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Electron Diffraction with the Transmission Electron Microscope as a Phase-Determining DiffractometerЧFrom Spatial Frequency Filtering to the Three-Dimensional Structure Analysis of Ribosomes.

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Electron Diffraction with the Transmission Electron Microscope
as a Phase-Determining DiffractometerFrom Spatial Frequency Filtering
to the Three-Dimensional Structure Analysis of Ribosomes
By Walter Hoppe*
Dedicated to Professor Adolf Butenandt on the occasion of his 80th birthday
Chemists recognize X-ray crystaI structure analysis and electron microscopy as powerful
methods of analysis. In the last 20 years the basic ideas of X-ray diffraction analysis have
been extended to the field of electron microscopy, whereby an image-forming apparatus is
converted into an electron diffractometer, and through which an old dream of crystallographers can be realized-the measurement of the phase shift of scattered waves, a prerequisite
for the direct calculation of structures. Its most important area of application, like that of
the X-ray diffractometer, is in three-dimensional structure analysis-in all fields of science.
However, beyond crystallography, aperiodic structures (comparable to crystals with a single
unit cell) can also be analyzed three-dimensionally. In this progress report, the development
of the first idea (spatial frequency filtering) to the analysis of ribosomal particles is outlined. Attention will be focused primarily on quantitative methods for the measurement of
scattered rays, which are also usable beyond the conventional limit of resolution, down to
atomic resolution. In the course of this work in 1968, the principle of the three-dimensional
analysis of native biological crystal structures using the electron microscope, as worked
with today in many laboratories, was developed. In Munich, however, further research focused on the three-dimensional analysis of aperiodic and individual (especially biological)
objects. The analysis of 50s-subunits of the procaryotic ribosome of E. coli showed surprisingly good reproducibility of the results (although only within the same orientation), allowing the deduction of almost ideal average model structures from a limited number of particles.
1. Introduction
It was not easy to find a suitable title for a report on the
research work which has been carried out in our laboratory
in the field of structural chemistry over the past number of
years. “Three-dimensional electron microscopy” soon
proved to be too narrow, and missed the important aspect
of quantitative analysis, i. e., the measurement of the amplitude and phase of scattered waves, which is important
for the determination of the potential distribution (which
corresponds to the electron density distribution in X-ray
diffraction). If the electron microscope is used as a phasedetermining diffractometer, then three-dimensional electron microscopy corresponds in principle to three-dimensional X-ray crystal structure analysis. Different types of
diffractometer have been developed using similar basic designs of electron microscope. Aside from the methodological aspects of our work, a selection of the structural findings (especially on ribosomal particles) which are of particular interest to the chemist are outlined, so as to give the
reader an idea of the “state of the art” of this technique.
Max-Planck-Institut fur Biochemie, Abfeiiung Strukturforschung I
Am KIopfenpitz, D-8033Martinsried bei Miinchen (Germany)
[*] Prof. Dr.
0 Verlag Chemie GmbH. 6940 Weinheim, 1983
2. The Development of Phase-Determining
Diffractometry with the Conventional
Transmission Electron Microscope (CTEM)
2.1. “Computers” that Work with Light
In the fifties, the light diffractometer was a popular tool
of crystallographers. The impetus behind its use stemmed
from the “two-wave microscopy” of Boerschr’*21,
who suggested that masks, fashioned according to the diffraction
diagram of a crystal, be brought into the diffraction plane
of a microscope working with monochromatic coherent
light. Theoretically, an image of the crystal lattice (more
exactly, a two dimensional projection of the crystal lattice)
should appear in the image plane of the microscope. In
two-wave microscopy, the diffraction diagram is created,
without using a lens, with the radiation of the first wavelength (X-rays); the function of the lens is reproduced by
the radiation of the second wavelength (light). This idea
fascinated many people at that time, including Sir W. L.
Two-wavelength microscopy illustrates, in a simple fashion, one of the fundamental features of structural analysis
with diffraction methods. The analysis proceeds in two
steps. In the first-physically important step-scattered
0570-0833/83/0606-0456 $02.50/0
Angew. Chem. Ini. Ed. Engl. 22 (1983) 456-485
rays are produced which contain the complete information
on the structure of the object. In the second step these data
are combined, in a way that is equivalent to the mathematical operation of Fourier transformation. The direct result
is the structure of the object being investigated. Actually,
once the data of the scattered waves have been collected, a
physical instrument is no longer needed. The combining of
the data can also be done using a suitably programmed
computer. Indeed, the coupled light lens has the function
of such a computer-the apparatus is therefore commonly
referred to as a “light-optical analogue computer”.
Although today the much more accurate digital computers (acting as “computer lenses”) have taken over this task
as well, the light-optical computer has not yet lost its value.
It should be remembered that both X-rays and light rays
have wave characteristics, and that the wavelength of light
is longer than that of X-rays by a factor of about lo’.
When a light-optical apparatus, corresponding geometrically to an X-ray diffractometer but working with mono-
chromatic light, is built, then in principle the same scattering
effects are produced as with X-rays if the objects are enlarged by this factor of about lo3. Such an apparatus is
called a light diffractometer. The light diffractometer (Fig.
la) enables rapid checking of structural models. All that is
needed is a mask with small holes in the presumed positions of the atoms. Naturally such a check can also be carried out very quickly today with a real computer. Despite
this, the light diffractometer has remained useful, especially in electron microscopy (see also Sections 2.5 to
The light diffractometer is especially useful for unravelling the inner symmetries of the object under examination.
Thus, for example, owing to the regular hexagonal arrangement of the atoms in arene molecules, characteristic
light diffractograms are obtained, typified by the hexagonal positioning of strong scattering maxima (Fig. lb).
However, in the case of a crystal, these molecular scattering diagrams are only seen through the “windows” of the
crystal reflections, which makes their investigation difficult. Even as long as thirty years ago, it was shown that
they also appear in the continuous scattering background
of the X-ray diagrams of single crystal^'^'. Figure lc shows
such a molecular scattering diagram in the background of
a “Weissenberg” diagram of an anthraquinone crystal. For
some time, the study of the diffuse background was relevant to the structural analysis of organic molecules, and
was actually used in the constitutional analysis of ecdysonec5I.Since the development of “direct methods”, however, the evaluation of additional scattering data (besides
the single crystal reflections) is only useful in special
2.2. Correction of the Spherical Aberration in the
Electron Microscope by Ring Diaphragms
Fig. 1. a) The principle of the light diffractometer. It produces a diffraction
image from the object 0. The lenses L, and L2are unimportant; they shouId
only ensure parallelism of the primary beam and of the scattered rays, despite the relatively short distance to the monochromatic light source L’ and
the detector (film) T. If they are left out, the distances have to be greatly enlarged. When using X-rays the lenses are left out, but the atomic dimensions
of the object are so small that the light source and detector can always he assumed to be infinitely far away. The dashed lines delineate the beam in the
absence of the lenses.-b) Light diffractometer diffraction image of a model
(mask with holes at the sites of atoms) of naphthalene.-c) Image of the Fourier transform of anthraquinone in the diffuse background scattering of crystals 141. Because of the geometry of the Weissenberg pictures, the strong “aromatic” maxima lie on lines.
Angew. Chem. Int. Ed. Engl. 22 (1983) 456-485
In 1961, a light diffractometer was also to be built in our
laboratory for the purpose of studying diffuse X-ray scattering. It was known that one of the main sources of error
in the electron microscope is spherical aberration (the refractive power of a magnetic lens increases strongly towards the outer edge, so the outer rays have a shorter focal
length than those near to the axis). Therefore, a student
named Menzel was given the task of testing, through analogous experiments with a home-built light diffractometer,
whether the spherical aberration could be eliminated by
simply combining a series of exposures which are recorded
with ring diaphragms of increasing radius. When this is
performed with an electron microscope, the position of the
focussing plane would have to be synchronously corrected
by changing the objective’s current strength. However, we
did not attach very great importance to this principle of
correcting the spherical aberration. Naturally, the large decrease in the working aperture of the lens is troublesome,
since all the scattered rays outside the transmitted rings are
lost through shielding. The given task nevertheless fulfilled
its purpose, and Menzelc6]not only built a good light diffractometer, but also was able to show that sharp image
points can indeed be depicted, albeit with additional appearance of a strong background. Strangely enough, the
idea of image forming with several ring diaphragms in
electron microscopy has also been discussed in more recent times.
2.3. Spatial Frequency Filtering in the Electron Microscope
Although we had never devoted a great deal of effort to
this problem, we could not dismiss it: if the temporal sequence of a series of ring diaphragms could be replaced by
a spatial sequence of concomitantly operating ring diaphragms, then the intensity of the transmitted light should
naturally increase dramatically. At this juncture a little
knowledge of wave optics is essential. When a point object-e.g. an atom-is irradiated, it acts as the center of a
spherical wave. The wavefront is then the surface of a
sphere with the point object as its origin. The optical function of a perfect lens is to invert this spherical surface so
that a new image-sided spherical wave surface is formed,
whose origin is the image-point. The detailed explanation
of how the lens does this (in the case of light, by retardation of the waves in the glass) is not necessary for this discussion. The characteristic of an imperfect lens is that it is
not able to produce a fully spherical surface. In the extreme case, i. e. if no lens is used at all, the wave surface of
the object acts at the same time as the wave surface of the
image, and this is actually curved in the wrong direction
(away from the image point). Fresnel had already found
that even in this case, an image will be possible if a system
of a sequence of ring diaphragms is placed between the
object and the image. This Fresnel lens is, of course, of
particular interest when working with rays for which there
are no lenses, e.g. with X-rays. The author had always
toyed a little with the idea of building an X-ray microscope
with Fresnel lenses, but had soon discovered that the ring
distances would have to be of the order of magnitude of
Fig. 2. Principle of the Fresnel lens (a) and of the zone correction plate (b). In
(a), the image-side wave surfaces W,, W,, W1.. ., at intervals of A intersect the
object-side wave surface W. at the Fresnel lens and in (b) the defective
image-side wave surface Wb at the zone correction plate. In both cases, correct imaging is obtained with a ring-shaped diaphragm system (not shown),
which allows passage of in-phase rays (phase shifting 0-x) (shaded), but
screens out oppositely phased rays (phase shifting n+2rr).
atomic distances[*].On incorporation of a magnetic lens in
an electron microscope, the image-sided wave surface is
not especially good, but at least it is properly curved. Thus,
the idea arose that it should be possible to place a ring
plate, working on the principle of the Fresnel lens, between the lens and the image. Owing to the very small discrepancy between real and ideal wave surfaces, in this
case, it was to be expected that such a correction plate
would show fewer and much wider rings than a real FresAs shown in Figure 2, this zone correction
plate is a “spatial frequency filter”.
