CTF determination and correction for low dose tomographic tilt series

The resolution of cryo-electron tomography can be limited by the first zero of the microscope’s contrast transfer function (CTF). To achieve higher resolution, it is critical to determine the CTF and correct its phase inversions. However, the extremely low signal-to-noise ratio (SNR) and the defocus gradient in the projections of tilted specimens make this process challenging. Two programs, CTFPLOTTER and CTFPHASEFLIP, have been developed to address these issues. CTFPLOTTER obtains a 1D power spectrum by periodogram averaging and rotational averaging and it estimates the noise background with a novel approach, which uses images taken with no specimen. The background-subtracted 1D power spectra from image regions at different defocus values are then shifted to align their first zeros and averaged together. This averaging improves the SNR sufficiently that it becomes possible to determine the defocus for subsets of the tilt series rather than just the entire series. CTFPHASEFLIP corrects images line-by-line by inverting phases appropriately in thin strips of the image at nearly constant defocus. CTF correction by these methods is shown to improve the resolution of aligned, averaged particles extracted from tomograms. However, some restoration of Fourier amplitudes at high frequencies is important for seeing the benefits from CTF correction.     

TomoAlign: A novel approach to correcting sample motion and 3D CTF in CryoET

TomoAlign is a software package that integrates tools to mitigate two important resolution limiting factors in cryoET, namely the beam-induced sample motion and the contrast transfer function (CTF) of the microscope. The package is especially focused on cryoET of thick specimens where fiducial markers are required for accurate tilt-series alignment and sample motion estimation. TomoAlign models the beam-induced sample motion undergone during the tilt-series acquisition. The motion models are used to produce motion-corrected subtilt-series centered on the particles of interest. In addition, the defocus of each particle at each tilt image is determined and can be corrected, resulting in motion-corrected and CTF-corrected subtilt-series from which the subtomograms can be computed. Alternatively, the CTF information can be passed on so that CTF correction can be carried out entirely within external packages like Relion. TomoAlign serves as a versatile tool that can streamline the cryoET workflow from initial alignment of tilt-series to final subtomogram averaging during in situ structure determination.     

goCTF: Geometrically optimized CTF determination for single-particle cryo-EM

Preferred particle orientation represents a recurring problem in single-particle cryogenic electron microcopy (cryo-EM). A specimen-independent approach through tilting has been attempted to increase particle orientation coverage, thus minimizing anisotropic three-dimensional (3D) reconstruction. However, focus gradient is a critical issue hindering tilt applications from being a general practice in single-particle cryo-EM. The present study describes a newly developed geometrically optimized approach, goCTF, to reliably determine the global focus gradient. A novel strategy of determining contrast transfer function (CTF) parameters from a sector of the signal preserved power spectrum is applied to increase reliability. Subsequently, per-particle based local focus refinement is conducted in an iterative manner to further improve the defocus accuracy. Novel diagnosis methods using a standard deviation defocus plot and goodness of fit heatmap have also been proposed to evaluate CTF fitting quality prior to 3D refinement. In a benchmark study, goCTF processed a published single-particle cryo-EM dataset for influenza hemagglutinin trimer collected at a 40-degree specimen tilt. The resulting 3D reconstruction map was improved from 4.1?Å to 3.7?Å resolution. The goCTF program is built on the open-source code of CTFFIND4, which adopts a consistent user interface for ease of use.     

Accurate determination of local defocus and specimen tilt in electron microscopy

Accurate knowledge of defocus and tilt parameters is essential for the determination of three-dimensional protein structures at high resolution using electron microscopy. We present two computer programs, CTFFIND3 and CTFTILT, which determine defocus parameters from images of untilted specimens, as well as defocus and tilt parameters from images of tilted specimens, respectively. Both programs use a simple algorithm that fits the amplitude modulations visible in a power spectrum with a calculated contrast transfer function (CTF). The background present in the power spectrum is calculated using a low-pass filter. The background is then subtracted from the original power spectrum, allowing the fitting of only the oscillatory component of the CTF. CTFTILT determines specimen tilt parameters by measuring the defocus at a series of locations on the image while constraining them to a single plane. We tested the algorithm on images of two-dimensional crystals by comparing the results with those obtained using crystallographic methods. The images also contained contrast from carbon support film that added to the visibility of the CTF oscillations. The tests suggest that the fitting procedure is able to determine the image defocus with an error of about 10nm, whereas tilt axis and tilt angle are determined with an error of about 2 degrees and 1 degrees, respectively. Further tests were performed on images of single protein particles embedded in ice that were recorded from untilted or slightly tilted specimens. The visibility of the CTF oscillations from these images was reduced due to the lack of a carbon support film. Nevertheless, the test results suggest that the fitting procedure is able to determine image defocus and tilt angle with errors of about 100 nm and 6 degrees, respectively.     

