Cross-Validation of Data Compatibility Between Small Angle X-ray Scattering and Cryo-Electron Microscopy

Fitting high-resolution electron density maps from atomic models to solution scattering data

Solution scattering techniques, such as small- and wide-angle X-ray scattering (SWAXS), provide valuable insights into the structure and dynamics of biological macromolecules in solution. In this study, we present an approach to accurately predict solution X-ray scattering profiles at wide angles from atomic models by generating high-resolution electron density maps. Our method accounts for the excluded volume of bulk solvent by calculating unique adjusted atomic volumes directly from the atomic coordinates. This approach eliminates the need for one of the free fitting parameters commonly used in existing algorithms, resulting in improved accuracy of the calculated SWAXS profile. An implicit model of the hydration shell is generated that uses the form factor of water. Two parameters, namely the bulk solvent density and the mean hydration shell contrast, are adjusted to best fit the data. Results using eight publicly available SWAXS profiles show high-quality fits to the data. In each case, the optimized parameter values show small adjustments demonstrating that the default values are close to the true solution. Disabling parameter optimization produces significantly more accurate predicted scattering profiles compared to the leading software. The algorithm is computationally efficient, comparable to the leading software and up to 10 times faster for large molecules. The algorithm is encoded in a command line script called denss.pdb2mrc.py and is available open source as part of the DENSS v1.7.0 software package. In addition to improving the ability to compare atomic models to experimental SWAXS data, these developments pave the way for increasing the accuracy of modeling algorithms using SWAXS data and decreasing the risk of overfitting.

Fitting high-resolution electron density maps from atomic models to solution scattering data

Solution scattering techniques, such as small and wide-angle X-ray scattering (SWAXS), provide valuable insights into the structure and dynamics of biological macromolecules in solution. In this study, we present an approach to accurately predict solution X-ray scattering profiles at wide angles from atomic models by generating high-resolution electron density maps. Our method accounts for the excluded volume of bulk solvent by calculating unique adjusted atomic volumes directly from the atomic coordinates. This approach eliminates the need for a free fitting parameter commonly used in existing algorithms, resulting in improved accuracy of the calculated SWAXS profile. An implicit model of the hydration shell is generated which uses the form factor of water. Two parameters, namely the bulk solvent density and the mean hydration shell contrast, are adjusted to best fit the data. Results using eight publicly available SWAXS profiles show high quality fits to the data. In each case, the optimized parameter values show small adjustments demonstrating that the default values are close to the true solution. Disabling parameter optimization results in a significant improvement of the calculated scattering profiles compared to the leading software. The algorithm is computationally efficient, showing more than tenfold reduction in execution time compared to the leading software. The algorithm is encoded in a command line script called denss.pdb2mrc.py and is available open source as part of the DENSS v1.7.0 software package (https://github.com/tdgrant1/denss). In addition to improving the ability to compare atomic models to experimental SWAXS data, these developments pave the way for increasing the accuracy of modeling algorithms utilizing SWAXS data while decreasing the risk of overfitting.

High Resolution Membrane Structures within Hybrid Lipid-Polymer Vesicles Revealed by Combining X-Ray Scattering and Electron Microscopy

Hybrid vesicles consisting of phospholipids and block-copolymers are increasingly finding applications in science and technology. Herein, small angle X-ray scattering (SAXS) and cryo-electron tomography (cryo-ET) are used to obtain detailed structural information about hybrid vesicles with different ratios of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and poly(1,2-butadiene-block-ethylene oxide) (PBd₂₂ -PEO₁₄ , M_s  = 1800 g mol^-1 ). Using single particle analysis (SPA) the authors are able to further interpret the information gained from SAXS and cryo-ET experiments, showing that increasing PBd₂₂ -PEO₁₄ mole fraction increases the membrane thickness from 52 Å for a pure lipid system to 97 Å for pure PBd₂₂ -PEO₁₄ vesicles. Two vesicle populations with different membrane thicknesses in hybrid vesicle samples are found. As these lipids and polymers are reported to homogeneously mix, bistability is inferred between weak and strong interdigitation regimes of PBd₂₂ -PEO₁₄ within the hybrid membranes. It is hypothesized that membranes of intermediate structure are not energetically favorable. Therefore, each vesicle exists in one of these two membrane structures, which are assumed to have comparable free energies. The authors conclude that, by combining biophysical methods, accurate determination of the influence of composition on the structural properties of hybrid membranes is achieved, revealing that two distinct membranes structures can coexist in homogeneously mixed lipid-polymer hybrid vesicles.