Spatial frequency filtering constitutes one of the most
decisive steps which have led to phase-determining diffractometry. In principle, the correction of spherical aberration with the zone correction plate enables improvement of
the resolving power of the microscope down to atomic resolution. Right at the outset, plates (with about ten rings)
were ~alculated[’~~~,
which should allow a resolution of
about 0.15 nm (see Section 2.7).
2.4. The CTEM-A Diffractorneter
A characteristic feature of the conventional transmission
electron microscope (CTEM) is that the object is illuminated by a parallel monochromatic primary beam (Fig. 3a).
This type of illumination, which would not be feasible with
the light microscope because of the appearance of Fresnel
fringes (there, a convergent polychromatic light beam is
used for illumination), is, in principle, exactly the same as
that which the crystallographer uses in his diffractometer.
Indeed, if the lower part of Figure 3a, including the lens, is
removed, then the scheme is that of a diffractometer: a parallel beam of radiation impinges on an object and sends
scattered rays out in all directions. For a complete diffractometer, only one more fitting (a Goniometer) is needed,
with which the object can be tilted with respect to the primary ray.
The principal similarity between the construction of an
electron microscope and that of an X-ray diffractometer
was realized early on by the electron microscopist. If a
small crystaI is used as the object and the image-forming
microscope lenses are omitted, or, put another way, the
image of the distribution of the rays is formed on the aperture diaphragm, then instead of photographing the image
of the crystal we can photograph its diffraction diagram in
the CTEM. The remarkable thing is that the electron microscope-using optical criteria-is actually a poor microscope but an excellent diffractometer. However, as experience in conventional electron microscopy has told us, good
microscopy is possible even with this poor microscope if
its peculiarities are taken into consideration.
Boersch noted in 1947 that atoms can be considered in
analogy to phase objects in light
Phase objects are
structures in which only the refractive index changes but
no absorption takes place. They are therefore invisible in
the light microscope, but Zernike showed that they can be
[‘I This idea was later taken up again with respect to an apparatus for far ultraviolet and soft X-rays, after new possibilities for the miniaturization of
such a ring diaphragm system became experimentally within reach, at
Schmahl, D. Rudolph, B.
least for wavelengths in the region of 10 nm [C.
Niemann, Phys. BI. 38 (1982) 2831.
Angew. Chem. In!. Ed. En.& 22 (1983) 456-485
Fig. 3. The “diffractometric” ray path of the conventional transmission electron microscope (CTEM). a) The primary beam P (parallel, monochromatic)
penetrates the object 0, which scatters rays within a scattering cone with
which are led through the lens L with the aperture A to give the image
1. b) Pictorial representation of-the scattering in the reciprocal sp2ce by
Ewald’s sphere of propagatio_n:so/A the vector of the primary wave, s / l the
vector of the scattered wave, r* the spatial vector in the reciprocal space, rgSx
the radius of Ewald‘s sphere of propagation (dashed), x*, y*, z* the coordinates of the reciprocal space. For very small wavelengths l (for 100 kV electrons, l is only 0.0037 nm!) the scattering angles 6 become very small, and
Ewald’s sphere-can be replaced by its tangential plane. The vectors of the reciprocal space r* then lie in this plane (x*, y* plane). In electron microscopy
they are also called spatial fie-quencies. Each scattered ray therefore corresponds to a reciprocal vector r* (spatial frequency). The amplitude /F/ and
phase shift @ of a scattered ray (referred to the primary beam) are designated,
in crystal structural analysis (also adopted by us for electron microscopy) as
the structural factor F;-=/Fp/expi@. Through the imaging process, @ becomes @ y ( y = wave aberration). A “spatial frequency filter” in the ray path
of the scattered rays can correct the phase error. The first electron microscopic spatial frequency filter was the zone correction plate. Since phase errors up to the maximum n can be allowed in an imaging process, the zone
correction plate filters out disturbing spatial frequencies having phase errors
between n and 2n (cf. Fig. 2 and Fig. 5). Later, zone correction plates were
also developed which corrected the phase error by deceleration of the scattered ray in carbon layers of different thicknesses.
made visible by additionally shifting the mutual phases of
irradiating rays and of scattered rays by 90”. This so-called
phase contrast method has been an important part of the
experimental procedure of light microscopy for decades. It
should be mentioned that atoms are also phase objects
with respect to X-rays. However, this is of no consequence
in crystal structure analysis, because here the primary ray
is screened off (i. e. one is performing a “dark field operation”). In bright-field electron microscopy with the CTEM
one reaches the surprising conclusion, however, that the
quest for an ideal lens is actually meaningless: no contrast
can be obtained in the imaging of an atomic object. Zernike’s trick-of inserting a small plate in the aperture
plane of the microscope, and thus enabling modification
of the phase between the primary and the scattered rays in
the desired way-meets with difficulties in the case of the
electron microscope. Surprisingly, however, phase contrast
(at least to a certain degree, and certain resolution) can
also be produced by replacing the ideal lens by a lens with
spherical aberration. This is because the spherical aberration produces an additional phase shift, and one must consider whether this phase shift can be exploited for phase
contrast imaging.
With regard to the imaging of atoms, Scherzer incorporated into the imaging theory the phase object character of
atoms””. Since the scattering of electrons is “weak” in the
usual voltage range (50-100 kv), the hypothetical atomic
Angew. Chern. h i . Ed. Engl. 22 (1983) 456-485
images are calculated in a linear approximation[*]. This
may seem paradoxical: it is the strong scattering of electrons (orders of magnitude stronger compared to X-rays)
which enables the imaging of an object consisting of few
atoms. However, the excited scattered rays are still substantially weaker than the exciting primary beam.
The fact that the linear theory suffices for thinner preparations in electron microscopy is of considerable practical
importance, similarly as in the X-ray structure analysis of
crystals, where the linear theory is known as the kinematic
theory. Linear approximations are also used in some-but
not all-holographic imaging procedures. One finds for
the contrast g in the center of an atomic image,
the relationships[’”:
(Z-f,)(sin y)B-’ d0
y=(nCs84/2/2)- (nAzBZ/L)
( I o=bright field intensity, I = intensity in the center of the
atom; e = electron charge, h = Planck’s constant, uo = electron velocity; Z = atomic number; fR = X-ray atomic scattering factor; @= scattering angle; emax
= maximum scattering angle allowed by the lens; C,=spherical aberration;
A= wavelength, A z = defocussing). In optics, y is called the
wave aberration (cf. Fig. 3b, see also [’,‘I).
Siny is the imaginary part of exp i y ; when using amplitude objects, sin y in
(2) has to be replaced by cosy. The function characterizing
the spherical aberration, exp i y, corresponds to the pupil
function in light optics. Its component describing the
imaging properties of weakly scattering objects (cosy in
the case of amplitude objects, sin y in the case of phase objects) is also called the transfer function. Figure 4 shows
exp i y for a voltage of 100 kV and a rotationally symmetrical magnetic lens with a spherical aberration constant of 1
mm (lenses with spherical aberration constants of this order of magnitude are used in the modem CTEM apparatus), as a function of the scattering angle 0 for different defocussings. Taking case a) first: here the image plane is
placed in the focussing plane of the paraxial rays (Gaussian focus). Notice that siny is almost zero up to
8 = 5 x l o p 3 rad. If an aperture diaphragm were to be
placed at this angle, then an atomic object would show no
contrast. In this region the lens acts practically as an ideal
lens without a Zernike’s phase plate, and thus cannot be
used for the imaging of phase objects. Only when the scattering angle is larger does siny have values larger than
zero, so that a contrast is built up in the center of the atom.
However, above 8 = 9 x
rad siny changes its signthe integral in (2) becomes smaller with increasing 8. It is
therefore advisable to limit the scattering rays building up
the image to this angle.
[‘I If a large bright-field amplitude A and a small (complex) image amplitude p are added, and the intensity is calculated by squaring
then the small term pp* can be
neglected. The image intensity is proportional to the real part of the amplitude.
,sin Y
sin Y
Fig. 4. Pupil functions expi y for different defocussings [30]: left, the amplitude component cosy, right, the phase component sin y. Defocussings: a) A z = O (Gaussian focus), b) Az=67,5 nm (Schemer focus), c) Az=310 nm (zonal correction
focus). U = 100 kV; C,= I mrn.
Hence, the phase contrast is indeed produced by the
spherical aberration; without the spherical aberration,
sin y would never vary from zero. Scherzer"'] tried to improve the contrast by additional defocussing, and succeede d in doing so at a certain value (underfocus) (Fig. 4b):
this was found to be 67.5 nm for a spherical aberration of 1
mm; for other spherical aberrations this value changes in
accordance with a formula given by Scherzer. The range up
to the change of sign of sin y is thereby enIarged, and the
scattered rays with low scattering angles can also contribute more to the formation of the image than in the case of
the Gaussian focus.
In order to extend the phase contrast principle to our
zone correction plate it is necessary to calculate sin y for
even larger defocussings (see image point calculations1"14]), so that the wave aberration y oscillates strongly (Fig.
4c). If sin y is now "filtered" through a ring diaphragm system so that the sign is not changed (with gaps in the
screened-out places), then in the image point integral (2)
all terms of the same sign with increasing B are added, and
increase both the contrast and the resolution. Figure 5 illustrates how the zone correction plate screens out the unwanted parts of sin y with opposite sign.
