three-dimensional structure determination by electron ...

PeoU.Biophys~molec.Biol. 1982,Vol.39, pp. 183-231.

0079-.6107/82./030183.-49524.50/0

Copyright "~ 1982Pergamon Press Ltd.

Printed in Great Britain.All rillhtl reserved.

THREE-DIMENSIONAL STRUCTURE DETERMINATION BY ELECTRON MICROSCOPY OF TWO-DIMENSIONAL CRYSTALS L. A. AMOS*,RICHARDHENDERSON* and P. N. T. UNWlN? *MRC Laboratory of Molecular Biology, Hills Road, Cambridge CB2 2QH, U.K. tStanford University School of Medicine, Stanford, California 94305, U.S.A.

CONTENTS I. INTRODUCTION II. HISTORICALBACKGROUND IlL ELECTRONMICROSCOPYAND DIFFRACTION

I. 2. 3. 4. 5. 6.

184 184 185 185 186 189 190 191 193

Electron Scattering Radiation Damage Image Formation Specimen Preparation Diffraction Patterns Experimental Recording of Micrographs

IV. STRUCTUREDETERMINATIONIN THREE DIMENSIONS

1. Two Dimensional Crystal Terminology 2. Mathematical Concepts and Terms 3. Space Groups and Plane Groups V. THE ELECTRONMICROGRAPHS

1. 2. 3. 4. 5.

Stained or Unstained Specimens Optimal Defocus Correction for CTF in Images of Untilted Specimens Correction for CTF in Images of Tilted Specimens The Number of Tilted Images Required to De/ine the Three-Dimensional Transform Accurately • 6. Optical Diffraction in the Evaluation of Images VI. ANALYSISOF EACH IMAGEINTO FOURIERCOMPONENTS

1. Transform of an Image of a 2-D Crystal 2. Extraction of Amplitudes and Phases of Fourier Components and Calculation of 2-D Filtered Images 3. Refinement of Parameters of Reciprocal Lattice 4. Shape of Diffraction Spots 5. Distortions and Defects in Real Crystals 6. Uneven Staining or Preservation 7. Phase Gradients Across Spots 8. Application of Crystallographic Symmetry 9. Phase Origin Refinement in Projection 10. Space Group Determination in Projection VII. COMBINATIONOF IMAGESTO FORM 3-D TRANSFORM

1. Determination of Scale Factor 2. Determination of Common 3-D Phase Origin 3. How Closely Spaced Need Spots be in z* ? 4. Absolute Hand of Structure 5. Space Group Determination in Three-Dimensions VIII. CALCULATIONOF THE STRUCTURE

1. Selection of Amplitudes and Phases of Continuous Transform 2. Missing Cone Problem IX. EXPERIENCESWITH 3-D ANALYSESOF 2-D CRYSTALS

1. 2. 3. 4.

Strategies for Data Collection Contrast Variation in the Computed Structures Interpretation of the 3-D Map Experience with Different Negative Stains and Embedding Media 183

194 194 195 195 196 196 196 198 198 199 201 202 202 202 203 205 205 206 207 207 207 207 208 209 210 211 215 215 215 216 216 217 217 220 220 221

184

L.A. AMOS, R. HENDERSONand P. N. T. UNWIN

X. SOME RESULTS

1. 2. 3. 4. 5. 6. 7.

Purple Membrane Cytochrome Oxidase Ribosomes Tubulin Gap Junctions Cell Wall of Sulfolobus acidocaldarius Thin 3-D Crystals

XI. RESULTS ON OTHER STRUCTURES OF SPECIAL INTEREST IN THE FORM OF 2-D ARRAYS

1. 2. 3. 4. 5.

