Pushing the resolution limit by correcting the Ewald sphere effect in single-particle Cryo-EM reconstructions

Abstract

The Ewald sphere effect is generally neglected when using the Central Projection Theorem for cryo electron microscopy single-particle reconstructions. This can reduce the resolution of a reconstruction. Here we estimate the attainable resolution and report a "block-based" reconstruction method for extending the resolution limit. We find the Ewald sphere effect limits the resolution of large objects, especially large viruses. After processing two real datasets of large viruses, we show that our procedure can extend the resolution for both datasets and can accommodate the flexibility associated with large protein complexes.

Fig. 1

The resolution limit caused by the effect of depth of field. a Positions marked with a cross (x) represent the calculated resolution limit of protein complexes of variable sizes by using the simulated 300 kV (black), 200 kV (red), and 120 kV (blue) cryo-EM data. The corresponding black, red, and blue lines are the resolution limits calculated using the modified empirical formula. Values for the dashed black line were obtained by applying the DeRoiser’s empirical formula that was used as a reference for comparison^, . The black-edged square is the simulation result performed by Kenneth et al.. b Black and red circles with EMDB codes represent the resolutions of typical high-resolution protein complexes generated by cryo-EM SPA at 300 kV and 200 kV, respectively. Black squares represent the resolutions of PBCV-1 virus and HSV-2 virus that were reconstructed by using a block-based reconstruction method. Gray squares represent the resolution of these two viruses that were reconstructed by using a conventional method

Fig. 2

The block-based reconstruction, particle defocus, and local mean defoci of blocks. a To show how block-based reconstruction works, a density map (EMD-6775) was divided into four blocks, which are circled with red dashes. The distance between the center of mass of the model and the focal plane of objective lens along the Z axis is the particle defocus. Each block has its own local mean focus, which is the sum of the particle defocus values with the distance from the center of the block to the center of the model along the Z axis. b The Thon rings calculated from the whole virus (left) or after excluding the central part (right). The region of the virus in the 2D image (up right) corresponds to the part of the virus that is near the particle defocus plane in the 3D virus (down right). c The resolutions determined by gold standard FSC at threshold 0.143 of HSV-2 capsid reconstructions by a conventional reconstruction method (colored in black), by block-based reconstruction with local refinement of translational and rotational parameters of each block but without applying local mean defocus (colored in blue), and by block-based reconstruction with local refinement and local mean defocus being applied to overcome the Ewald sphere effect (colored in red). d The resolutions determined by gold standard FSC at threshold 0.143 of PBCV-1 virus reconstructions by a conventional reconstruction method (colored in black), by block-based reconstruction with local refinement of translational and rotational parameters of each block but without applying local mean defocus (colored in blue), and by block-based reconstruction with local refinement and local mean defocus being applied to overcome Ewald sphere effect (colored in red)

Fig. 3

Comparison of cryo-EM densities from block-based and conventional reconstruction methods. a The densities belong to the major capsid protein in the 3.1 Å resolution HSV-2 reconstruction by block-based reconstruction method (left) and the densities that were from the same areas in the 4.0 Å resolution reconstruction by conventional method (right). The HSV-2 virus structure data are deposited in the Protein Databank with accession code 5ZAP (HSV-2 icosahedral reconstruction after block-based refinement) and in the Electron Microscopy Database with accession code EMD-6907. b The densities belong to the major capsid protein Vp54 in the 3.5 Å resolution PBCV-1 reconstruction by the block-based reconstruction method (left) and the densities that were from the same areas in the 4.2 Å resolution reconstruction by the conventional method (right)