The question then arises of whether the screened-out
parts have a disruptive influence on the image. According
to image point calculations" '-14], the background variations are somewhat increased, but the form of the image
points remains unaffected. Figure 4c shows that with a
given defocussing of 310 nm, almost a doubling of the resolution limit compared with Scherzer focus can be
reached with 8 oscillations of sin y (comparable to 8 dark
rings). A further increase of resolution, however, soon
leads to difficulties, since the number of oscillations increases very rapidly. But, a factor of more than 2 is unnecessary in order to analyze atomic structures. On the other
ainr 0
Fig. 5. Phase component of the pupil function (phase contrast transfer function) and design of the zone correction plate. The positive regions of siny are
screened out. Note that in contrast to the general case (cf. Fig. 2 and Fig. 3),
the phase error y (wave aberration) of the transferred structural factors F;no longer changes continuously, but jumps from band t? band by A (three
*,; *,;- primary ray); the strucray interference of the spatial frequency +
tural factor amplitudes Fr. are therefore weighted by a function (/shy/).
U = 100 kV; C,= 1 mm: ,i/O,,,,ax =0.18 nm.
Angew. Chern. Int. Ed. Engl. 22 (1983) 456-482
hand, the spherical aberration of round magnetic lenses
can be pushed only a little under the limit of 1 mm (using
100 kV), (Scherzer’s the~rem“~]).
2.5. The Imaging of the Transfer Function in the
Light Diffractogram
As deliberations on the zone correction plate were coming to maturity we still did not possess an electron microscope in our laboratory. On discussing the experimental
realization of our ideas, experts told us that secondary errors in electron microscopy (current instability, voltage instability, mechanical drift in the object stage) already made
it very difficult to reach double the theoretical minimal
image point distance (Scherzer’s resolution distance). During a visit to the Siemens’ electron microscopy research
and development laboratories in Berlin, I was informed
about the work of Thon, who was studying the dependence
of carbon foil granulation on the defocussing of the objective. Electron microscopic investigations on carbon foils
had shown that the granular-like image is strongly dependent on the defocussing.
had developed a theory explaining the different granulations by changes in the properties of the lens with different defocussing, in which Thon
incorporated the spherical aberration. To test this theory,
the most often occurring distances in many micrographs
were measured and their statistical average compared to
the theoretical mean‘”]. The technical quality of the series
of micrographs was excellent. Point distances in the range
of Scherzer’s resolution distances could be measured. I
suggested replacement of the troublesome single measurement of the distances by an investigation of the autocorrelation function (which directly yields a statistic of the distances), or by an investigation of the square of the image
Fourier transform (equivalent to the autocorrelation function). This last type of analysis seemed to be especially
convenient experimentally. Its execution is simple, if the
plate with the electron micrograph is used directly as an
object in the light diffractometer. The light diffractometer
then directly forms an image of the square of the Fourier
transform. Thon accepted an invitation to carry out experiments on this in our laboratory. For the experiments, the
light diffractometer that Menzel had already built was used
(see Section 2.2). Even the first pictures showed ringshaped structures in the light diffractogram. Afterwards
Thon systematically continued these experiments in Berlin
using a light diffractometer with a laser instead of a highpressure mercury lampr’*].The light diffractograms showed
(as expected from theory) ring-shaped structures modulated by the square of siny (see Fig. 6a). These diagrams
immediately proved that atoms are phase objects and that
the linear theory suffices for the description of the scattering. If the atoms had been amplitude objects (that is, if the
electron beam had been absorbed in the atoms), then the
light diffractograrn would have had to have been modulated by cosy (cf. left side of Fig. 4). If the Iinear theory of
the phase contrast had not sufficed, then the ring structure
would have disappeared.
Angew. Chem. Inr. Ed. Engl. 22 (1983) 456-485
2.6. Spatial Frequency Filtering in the CTEM using the
Zone Correction Plate
Some time later, in collaboration with our colleagues in
Berlin and Tiibingen (we had by then also become involved with experimental electron microscopy), investigations were carried out on filtering by the zone correction
plate in the CTEM (see Section 2.3)f’9.201.
Mollensredt et al.
in Tiibingen had developed a special electron-optical technique for etching very fine diaphragm systems[”], which
enabled the production of suitable zone correction plates.
The direct imaging of sin’y in light diffractograms of carbon foils allows adjustment of the filter with control of the
proper positioning of the open rings, and rings to be covered up in the light diffractogram. Figure 6 shows the light
diffractograms of the same foil before and after the positioning of the zone correction plate; each even-numbered
ring zone in Figure 6a is screened off in Figure 6b. Naturally, it is the linear transfer of the real part of the amplitude (see footnote p. 459), after the phase shifting of n/2
(phase contrast), that enables the direct imaging of the
zone correction plate. In Figure 6b, even the clamps on the
sides of the rings are pictured.
Fig. 6. Light diffractogram of a carbon foil: a) before insertion, b) after insertion of a zone correction plate.
Figure 7 shows one of the first successful spatial frequency filterings in electron microscopy. Here, as in other
optics, the resolution is limited by the aperture of the lens,
which itself limits the maximum scattering angle B,,.
law has already been used in the discussion of the function
expi y (pupil function; cf. Fig. 4), where it was shown how
the largest usable aperture angle 6,,, increases on going
from the Gaussian focus to the Scherzer focus, and finally
to the spatial frequency filter focus.
The spatial frequency of a scattered ray according to
Figure 3, is a two-dimensional vector in the x*,y*-plane.
Due to the small scattering angles in electron microscopy,
its absolute value corresponds to the scattering angle of the
scattered electron beam 8, divided by the wavelength A.
We always use the reciprocal value of the maximum spatial frequency (the radial limitation in the spatial frequency plane) A/8,,,, as the limit of resolution. The resolution defined in this way (dimension length) is also called
the crystallographic resolution dcryst,
since the analogous
term is used in crystallography for the definition of resolution (e.g. in the crystal structure analysis of proteins). In
analogy to light-optical resolution, dcryst
corresponds to the
smallest distance with which two image points in an image
46 1
Fig. 7. Spatial frequency filtering in the electron microscope (Elmiscop 101
with a C,=l.35 mm special objective). Above left: zonal correction plate
(after Mollenstedf ef al.) photographed in the electron diffraction image of
the foil; below right: light diffractogram of the foil. The light diffractogram
of the foil does not encompass the boundaries of the electron diffraction diagram (limited monochromaticity to the thermal cathode).
can be separated. Note, that this definition is somewhat
pessimistic, the exact calculation yields an additional factor of 0.85 when using the light-optical definition of resolution for coherent illumination. Sometimes, in electron
microscopy publications, even the factor of 0.6 is placed
before MO,,, (called nominal resolution). However, this
definition of resolution is somewhat confusing, since this
factor corresponds to incoherent illumination, which does
not apply in the CTEM. Hence, on studying the literature
of electron microscopy, care must be taken that the different definitions of resolution do not lead to false conclusions. The crystallographic resolution has the advantage
that it allows the direct comparison between electron microscopy and X-ray crystallography. In the right-hand part
of Figure 4 the (crystallographic) limits of resolution under
the three different conditions are 0.4, 0.33, and 0.18 nm.
When dc,,,,=0.18 nm, the atomic structure can be excellently interpreted-as protein crystallography has shownassuming, naturally, that the protein structure has been determined three-dimensionally. Even atomic models down
to a resolution of 0.28 nm are routinely constructed; however, the atomic maxima in the electron density synthesis
are no longer resolved. Because of the known, and limited,
atomic configurations, simple “pattern recognition” models can, however, be established. It follows from this, that
with spatial frequency filtering, the barrier to atomic resolution can indeed be broken through.
In Figure 7, however, the light diffractogram (bottom
right) of the CTEM-micrographs is only sufficient for a resolution of 0.3 nm (rather than of 0.2 nm). This was disappointing, because we had hoped that contrast would be extended at least to the edge of the strong area of the electron scattering diagram. Since the light diffractogram
images the square of the Fourier transform (see Section
2.5), the image will at best give a resolution that corresponds to the reciprocal limit of the light diffractogram.
The limit of resolution is not defined by the aperture
diaphragm of the objective, but by the expansion of the
scattering diagram in the spatial frequency area; beyond
this limit, even the best lens cannot improve on the resolution. This effect was investigated in more detail by
The Maxwellian distribution of the electron velocities at
the hot cathode prevents the radiation from being totally
monochromatic, even with the best possible stabilization.
With a larger scattering angle, the scattering intensity will
be diminished, and will finally become immeasureably
small. By using a cold cathode (field emission gun) the
range of speed of the electrons can be narrowed to such an
extent that intense scattering appears up to the edges of the
zone correction plate. An increase in the accelerating voltage also leads to a better monochromaticity of the radiation; for example, it was possible to demonstrate a crystallographic resolution of 0.18 nm (Scherzer’s resolution 0.28
nm) in the light diffractogram using CTEM pictures at 200
kVZ3]. For these pictures (Fig. 8) a cryomicroscope was
used (T=4.2 K), which offers a further advantage: decreasing of the thermal vibrations of the atoms, and therefore a genera1 increase in the scattering intensities.
2.7. Replacement of Light Diffractometry by
Computer Calculations
As before, the readily obtainable diffractogram serves as
an invaluable aid for the assessment of the quality of an
electron micrograph (see Fig. 9).
However, for quantitative analysis, light diffractometry
is too imprecise, and has to be replaced by calculations.
For this, it is necessary to bring an electron micrograph
into a computer retrievable form. The micrograph is therefore scanned, in the course of which the length of the sides
of the scanning elements (Pixel) must not surpass half, at
most, of the linear resolution. The density of the micrograph in each of these Pixels is determined. Since electron
rays, the same as X-rays but in contrast to light rays, increase the density of the photoplate proportionally to the
intensity (linear relationship up to a density of S = I), it is
possible to determine the intensity profile of the picture
with a densitometer. The large amount of data being handled necessitates that the densitometer should scan automatically. Fourier analysis, which can be carried out using
a routine program for Fourier transformation, leads to a
two-dimensional density diagram that is equivalent to the
light diffractogram but which not only produces the square
of the Fourier transform, but also the Fourier transform itself (with amplitude and phase).
