CTF Correction in Cryo-Electron Tomography

Abstract

Nanometer resolution inside the cell will allow us to study the fundamentals of life at the smallest scale. This thesis addresses what is needed to obtain this resolution using cryo-electron tomography (CET). CET is a microscopy modality with the unique potential to visualize proteins, protein-complexes and other molecular assemblies in a close-to-native environment at a high resolution in three dimensions. In CET, a thin specimen embedded in vitreous ice is tilted in the electron beam to acquire projections under different angles. The primary contrast mechanism is phase contrast which is obtained by intentionally defocussing the specimen. The contrast transfer function (CTF) describes how aberrations, such as defocussing, generate detectable intensity contrast. The CTF is an oscillating function of spatial frequency, resulting in contrast inversions at certain spatial frequencies. To interpret structures at a resolution beyond the first zero-crossing, it is necessary to correct for the CTF. In this thesis we answer the questions: how can we model the CTF for tomographic geometries, what is the influence of CTF correction, which processing steps need to be improved to fully exploit CTF correction in combination with subtomogram averaging, and how big is the improvement in resolution? This thesis presents fast and efficient algorithms for both forward modeling and correction of the CTF for tilted geometries of various thicknesses, as well as methods to model the specimen-beam interaction. To avoid a brute-force multislice procedure to model the specimen-beam interaction, we study the influence of the projection assumption, the weak-phase object approximation, and the thick-phase grating approximation, as well as their limits of applicability. Fast algorithms for computing and correcting the CTF in tilted geometries are mandatory for practical use. Our algorithm reduces the computation time for a tilt-series from ~100 hours down to ~45 minutes. Using simulations, we also study how different CTF models influence the projections and what the influence of CTF correction is on the final reconstruction. We quantify the influence of the developed CTF correction methods in subtomogram averaged CET. Subtomogram averaging is the solution to raise the signal-to-noise ratio for high spatial frequencies above the noise floor. To achieve the required defocus estimation accuracy under realistic experimental conditions, we present an extended acquisition scheme in combination with a previously developed defocus estimation procedure. Using simulations and experimental data of ribosomes, acquired on a Titan microscope (FEI Company) at the NeCEN, we study the influence on the achievable resolution of different processing steps, including CTF correction, as well as the number of subtomograms. A comparison of simulations and experiments allows us to identify the factors that limit the resolution as well as the effect of tilted CTF correction. We obtained a final average using 3198 ribosomes with a resolution of 2.2 nm on the experimental data. Our simulations suggest that with the same number of particles a resolution of 1.2 nm could be achieved by improving the tilt-series alignment.