The Ewald sphere/focus gradient does not limit the resolution of cryoEM reconstructions

Area of Science:

• Structural Biology
• Electron Microscopy
• Biophysics

Background:

• Accurate biomolecular structure determination using cryo-electron microscopy (cryo-EM) requires addressing all image formation aspects.
• The Ewald sphere and focus gradient, arising from scattering geometry, significantly impact high-resolution recovery and handedness determination in cryo-EM.
• Traditional projection approximations in cryo-EM break down at resolutions around 2-3 Å, especially for large particles, hindering the study of fine molecular details.

Purpose of the Study:

• To investigate the impact of the Ewald sphere/focus gradient on high-resolution cryo-EM data.
• To evaluate methods for dealing with the Ewald sphere effect in cryo-EM reconstruction.
• To determine the feasibility of recovering high resolution and handedness information in cryo-EM.

Main Methods:

• Simulations were used to analyze the effect of the Ewald sphere on image formation and reconstruction.
• Integration along Ewald spheres in frequency space was employed during reconstruction using the 'simple insertion method'.
• Theoretical analysis and simulations were conducted to assess phase information and handedness recovery.

Main Results:

• The 'simple insertion method' of integrating along Ewald spheres in frequency space allows reconstruction to the Nyquist frequency.
• Simulations demonstrate that the Ewald sphere effect breaks down the projection approximation at resolutions of 2-3 Å and for large particles.
• Both theoretical analysis and simulations indicate that handedness information is irreversibly lost during real-space image formation.

Conclusions:

• Correct reconstruction along the Ewald spheres circumvents the limitations imposed by the traditional projection approximation in cryo-EM.
• While high-resolution data can be recovered by accounting for the Ewald sphere, handedness information is not recoverable.
• Understanding and implementing Ewald sphere corrections are crucial for advancing high-resolution cryo-EM studies.