Acetylcholine Receptors A TPase (Coupling Factor F1) Antibody Labelling Correction of Distorted Lattices and Analysis of Disordered Crystals Limited 3-D Information from Shadowed Specimens

221 221 221 222 222 223 224 224 225 226 226 226 226 226

ACKNOWLEDGEMENTS

227

APPENDIX I: ESTIMATION OF TILT ANGLES AND TILT AXES

230

APPENDIX II: DENSIT()METRY

230

I. I N T R O D U C T I O N We give here a review of the electron microscope methods we have been using to determine the three-dimensional distribution of scattering matter in the average unit cell of a twodimensional crystal. The account, which is derived from material prepared for an EMBO practical course held at the Laboratory of Molecular Biology in September 1980, includes a section on the basic properties of the electron microscope and how it may be used to best advantage in analysing structure of biological molecules together with a section reviewing published work in electron microscopy of two-dimensional crystals. Thus, although the review is specifically aimed at those interested in the structure of 2-D crystalline arrays, much of the material is of general interest to anyone working on electron microscopy of biological specimens. The concepts and terminology stem largely from X-ray crystallography, with which we are assuming the reader has a basic familiarity. Lipson (1972) or Lipson and Taylor (1958) provide a good introduction to Fourier transforms as used in crystallography. The review is intended to be a descriptive guide with only the essential minimum of mathematics. The mathematical detail is given in various references which are cited below. II. H I S T O R I C A L B A C K G R O U N D Interest in the structure of biological molecules and assemblies dates to the first attempts at X-ray diffraction from protein crystals. However, it was the invention of the electron microscope which made possible direct images of biological structure at a macromolecular level. The early use of shadowing casting (Williams and Wyckoff, 1945), of negative stains (Hall, 1955; Huxley, 1957; Brenner and Horne, 1959; Huxley and Zubay, 1960) and even positive staining of ultra thin sections (Pease and Baker, 1948; Gettner and Ornstein, 1955) all showed the arrangement of subunits in biological assemblies. The first application of the principle of image processing involving molecular averaging of images of identical structures came with the rotational and translational superposition work of Markham et al. (1963, 1964) and the use of optical diffraction (Klug and Berger, 1964) and optical filtering in the diffraction plane (Klug and DeRosier, 1966). These methods allow two-dimensional averaging to produce images with higher signal-to-noise ratios than the original electron micrograph. Optical filtering was also used to disentangle superimposed two layer structures. These two dimensional procedures have since been extended to sophisticated practical (Erickson et al., 1978) and computer methods of both two-dimensional lattice (Amos and Klug, 1972; Aebi et al., 1973) and rotational (Crowther and Amos, 1971) filtering. Digital methods were first introduced by DeRosier and Klug (1968), who extended image processing to produce three-dimensional models of biological structures as seen in the electron microscope. The advantages of digitizing the images is that phases, as well as amplitudes, are readily available for analysis in the computed diffraction pattern or Fourier

3°D structure determination by electron microscopy of 2-D crystals

185

transform. DcRosier and Klug applied the principle to a helical structure of sufficient multiplicity (T4 phage tails) that a 3-D model could be obtained from a single electron micrograph. There have subsequently been many similar analyses on other particles with helical symmetry (e.g. Finch and Klug, 1971; Unwin and Klug, 1974; Wakabayashi et al., 1975; DeRosier et al., 1977; Dykes et al., 1978; Taylor and Amos, 1981). Structures with less symmetry than found in these helical structures require that more electron micrographs should be combined together to build up sufficient 3-D data to determine the structure accurately in 3D. This is so for the case of icosahedral viruses (Crowther et al., 1970; Crowther, 1971) for which three or more images were required. Finally, with the work on purple membrane (Henderson and Unwin, 1975; Unwin and Henderson, 1975) there began the analysis of 3-D structures of 2-D crystals, which requires a much larger number of views. Detailed references specifically to work on individual 2-D crystalline arrays are given later. General reference works on the analysis of electron micrographs, written over the last few years, include "a discussion on new developments in electron microscopy with special emphasis on their application in biology" (Huxley and Klug, 1971), the proceedings of a meeting organized by Huxley and Klug in 1970, with a number of authors, and a broadly based review (Crowther and Klug, 1975). More mathematical reviews have been published by Mellema (1980) and Misell (1978). The most recent survey, from a number of contributing authors (Baumeister and Vogell, 1980) reports the proceedings of a meeting at which 2dimensional crystals were the main topic. III. ELECTRON

