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6 Electron microscopy, image processing, and phasing methods
Phasing via electron and neutron diffraction data
images interpretable in terms of crystal structure projection, provided that the
effects of other parameters have been corrected. Point-to-point resolution is
between 1.5 and 2 Å for a conventional TEM operating at about 200–400kV.
In complex structures, atoms overlap (nearly or exactly) in any projection, and
therefore cannot be resolved in a single projection image. The way to overcome this problem is to collect several images from different directions and
to then combine the images to provide a model structure. This was the basic
contribution of de Rosier and Klug (1968), who described a method for the
reconstruction of three-dimensional structures from a set of two-dimensional
microscope images. Their work allowed the solution of hundreds of molecular
structures, including membrane proteins and viruses. Later on, it was found
that the contrast of a high-resolution electron microscopy (HREM) image
changes with optical conditions and crystal thickness. The so-called contrast
transfer function (CTF) plays a fundamental role in contrast changes. The
interpretation of contrast became simpler when simulation computer programs
(O’Keefe, 1973) using multislice methods, became available. It was then the
custom to interpret experimental images via image simulation. This method
was essentially a trial and error technique; a structural model is assumed, various optical parameters (thickness, defocus, etc.) are varied, and calculated
images are compared with the experimental image. The structural model is
modified, then simulation is started again.
The method is time consuming. Klug and his group revived the technique
by application of the crystallographic image processing method, which proved
capable of recovering the correct structure projection from each individual
image. The method has been further improved by Hovmöller and his group in
Stockolm (Hovmöller et al., 1984; Wang et al., 1988; Li and Hovmöller, 1988).
What is the accuracy and resolution with which the projection of a structure can be deduced from an image obtained via the back Fourier transform
performed by electromagnetic lenses? There are two main factors limiting the
immediate use of the electron micrograph:
1. The image does not represent the projection of the crystal potential, but
instead, its convolution with the Fourier transform of the contrast transfer
function. Therefore, a deconvolution operation is necessary to restore the
2. Widely scattered electrons are focused at positions other than those to
which electrons travelling close to the lens axis (spherical aberration) are
focused. As a consequence a point object is spread over length r in the
image plane, so that the real resolution of an electron microscope is no
less than about 100 times the electron wavelength. In practice, 1 Å resolution images can seldom be obtained by high-resolution microscopes; more
often the image resolution for organic crystals is 2−3 Å or lower, and from
4 to 15 Å for a two-dimensional protein crystal.
Images with a resolution of 1 Å are only obtained for special inorganic
structures. Then, atoms are resolved; since images are projections of the threedimensional structure, peak overlapping could, even in this case, hinder correct
three-dimensional location of the atoms. Several projections are therefore
needed for a three-dimensional reconstruction of the structure (Wenk et al.,
Electron microscopy, image processing, and phasing methods
1992). However, if the projection axis is short, packing considerations can lead
to solution, even from a single projection.
The effectiveness of high-resolution images for crystal structure solution
of macromolecules is limited by radiation sensitivity and poor crystal ordering. Membrane proteins are particularly suited to electron microscopy, because
they often form two-dimensional crystals. A first significant result was the resolution (at 7 Å resolution) of the purple membrane (Hendersson and Unwin,
1975; Unwin and Hendersson, 1975); the model was further refined at 3.5 Å
resolution by combining electron microscope images and electron diffraction
In spite of the above limitations, Fourier transformation of electron micrography is quite an important branch of electron crystallography devoted to
crystal structure. However, the image intensities constitute a non-linear representation of the projected potential and depend on crystal specimen (e.g.
thickness and orientation) and on instrumental parameters (e.g. aberration,
alignment, defocusing, etc.). Interpretation of the image in terms of charge
density distribution is meaningful only when all of the experimental parameters
have been correctly adjusted, and/or when it is supported by the image calculated via many-beam dynamic diffraction theory. If this process turns out to be
successful, the image may be quite useful for determination of crystallographic
phases; it may also be employed as prior information towards extending the
phasing process to higher resolution or to a different set of reflections.
Direct methods can play an essential role in this field. Among the various
recent achievements we quote the following:
1. Image processing methods have been combined with direct methods (Fan
et al., 1985; Hu et al., 1992) and maximum entropy methods (Bricogne
1984, 1988a,b, 1991; Dong et al., 1992; Gilmore et al., 1993; Voigt-Martin
et al., 1995).
2. Structure factor statistics has been used to estimate crystal thickness under
near-kinematic conditions (Tang et al., 1995).
3. Phases derived from a 10 Å resolution image of a two-dimensional E. coli
Omp F outer membrane porin (space group P31m) have been expanded
to 6 Å resolution by the tangent formula. The mean phase error for the
25 determined reflections was about 43◦ (Dorset, 1996).
4. Phases derived from 15 Å resolution images from bacteriorhodopsin have
been extended by maximum entropy and likelihood procedures to the
diffraction limit (Gilmore et al., 1993).
5. Useful results were obtained by Dorset (1996) for phasing ab initio, via
tangent methods, the centrosymmetric projection of halorhodopsin to 6 Å
6. Maximum entropy and likelihood methods have been used for an ab initio phase determination (at about 6−10 Å resolution) for two membrane
proteins, the Omp F porin from the outer membrane of E. coli and for halorhodopsin (Gilmore et al., 1996). Potential maps revealed the essential
structural details of the macromolecules.
