High-resolution single-particle orientation refinement based on spectrally self-adapting common lines.

Three-dimensional (3D) structure determination from electron microscopic images of single molecules can be difficult for particles with low or no internal symmetry, and for images with low signal-to-noise ratio (SNR), due to the existence of false maxima in the scoring function used for orientation search. In attempt to improve robustness of orientation parameter refinement towards noise and poor starting reconstruction quality, we have developed a method for common lines-based orientation search in Fourier space. The Fourier-space formulation enables inclusion of resolution (spatial frequency of the low-pass limit) as a variable that is adjusted in a particle-dependent, self-adaptive manner. The method allows for the underlying 3D structure to be estimated to high resolution, and requires only a crude, low-resolution reconstruction as starting-point for refinement. Benchmarking of the method is performed on experimental and synthetic data.