MICROSCOPY

AND DIFFRACTION

We come first to a description of some basic properties of electrons and how they are used in the electron microscope. At the present (1981 ) stage of development, electron microscopy combined with image analysis is considered to be useful for solving three-dimensional structures at moderate levels of resolution. Limitations arise from the difficulty of preserving specimens in the microscope vacuum, from radiation damage and from the requirement that the specimen be composed of ordered arrays of equivalent molecules which are extensive in one or two dimensions, but not more than a few hundred angstroms thick (see below). At higher resolution, sufficient to resolve atomic detail, X-ray diffraction of 3-D crystals is still the method of choice. In the following paragraphs we have to take account of the dual particle/wave nature of the electron. When dealing with subjects such as electron scattering, radiation damage and photographic recording it normally suffices to .regard electrons as charged particles. However with the processes of diffraction and image formation (particularly at high resolution) this treatment becomes inadequate, and effects need to be considered which can only be explained in terms of waves. 1. Electron Scattering The electron beam is modified during its passage through the specimen by both elastic and inelastic interactions. Electrons interacting with the potential field of atomic nuclei usually undergo elastic collisions. They emerge with their wavelength unchanged, but suffer a directional change and an associated ~ ~/2 phase shift. Electrons interacting with the outer (valence and bonding) electrons undergo inelastic collisions. They emerge with small changes in wavelength and transfer some of their energy to the specimen (typically about 25 eV). Only the elastic process is important in producing the interference effects responsible for contrast in the images and in forming diffraction patterns similar to those obtained with X-rays. Inelastically scattered electrons are poorly focused in the images (because of their lower energy and consequent greater deflection by the magnetic lenses) and they give rise to a background in the diffraction pattern which is strongly concentrated in the forward direction. This is illustrated by the scattering curves for carbon in Fig. 1. The ratio of the total elastic (ae) to inelastic (gi) cross-section (which is not much affected by the accelerating voltage) behaves roughly as: O'.._e_ _Z

gi

19

186

L.A. AMOS, R. HENDERSON and P. N. T. UNWIN

Inelastic

1~0

1'5

e (tO "s radians)

FIG.1.Theoreticalelasticand inelasticelectronscatteringcross-sectionsfor carbonplottedon a linear scale as a function of scattering angle 0, for 75 kV electrons. (Burgeand Smith, 1962.) where Z is the atomic number (Crewe et al., 1970). Thus inelastic scattering predominates with biological molecules, causing extensive damage (see below). Electrons interact much more strongly with matter than do X-rays. There is a difference by a factor of ,-, 10,000 between atomic scattering amplitudes in the two cases. Electron scattering amplitudes also differ in that they decrease more rapidly with scattering angle and show less discrimination between heavy and light atoms. Thus whereas with X-rays Au atoms scatter 14 times more strongly than C atoms, with electrons they scatter only 5 times more strongly. Likewise, the disparity between the electron scattering amplitudes for H atoms and those for C, N and O is less marked. Electrons discriminate poorly between heavy and light atoms because the atomic nucleus is screened by the,surrounding electron cloud, so that its potential falls off more rapidly than would be the case otherwise. With heavy atoms this screening effect is accentuated and they therefore scatter less strongly than would be expected on the basis of atomic number alone. For C atoms and 100 kV electrons the mean free paths for elastic and inelastic scattering are 1300 ~, and 750 A respectively; for heavier atoms they are shorter (values for Au are 60 A and 600 A respectively) (Misell, 1973). Since the fidelity of the image decreases the more times the electron is scattered (multiple scattering introduces erroneous features) and the quality deteriorates (because of the relatively greater contribution from electrons which have been inelastically scattered) it is advantageous to have the specimen as thin as possible. But this is not critical. With stained molecules the fidelity and quality tend to be limited by the extent of preservation. Only occasionally is a specimen both sufficiently thick and well ordered to show evidence of multiple scattering; for example, the optical diffraction pattern of double layers of the bacterial cell wall studied by Finch et al. (1967) showed an extra reflection due to double scattering. With unstained molecules, the low atomic weights make multiple scattering events less frequent. Thus it generally works well in practice to assum~ tltat all biological specimens are weakly scattering objects. Such an assumption greatly ~mlifies the description of the process of image formation.