2.8. A posteriori Spatial Frequency Filtering Outside the
Let us look again at Figure 6. As previously explained,
in the right-hand part (b), the even numbered (misphased)
spatial frequency rings are screened off by the zone correction plate (filtering off), and are therefore missing in the
formation of the image. The Fourier transform of a normal
bright-field micrograph could also be produced by calculation, and on image formation (by calculation), the misAngew. Chem. Inf. Ed. Engl. 22 (1983) 456-485
Az= 60 nm
Fig. 8. Exceeding the conventional limit of resolution with central illumination [23] (for inclined illumination, cf. Fig. 11). Photographs taken with the cryomicroscope using an acceleration voltage of 200 kV and C,= 1.35 mm: a) in the proximity of the Scherzer focus (Az=40 nm), b) defocussed for image reconstruction.
Note in a) and b) the parallel dark fringes produced by overlaying of two equal, slightly shifted micrographs (resolution test with Young’s fringes, see [24b]).-c)
and d), phase contrast transfer functions for a) and b). The transfer function c) shows narrow oscillations outside the central region (Scherzer region) that can be
scarcely resolved for reconstruction. In contrast to this, the zones in d) are considerably broader (cf. also Fig. 4). which-with regions of sufficient size (see 1301)allows reconstructions. The resolution test with Young’s fringes indicates significant regions also in the frequency filtering regions with non-resolvable zones,
therefore they are recognizable in a) also outside the strong mid region (Scherzer region). The resolution in the diffractogram (reduction of speckle) can be increased, according to [30], by increasing the illuminated region of the specimen, so that the delineation of the zones (and therefore also the reconstructability) can
be improved. An increase in the resolution of the image by reconstruction in case a) should however only be possible to a limited extent, whereas the broad zones
in case b) allow reconstruction up to the limit of the Young’s fringes (corresponding to 0.18 nm resolution).
Fig. 9. Light diffractograms for the diagnosis of electron micrographs. a) The light diffractogram has elliptical zones: axial astigmatism
(magnetic field non-spherical, adjustment of stigmator inexact); this causes no disturbance with suitable reconstruction. b) Lateral drift
of the specimen. Light diffractogram extended in one direction only, micrograph unusable. The reconstructable resolution can be recognized from the extension of the diffractogram. For determination of the absolute limit of significant details (also in non-reconstructable
regions), Young’s resolution test is necessary (cf. Fig. 8).
phased areas are simply omitted. The picture formed in
this way and the image produced by the zonal correction
diaphragm should be the same (within the scope of the linear approximation). It is more advantageous to include
Angew. Chem. Inl. Ed. Engl. 22 (1983) 456-485
the misphased scattering areas for the image formation,
but then to shift (correct) their phase by the amount 71. In
addition, even the weakening of Fourier amplitudes near
the zero positions can be compensated for by calculation
(amplitude filtering), but care must be taken, as the noise
in these regions is increased at the same time.
Our first calculations of this kind were discussed in 1970 at
symposia on new electron microscopic methods in Hirschegg[241and in
Soon after the publication of
the work on zone correction
Hanssen et a1.[26‘
pointed out that spatial frequency filtering-in the optical
instrument and a posteriori-had already been developed
in light-optics, although for entirely different physical
tasks. They applied the light-optical “Linear Transfer Theory” to the situation in the electron miscoscope, whereby
essentially the relations inferred by Scherzer[Io’and our~ e l v e s ‘ ~had
, ~ ’ only to be reinterpreted in another way[261.
S c h i ~ k e [and
~ ~ ]Hanssen[”] independently proposed transfer of the a posteriori filtering from light-optics to electron
microscopy. This was realized experimentally in the works
previously m e n t i ~ n e d l ~ and
~ , * ~in~ “analogue computations” in a double light d i f f r a ~ t o m e t e r A
~ ~further
~ ~ . proposal[27*281
suggested that the corrected image should not be
constructed from a single micrograph, but rather from a series of micrographs of the same part of the object taken at
a different focus. In this way, the influence of the gaps in
the spatial frequency spectrum on the quality of the corrected image should be eliminated (see Section 3.4.2).
2.9. A Consistent Theory
Of fundamental signifi~ance[~~-~‘’
in the use of the electron microscope as a phase-determining diffractometer, is
that the microscope is no longer needed to form an image,
but is used purely as a measuring instrument for the collection of the characteristic data (structure factors) of the
rays scattered by the object under study. As in X-ray structure analysis, these scattering data can be used in various
If it is indeed true that the atoms can be interpreted as
pure phase objects, then for electron rays, as with X-rays,
Friedel’s law applies: the centrosymmetrically related spatial frequencies of a diffractogram show the same intensities, and the corresponding (equally sized) phases have opposite signs. In the case of bright-field image formation,
the linear approximation means that, physically, the interferences between the individual scattered rays can be neglected“’. Therefore, corresponding to the classical definition of the phase in X-ray crystal structure analysis, onIy
the phase difference between the primary and the scattered
ray is measured. Luckily, a separate experiment is not necessary for each scattered ray (from the standpoint of the
optimal usage of the primary electrons, this would be disastrous); the phases can be determined from the superposition of all the scattered rays with the primary ray by Fourier analysis. However, with a limitation: centrosymmetrically related spatial frequency vectors lead to similar kinds
of interference images that coalesce. They can no longer be
separated (“three-ray interference”). This can be ignored if
Friedel’s law is applicable, since the one spatial frequency
will be ascribable to the other. The phase-determining dif[*I
They only have to be considered in the case of an approximation to the
second order of magnitude.
fractometer/electron microscope is therefore basically
only suited for scattering diagrams for which Friedel’s law
2.9.1. Anomalous Scattering
It is already known from X-ray crystallography that
both sides of the scattering diagrams can show different intensities and phases. This “non-Friedel” case occurs if
some of the atoms in the structure scatter anomalously.
This concerns heavy atoms which have an absorption edge
in the wavelength region of the rays being used. The scattering from these atoms proceeds with a certain (small)
phase shift 77 with respect to that of the non-anomalously
scattering atoms, and this effect leads to the inequality of
both halves of the scattering diagram. Such anomalous
scattering also occurs with electron rays, albeit likewise
weak, but significantly stronger than with X-rays. In practice, this too is only noticeable with heavy atoms. It was
first noticed in the electron diffraction of gases. Similarly
as in X-ray diffraction, it can be described by complex
atomic scattering factors. However, there is a special case
of anomalously scattering atoms in which Friedel’s law applies, namely when only one kind of atom is present. The
electron microscope is then once again a perfect interferometer which accurately records the diffraction spectrum
of the object (naturally, within the limits of the linear approximation). The phase shifting of the anomalous scattering 77 can easily be taken account of if y in equation (3) is
replaced by y - 7 (in the special case of a pure amplitude
object, with 71 = n/2)l3’].
What do we do when mixed structures, i.e. structures
with various kinds of atoms are present? This is the case,
for example, in the structure analysis of “heavy atom
stained” organic compounds. As already mentioned, the
centrosymmetrically related spatial frequency vectors of
both halves of the diffraction diagram together make a
sum whose single components can no longer be discerned.
If, however, at least two micrographs with different defocussings are used, then the weighting of the components
will be different due to the influence of the transfer function, through which a separation becomes p o ~ s i b l e ‘ ~ ’ , ~ ~ ~ .
This becomes even
if only one of the two centrosymmetrically coupled rays is allowed entry to the image
plane. If half a plane is covered in the aperture diaphragm,
then only half of the diffraction pattern will be recorded,
and a second micrograph is necessary for recording the
other half, with the complementary half-plane being concealed. Admittedly two micrographs are necessary in order
to transfer the complete experimental information, but calculations show that-other than with the central beam
bright-field micrograph -no weakening of scattered wave
amplitudes takes place. However, all the phases of the
Fourier spectrum of the spatial frequencies are now wrong,
but by knowing the transfer function, the phase errors can
be calculated and corrected. The transfer function can
either be determined from a third micrograph (with central
beam illumination), or be calculated from both the halfplane micrographs. The latter procedure, however, is only
exact in the case of a centrosymmetrical diffraction diaAngew. Chem. I n t . Ed. Engf. 22 (1983) 456-485
gram (e.g. of a pure phase object), but it should also be
possible in other cases, since y is only dependent on a few
parameters according to equation (3) (cf. Figures 10 and 11
for procedures with oblique illumination). With the exception of experiments on the discrimination of heavy
atoms[361,this possibility has not yet been exhausted in
structural analyses, but belongs to the reservoir of methods
for the future. Besides determinations of the complex function, the unweighted recording of the amplitude of the
scattered rays is of special interest.
S c a t t e r e d wave
Primary beam
Fig. 10. Complex image reconstruction according to the complementary halfplane procedure [31]. a) Schematic construction of the imaging arrangement.-b) Half-diaphragm (the small ring marks the penetration point of the
primary ray). For the second micrograph, the diaphragm must be removed,
and a complementary diaphragm inserted.
into phase and amplitude objects, but into “differently
mixed” objects with the extreme case of the pure phase object (pure amplitude objects do not appear in electron microscopy). In this way, not only is the important link between phase and amplitude parts of anomalously scattering atoms taken into account, but also, the influence on the
transfer function can easily be surveyed. Figure 12 shows,
for example, the transfer functions at different defocussings for 7 = 0.25 (corresponding approximately to platinum
according to the table of atomic scattering
for q = 0 (light atoms). It can be seen that the differenceswith the exception of the immediate proximity of the primary ray-are not very great. The experimental zero positions will lie somewhere between the zero transition points
of both transfer functions. It can also be seen that the weakening of the amplitudes of the scattered rays near to the
zero positions is greatly advantageous here, for the unstable phases, which are anyway in a very narrow range, are
associated with a strong weakening of the amplitudes, so
that the form of the image is little influenced. Despite renunciation of a complex reconstruction, both heavy atoms
as well as light atoms are well reproduced; the errors of
this approximation procedure play hardly any role. A
short time ago, in our laboratory, Typke et u I . [ ~ * ~experimentally determined the magnitude of the anomalous scattering for some heavy atoms (cf. Fig. 13).
Fig. 1 1. Complex image reconstruction with inclined illumination [33-351.
