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Free keywords:
fast Fourier methods; rigid-body motions; match and fit; exhaustive search; fast correlations
Abstract:
The task of evaluating correlations is central to computational structural biology.
The rigid-body correlation problem seeks the rigid-body transformation (R, t), R ∈ SO(3), t ∈ R3,
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 with respect to either the sought translation or rotation. We
present PFcorr, a new exhaustive solution, based on the nonequispaced 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. PFcorr 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 analogues of the above problems in which the flexibility of the
protein is relevant.