2. Radiation Damage Biological molecules, like most organic materials, are highly susceptible to radiation damage. The incident electrons lose large amounts of energy by inelastic int~actions, leading to the formation of numerous highly reactive ions and free radicals. These excited species cause alterations by rupturing bonds, fragmenting molecules and forming new, stable, crosslinks. Direct transfer of momentum from the incident electron to the atomic nucleus, causing

3-D structure determination by electron microscopy of 2-D crystals

187

its displacement, may also occur (the threshold accelerating voltages for direct displacement of H and C atoms are ~ 3 and ~ 30 kV respectively) but the cross-section for this process is very much smaller than that for ionization, and excitation. Gross consequences of these reactions are heating of the specimen, mass loss and changes in chemical composition (H and O are more readily lost than C and N) (Bahr et al., 1965), as shown for gelatin in Fig. 2. Normal exposures in electron microscopy (about 500 electrons/A 2 to locate, focus and image a specimen at high magnification) result in radiation doses to the specimen of 1010_101 t rads (about equivalent to what it would receive if placed in the collimated beam of a rotating anode X-ray set for 1000 years!) and transform it into a highly cross-linked product, bearing little resemblance to the original material. Fortunately, these drastic alterations are not of great concern with stained specimens where one is just interested in molecular boundaries and it is more the properties of the stain than the biological matter it outlines which govern the appearance of the imag e . The stain is relatively stable and remains more or less in position during irradiation, although there is some movement, predominantly shrinkage, which decreases fidelity as the dose increases (Unwin, 1974). So-called "minimal dose" electron microscopy, referring to the 10-20 electrons/A 2 required to record a statistically reliable image, in which the specimen is located at low magnification and focusing at high magnification is carried out on an adjacent area, is therefore quite adequate for negatively stained preparations (Williams and Fisher (1970) and see later). But if one wishes instead to visualize, say, secondary protein structure in an unstained specimen, even minimal exposures, in the statistical sense, are too high. Measurements made from fading of electron diffraction patterns (see for example the fading, of the purple membrane diffraction pattern in Fig. 3) indicate that incident doses of the order of loo

~

i

i

H . m -

4c

-

q

~

)

-

~

-

lb

Dose- electrons/~2 FIG. 2. Changes in the chemical composition of gelatin as a function of electron dose. (Adapted from Bahr et al., 1965).

50

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i ,3)

0

t 0.5

1.0

Dose - electrons/~2 FIG. 3. Fading of some typical reflections in the electron diffraction patterns of purple membrane embedded in glucose. (From Unwin and Henderson, 1975.)

L. A. AMOS,R. HENDERSON and P. N. T. UNwn~

188

0.5 electrons/A z or less would be more appropriate. The use of an exposure less than that required to completely destroy the specimen, as judged from the diffraction pattern, we refer to rather unutti~actorily as a very low dose exposure. With only 0.5 electrons/A 2 however, the number of elastic scattering events will be insufficient to allow the secondary structure to be directly vimafized with good counting statistics especially since the contrast expected from unstained structures is also much lower than that obtained with stained specimens. For accurate definition, a much higher and therefore completely destructive exposure would be needed. Table la gives the details in a more comparative way of the level of electron dose involved in different types of microscopy. It is thus impossible to observe secondary structure directly by electron microscopy without destroying it in the process. The only feasible way tO obtain the high resolution information is to combine data from different, equivalent, molecules so as to reinforce the genuine features in each of them and average out the statistical fluctuations. A two-dimensional crystalline array composed of 103-104 equivalent molecules is a particularly appropriate object for achieving this task. Combination of information from many different molecules is carried to extremes in X-ray crystallography of protein crystals. Protein crystals contain as many as 101~ equivalent molecules and a complete X-ray diffraction pattern is built up with few, if any, of these molecules being hit by the X-ray quanta more than once. It is the greater number of unit.cells involved, not the source of radiation, that makes X-rays appear less damaging than electrons. In fact, the damaging effect of X-rays expressed as the ratio of inelastic to elastic cross sections, is greater than that of electrons (Hoppe, 1971). TABLE l(a). SoME TYPICAL EXPOSURE LEVELS INVOLVED IN VARIOUS TYPES OF ELECTRON MICROSCOPY