Using inclined illumination a resolution down to the atomic limit can be
achieved, even with thermic cathodes (with 100 kV). However, the total
image must then be compiled from several partial images (synthetic aperture). Light diffractograms reveal the (anisotropic) increase in the transferred
spatial frequency area on increasing the angle from 0” (a, b, c) to 0.66” (g, h,
i). I n the latter case, a limit of resolution of 0.16 nm can be measured. The
procedure is complicated and of low intensity, but excellently demonstrates
the possibilities that an electron microscope offers on its use as a phase-determining diffractometer.
Another possibility for the analysis of structures with
different kinds of atoms is offered by approximation procedures, in which the separation of phase and amplitude
parts of the scattering is dispensed with. Such a procedure
is usual in X-ray structural analysis, where, however, the
influence of anomalous scattering is much smaller. Approximation is also used in our analysis of “heavy atom
stained” Organic compounds. Here-in contrast to what is
usual in light optics-it is important not to discriminate
Angew Chem. Int Ed Engl 22 (1983) 456-485
---sin(y-~ )
Fig 12. f i e function sin(y-7) for v=o and
cussed, b) overfocussed
~ = 0 2 5
7 =O
v=o 25 (from [361): a) underfo465
Az =-131nm
= 2nm, ~z,=ll60nm, y = O 3 8
Fig. 13. Light-optical diffractograms of electron micrographs of a carbon foil
shadowed with platinum. Due to the relatively large astigmatic difference
AzA (I 160 nm), the zero lines in the diffractogram (corresponding to the gaps
in the transfer function) are hyperbolic in the inner region (shown for three
defocussing values of Az in comparison with the calculated curves). Because
of the anomalous scattering of the platinum atoms, this also applies for the
innermost zero line, which with a pure weak phase object, would go through
the center (cf. [38]). The images show that the electron microscope is also utilizable as a Fourier interferometer for the study of physical parameters (for
further refinement of our methods, a more exact knowledge of the anomalous scattering IS important).
At the “double symposia” in Hirschegg and in London
in 1970, Erickson and KIug reported on the influence of
amplitude filtering on the defocussing-dependency of the
reflections of catalase crystals stained with uranyl acetate[’’], and thereby experimentally proved“’ the concept
which we had formulated the previous year[30-321.
Particularly noteworthy was the finding that the linear theory
even remains valid for strongly scattering specimens- we
had previously only experimented with light-atom structures.
2.9.2. Consideration of the Curvature of
Ewald’s Sphere of Propagation
Discrete formulation with spatial vectors and atomic
scattering factors had proven especially useful for the
handling of structural analysis problems in X-ray diffraction. Consequently introduced into our work since 1969[’01,
it led to the separation of “partial amplitude scattering
(angle 7)” and “phase scattering”-a separation which
would have made little sense in light optics. On extension
of the theory of electron diffraction to thick specimens
(within the validity of single scattering)[301,the complication arose that the transfer functions of the atoms become
dependent on their position along the optical axes of the
instrument. This complication could be eliminated by replacement of the two-dimensional spatial frequency area
[*] The theoretical basis of this contribution was inaccurate: in the basic
equation (9, in which the influence of the light atoms has apparently
been neglected, the authors have added the phase part and amplitude
part of the heavy atom scattering as if they had been independent of each
other, whereby the correct transfer function sin(y-7) is obtained as an
approximation. With a small amplitude part, this has scarcely any influence on the numerical results; only when 7=n/4 (for uranium from
about 8/1=7.5 nm-’) do incorrect factors, of the order of magnitude of
fi,and phase errors, emerge.
by the three-dimensional reciprocal space (Fourier
space)[301.The Ewald’s sphere of propagation (see Fig. 3b)
then comes back into play, and thus, electron microscopy
becomes now, in every detail, a variant of the diffraction
methods in structure research. When dealing with scattering at the surface of the sphere of propagation, complex
image reconstruction is unavoidable even with pure phase
objects-and one must fall back on the “methods in store”
(cf. Figs. 10 and 11). “Phase-determining diffractometry
with the electron microscope as a tool” is still a recent
method, but the door to three-dimensional analysis down
to atomic resolution, in analogy to X-ray structural analysis, is open. This also applies for the aperiodic case; even it
can be considered as “crystal structure analysis” in the
widest sense, if a small piece of aperiodic material is regarded as a “crystal with one unit cell”. The electron microscope thereby loses its property as an image-forming
apparatus (however, it can be further used as such for
readout and presorting of the submicroscopic entities) and
the lens is replaced by the computer for generally three-dimensional images.
2.10. Automation of Phase-Determining Diffractometry
The development of the electron microscope into a “robot” is therefore indicated. A robot works not only fast
and reliably, but also enables any chemist, biologist, mineralogist etc. to carry out complicated physical procedures without any specialist knowledge, using a “black
It is remarkable that the prerequisites for the automation of phase-determining diffractometry are even better than in X-ray structure analysis; the phases can be
measured directly, whereas in the latter case they have to
be determined indirectly. Although the demands on the
computer are greater, the incredible advances in computer
technology allow for no faint-heartedness even if the conditions of a dedicated computer-now common in X-ray
diffraction analysis-are imposed. Of interest is the shift in
the problems of development. Whereas formerly, in the
case of X-ray structural analysis, the translation of the relatively simple measuring methods into the robot’s technology gave difficulties, today these are marginal. On the
other hand, articulation of the meticulous adjustment and
measuring operations in conformity with robots, which are
so difficult in electron microscopy, requires special attention“].
An electron microscopist of the good old stamp may at
first pity the “degradation” of the electron microscope to a
measuring instrument. But, is it not true that the computer
creates new, incredible, possibilities for the electron microscope? Phase-determining diffractometry is-within the
framework of kinematic approximation-just as quantitative a procedure as X-ray crystal structure analysis. Both
are based on measurements; it should be noticed that even
the density curves of X-rays and electron rays are analogous, and that in both cases quantum-counting direct detectors can also be
Phase-determining diffractom[*I It can only be remarked in passing that the on-line diffractometer [41,42]
and the on-line correlation computer (401 are important aids to adjustment.
Angew. Chem.
Ed. Engl. 22 (1983) 454-485
etry is not limited to periodic structures, and can be used
in all areas of chemistry, from inorganic chemistry to biochemistry. It also offers the prospect of atomic analysisnot as a vague presumption, but rather as a precise, theoreticall y-founded procedure, and one that is, experimentally, already realizable for the most part.
2.11. The Scattering Absorption Contrast
Looking back, it seems remarkable that the fundamental
relationship between electron microscopy and light-optic
phase contrast microscopy was not fully utilized until the
sixties, although Boersch had already noted in 1947 that
atoms scatter and do not absorb[’]. For sure, a reason for
this was that, even in the light microscope, the method of
phase contrast is not trivial-it is so much easier to view an
object as it is (if necessary also after staining). Actually,
even thin structures, stained with heavy atoms, show some
contrast in the Gaussian focus of the electron microscope
at low resolution. Because of the anomalous scattering,
heavy atoms are not colorless, but light grey. But strong
phase objects (thick objects) can also behave as amplitude
objects (non-applicability of the linear approximation,
quadratic phase contrast), similarly as to how air bubbles
can easily be seen in water when using the light microscope. This becomes more complicated if multiple scattering takes place. In earlier electron microscopy, the source
of the contrast was not important, the images being seen
“as i f ’ they came from absorbing material. Even today,
one must revert to the phenomenological approach if the
range of applicability of the linear theory is relinquished;
but nowadays, attempts are made when calculating the
bright-field intensity, to take the quadratic terms into account.
2.12. What is “Ptychography”?
This name describes some (almost forgotten) procedures
for determining the amplitudes and phases of scattered
electron waves without lenses, which with today’s knowledge are especially applicable in the case of crystals[441.
They are based on the mutual interference of scattered
rays-in contrast to holography, in which all scattered rays
are superimposed with one reference wave. A variant of
these procedures has recently been realized[451.Another
variant should be relatively easily realizable in the scanning transmission electron microscope, and should enable
the evaluation of diffractograms with almost any resolution that is needed (Fig. 14)[461.In the case of inorganic
crystals, and perhaps also in the case of radiation-sensitive
organic crystals, these procedures could easily develop
into being competitors for the methods described in Sections 2.3-2.10.
2.13. Highly Ordered Biological Structures
In crystallography textbooks, the laws of diffraction are
usually “amalgamated” with periodicity and symmetry.
But, just as the laws of diffraction can be abstracted from
periodicity and symmetryr6’],using periodic and/or symAngew. Chem. Int. Ed. Engl. 22 (1983) 456-485
Fig. 14. “Phenomenological” description of a variant of ptychography 1461.
In a scanning transmission electron microscope, a structure is impressed, according to a), o n the (coherent) scanning probe. The lattice reflections enlarge according to b) lo sharply defined spots, which overlap one another
(with interference). On scanning, the intensities in the overlapping regions
vary in unison with the phase differences of the reflections. For recording the
micrographs, the usual one-channel detector has to be replaced by a position-sensitive area detector for electrons (e.g. according to [43]).
metrical patterns, the laws of symmetry can be abstracted
from the diffraction theory. X-ray crystallography has led
to the study of objects transformed into the reciprocal
space (Fourier space). Periodicity and symmetry produce
certain Fourier structures in which it does not matter
whether the object is an electron density distribution or another-even macroscopic-density distribution. This naturally also applies for micrographs obtained by imaging the
respective objects in the electron microscope. Once again,
it does not matter whether it is a question of qualitatively
correct images, or-as in the extension of the kinematic
theory to electron microscopy outlined in this review-of
parallel projections of potential distributions.
