Molecular Salad: multi‐slice simulation of particles for cryo‐
TEM
Authors: McLeod Robert 
Published: December 2016

The combination of counting, direct electron detectors, such as the DE‐20, Gatan K‐2, and FEI Falcon 3 and Bayesian maximum‐likelihood reconstruction tools embodied by Relion and Frealign, have revolutionized the technique of single particle analysis in cryo‐TEM. Only a handful of years before, 10 Å results from film or scintillator‐coupled CCDs represented the state‐of‐the‐art. At present, many structures are being published with resolutions of 3 Å and the current world record stands at 2.2 Å.

However, many of the physics assumptions that are used throughout cryo‐TEM are left‐over from the previous, low‐resolution era. In particular, the Weak‐Phase Object (WPO) approximation is widely used, in that all reconstruction tools back‐project 2D projections to a 3D map of electrostatic potential using the Central Projection Theorem (CPT). The WPO approximation is much poorer at higher spatial frequencies, in particular when resolution exceeds inter‐atomic spacing and/or high electron wavefront curvature is present in the projection system optics. Thus to proceed to further improved resolution with confidence the accuracy of the underlying physics assumptions must be assessed.

Results will be presented from a plug‐in for C. Koch's QSTEM multislice simulation package, called Molecular Salad (MS). MS can take a structure from the Protein DataBank (PDB), randomly orientate it, merge the particle with a vitreous ice matrix, determine the exit‐wave function by multi‐slice, and then apply an aberration waveplate up to spherical aberration (C3). Many particle groups are generated by a multi‐processed approach, which permits generation of thousands of synthetic particles that may be reconstructed by Relion or similar packages for independent verification of techniques. Multislice‐simulated particles can also have simulated radiation damage using B‐factors in the same code that is typically used for thermal diffuse scattering for phonon calculations.

In Fig. 1 the Fourier Ring Correlation (FRC) is shown between the projected potential (i.e. WPO) and the multislice Exit Wave Function (EWF) averaged over many random orientations of protein 2QI9. The shaded area represents the range of correlations over different angles. The correlation between the WPO and the EWF rapidly drops, being approximately 0.6 at 2.0 Å and negatively correlated at 1.0 Å resolution. This suggests strongly that the current generation of CPT backprojection algorithms will not suffice for sub‐2.0 Å resolution. Examples are shown in Fig. 2 of a 2QI9 particle, and in Fig. 3 the same particle with 1 µm defocus. Especially large defocus values require special treatment of aliasing that occurs when high curvature phase‐plates are applied.

The limits to resolution in single particle analysis are also thought to include the uncertainty in defocus. The ensemble average defocus is estimated from entire micrographs, but particles are embedded at different heights in the ice block which can generate a per‐particle defocus error of ± 50 nm. With simulated particles this effect can be tested. The introduction of reliable simulation into the field of single particle analysis would be a valuable addition to the field for validation of algorithms.