Purpose of exposure Routine photograph Minimal beam

Electron dose required for focusing and preliminary adjustments

Electron dose requiredfor exposure el/,~2

Magnification

Optical density of film

200-500 0.01-0.03"

10-20 10-20

30,000-40,000 30,000-40,000

1 1

exposure of

Reference --

Williams and Fisher (1970)

1

stained specimen Very low dose exposure of unstained specimen Higher dose exposure to accompany the the above

0.01-0.03"

0.5-4

40,000-50,000

0.05-0.3 "~

t 0

15-30

40,000-50,000

1

Unwin and Henderson (1975)

* Focusing is performed on an adjacent area, so the exposure in this case is only that required to locate the specimen at low magnification (say ~ 1000 × ). TABLE l(b). OPTICAL DL~srrY AND RESOLUTIONTO BE Exv~cleu

wrrH SOMETYPICAL EM FILM DEVELOPEDFOR MAXIMUMSI~ED (e.g. KODAK 4463, AGFA SCIENTIA,DUPONT GRAPHIC ARTS)

Magnification IO,OO0 I0,000 40~000 401000 200,000 200,000

Dose (e/A 2)

0.5 I0 0..._55 I0 0.5 I0

OD

I > 5 0.06 1.25 0.002 0.05

d~(A)*

I0 I0 2.5 2.5 0.5 0.5

* Spacing related to object at which contrast is diminished by the photographic emulsion to 50~. (The corresponding spacing on the film is 10 ~. This dimension is determined by the spread of electrons within the emulsion (Valentine, 1966; Famell and Flint, 1975). In practice, other factors, e.g. magnetic fields, may make this figure closer to ~ 25 in which case d ~ would be multipfied by 2.5.)


