NONUNIFORM FOURIER TRANSFORMS FOR RIGID-BODY AND MULTI-DIMENSIONAL ROTATIONAL CORRELATIONS

Area of Science:

• Computational structural biology
• Biophysics
• Structural bioinformatics

Background:

• Evaluating correlations is crucial in computational structural biology.
• The rigid-body correlation problem aims to find transformations that maximize structural correlation.
• Existing methods offer speedups for translation or rotation but not both simultaneously.

Purpose of the Study:

• To introduce PFcorr, an exhaustive solution to the rigid-body correlation problem.
• To achieve combined translational and rotational speedups without requiring equispaced grids.
• To demonstrate the applicability of PFcorr to protein structure prediction and refinement.

Main Methods:

• Utilizing the non-equispaced SO(3) Fourier transform for rigid-body correlation.
• Implementing an exhaustive search for optimal rigid-body transformations (R, t).
• Adapting the method for problems involving protein flexibility.

Main Results:

• PFcorr provides simultaneous translational and rotational speedups.
• The method does not require equispaced grids, offering greater flexibility.
• PFcorr is applicable to various protein structure analysis tasks.

Conclusions:

• PFcorr offers a significant advancement in solving the rigid-body correlation problem.
• The method enhances efficiency in protein structure prediction and refinement.
• PFcorr provides a flexible framework for analyzing molecular structures, including flexible proteins.