Qualitative electron microscopical images of contrasted,
periodic and symmetrical biostructures have been investigated since the early sixties using Fourier principles,
whereby the light diffractometer (see Section 2.1) has
served as an especially convenient “calculating machine”
for Fourier trans for ma ti or^^^'^. By exploiting the Fourierdistribution of the object-known as filtering-certain
structural properties are especially accentuated. This filtering, which concerns the object under investigation, has
nothing to do with the spatial frequency filtering that we
introduced, which concerns the optical properties of the
objective. A special kind of “object filtering” is possible in
the case of two-dimensional lattices, whose Fourier transform shows strong, grid-like arranged maxima (corresponding to the periodicity), and a background (arising
from individual differences in the unit cell pictures). By filtering out the background, and averaging all the distorted
entities by a further Fourier transformation (e.g. in a light
diffractometer), a strictly periodic structure can be produced. The averaging was first carried out on high-dose
micrographs (good electron statistics, but preparation and
irradiation artefacts). Electron microscopic work on periodic unstained and native biostructures has been published since 1968 (see Section 3.3).
different angles are superimposed on top of one another in
such a way that single layers of the specimen are thrown
into sharp relief. By changing the overlapping parameters,
different layers can be rendered predominant. A similar
principle had been referred to much earlier in X-ray diagnostics as “tomography”. If X-ray shadow pictures of a
body are made at different angles, then they contain projections of all the superimposed layers, which are, however, overlaid using different amounts of shifting. If such
pictures are superimposed in such a way that one layer is
placed in the same orientation in all the pictures, then this
layer will predominate, whilst the other layers are shifted
with respect to each other, and, to a certain degree, average
themselves out (Fig. 15).
3. Three-Dimensional Analysis
3.1. The Problem
Considering the electron microscope and the X-ray diffractometer as analogue instruments already implicates all
applications which are possible with a diffractometer.
These include, above all, the three-dimensional analysis of
the structures under study. In the fifties, X-ray crystal
structure analysis of projections (along the edges of the
unit cell) was followed by three-dimensional analysis of
the electron density in the unit cell, since it was clear that
only the true[’] three-dimensional analysis (for which the
kinematic theory had afforded the theoretical background)
could lead to elucidation of the construction of complicated structures. Fortunately, the tools which were necessary for complex information processing were developed
at the same time, namely, automatic measuring machines
and electronic calculating machines. In electron microscopy, as in crystal structure analyses, the object specimens
are far too thick, relative to the lateral resolution, so that
overlapping of the structural details prevents a consequent
analysis. Three-dimensional electron microscopy was not
simply achieved in an analogous way, but had its origin, in
part, in general procedures of image p r o ~ e s s i n g [ ~ * - ~ ~ ~ .
This is not surprising, due to the original image-forming
character of the electron microscope. The “transfunctionalization” of the bright-field electron microscope into a
phase-determining diffractometer for electron diffraction
signifies a development away from the admittedly attractive, but only qualitative “peep” microscopy (a term given
by Ernst Ruska), to quantitative structural research.
3.2. Tomographic Procedures
3.2.1. The Poktropic Montage
In Hurt’s contribution[491,the term “three-dimensional”
does not even appear. He describes his method a “polytropic montage”, with which electron micrographs taken at
This means the substitution of the two-dimensional image function p(x, y)
(e. g. on an electron micrograph) by the three-dimensional image function
p(x,y,r) (in electron microscopy, z extends along the optical axis). To be
distinguished from image stereoscopy, in which a two-dimensional image
is replaced by two two-dimensional images slightly tilted towards one another, whose view gives a spatial impression, but does not give the inner
Fig. IS. Principle of circular tomography. The layers oC the body K (e.9. I , 2,
3) are imaged with shifts in the X-ray shadow diagram. The shifts depend on
the location of the X-ray tube (e. 9. position R’ or R‘?. If the pictures P’and
P are shifted one over the other in such a way that the layer pictures 2’ and
2” become congruent, then only 2 is highlighted in the overlapping image. In
circular tomography, R rotates about the axis A. In the electron microscope,
central projection is replaced by parallel projection (R infinitely far away;
imaging of the object at large depth of focus). W e change in direction of projection is achieved by tilting of the specimen. The plane of the image (P’, p”)
is therefore perpendicular to the direction of the projection. A certain, but
easily managable, distortion of the projection images is produced (squares
are imaged as rectangles).
3.2.2. Electron Microscopic Computer Tomography
In the sixties, it was found that disturbances caused by
insufficient averaging-out of the unwanted layers in tomography, are largely mathematically correctable, especially
when one kept to parallel projections, instead of central
projections (which called for new X-ray imaging apparatus). The “reconstruction” of a three-dimensional image of
a body becomes especially easy to view if different directions of projection are adjusted by the rotation of the body
about one axis; with an asymmetrical body, the axis of
choice does not, in principIe, matter (computerized tomography, see Figure 16).
This computerized tomography is very well suited for
extension to electron microscopy[4s1.The parallel projection is guaranteed by image formation with great depth of
focus[491,through which superimposed layers of the specimen appear projected over one another in the electron micrograph. Microgoniometers can be used to rotate the specimen (e.9. in the way that “tilt cartridges” are used in
electron microscopy) and finally, the computerized analysis follows in analogy with calculation methods, if the
Angew. Chem. I n f . Ed. Engl. 22 (1983) 456-485
Fig. 16. “Tomographic chicken grill”. The chicken H on the skewer S is
grilled by the fire F. On turning the skewer, pictures of the chicken at equal
angular increments Aa are produced on the plates P with parallel X-rays. In
electron microscopy, the X-rays are replaced by electron rays; parallel projection is achieved by imaging with great depth of focus. The “grilling” of
the “chicken” is (unfortunately) done by the electrons themselves.
image is transformed into a digital field of numbers, e . g .
by densitometry. The “grilling”, which is not normally the
case in X-ray tomography, is (unfortunately) brought
about by the electron rays themselves: at a dose necessary
for image formation, they destroy the organic substance
(e.g. biological macromolecules), which means that special
methods of specimen preparation must be used.
Thus, irradiation-resistant inorganic structures are imprinted on the specimen (positive and negative staining),
which allows recognition of the primarily interesting features of the organic structure. They can also be imaged
with high irradiation doses, where generally, structural details are only relevant down to the so-called biological resolution (31.5 nm). Care must always be taken, because,
even on stabilization of the structure after the very rapid
destruction of the organic substance, slow changes cannot
be ruled
and the laws of “staining” are in no way
trivial-the principle of the filling of gaps with an amorphous heavy-atom glass in negative contrasting is, e. g.,
certainly only approximate[’].
[*] To define the term “computerized tomography” more precisely (to differ-
entiate it from “diffractometry”): Tomography can be carried out both in
real, as well as in reciprocal space, whereby the mathematical procedures
of image processing are formally related to the procedures of crystallography. All three-dimensional methods necessitate a set of pictures taken
with the illuminating rays in different directions (cf. Fig. 15 and 16 and
[Sol). There are, however, characteristic differences: (a) Tomography is
based on central or parallel projections, (b) in tomography the physics of
the imaging process is unimportant.-Tomography can be used in such
diverse areas as X-ray diagnostics and radio astronomy (corresponding to
(b)). In contrast, in diffractometry the physical imaging process (scattering process) is important; in X-ray diffractometry the requisites of “projections” (see (a), planar sections in the reciprocal space in the case of parallel projections) are only applicable in an approximate way, in special
cases (small angle scattering). The reciprocal space is transected by a
spherical surface. This also applies in diffractometry using the electron
microscope. Of course, it is useful in practice that the spherical surface
can be approximated by a plane, owing to the short wavelength of the
electrons at a not too high resolution. In a diffractometry theory, there
must be a defined correlation between scattering and structure. It can
only be applicable to an approximation (neglect of multiple scattering in
the kinematic theory, use of h e a r theory for phase measuring). Using
these criteria, the procedure of &Rosier and H u g 1481 is “tomographic”,
not only because it absolutely necessitates parallel projections, but primarily because here, a phenomenological imaging theory (scattering absorption contrast based on the logarithms of the densities) is used, without
taking spherical aberration into account. In our image-point calculations
with spatial frequency filtering the kinematic scattering theory and the liAngew. Chem. Int. Ed. Engl. 22 (1983) 456-485
3.2.3. l%ree-Dimensional Analysis via Symmetry
The experimental work on three-dimensional electron
~ ~ ’not, however,
microscopy by DeRosier and K I U ~ ‘ did
correspond exactly to the model in Figure 16. With respect
to the analysis of highly-ordered biological structures (especially helical structures)[481, in the model case the
chicken would have to be replaced by a macroscopical helix, e.g. a helical spring whose axis is identical to the
skewer axis. Simple geometric considerations show that a
sinusoidal curve must appear as the image (parallel projection). When the skewer is rotated, the sinusoidal curve retains its shape, but appears to move along the axis, one full
turn corresponding to a shift of the sine curve by one period. This means that, in such a case, all tomographic pictures can be derived from a single image, and so, of course,
for three-dimensional analysis, one X-ray or electron diffraction picture would suffice. However, if this model is refined to a helix on which identical subunits are threaded
like pearls, then identical projections appear merely on rotation through small, discrete angle increments Aa (e.g. for
tobacco mosaic virus ha = 3.7 ”). A discrete set of tomographic pictures is obtained (e.g. 49 pictures with tobacco
mosaic virus), which, in most cases, suffice for a three-dimensional analysis at biologically-significant resolution.
With anglular increments that are too large, intermediate
layers can either be taken from images with incidentally
different positions of the objects, or the specimen can be
tilted inside the region of the anglular increments. The
three-dimensional structure of the tail of the T4 phage was
determined in this wayc4’].
The method of producing projections by symmetry relationships (instead of by measuring) can aiso be used with
other highly symmetrical structures (e.g. with spherical viruses). The experimental simplicity of the analysis is fascinating, especially in the case of helical structures with
small angle increments-no tilting of the specimen is necessary, and the micrographs can be taken with a conventional microscope[52’.
This does not yet constitute a three-dimensional analysis
in the strictest sense, since the identity of experimentally
determined projections and projections deduced via symmetry is correct only to a relatively crude approximation.
