Statistical Inference of cryo-EM Maps

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

Permutation testing of Fourier shell correlation for resolution estimation of cryo-EM maps

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)

Cover art to "25 years of small molecule optimization at Novartis: A retrospective analysis of chemical series evolution"

In the internal Novartis compound databases, a set of ~3000 chemical series has been retrospectively reconstructed. Using the registration dates of the compounds, the evolution over time of structural properties, ADMET and target activities during optimization of the compounds has been analyzed, which revealed multiple trends. Furthermore, general properties of the chemical series and their inter-relations are investigated

Structural interpretation of cryo-EM image reconstructions

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

25 Years of Small-Molecule Optimization at Novartis: A Retrospective Analysis of Chemical Series Evolution.

In the drug development process, optimization of properties and biological activities of small molecules is an important task to obtain drug candidates with optimal efficacy when first applied in subsequent clinical studies. However, despite its importance, large-scale investigations of the optimization process in early drug discovery are lacking, likely due to the absence of historical records of different chemical series used in past projects. Here, we report a retrospective reconstruction of ∼3000 chemical series from the Novartis compound database, which allows us to characterize the general properties of chemical series as well as the time evolution of structural properties, ADMET properties, and target activities. Our data-driven approach allows us to substantiate common MedChem knowledge. We find that size, fraction of sp3-hybridized carbon atoms (Fsp3), and the density of stereocenters tend to increase during optimization, while the aromaticity of the compounds decreases. On the ADMET side, solubility tends to increase and permeability decreases, while safety-related properties tend to improve. Importantly, while ligand efficiency decreases due to molecular growth over time, target activities and lipophilic efficiency tend to improve. This emphasizes the heavy-atom count and log D as important parameters to monitor, especially as we further show that the decrease in permeability can be explained with the increase in molecular size. We highlight overlaps, shortcomings, and differences of the computationally reconstructed chemical series compared to the series used in recent internal drug discovery projects and investigate the relation to historical projects

Thresholding of cryo-EM density maps by false discovery rate control

Cryo-EM now commonly generates close-to-atomic resolution as well as intermediate resolution maps from macromolecules observed in isolation and in situ. Interpreting these maps remains a challenging task owing to poor signal in the highest resolution shells and the necessity to select a threshold for density analysis. In order to facilitate this process, a statistical framework for the generation of confidence maps by multiple hypothesis testing and false discovery rate (FDR) control has been developed. In this way, three-dimensional confidence maps contain signal separated from background noise in the form of local detection rates of EM density values. It is demonstrated that confidence maps and FDR-based thresholding can be used for the interpretation of near-atomic resolution single-particle structures as well as lower resolution maps determined by subtomogram averaging. Confidence maps represent a conservative way of interpreting molecular structures owing to minimized noise. At the same time they provide a detection error with respect to background noise, which is associated with the density and is particularly beneficial for the interpretation of weaker cryo-EM densities in cases of conformational flexibility and lower occupancy of bound molecules and ions in the structure

Confidence maps: statistical inference of cryo-EM maps

Confidence maps provide complementary information for interpreting cryo-EM densities as they indicate statistical significance with respect to background noise. They can be thresholded by specifying the expected false-discovery rate (FDR), and the displayed volume shows the parts of the map that have the corresponding level of significance. Here, the basic statistical concepts of confidence maps are reviewed and practical guidance is provided for their interpretation and usage inside the CCP-EM suite. Limitations of the approach are discussed and extensions towards other error criteria such as the family-wise error rate are presented. The observed map features can be rendered at a common isosurface threshold, which is particularly beneficial for the interpretation of weak and noisy densities. In the current article, a practical guide is provided to the recommended usage of confidence maps

Elucidation of the viral disassembly switch of tobacco mosaic virus

Stable capsid structures of viruses protect viral RNA while they also require controlled disassembly for releasing the viral genome in the host cell. A detailed understanding of viral disassembly processes and the involved structural switches is still lacking. This process has been extensively studied using tobacco mosaic virus (TMV), and carboxylate interactions are assumed to play a critical part in this process. Here, we present two cryo‐EM structures of the helical TMV assembly at 2.0 and 1.9 Å resolution in conditions of high Ca2+ concentration at low pH and in water. Based on our atomic models, we identify the conformational details of the disassembly switch mechanism: In high Ca2+/acidic pH environment, the virion is stabilized between neighboring subunits through carboxyl groups E95 and E97 in close proximity to a Ca2+ binding site that is shared between two subunits. Upon increase in pH and lower Ca2+ levels, mutual repulsion of the E95/E97 pair and Ca2+ removal destabilize the network of interactions between adjacent subunits at lower radius and release the switch for viral disassembly