Automatic lattice determination for two-dimensional crystal images

https://doi.org/10.1016/j.jsb.2007.08.008Get rights and content

Abstract

Electron crystallography determines the structure of membrane proteins and other periodic samples by recording either images or diffraction patterns. Computer processing of recorded images requires the determination of the reciprocal lattice parameters in the Fourier transform of the image. We have developed a set of three programs 2dx_peaksearch, 2dx_findlat and 2dx_getlat, which can determine the reciprocal lattice from a Fourier transformation of a 2D crystal image automatically. 2dx_peaksearch determines a list of Fourier peak coordinates from a processed calculated diffraction pattern. These coordinates are evaluated by 2dx_findlat to determine one or more lattices, using a-priori knowledge of the real-space crystal unit cell dimensions, and the sample tilt geometry. If these are unknown, then the program 2dx_getlat can be used to obtain a guess for the unit cell dimensions. These programs are available as part of the 2dx software package for the image processing of 2D crystal images at http://2dx.org.

Introduction

Electron crystallography determines the structure of two-dimensional (2D) crystals of membrane proteins or other periodically arranged samples, using cryo-electron microscopy (cryo-EM) data collection and computer image processing (Henderson et al., 1990, Henderson and Unwin, 1975). The electron microscope can be used in either the imaging or the diffraction mode. In imaging mode, real-space images of the crystalline samples are recorded on the instrument’s CCD camera or photographic film. The latter needs to be digitized with a scanner before further processing. Digitized images can then be numerically Fourier transformed, producing complex datasets, which contain amplitudes and phases. Since computational correction of 2D crystal defects in the image can be done by computational “unbending” (Crowther et al., 1996), useful real-space images can also be recorded for crystal samples of limited order. Nevertheless, the resolution of such real-space images is affected by beam-induced sample charging and drum-head movement, as well as by sample vibration or drift. While phases obtained from Fourier-transformed 2D crystal real-space images are of relatively good quality, the amplitudes are affected by the electron microscope’s contrast transfer function, and are therefore less well determined.

Alternatively, the electron microscope can record electron diffraction patterns of the 2D crystal samples, which are preferably recorded onto CCD cameras due to their superior dynamic range. The electron diffraction patterns are then evaluated similarly to X-ray diffraction (XRD) patterns in X-ray crystallography; which yield the intensities of the diffracted rays, and thereby contain the information about the structure’s amplitudes. Phase information is not contained in the diffraction pattern, and has to be acquired by different means. Electron diffraction data collection, in contrast, generally does not suffer from sample charging or sample movement during the data collection. Since 2D crystal image unbending cannot be done with a diffraction pattern, in practical terms electron diffraction can only be done with larger, well-ordered 2D crystal samples.

Electron crystallography structure reconstruction of membrane proteins ideally utilizes real-space images to obtain an initial dataset with amplitudes and phases, and then continues completing the dataset with high-resolution amplitudes from electron diffraction patterns alone. The phases for the high-resolution components are then generated or refined by phase extension or molecular replacement, similar to the procedures used in X-ray diffraction structure determination (Grigorieff et al., 1996).

The atomic models for seven membrane proteins and tubulin have so far been determined by electron crystallography: BR (Henderson et al., 1990) LHCII (Kühlbrandt et al., 1994), AQP1 (Murata et al., 2000, Ren et al., 2001), nAChR (Miyazawa et al., 2003), AQP0 (Gonen et al., 2004, Gonen et al., 2005), AQP4 (Hiroaki et al., 2006), MGST1 (Holm et al., 2006), and Tubulin (Nogales et al., 1998). Several other membrane proteins classified as transporters, ion pumps, receptors and membrane bound enzymes have been studied by electron crystallography at lower resolution allowing localization of secondary structure motifs such as transmembrane helices, and are likely to produce atomic models in the near future (e.g. Hirai et al., 2002, Kukulski et al., 2005, Schenk et al., 2005, Tate et al., 2003, Vinothkumar et al., 2005). Computer image processing in almost all above-mentioned cases has been performed with the so-called “MRC programs” for image processing (Crowther et al., 1996). Computer processing of recorded images generally requires the determination of the crystal lattice using spots visible in the Fourier transform of the images. For the processing of electron crystallography images, this determination of the lattice vectors is usually done manually, and represents a time-intensive step, especially if many images are to be processed.