The specimen lies on a foil, and is covered with contrast
medium; these components certainly have no helical, nor
even cylindrical, structure. The helix in the specimen could
also have been squashed; this is not revealed in every case
on enlarging the micrograph[*]. Despite these limitations,
near approximation had already been used since 1965 11 1-14]. This theory (with spatial frequency filtering), was adopted in Cambridge in 1970
1391. In electron microscopy, however, consideration of the lens properties is especially important, since different kinds of “images” are obtained using different defocussing. In the Gaussian focus, for example,
the linear approximation is not applicable. The first three-dimensional
image reconstructions in electron microscopy (fatty acid synthetase [all)
are consistent with diffractometry theory. A phenomenological imaging
theory is completely unusable at high resolution (accelerating voltage of
the order of magnitude of 100 kv), because, in such a case, the curvature
of the sphere of reflection, as well as the change of sign in the spatial frequency spectrum, has to be taken into consideration. However, there are
conditions under which work can only be qualitative: thick objects, multiple scattering (see Section 2.1 1). Qualitative analyses have recently been
described 1931.
these kinds of experiments have yielded a lot of valuable
information on the structure and function of macromolecules-e.g. on the mechanism of contraction of the phage
Regarding the term “macromolecule”, it should be
noted that from the standpoint of the content of information (expressed, for example, by the sum of all atomic
coordinates), it is of great importance whether a highly
symmetrical molecule (e.g. tobacco mosaic virus (TMV)),
or an unsymmetrical molecule (e.g. ribosome), is under
study. The content of information in the former case can
be lower by orders of magnitude. Often a small subunit
(the truly unsymmetrical structure-like the base sequence
of the RNA in viruses-is neglected) repeats itself, according to a law of symmetry, which can usually be given with
few parameters-in the case of a helix, with its polarity, diameter, pitch, and number of subunits per turn. Their
number plays hardly any role compared to the considerably larger numbers of parameters necessary to describe the
subunit, so-according to information theory-such a
macromolecule can practically be taken as the “subunit
molecule”. This concept can be extended even further. As
already mentioned, a biological helix is a “string of pearls”
consisting of “equal” subunits wound in the form of a
screw. From the viewpoint of three-dimensional analysis,
such a helix can directly be seen as a “tilting device”,
which brings single subunits into the orientations necessary for structural analysis. This is associated with both an
advantage, as well as a disadvantage: on the one hand,
many subunits form an image, whereby averaging takes
place on artefacts of preparation and irradiation damage
(object filteringf4’]); on the other hand, this principle apparently functions only for smaller structures-a helix similar to TMV with ribosomes as subunits would be so enormous, that this would go far beyond the applicability of
the kinematic theory, because of its thickness. This has the
consequence that the proper three-dimensional information-expressed, e.g., as the number of resolution elements N in the “reconstruction volume” of the subunit-is
very small (order of magnitude 10) because of the limited
biological resolution.
Nevertheless, the aesthetic charm of highly symmetrical
helical and spherical ornaments is immense-it is pleasing,
in a certain way, that the long-forgotten dreams of Dorothy
Wrinch. who had postulated extremely symmetrical protein structures in her cyclol theory[531,have come true, at
least in this field.
Furthermore, this information-based description of the
molecule also applies for the X-ray diffraction experiments of highly symmetrical macromolecules like the TMV
protein[54J.However, the high molecular weight complicates the measurement-an immense number of scattering
data have to be determined-but the high symmetry facilitates the analysis. On discussing helical structures, the possibility of three-dimensional X-ray analysis of fiber diagrams must be mentioned. It was the precursor of electron
microscopic analysis, and could be carried very far, for example, with TMV[551.
[*I Recent investigations on a spherical virus (turnip yellow mosaic virus)
seem to confirm these fears.
3.3. The Analysis of Native Periodic Structures
The tomographic procedure^^^"^^] and our contributionf5’] to three-dimensional electron microscopy had different origins. Dissatisfaction with the fact that in the case
of biological specimens irradiation damage necessitated
contrasting tricks, and bad resolution seemed to be inevitable, stimulated a search for ways which could lead, in analogy to X-ray crystallography, to an electron-ray crystallography of native proteins. We immediately directed our attention to the possibility of the diffractometric determination of amplitude and phase of the crystal reflections using
electron-microscopic methods, for the methods of spatial
frequency filtering, and hence electron-microscopical diffractometry, had been developed in our laboratory.
The first hurdle was specimen preparation. Protein crystals contain about the same amount of solvent as the protein itself. On drying, the crystalline order is almost completely lost. It was therefore necessary to find a vacuum-resistant material that could replace the solvent without disturbing the crystalline order. Of the known embedding materials for electron microscopy, hydrophilic polymers
proved to be the most useful. The alternative, that water
should be left in the crystal and its evaporation prevented‘56Jby modified experimental procedures, such as
electron microscopy with humid object chambers, or lowtemperature microscopy (at - 180 “C, ice has a vapor presbar), seemed far from promising in the initial
sure of
stages of research. As test structures, we used crystals of
myoglobin and erythrocruorin, and tested the preservation
of their structure X-ray crystallographically. For specimen
preparation, special procedures were developed (for example, cross-linking of the proteins with glutaraldehyde to
render them insoluble).
Figure 17b shows a precession diagram of a myoglobin
crystal embedded in Vestopal. Here, it can be seen that the
order is much worse than in a water-containing crystal
(Fig. 17a). The disturbance of the crystal order takes place
only in the last step of the preparation, on transformation
of the monomeric embedding material into the polymer;
diagrams of the crystal soaked with the monomer show an
unchanged order of the protein moleculesi571.It is therefore
recommended to lower the vapor pressure by non-covalent
forces (lowering of the temperature) instead of by polymerization through covalent cross-linking. The range of
materials that can be used as substitutes for water is therefore broader. Of course, water itself-as already mentioned, and as was later proven e~perimentally[~~~-can
also be used. Its anomalous behavior on crystallization,
however, can only be overcome by certain tricks, for example, by supercooling (shock-like deep-freezing), or by the
generation of a non-anomalous ice modification at high
pressure[”! On substitution of the water, new parameters
can be varied ?vapor pressure curve), and also mixtures
(partial distillation) can be tried out. In any case, tod,ay
there is scarcely any doubt-for ice158Jand organic mono m e r ~ it[ ~
been proven-that a preparation of native
structures of biomolecules for high resolution electron microscopy is possible.
As a temporary aim of our work[*’], the X-ray crystallographic resolution of 0.8 nm that we reached, was considAngew. Chem. Inf. Ed. Engl. 22 (1983) 456-485
ered satisfactory (Fig. 17). Electron diffraction on thin
layers of crystals prepared without contrasting yielded
clear crystal reflections, which on comparison with the Xray diagrams showed an analogous intensity distribution.
These diffraction diagrams using the normal conditions of
irradiation in the electron microscope-still without the
minimal dose technique introduced by Williams et al.[6v1
(not to be confused with the low dose technique)-were
Fig. 17. a) X-ray diffraction diagram (precession diagram) of a sperm whale
myoglobin crystal (hkO projection) in mother liquor. b) Precession diagram
after crosslinking of the proteins with glutaraldehyde, and dehydration and
embedding in Vestopal (polymerized). c) Electron diffractogram of a thin ultramicrotome section of a crystal embedded in Vestopal (schematic). In addition to the indexing, absolute values of the structural factors measured by Xrays and (beneath) the estimated electron ray intensities (st = strong, m = middle, s=weak) are given (after [5O]).-In a “supplement” [57], different embedding materials, primarily water soluble materials, were also tested, and an
electron micrograph of an unstained microtome section was shown, which
seemed to be unordered (“granulated”), but showed single reflections in the
light diffractogram.
Angew. Chem. Inr. Ed. Engl. 22 (1983) 456-485
visible for only a few seconds. The poorer resolution in the
electron diffraction diagram (1.2 nm instead of 0.8 nm) can
perhaps be attributed to radiation damage during the adjustment operation. However, most important was the fact
that the possibility of carrying out an electron ray analysis
of native proteins (and therefore also that of other biogenic macromolecules) had been demonstrated.
A law in structure research, the reciprocity law, states
that structural information in one of the two dual spacesreal space and reciprocal space-must always correspond
to an analogous information (transformed into the other
space). When applied to our problem, it means that the
same information o n the structure of the crystal must be
contained in the image of the native crystal lattice in the
electron microscope as in the diffraction diagram. However, it contains information about the phases, which indeed
the diffraction diagram also contains, but which is lost on
the transformation of the amplitude into intensity (in contrast to the intensity formation in the image plane)[”’.
However, the influence of the measuring instrument, the
electron microscope (phase object, spherical aberration)
must be taken into account (cf. Sections 2.3-2.10). For the
changing of direction of the projection (for three-dimensional analysis) differently orientated ultramicrotome sections of the crystal were pr~posed‘”~,
with which, in electron microscopy also, the whole reciprocal space is accessible. The same goal can be achieved by changing the
orientation with the aid of a goniometer (“tilting”), as is
otherwise usual in crystallography.
Why a crystal structure analysis of native biogenic macromolecules is possible with the electron microscope is
made clear in the following referen~e”~”’:
“Let us first start
with a not very encouraging discussion concerning the
physical possibility of “molecular microscopy”. It is the
strong interaction of electrons with atoms which makes it
possible to collect in a reasonable time enough scattered
electrons for the recognition of single atoms. But there is
also the unhappy situation that for light atoms the crosssections for elastic and inelastic scattering are of the same
order of magnitude. That means that the number of elastic
and inelastic collisions is approximately the same. In crystal structure analysis there are many equivalent molecules-in a small protein crystal, e. g.,
It is therefore
highly improbable that a molecule will be hit more than
once by an incident quantum. Therefore the elastically
scattered quanta will find untouched molecules and can
build up diffraction patterns of the non-distorted molecule”. Now, the averaging principle is a fundamental principle of crystallography; it is dealt with in text
used in the X-ray diffraction analysis of statistical superpositions of molecules with different conformationsi621,
and is applied to stained electron microscopical molecular
pictures, which show differences produced by preparation
and radiation damage (high dose pict~res)[~’,~*~.
Remarkably, however, it was not until much later that averaging to
eliminate irradiation damage was given any a t t e n t i ~ n [ ’ ~ . ~ ~ ~ ]
(work on information theory[631cited in this contextIs81contains no remark on this possibility), perhaps because it
only became known I a t e ~ [that
~ ~ ] the ratio of inelastic to
elastic collisions with atoms, also in the case of X-rays
(substitution of the electrons by X-ray quanta) is very
47 1
large. It is actually almost larger by a factor of 10 compared with electron rays, i.e. X-rays are very destructive“].
