Towards a Protein-Size Dependent Resolution Limit due to Dynamical Scattering in Cryo-transmission Electron Microscopy

In cryo-transmission electron microscopy, single-particle reconstructions exploit the weak phase object approximation. A decisive aspect to be studied systematically is to what extent underlying scattering assumptions limit the resolution, whether theoretical limits are compatible with experimental observations, and if current experimental benchmarks achieve this limit. Single-, multislice, and hybrid scattering models are employed in this work for simulating eight protein complexes up to 97.5 nm in thickness, embedded in low-density amorphous ice obtained from molecular dynamics. With the multislice scheme providing an accurate solution to the multiple scattering problem as reference, the reliability of the different models is assessed in both real and Fourier space, particularly via Fourier ring correlations at the specimen exit wave level. A comparison with benchmarking literature resolutions is performed. Our results show proportionality of the attainable resolution to the square root of the projection thickness. This is in reasonable quantitative agreement with the highest resolution published experimentally for proteins with at least the size of apoferritin. The study provides a rationale for the expectable resolution for a protein complex of known size. The implications of structural noise due to the ice background for the minimal ice thickness on protein size-dependent resolution are discussed, as well as efficient methods to approximate multiple scattering and propagation in thick proteins.