Development of a new protein labeling system to map subunits and domains of macromolecular complexes for electron microscopy

Several gene fusion technologies have been successfully applied to label particular subunits or domains within macromolecular complexes to enable positional mapping of electron microscopy (EM) density maps, but exogenous fusion of a protein domain into the target polypeptide can cause unwanted structural and functional outcomes. Fab fragments from antibodies can be used as labeling reagents during EM visualization without gene manipulation of the target protein, but this method requires a panel of high-affinity antibodies that recognize a wide variety of epitopes. Linear peptide tags and their anti-tag antibodies can be used but they have a limited mapping ability as their placement is usually limited to the terminal regions of a protein. The PA dodecapeptide epitope tag (GVAMPGAEDDVV), forms a tight β-turn in the antigen binding pocket of its antibody (NZ-1). This capability allows for insertion of the PA tag into various surface-exposed loops within a multi-domain cell adhesion receptor, α_IIbβ₃ integrin. We confirmed that the purified PA-tagged integrin ectodomain fragments can form a stable complex with NZ-1 Fab. Negative stain EM of the various integrin-NZ-1 complexes revealed that a majority of the particles exhibited a clear density corresponding to the NZ-1 Fab; and the positions of the bound Fab were in good agreement with the predicted location of the inserted PA tag. The high-affinity and insertion-compatibility of the PA tag system allowed us to develop a new EM labeling methodology applicable to proteins for which good antibodies are not available.     

Recognition and separation of single particles with size variation by statistical analysis of their images

Macromolecules may occupy conformations with structural differences that cannot be resolved biochemically. The separation of mixed molecular populations is a pressing problem in single-particle analysis. Until recently, the task of distinguishing small structural variations was intractable, but developments in cryo-electron microscopy hardware and software now make it possible to address this problem. We have developed a general strategy for recognizing and separating structures of variable size from cryo-electron micrographs of single particles. The method uses a combination of statistical analysis and projection matching to multiple models. Identification of size variations by multivariate statistical analysis was used to do an initial separation of the data and generate starting models by angular reconstitution. Refinement was performed using alternate projection matching to models and angular reconstitution of the separated subsets. The approach has been successful at intermediate resolution, taking it within range of resolving secondary structure elements of proteins. Analysis of simulated and real data sets is used to illustrate the problems encountered and possible solutions. The strategy developed was used to resolve the structures of two forms of a small heat shock protein (Hsp26) that vary slightly in diameter and subunit packing.     

An adaptation of the Wiener filter suitable for analyzing images of isolated single particles

The Wiener filter is a standard means of optimizing the signal in sums of aligned, noisy images obtained by electron cryo-microscopy (cryo-EM). However, estimation of the resolution-dependent (“spectral”) signal-to-noise ratio (SSNR) from the input data has remained problematic, and error reduction due to specific application of the SSNR term within a Wiener filter has not been reported. Here we describe an adjustment to the Wiener filter for optimal summation of images of isolated particles surrounded by large regions of featureless background, as is typically the case in single-particle cryo-EM applications. We show that the density within the particle area can be optimized, in the least-squares sense, by scaling the SSNR term found in the conventional Wiener filter by a factor that reflects the fraction of the image field occupied by the particle. We also give related expressions that allow the SSNR to be computed for application in this new filter, by incorporating a masking step into a Fourier Ring Correlation (FRC), a standard resolution measure. Furthermore, we show that this masked FRC estimation scheme substantially improves on the accuracy of conventional SSNR estimation methods. We demonstrate the validity of our new approach in numeric tests with simulated data corresponding to realistic cryo-EM imaging conditions. This variation of the Wiener filter and accompanying derivation should prove useful for a variety of single-particle cryo-EM applications, including 3D reconstruction.     

An improved algorithm for fast resonant Mie scatter correction of infrared spectra of cells and tissues

Mie scattering effects create serious problems for the interpretation of Fourier‐transform infrared spectroscopy spectra of single cells and tissues. During recent years, different techniques were proposed to retrieve pure absorbance spectra from spectra with Mie distortions. Recently, we published an iterative algorithm for correcting Mie scattering in spectra of single cells and tissues, which we called “the fast resonant Mie scatter correction algorithm.” The algorithm is based on extended multiplicative signal correction (EMSC) and employs a meta‐model for a parameter range of refractive index and size parameters. In the present study, we suggest several improvements of the algorithm. We demonstrate that the improved algorithm reestablishes chemical features of the measured spectra, and show that it tends away from the reference spectrum employed in the EMSC. We suggest strategies for choosing parameter ranges and other model parameters such as the number of principal components of the meta‐model and the number of iterations. We demonstrate that the suggested algorithm optimizes an error function of the refractive index in a forward Mie model. We suggest a stop criterion for the iterative algorithm based on the error function of the forward model.      