7. Three-dimensional reconstruction of ordered materials from diffraction
images. Particularly interesting was the combination of 13 zone axes for
Phasing via electron and neutron diffraction data
the structure of a very complex intermetallic compound, ν-AlCrFe, with
129 atoms in the asymmetric unit (Zou et al., 2003).
11.7 New experimental approaches: precession
and rotation cameras
In the preceding sections we have emphasized the limitations of the traditional
experimental ED techniques:
(i) data resolution is limited (only low-index zones are recorded);
(ii) experimental procedures are very time consuming (crystal orientation
is in itself time consuming and contributes to a deterioration of beam
(iii) since conventional manual techniques allow collection of reflections from
a few well-oriented zone axes, a diffraction experiment usually provides
less than 30% of the full three-dimensional reciprocal space. Owing to the
scarcity of observations phasing is difficult, the electron density maps are
poor, and least squares refinement is not effective.
(iv) the diffraction intensities (which carry information about the crystal
structure) are of poor quality due to multiple/dynamic scattering of the
The precession electron diffraction technique, recently developed by Vincent
and Midgley (1994), allows us to significantly reduce the dynamic effects and
improve data resolution. The technical bases of the precession camera are the
following: the electron beam is tilted by a small angle, typically 1–3 degrees,
and then rotated around the TEM optical axis. The precession movement of
the reciprocal plane in diffraction allows only a small number of reflections
to be excited at any time (which reduces the multiple/dynamic scattering).
Furthermore, the movement integrates over the excitation error because a
volume of reciprocal space is explored, not just a surface.
Although the precession technique curtails the problem of dynamic diffraction, another important problem remains: how to collect full 3D reflection data,
or, in other words, how to collect data as in automated X-ray diffractometry?
If such a technique should become available, ED would show an important
advantage over X-ray diffraction and it may be extendable to nanocrystals.
A sequential electron diffraction data collection (automated diffraction
tomography, ADT) and related data processing routines have been developed
by Kolb et al. (2007a,b). The technique uses tilts around an arbitrary axis; the
reciprocal space is sequentially sampled in fine steps, so that most of the reflections lying in the covered reciprocal space may be collected. The technique
combines well with precession techniques; as stated above, better integration
of the diffraction intensities may be performed because several cuts through the
reflection body can be collected and, in this way, the true reflection intensities
are more accurately reconstructed.
One of the most complex systems solved so far, via ADT + precession, is
the mineral charoite (Rozhdestvenskaya et al., 2010; V = 4500 Å3 , 90 non-H
atoms in the asymmetric unit), a silicate structurally close to a zeolite. The
structure was solved by direct methods, as implemented in the program,
SIR2008. Around 9000 reflections with 97% coverage up to 1.1 Å resolution
were measured and used and the final crystallographic residual was 17%.
Electron rotation uses a technique rather similar to that employed by electron precession (Zhang et al., 2010), but the main difference is that, in the
rotation technique the electron beam is tilted along a straight line, like a pendulum, whereas it is tilted around a circle in precession. Rotations up to 5◦ may
be used and the line can be along the x or the y direction, or along any diagonal in between. Data are collected in small angular steps, in order to handle
partially recorded reflections. Measurements can start from any orientation of
the crystal, because there is no need to align it.
11.8 Neutron scattering
A neutron is a heavy particle with spin 1/2 and magnetic moment of
1.9132 nuclear magnetrons. The most common sources of neutrons suitable
for scattering experiments are nuclear reactors and spallation sources. Nuclear
reactors are based on a continuous fission reaction; fast neutrons are produced
whose energy is reduced by collisions in a moderator of heavy water and graphite (thermalization process). The neutrons, thus retarded, obey the Maxwell
distribution and the wavelength for the scattering experiment is selected by a
monochromator, usually a single crystal of Ge, Cu, Zn, or Pb.
Neutrons are also produced by striking target nuclei (usually tungsten or
uranium) with charged particles (protons, α-particles). These are accelerated in
short pulses (<1 µs) to 500–1000 MeV and cause, by impact with the target,
the ‘evaporation’ of high-energy neutrons. Hydrogenous moderators (typically polyethylene) thermalize the fast neutrons, making them suitable for the
There are two basic differences between the neutrons produced by a reactor
and those from a spallation source: the neutron flux is pulsed when obtained
from a spallation source, consequently the experiments must be performed by
time-of-flight techniques; high intensities at short wavelength (λ < 1 Å) is a
very significant characteristic of spallation sources.
The scattering of neutrons by atoms comprises interaction with the nucleus
and interaction with the magnetic moment of the neutron-magnetic moment of
the atom. This last effect mainly occurs in atoms with incompletely occupied
outer electron shells; since the usefulness of phasing methods to diffraction
effects caused by magnetic interaction is marginal, this topic will not be
covered in this book.
Since the nuclear radius is of the order of 10−15 cm (several orders of magnitude less than the wavelength associated with the incident neutrons), the
nucleus behaves like a point scatterer and its scattering factor, b0 , will be isotropic and not dependent on θ/λ. In a gas, the nucleus is free to recoil under the
impact of the neutrons; then the free-scattering length should be calculated by
mn + M