Search

The productivity of single-particle cryo-EM as a structure determination method has rapidly increased as many novel biological structures are being elucidated. The ultimate result of the cryo-EM experiment is an atomic model that should faithfully represent the computed image reconstruction. Although the principal approach of atomic model building and refinement from maps resembles that of the X-ray crystallographic methods, there are important differences due to the unique properties resulting from the 3D image reconstructions. In this review, we discuss the practiced work-flow from the cryo-EM image reconstruction to the atomic model. We give an overview of (i) resolution determination methods in cryo-EM including local and directional resolution variation, (ii) cryo-EM map contrast optimization including complementary map types that can help in identifying ambiguous density features, (iii) atomic model building and (iv) refinement in various resolution regimes including (v) their validation and (vi) discuss differences between X-ray and cryo-EM maps. Based on the methods originally developed for X-ray crystallography, the path from 3D image reconstruction to atomic coordinates has become an integral and important part of the cryo-EM structure determination work-flow that routinely delivers atomic models.

Fourier shell correlation (FSC) has become a standard quantity for resolution estimation in electron cryo-microscopy. However, the resolution determination step is still subjective and not fully automated as it involves a series of map interventions before FSC computation and includes the selection of a common threshold. Here, we apply the statistical methods of permutation testing and false discovery rate (FDR) control to the resolution-dependent correlation measure. The approach allows fully automated and mask-free resolution determination based on statistical thresholding of FSC curves. We demonstrate the applicability for global, local and directional resolution estimation and show that the developed criterion termed FDR-FSC gives realistic resolution estimates based on statistical significance while eliminating the need of any map manipulations. The algorithms are implemented in a user-friendly GUI based software tool termed SPoC (https://github.com/MaximilianBeckers/SPOC).

Investigation of the structure and function of biological matter provides one of the most fascinating aspects of nature: how life with all its complex processes evolves from simple wiggling and jiggling of atoms. Structural Biology is especially interesting, as it involves all three major fields of the natural sciences: the physics of atoms and the scattering of incident radiation, the chemistry of bonding, reactions and interactions and finally the biological interpretation of the chemical structures. However, tools from statistical decision theory are still rare in structural biology compared to their applications in e.g. "omics"-technologies. Especially when it comes to the interpretation of 3D maps of single particles, more rigorous approaches would be highly desired. In this thesis, I developed new methodology for the statistical inference of three-dimensional molecular maps generated with cryogenic electron microscopy (cryo-EM), which is becoming the method of choice for high-resolution structure determination. The aspects I focused on are very basic topics of the method and were not properly solved so far. The first part of the dissertation deals with the problem of assigning molecules and molecular parts in noisy 3D densities. Based on multiple hypothesis testing and false discovery rate control, the cryo-EM map is transformed in a map containing detection probabilities, termed confidence map. Confidence maps allow the assignment of map features by means of statistical significance and avoid rather arbitrary thresholds, as they have to be used for the analysis of cryo-EM maps. Another important quantity that has to be inferred from cryo-EM maps is their resolution. It is probably the most important number regarding the quality of the map and describes up to which spatial frequency we can faithfully interpret the data. However, despite its importance and implications for map processing, resolution estimation remains a highly controversial issue. I describe how the resolution estimation problem can be reformulated into multiple hypothesis testing of Fourier shell correlation coefficients and how this results in a unified threshold criterion applicable to global, local, directional and map-model resolution estimation. The last chapter provides a high-resolution study of tobacco mosaic virus (TMV). Although structural studies of tobacco mosaic virus by Rosalind Franklin marked one of the birth events of structural biology, the most important biological aspect of controlled release of the viral genome remained a mystery for more than 50 years. Two cryo-EM structures at 1.9 and 2 A resolution together with the developed confidence maps allowed us to elucidate the structural mechanism of the disassembly switch of TMV. Moreover, it may also serve as a general case study how careful interpretation with state-of-the art methods can be used to deal with densities that are notoriously difficult to model.