刚体相关性问题寻求刚体变换（，），∈SO(3)，∈ℝ，该变换能使表示分子结构的一对输入标量值函数之间的相关性最大化。刚体相关性问题的详尽解决方案利用快速傅里叶变换，在寻找平移或旋转时实现加速。我们提出了PF，一种基于非等间距SO(3)傅里叶变换的新的详尽解决方案，用于刚体相关性问题；与以前的解决方案不同，我们的方案在不需要等间距网格的情况下实现了平移和旋转加速的结合。PF可以直接应用于蛋白质结构预测和优化中的各种问题，这些问题涉及蛋白质刚体运动下的相关性。此外，我们展示了它如何与适当的灵活性模型一起应用于上述问题的类似问题，其中蛋白质的灵活性是相关的。
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