title: NONUNIFORM FOURIER TRANSFORMS FOR RIGID-BODY AND MULTI-DIMENSIONAL ROTATIONAL 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∈ ℝ3that 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 PFcorr, 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. PFcorrcan 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.
authors.affiliation: 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.
authors.forename: Chandrajit
authors.initials: C
authors.lastname: Bajaj
authors.affiliation: Max Planck Institute for Evolutionary Biology. Plön, Germany.
authors.forename: Benedikt
authors.initials: B
authors.lastname: Bauer
authors.affiliation: Computational Visualization Center, Department of Mechanical Engineering, The University of Texas at Austin, 1 University Station C0200, Austin, Texas 78712, USA.
authors.forename: Radhakrishna
authors.initials: R
authors.lastname: Bettadapura
authors.affiliation: Institute of Computational Mathematics, TU Braunschweig, Pockelsstr 14, 38106 Braunschweig, Germany.
authors.forename: Antje
authors.initials: A
authors.lastname: Vollrath
keywords: Exhaustive search; Fast Fourier methods; Fast correlations; Match and Fit; Rigid-body motions