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6 Electron microscopy, image processing, and phasing methods

6 Electron microscopy, image processing, and phasing methods

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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

desired image.

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

sensitive samples);

(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

Neutron scattering

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

scattering experiment.

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


bfree =

b0 ,

mn + M


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