189

3. Image Formation Similar principles of image formation apply to electron microscopy of thin biological specimens as apply to ordinary bright field light microscopy. Strictly, there is no absorption ofdectrons as there is of photons; however, loss of electrons from the image, apparent or real, through inelastic scattering or interception by the objective aperture has an analogous effect. One has to deal with much smaller numerical apertures in electron microscopy because of the inferior quality of magnetic lenses over glass ones, and this limits the resolution attainable to about 50 times the wavelength (2=0.037 A for 100 kV electrons) instead of I or 2 times as with light microscopy. A formal description of the process of image formation from the standpoint of Fourier optical theory can be found in a number of books or references (e.g. Brag,g, 1939; Heidenreich, 1964; Grimstone, 1968; Hawkes, 1972; Misell, 1978) but here it is appropriate to state only a few things by way of introduction. "Phase contrast" (i.e. constructive or destructive interference between the elastically scattered waves and the unscattered, transmitted, wave) is the dominant contrast mechanism for thin stained and unstained specimens at most spacings. It is almost zero when the optical path lengths of the scattered and unscattered waves are the same (because of the n/2 phase shift upon scattering which means that the scattered wave is in quadrature with the unscattered). Thus, with an aberration-free microscope and the object exactly in focus there is no difference in optical path lengths between the two waves (Fermat's principle) and therefore no phase contrast. In a real situation, however, the image is out of focus and spherical aberration is present. These defects combine to produce a phase shift in the scattered wave given by: Z = 2n2-1(6f02/2- C~ 0"/4) where 0 is the scattering angle, 6fis the degree of underfocus and C, is the spherical aberration coefficient of the objective lens (typically 1-4 mm). The effect of this phase shift, as a function of the reciprocal of the object spacing, 0/2, is referred to as the phase contrast transfer function (CTF). The phase shift in the scattered waves produces phase contrast, which is strongest when X= -+ n/2, because the scattered wave has been brought exactly into or exactly out of phase with the unscattered wave and now interferes with it. For a moderately underfocused image (obtained by weakening the objective lens) the effects of defocus and spherical aberration balance one another in such a way that X is approximately n/2 over a wide range of object spacings. This sort of setting will therefore be the most appropriate one to use in practice. The function, - 2 sin X, which provides a simple way of representing the effect of these phase shifts, is known as the phase contrast transfer function and is illustrated in Fig. 4 for a particular set of conditions. The product of the phase CTF and the Fourier transform of (the potential distribution in) the object gives the amplitude and phase of each Fourier term contributing to the image. In practice the CTF is modified by several optical factors besides 6f and C~: (a) Chromatic aberration of the objective lens Chromatic errors (i.e. energy differences in the electron beam) may arise from several sources, e.g. fluctuations in the HT supply, variation in the energy of the electrons emitted from the hot cathode (typically +0.4 eV) and energy losses as a result of inelastic scatt~'ing. The focus change is Co"6E/E (where E is the energy of the electrons and C¢ is the chromatic aberration constant of the objective lens--typically about 3 mm). The main effect is to smear out the CTF at high resolution, so that for these spacings the contrast becomes very weak.

Co) Partial coherence of the illuminatino beam The finite angular spread of the beam incident on the object causes diffracted waves corresponding to a given spacing to pass through a range of angles in the objective lens field. This predominantly causes the CTF to be attenuated in regions where the phase shifts are changing most rapidly. The effect of partial coherence is small if relatively small second condenser apertures are used (< 200/t) and if the object is not unduly out of focus.

190

L.A. AMOS, R. HENDERSON and P. N. T. UNWIN (a)

X

0~x 20 A) over a wide range of underfocus values (up to about I0,000 A). Note that the amplitude and phase contrast mechanisms oppose each other if the image is overfocused, making it difficult to interpret directly. Useful discussions of the relative importance of amplitude and phase contrast for light and heavy atoms are given by Unwin {1972) and Erickson and Klug (1971).

4. Specimen Preparation Specimen preparation plays a key role in successful electron structure determination and it is well worth spending much time and care on this aspect of the work. We assume you are familiar with the preparative procedures involved (see e.g. Hall, 1966; Kay, 1965; Valentine, 1961) and aim just to give some of the general guidelines we use in our attempts to optimize results. It is best to be flexible, as each specimen is different, having problems peculiar to itself. Some sort of protective medium generally needs to be appfied to surround the specimen and preserve its shape or higher order structure in the microscope vacuum. Heavy metal negative stains are of great value because they preserve shape, provide contrast and are