An open‐source code for Mie extinction extended multiplicative signal correction for infrared microscopy spectra of cells and tissues

Infrared spectroscopy of single cells and tissue is affected by Mie scattering. During recent years, several methods have been proposed for retrieving pure absorbance spectra from such measurements, while currently no user‐friendly version of the state‐of‐the‐art algorithm is available. In this work, an open‐source code for correcting highly scatter‐distorted absorbance spectra of cells and tissues is presented, as well as several improvements of the latest version of the Mie correction algorithm based on extended multiplicative signal correction (EMSC) published by Konevskikh et al. In order to test the stability of the code, a set of apparent absorbance spectra was simulated. To this purpose, pure absorbance spectra based on a Matrigel spectrum are simulated. Scattering contributions where obtained by mimicking the scattering features observed in a set of experimentally obtained spectra . It can be concluded that the algorithm is not depending strongly on the reference spectrum used for initializing the algorithm and retrieves well the underlying pure absorbance spectrum. The calculation time of the algorithm is considerably improved with respect to the resonant Mie scattering EMSC algorithm used by the community today.      

Structural analysis of vimentin and keratin intermediate filaments by cryo-electron tomography

Intermediate filaments are a large and structurally diverse group of cellular filaments that are classified into five different groups. They are referred to as intermediate filaments (IFs) because they are intermediate in diameter between the two other cytoskeletal filament systems that is filamentous actin and microtubules. The basic building block of IFs is a predominantly alpha-helical rod with variable length globular N- and C-terminal domains. On the ultra-structural level there are two major differences between IFs and microtubules or actin filaments: IFs are non-polar, and they do not exhibit large globular domains. IF molecules associate via a coiled-coil interaction into dimers and higher oligomers. Structural investigations into the molecular building plan of IFs have been performed with a variety of biophysical and imaging methods such as negative staining and metal-shadowing electron microscopy (EM), mass determination by scanning transmission EM, X-ray crystallography on fragments of the IF stalk and low-angle X-ray scattering. The actual packing of IF dimers into a long filament varies between the different families. Typically the dimers form so called protofibrils that further assemble into a filament. Here we introduce new cryo-imaging methods for structural investigations of IFs in vitro and in vivo, i.e., cryo-electron microscopy and cryo-electron tomography, as well as associated techniques such as the preparation and handling of vitrified sections of cellular specimens.     

Structural analysis of the Saf pilus by electron microscopy and image processing

Bacterial pili are important virulence factors involved in host cell attachment and/or biofilm formation, key steps in establishing and maintaining successful infection. Here we studied Salmonella atypical fimbriae (or Saf pili), formed by the conserved chaperone/usher pathway. In contrast to the well-established quaternary structure of typical/FGS-chaperone assembled, rod-shaped, chaperone/usher pili, little is known about the supramolecular organisation in atypical/FGL-chaperone assembled fimbriae. In our study, we have used negative stain electron microscopy and single-particle image analysis to determine the three-dimensional structure of the Salmonella typhimurium Saf pilus. Our results show atypical/FGL-chaperone assembled fimbriae are composed of highly flexible linear multi-subunit fibres that are formed by globular subunits connected to each other by short links giving a “beads on a string”-like appearance. Quantitative fitting of the atomic structure of the SafA pilus subunit into the electron density maps, in combination with linker modelling and energy minimisation, has enabled analysis of subunit arrangement and intersubunit interactions in the Saf pilus. Short intersubunit linker regions provide the molecular basis for flexibility of the Saf pilus by acting as molecular hinges allowing a large range of movement between consecutive subunits in the fibre.     

Single particle 3D reconstruction for 2D crystal images of membrane proteins

In cases where ultra-flat cryo-preparations of well-ordered two-dimensional (2D) crystals are available, electron crystallography is a powerful method for the determination of the high-resolution structures of membrane and soluble proteins. However, crystal unbending and Fourier-filtering methods in electron crystallography three-dimensional (3D) image processing are generally limited in their performance for 2D crystals that are badly ordered or non-flat. Here we present a single particle image processing approach, which is implemented as an extension of the 2D crystallographic pipeline realized in the 2dx software package, for the determination of high-resolution 3D structures of membrane proteins. The algorithm presented, addresses the low single-to-noise ratio (SNR) of 2D crystal images by exploiting neighborhood correlation between adjacent proteins in the 2D crystal. Compared with conventional single particle processing for randomly oriented particles, the computational costs are greatly reduced due to the crystal-induced limited search space, which allows a much finer search space compared to classical single particle processing. To reduce the considerable computational costs, our software features a hybrid parallelization scheme for multi-CPU clusters and computer with high-end graphic processing units (GPUs). We successfully apply the new refinement method to the structure of the potassium channel MloK1. The calculated 3D reconstruction shows more structural details and contains less noise than the map obtained by conventional Fourier-filtering based processing of the same 2D crystal images.