that embedding the sample in vitreous ice eliminated drying and
fixation artifacts and reduced the impact of radiation damage [2],
electron crystallography became the method of choice for solving
membrane protein structures, reaching near-atomic resolution in a
number of cases, such as bacteriorhodopsin [3], the plant lightharvesting complex [4], αβ-tubulin [5], and aquaporin-0[6]. Unfortunately, it was also realized that satisfying the sample
quality requirements for achieving high-resolution diffraction,
namely the perfect ordering and flatness of the 2D crystals, in
most cases was very difficult or even impossible.
While it is possible in some cases to employ X-ray crystallography [7, 8] or nuclear magnetic resonance (NMR) [9] to solve
structures of membrane proteins, these techniques also have their
own shortcomings, namely the need for suitably large 3D crystals,
or being constrained to small molecular weights, respectively. Furthermore, in both techniques, the membrane protein environment
is often not comparable to the native cellular membrane. In single
particle cryo-electron microscopy (cryo-EM), however, most of
these technical challenges are overcome by performing 3D reconstructions from proteins randomly oriented in solution
[10, 11]. Membrane proteins, specifically, can be solubilized if
surrounded by detergent micelles [12] or a lipid nanodisc [13].
Nevertheless, there are specific cases where working with 2D
crystals is necessary or even advantageous compared to these other
techniques. One example is when such periodical arrangements
occur natively in the cell membrane [1, 3], or when their natural
formation is associated with a biological specific function
[14]. Another example is when the 2D array is designed artificially,
enabling studies of proteins and other molecules that would be
difficult otherwise [15, 16]. Other advantages are that 2D crystallography offers the highest possible efficiency in terms of number of
particles in the field of view and allows reconstructions from arbitrarily small proteins, which can be challenging for conventional
single particle analysis (SPA). These are particularly interesting
aspects if combined with the single particle approach outlined in
this chapter.
2D electron crystallography can be performed both in the
diffraction or the imaging mode of the TEM [17]. In this chapter,
we will cover only the imaging mode, in which several projection
images of 2D crystals at different orientations are recorded. As in
single particle analysis, the principle of 3D reconstruction is based
on the central section theorem [10, 18]. The periodical nature of
the two-dimensional array in real space appears as diffraction spots
(Bragg peaks) in reciprocal space. These spots can then be indexed,
measured, and corrected for the contrast transfer function (CTF) of
the microscope. After merging the detected spots in 3D reciprocal
space, a real space map of the protein can be obtained by Fourier
inversion [17, 19]. Algorithms for performing these operations
268
Ricardo Righetto and Henning Stahlberg
fixation artifacts and reduced the impact of radiation damage [2],
electron crystallography became the method of choice for solving
membrane protein structures, reaching near-atomic resolution in a
number of cases, such as bacteriorhodopsin [3], the plant lightharvesting complex [4], αβ-tubulin [5], and aquaporin-0[6]. Unfortunately, it was also realized that satisfying the sample
quality requirements for achieving high-resolution diffraction,
namely the perfect ordering and flatness of the 2D crystals, in
most cases was very difficult or even impossible.
While it is possible in some cases to employ X-ray crystallography [7, 8] or nuclear magnetic resonance (NMR) [9] to solve
structures of membrane proteins, these techniques also have their
own shortcomings, namely the need for suitably large 3D crystals,
or being constrained to small molecular weights, respectively. Furthermore, in both techniques, the membrane protein environment
is often not comparable to the native cellular membrane. In single
particle cryo-electron microscopy (cryo-EM), however, most of
these technical challenges are overcome by performing 3D reconstructions from proteins randomly oriented in solution
[10, 11]. Membrane proteins, specifically, can be solubilized if
surrounded by detergent micelles [12] or a lipid nanodisc [13].
Nevertheless, there are specific cases where working with 2D
crystals is necessary or even advantageous compared to these other
techniques. One example is when such periodical arrangements
occur natively in the cell membrane [1, 3], or when their natural
formation is associated with a biological specific function
[14]. Another example is when the 2D array is designed artificially,
enabling studies of proteins and other molecules that would be
difficult otherwise [15, 16]. Other advantages are that 2D crystallography offers the highest possible efficiency in terms of number of
particles in the field of view and allows reconstructions from arbitrarily small proteins, which can be challenging for conventional
single particle analysis (SPA). These are particularly interesting
aspects if combined with the single particle approach outlined in
this chapter.
2D electron crystallography can be performed both in the
diffraction or the imaging mode of the TEM [17]. In this chapter,
we will cover only the imaging mode, in which several projection
images of 2D crystals at different orientations are recorded. As in
single particle analysis, the principle of 3D reconstruction is based
on the central section theorem [10, 18]. The periodical nature of
the two-dimensional array in real space appears as diffraction spots
(Bragg peaks) in reciprocal space. These spots can then be indexed,
measured, and corrected for the contrast transfer function (CTF) of
the microscope. After merging the detected spots in 3D reciprocal
space, a real space map of the protein can be obtained by Fourier
inversion [17, 19]. Algorithms for performing these operations
268
Ricardo Righetto and Henning Stahlberg