191

relatively stable under the electron beam. But they are only of value in examining gross structural features--to a resolution of about 20 A. To preserve detail within a protein molecule more appropriate environments are provided by non-ionic hydrophilic media such as glucose or ice (ifa cold stage is available). These latter media have the potential of bringing the resolution to near atomic dimensions, but their value in practice is complicated by the problem of radiation damage. Two aspects of primary importance are the properties of the support film and of the protective medium itself. Carbon and plastic (collodion or formvar) are the most widely used materials for support film. Carbon is almost invariably the more suitable since it is the better conductor and the most stable in the electron beam. Plastic films and thin carbon films (very light brown on filter paper) are susceptible to drift and breakage, making high image resolutions difficult to achieve. They are also susceptible to electrical charging effects, making them unsuitable supports for electron diffraction experiments. Carbon films when freshly prepared are usually fairly hydrophilic, but they become increasingly hydrophobic with time, especially if kept outside a dessicator. These properties influence the adhesion (and sometimes the preservation) of the specimens. Fresh films generally give best results for most specimens. Adhesion to old films can usually be improved by pre-soaking them in a ~0.1% solution of polylysine (Williams, 1977), cytochrome c or by ion bombardment ("glow discharging"). Films treated in the latter way can however disrupt fragile specimens and severely distort others. "Holey" support films (where the specimen ends up over openings in the film) are particularly useful where it is important to minimize distortions such as particle flattening or to ensure that the staining is even from both sides. Sometimes one might like to prepare a thin carbon film overlying a thick "holey" support film so that one can simultaneously minimize the amount of background noise and retain a certain degree of rigidity. The spreading of negative stains (or media such as glucose) is influenced by the properties of the support film and the specimen. Spreading, as well as adhesion, may be improved considerably by the addition of surfactant molecules such as serum albumin, cytochrome c or bacitracin to a concentration of ~ 0.1% in one or other of the solutions applied to the grid, by glow discharging or by the application of octadecanol (Gordon, 1972). Of the variety of negative stains which could be used, uranyl acetate or formate (at pH ~4.0) is very likely to give best results in terms of preservation and resistance to radiation damage. Sodium phosphotungstate (at pH ~ 7.0) may lead to significant improvements ifthe specimen is unstable at low pH, and methylamine tungstate (Faberg~ and Oliver, 1974), a nonionic stain, may well be less disruptive to specimens in which the degree of order is high only when ionic strength is low. Prior fixation of the specimen with glutaraldehyde, formaldehyde and/or osmium tetroxide may help in some cases. Auro-thio-glucose (available from Sigma) is potentially very useful as a non-ionic stain (see Section IX). It has the property of preserving molecular detail to high resolution at low doses like glucose and the advantage of providing more contrast than glucose (although less than the heavier metal stains). 5. Diffraction Patterns The short wavelength of high energy electrons makes the Ewald sphere much less curved than in the X-ray (Cu k~, 8 keV) case, and the electron diffraction pattern, for all practical purposes, is simply a plane through the three-dimensional reciprocal lattice (see below). Electron diffraction patterns can be used to provide structure factor amplitudes (see e.g. Fig. 5b) from crystals directly (rather than by Fourier transformation of micrographs), and to show up non-crystalline detail (e.g. from ordered secondary structure) which would be difficult to resolve in the image. The example shown in Fig. 5a is an illustration of a diffraction pattern containing this type of information. Such diffraction patterns may be more informative than images in the respect that they are created before the electrons interfere and therefore are not degraded or limited in terms of resolution by effects of the CTF, described above. On the other hand: (i) they contain no phase information, (ii) they tend to be swamped out at low resolution by inelastic scatter, (iii) they do not allow one to select sensitively for the

192

L.A. AMOS, R. HENDERSONand P. N. T. UNWn~

FIG. 5. Electron diffraction patterns from non-crystalline and crystalline specimens embedded in glucose and recorded with doses of < 0.5 el/At. (a) 4.7 A ring arising from cross B-structure in a T4 tail fibre aggregate (Earnshaw et al., 1979).

FI~. 5(b). Pattern from a thin crystal of catalase (unit cell dimensions 69 x 173 A). (Unwin, 1975; Unwin and Henderson, 1975.)


193

best areas of a specimen (as can be done, for example, by optical diffraction of micrographs). Also many specimens, because of their shape and size are not well suited to this technique (normally the illuminated area in electron diffraction is circular and of diameter >0.5 ~). Coherence is an important parameter when recording diffraction patterns. With typical illumination conditions for imaging (a 200 ~ condenser aperture and focused beam) the beam divergence at the specimen is ~ 10- 3 radians. This is inappropriate since it would give rise to a peak width in the diffraction plane of 10- 3/0.037 (= 1/27 A- 1), which is comparable to the spacing between peaks for most specimens. Very small divergences (< l0 s radians) are obtained by reducing the second condenser aperture size (to _