X-ray crystallography diffraction patterns show spots if their reciprocal position overlaps sufficiently with the Ewald sphere. The complex indexing process of XRD is done with robust automated software, such as the program DENZO as a part of the diffraction-image processing suite HKL2000 (Otwinowski and Minor, 1997, Otwinowski and Minor, 2001, Rossmann and van Beek, 1999), MOSFLM (Leslie, 1992), and dTREK (Pflugrath, 1999). Important representatives of autoindexing algorithms are either based on Fourier analysis (Steller et al., 1997) or direct indexing of difference vectors (Higashi, 1990, Kabsch, 1988, Kim, 1989). The general principle behind Fourier analysis methods is that the projection of a protein lattice in a chosen direction has a periodic distribution. The periodicity is determined by Fourier analysis. Structural details are encoded in the regular lattice in Fourier space. The basis vectors defining the reciprocal lattice in Fourier space are found by exploring all possible directions. In XRD autoindexing, Fourier-based methods need a few hundred spots to get reliable results, although in some favorable cases as few as 50 can be sufficient (Leslie, 2006). Difference vector methods first sort and estimate the crude base vectors according to their lengths and angle constraints. The selected bases are iteratively refined using estimated positions of observed diffraction spots. Both, Fourier-based and difference vector methods cannot identify single lattices in double- or poly-crystals. In this case, spots of a single lattice have to be selected manually beforehand.

There exist many algorithms for indexing diffraction spots in X-ray crystallography. However, little work is reported for that task in electron crystallography. Unlike X-ray diffraction patterns, electron crystallography gives real space images that have a very low signal to noise ratio, and the Fourier transformations show usually less than 100 visible spots. The common methods of difference vector analysis may not find the accurate basis. Kabsch, 1993, has proposed a robust solution that takes into account the moderate accuracy of the automatically determined lattice points and tolerates a small number of artifacts among them. This approach, however, cannot handle multiple crystal lattices.

We present here two new algorithms for determination of the reciprocal lattice of a 2D crystal image. These algorithms are also applicable to poly-crystal images. In addition, we present a refined tool for manual lattice identification in 2dx_image.

Section snippets

The lattice determination algorithm

The first algorithm presented requires and makes use of a-priori knowledge of the lattice dimensions and lattice angle of the crystal sample in real-space, as well as of the sample tilt geometry under which the image was recorded. This algorithm determines the reciprocal lattice in the Fourier transformation (FFT) of the image in two steps: A first program 2dx_peaksearch compiles a list of peak coordinates from the FFT, and another program 2dx_findlat uses these peak coordinates to determine

Results

The performance of these algorithms has been tested on a variety of images from non-tilted and tilted 2D crystals of various lattice dimensions and signal-to-noise levels.

Table 1 shows the results of applying the first algorithm (2dx_findlat) to different electron micrographs of 2D membrane protein crystals. For the first peak search in the original PS, 40 peaks were selected to generate the average shifted PS image and 140 peaks were selected from the latter to determine the lattice vectors.

Discussions

The peaks from the averaged PS allow much better identification of the lattice than the peaks from the original PS. Our algorithm as implemented in 2dx_peaksearch follows the developments for the average PS that were also implemented in the MRC program autoindex before (Crowther et al., 1996). In addition, 2dx_peaksearch also removes streaks, which can arise from image edge effects, or, as in the case for Fig. 1, from the edges of a negatively stained 2D crystal itself. The resulting averaged

Conclusions

A set of three programs 2dx_peaksearch, 2dx_findlat and 2dx_getlat was created, which allow the automatic determination of a 2D crystal lattice from a real-space image. 2dx_peaksearch determines a list of Fourier peak coordinates, which are used by 2dx_findlat to determine one or more lattices, using a-priori knowledge of the real-space crystal unit cell dimensions and the sample tilt geometry. If these are unknown, the program 2dx_getlat can be used to rapidly determine the most likely

Acknowledgments

This work was supported by the NSF, Grant No. MCB-0447860 and by the NIH, Grant No. U54-GM074929. We thank Richard Henderson for his explanations of the algorithms used in autoindex. Development of some of these algorithms was started in the laboratories of Jacques Dubochet in Lausanne, and Andreas Engel in Basel, Switzerland.

