Quantifying resolution limiting factors in subtomogram averaged cryo-electron tomography using simulations.

Cryo-electron tomography (CET) is the only available technique capable of characterizing the structure of biological macromolecules in conditions close to the native state. With the advent of subtomogram averaging, as a post-processing step to CET, resolutions in the (sub-) nanometer range have become within reach. In addition to advances in instrumentation and experiments, the reconstruction scheme has improved by inclusion of more accurate contrast transfer function (CTF) correction methods, better defocus estimation, and better alignments of the tilt-series and subtomograms. To quantify the importance of each contribution, we have split the full process from data collection to reconstruction into different steps. For the purpose of evaluation we have acquired tilt-series of ribosomes in such a way that we could precisely determine the defocus of each macromolecule. Then, we simulated tilt-series using the InSilicoTEM package and applied tomogram reconstruction and subtomogram averaging. Through large scale simulations under different conditions and parameter settings we find that tilt-series alignment is the resolution limiting factor for our experimental data. Using simulations, we find that when this alignment inaccuracy is alleviated, tilted CTF correction improves the final resolution, or equivalently, the same resolution can be achieved using less particles. Furthermore, we predict from which resolution onwards better CTF correction and defocus estimation methods are required. We obtain a final average using 3198 ribosomes with a resolution of 2.2nm on the experimental data. Our simulations suggest that with the same number of particles a resolution of 1.2nm could be achieved by improving the tilt-series alignment.

When to use the projection assumption and the weak-phase object approximation in phase contrast cryo-EM.

The projection assumption (PA) and the weak-phase object approximation (WPOA) are commonly used to model image formation in cryo-electron microscopy. For simulating the next step in resolution improvement we show that it is important to revisit these two approximations as well as their limitations. Here we start off by inspecting both approximations separately to derive their respective conditions of applicability. The thick-phase grating approximation (TPGA) imposes less strict conditions on the interaction potential than PA or WPOA and gives comparable exit waves as a multislice calculation. We suggest the ranges of applicability for four models (PA, PA+WPOA, WPOA, and TPGA) given different interaction potentials using exit wave simulations. The conditions of applicability for the models are based on two measures, a worst-case (safest) and an average criterion. This allows us to present a practical guideline for when to use each image formation model depending on the spatial frequency, thickness and strength of the interaction potential of a macromolecular complex.

Image formation modeling in cryo-electron microscopy.

Accurate modeling of image formation in cryo-electron microscopy is an important requirement for quantitative image interpretation and optimization of the data acquisition strategy. Here we present a forward model that accounts for the specimen's scattering properties, microscope optics, and detector response. The specimen interaction potential is calculated with the isolated atom superposition approximation (IASA) and extended with the influences of solvent's dielectric and ionic properties as well as the molecular electrostatic distribution. We account for an effective charge redistribution via the Poisson-Boltzmann approach and find that the IASA-based potential forms the dominant part of the interaction potential, as the contribution of the redistribution is less than 10%. The electron wave is propagated through the specimen by a multislice approach and the influence of the optics is included via the contrast transfer function. We incorporate the detective quantum efficiency of the camera due to the difference between signal and noise transfer characteristics, instead of using only the modulation transfer function. The full model was validated against experimental images of 20S proteasome, hemoglobin, and GroEL. The simulations adequately predict the effects of phase contrast, changes due to the integrated electron flux, thickness, inelastic scattering, detective quantum efficiency and acceleration voltage. We suggest that beam-induced specimen movements are relevant in the experiments whereas the influence of the solvent amorphousness can be neglected. All simulation parameters are based on physical principles and, when necessary, experimentally determined.

Radiation damage in single-particle cryo-electron microscopy: effects of dose and dose rate.

Radiation damage is an important resolution limiting factor both in macromolecular X-ray crystallography and cryo-electron microscopy. Systematic studies in macromolecular X-ray crystallography greatly benefited from the use of dose, expressed as energy deposited per mass unit, which is derived from parameters including incident flux, beam energy, beam size, sample composition and sample size. In here, the use of dose is reintroduced for electron microscopy, accounting for the electron energy, incident flux and measured sample thickness and composition. Knowledge of the amount of energy deposited allowed us to compare doses with experimental limits in macromolecular X-ray crystallography, to obtain an upper estimate of radical concentrations that build up in the vitreous sample, and to translate heat-transfer simulations carried out for macromolecular X-ray crystallography to cryo-electron microscopy. Stroboscopic exposure series of 50-250 images were collected for different incident flux densities and integration times from Lumbricus terrestris extracellular hemoglobin. The images within each series were computationally aligned and analyzed with similarity metrics such as Fourier ring correlation, Fourier ring phase residual and figure of merit. Prior to gas bubble formation, the images become linearly brighter with dose, at a rate of approximately 0.1% per 10 MGy. The gradual decomposition of a vitrified hemoglobin sample could be visualized at a series of doses up to 5500 MGy, by which dose the sample was sublimed. Comparison of equal-dose series collected with different incident flux densities showed a dose-rate effect favoring lower flux densities. Heat simulations predict that sample heating will only become an issue for very large dose rates (50 e(-)Å(-2) s(-1) or higher) combined with poor thermal contact between the grid and cryo-holder. Secondary radiolytic effects are likely to play a role in dose-rate effects. Stroboscopic data collection combined with an improved understanding of the effects of dose and dose rate will aid single-particle cryo-electron microscopists to have better control of the outcome of their experiments.