Emerging Themes in CryoEM─Single Particle Analysis Image Processing

Cryo-electron microscopy (CryoEM) has become a vital technique in structural biology. It is an interdisciplinary field that takes advantage of advances in biochemistry, physics, and image processing, among other disciplines. Innovations in these three basic pillars have contributed to the boosting of CryoEM in the past decade. This work reviews the main contributions in image processing to the current reconstruction workflow of single particle analysis (SPA) by CryoEM. Our review emphasizes the time evolution of the algorithms across the different steps of the workflow differentiating between two groups of approaches: analytical methods and deep learning algorithms. We present an analysis of the current state of the art. Finally, we discuss the emerging problems and challenges still to be addressed in the evolution of CryoEM image processing methods in SPA.

Calculating small-angle scattering intensity functions from electron-microscopy images

We outline procedures to calculate small-angle scattering (SAS) intensity functions from 2-dimensional electron-microscopy (EM) images. Two types of scattering systems were considered: (a) the sample is a set of particles confined to a plane; or (b) the sample is modelled as parallel, infinitely long cylinders that extend into the image plane. In each case, an EM image is segmented into particle instances and the background, whereby coordinates and morphological parameters are computed and used to calculate the constituents of the SAS-intensity function. We compare our results with experimental SAS data, discuss limitations, both general and case specific, and outline some applications of this method which could potentially complement experimental SAS.

We outline procedures to calculate small-angle scattering (SAS) intensity functions from 2-dimensional electron-microscopy (EM) images for two types of scattering systems.

Protein Footprinting: Auxiliary Engine to Power the Structural Biology Revolution

Structural biology is entering an exciting time where many new high-resolution structures of large complexes and membrane proteins are determined regularly. These advances have been driven by over fifteen years of technology advancements, first in macromolecular crystallography, and recently in Cryo-electron microscopy. These structures are allowing detailed questions about functional mechanisms of the structures, and the biology enabled by these structures, to be addressed for the first time. At the same time, mass spectrometry technologies for protein structure analysis, "footprinting" studies, have improved their sensitivity and resolution dramatically and can provide detailed sub-peptide and residue level information for validating structures and interactions or understanding the dynamics of structures in the context of ligand binding or assembly. In this perspective, we review the use of protein footprinting to extend our understanding of macromolecular systems, particularly for systems challenging for analysis by other techniques, such as intrinsically disordered proteins, amyloidogenic proteins, and other proteins/complexes so far recalcitrant to existing methods. We also illustrate how the availability of high-resolution structural information can be a foundation for a suite of hybrid approaches to divine structure-function relationships beyond what individual techniques can deliver.

Need for Cross-Validation of Single Particle Cryo-EM

Cross-validation is used to determine the validity of a model on unseen data by assessing if the model is overfitted to noise. It is widely used in many fields, from artificial intelligence to structural biology in X-ray crystallography and nuclear magnetic resonance. Although there are concerns of map overfitting in cryo-electron microscopy (cryo-EM), cross-validation is rarely used. The problem is that establishing a performance metric of the maps over unseen data (given by 2D-projection images) is difficult due to the low signal-to-noise ratios in the individual particles. Here, I present recent advances for cryo-EM map reconstruction. I highlight that the gold-standard procedure can fail to detect map overfitting in certain cases, showing the necessity of assessing the map quality on unbiased data. Finally, I describe the challenges and advantages of developing a robust cross-validation methodology for cryo-EM.