References (34)

  • P.J. Shaw et al.

    Tilted specimen in the electron microscope: A simple specimen holder and the calculation of tilt angles for crystalline specimens

    Micron

    (1981)
  • J.M. Smith

    Ximdisp–A visualization tool to aid structure determination from electron microscope images

    J. Struct. Biol.

    (1999)
  • C.G. Tate et al.

    Conformational changes in the multidrug transporter EmrE associated with substrate binding

    J. Mol. Biol.

    (2003)
  • J.M. Valpuesta et al.

    Analysis of electron microscope images and electron diffraction patterns of thin crystals of phi 29 connectors in ice

    J. Mol. Biol.

    (1994)
  • T. Gonen et al.

    Lipid-protein interactions in double-layered two-dimensional AQP0 crystals

    Nature

    (2005)
  • T. Gonen et al.

    Aquaporin-0 membrane junctions reveal the structure of a closed water pore

    Nature

    (2004)
  • R. Henderson et al.

    Three-dimensional model of purple membrane obtained by electron microscopy

    Nature

    (1975)
  • Cited by (21)

    • 3D reconstruction of two-dimensional crystals

      2015, Archives of Biochemistry and Biophysics
      Citation Excerpt :

      This leads to a power spectrum pattern that shows a full set of diffraction peaks without systematic absences and usually full occupancy of low-resolution spots. Two different algorithms can then be used to find one or several 2D crystal lattice patterns in the peaks in this power spectrum [52]: The algorithm “getlattice” will determine the most frequently occurring difference vector among the identified peaks, which is interpreted as the first lattice vector “a∗”. The second, most frequently occurring difference vector that is linearly independent from “a∗” is then taken as “b∗”.

    • 2dx_automator: Implementation of a semiautomatic high-throughput high-resolution cryo-electron crystallography pipeline

      2014, Journal of Structural Biology
      Citation Excerpt :

      Due to the new detector and the significant improvements of the version from 2013 of CTFFIND3, the success rate of this procedure is almost 100% (Section 6). The remaining processing tasks: (i) lattice determination (Zeng et al., 2007), (ii) crystal unbending, (iii) CTF-correction and (iv) map-generation, are automatically conducted in exactly the same way as for a classical 2dx-project (Arheit et al., 2013c). The automation pipeline also offers the possibility to test for potential second crystallographic lattices in the crystal images, which can then be processed within 2dx either fully automatically or manually.

    • Offline estimation of 2D crystal lattice parameters by processing the electron diffraction image

      2012, Optics Communications
      Citation Excerpt :

      The package has two components, viz. MICRO and INDEX. While it extracts and records the intensity, the latter indexes 3D information on the basis of 2D projection image. [16] proposed a software tool (2dx) that extract lattice points and determine the lattice corresponding to materials by electron microscope diffraction images.

    • Electron cryomicroscopy of membrane proteins: Specimen preparation for two-dimensional crystals and single particles

      2011, Micron
      Citation Excerpt :

      In fact, because membrane protein complexes are highly refractory to most other forms of structural analysis, the excitement about single particle methods is particularly warranted for these important protein complexes. There continue to be critical method developments in data collection and image processing methods for 2D crystals (Henderson et al., 1990; Downing, 1991; Crowther et al., 1996; Fujiyoshi, 1998; Gipson et al., 2007; Cheng et al., 2007; Zeng et al., 2007), which help to extend the resolution obtained as evidenced by the aquaporin-0 structure at 1.9 Å resolution (Gonen et al., 2005). The carbon sandwich is one of the most significant recent developments in sample preparation and preservation for 2D crystals.

    View all citing articles on Scopus
    View full text