From 1970 onwards G l u e ~ e r ‘ ~systematically
investigated the radiation damage of organic structures, and demonstrated in computer simulations how the influence of
the radiation damage can be reduced by crystallographic
averaging. Using these preliminary studies as a basis, Henderson and Unwin succeeded in performing the diffractometric three-dimensional analysis of a native crystal (purple membrane from H . habbiurn) by the use of spatial frequency filtering (see Sections 2.2-2. lo)‘”]. Such structural
analyses have become very popular in recent years[661.
However, it soon became obvious that preparation of a
specimen suitable for high resolution encountered difficulties in the case of very large molecules; even without radiation damage, resolutions of less than or equal to 2 nm are
difficult to obtain. Similar difficulties are also encountered
in the X-ray crystallography of macromolecular structures.
Highly symmetrical organic macromolecules (e.g. helical
structures) could easily be investigated in their native
states using the low-dose technique. Low-dose experiments
on stained TMV[67,681
have demonstrated how new details
(above all in the nucleic acid sector) become visible on
changing to the non-damaged molecule.
3.4. Three-Dimensional Electron Microscopy of
Individual Structures
(“Real” Three-Dimensional Electron Microscopy)
3.4.1. Why “Individual” Structures?
X-ray crystallography has developed from small beginnings to be one of the most important branches of science.
What would our understanding of matter (and therefore,
of chemistry) be today if the diffraction method had not
given us such a detailed knowledge of the atomic architecture of compounds-up to the proteins? This is true, of
course, only for highly ordered, periodic aggregates (like
single crystals). However, there also exists the world of individual structures which are not exactly reproducible, but
which are of importance not only in biology (although
there especially) but also for chemical reactions in the
most general sense. How paltry is our knowledge here!
Just think of “platinum black”, an inorganic catalyst for
reactions of organic molecules, whose particulate form
hardly ever repeats itself. Or a biological membrane: its
[*] A measure of the damage caused by the rays is given by the ratio of in-
elastic collisions-which are able to but do not have to change a structure-to the elastic collisions. Formerly, the damage caused by the rays
was often correlated (also in high-voltage electron microscopy) with the
reciprocal scattering cross-section. Naturally, this is meaningless regarding imaging problems, where the number of the scattered quanta (electrons) is important.
Compared to the first experiments on the structure analysis of native
crystal^'^", it is methodologically noteworthy that the analysis on a twodimensional crystal (membrane crystal) has been carried out, enabling a
link to the methods of analysis for individual structures (cf., e.g., [Sl]);
even the determination of the common origin (after translation into reciprocal space; cf. Section 3.4.2). This holds for three-dimensional crystals
(such as in [SO]) only with limitations (cf. 177, 961).
enzyme pattern on the surface leads us to suspect topological interactions, which optimize sequences of enzyme reactions. Enzyme complexes like fatty acid synthetase may be
precursors of such “factories”. Again, the structure is not
repeatable, but its principle of construction is important
for biochemistry.
A method which is fundamentally suited to experiments
in this problematical sector is to be found in microscopy.
For example, cells, which are individually so different, but
which also show structural similarities, can be identified
under the light microscope. On investigating individual
structures by conventional electron microscopy, the molecular, but not of course the atomic region, was approximated. But even this method had in many ways its limitations. One of its most important being the information-destroying restriction to projections of spatial bodies.
Phase-determining diffractometry, with its combination
of the principles of structural research and microscopy,
promised to provide the most interesting insights into the
wide field of aperiodic and individual structures (with possibilities for use in all areas of chemistry).
In Munich, therefore, although X-ray diffraction and
neutron diffra~tion[~~’-as
well as protein crystal structure
analysis in the electron microscope~501-werenot totally ignored, our efforts were concentrated on the further methodological development of electron diffraction for the investigation of individual and aperiodic structures in the
electron microscope. Atomic resolution was not attainable
using thermal cathodes, or, only incompletely so, (with
synthetic aperture technique~[~~-~’]).
The laborious development of better monochromatic field emission guns in
our own laboratory would have been unjustified, as such a
program of studies was already under way and proving
successful elsewhere; today, field emission cathodes are
commercially available (although they are costly). Threedimensional analysis, however, was fascinating at any resolution; it was also to be expected that in lower resolution
investigations the general stability problems would be of
less trouble. A self-imposed handicap was the concentrating of our efforts on biological structures, for that presented the complex problem of radiation damage. It is not
without envy that we look at inorganic electron microscopy, in which, completely conventionally and with incredibly high irradiation doses, imaged crystal projections yield
practicable contributions to topological chemical question~”’~.The energy transferred in elastic scattering processes is carried off without damage to the object. But, on
the other hand, biochemical and biophysical investigations
are especially interesting. Moreover, conventional electron
microscopy had already shown what valuable information
can be won in spite of radiation damage, if the object is
prepared in a suitable way (cf. Fig. 18).
The success of the low-dose analysis of native periodic
structures (Section 3.3) has unfortunately misled many into
regarding high-dose analysis of contrasted structures as being “retrogressive”. However, in the case of individual
structures, high-dose analysis must be resorted to. The object to be studied, e. g., a macromolecule, is by no means to
be regarded as isolated. In reality, reaction products are
observed, from the reactions of the compounds actually of
interest with the reagent of preparation, the supporting
Angew. Chern. h i . Ed. Engl. 22 (1983) 456-485
Fig. IS. Discovery o f bacteriophages with the electron microscope. As long
ago as the 16th December 1939, H. Ruska had submitted an article for publication (Narunvissenschaften 28 (1940) 45) in which it was reported that bacteriophages had been discovered o n lysis of E . coli cells. The micrograph
shown here is reproduced from a later communication (H. Ruska, Natunvissenschaften 29 (1941) 367) after the phage tails, which were “often pointed
into the inside of the bacteria” had been observed for the first time, on the attack of bacteriophages on Proreus cells. [I thank C. Ruska. Institut fur Biophysik der Medizinischen Akademie, Dusseldorf, for permission to reproduce this micrograph.]
foil, and the radiation. “Radiation damage” is also chemistry. Even if the radiation reactions can be eliminated in
any way, the preparation reactions are still there. And
these can highly influence the structure of the object. Even
with identical molecules the reaction product is only reproducible under exactly the same reaction conditions. For
comparison: if several people write the letter “a”, it can
look different in each case, although it is still “a”. Here,
we are dealing with one of the fundamental problems of
computerized character recognition, which in information
theory is studied as “pattern recognition”. By varying common structural characteristics the concept of the letter “a”
is reached. Primitive comparisons and averaging have to
be replaced by the ideas of “pattern recognition” in the
electron microscopy of individual structures too. As a calculable reaction product, “radiation damage” loses its horror; the electrons are simply a further, although undesired,
partner in the reaction. The reaction conditions can be
controllably varied, e. g. by trapping the emitted electrons
with acceptors or by lowering the temperature.
Only three-dimensional investigations lead to inequivocal structural results. For a given projection, as many
structurgs as wanted can be produced by exchanging
image elements along the direction of projection. In addition, there are components lying, accidentally, above or beneath this prijection (e.9. support foil). It is also important that a high enough radiation dose should be used, to
ensure significant imaging of the spatial structure. Only
then can changes in the structure be assigned to chemical
changes, for example, in the distribution of contrasting
material. With the necessarily high doses, a slow change of
the structure during the exposure (after the rapid destruction of the native structure) cannot be ruled out. The threedimensional procedure should therefore work in such a
way that it yields the average structure (as in conventional
microscopy). And finally, the electron microscope itself
Angew. Chem. Inr. Ed. Engl. 22 (1983) 456-485
should be free of errors, otherwise no decision can be
made as to whether a structural change is due to the object,
or is simulated by the spherical aberration. For this reason,
the tomographic procedures are incomplete. Only correct
spatial frequency filtering with determination of the structure of the image points, guarantees a sufficiently quantitative procedure.
This is often misunderstood; only recently, it was suggested that individual structures of identical particles
should be made more “similar” by reducing the resolution,
and thereby reducing the “noise”. This is something like
proposing to a cell biologist to image his cells less sharply
in order to iron out their individual differences (which are
designated as “noise”). He can of course do this, and in
this way gets a “unit cell” by subsequent superimposition,
but all the fine details-e.g. in the nucleus-are lost.
The light microscopist, studying his cells individually,
can do it better: he does “pattern recognition” intuitively.
One only has to bear in mind the really quite crude preparation procedures in order to understand how different
“identical” particles can look. However, the rich preparative experience potential collected in conventional electron
microscopy, should also not be underestimated. But only
by three-dimensional analysis can it be thoroughly explored and made usable. In the future, directed improvements of the preparation methods are therefore to be expected.
Naturally, this should not mean that the averaging of the
same kinds of “reaction products” of identical particles is
unnecessary. Statistical procedures will always be necessary in order to study the regularities in a population of
entities. But the chemistry involved should not be forgotten. From the development of low-dose analysis, it can be
seen how errors of judgement in the microscopy of individual structures were made. The individual image consists
practically only of real, uninterpretable electron noise.
However, for example, the “granulation” so characteristic
of each electron micrograph with high resolution (cf. Fig.
23) is not noise, even if the electron microscopist refers to
it as “structural noise”‘’].
3.4.2. MethodologicalAspects
The Necessary Radiation Dose
On going from two-dimensional diffractometry (fixed
direction of the primary ray) to three-dimensional diffractometry, some new questions arise. Thus, it was feared that
the large number of pictures on rotating the object (cf. Fig.
16) would result in an extreme radiation load on the speci[‘I The averaging described concerns particles which were measured to an
electron-statistically significant degree. But naturally the integral dose per
particle can also be reduced, whereby the single particles show strong
electron noise that can only be reduced on averaging. Thereby, the influence of radiation can be studied. In the borderline case of very low radiation doses (analysis of native structures), the projections necessary for
the carrying out of the three-dimensional reconstruction can, because of
the interchangability of the operations, also be averaged first of all, and
afterwards, reconstruction can be made with the averaged projection‘941.
This procedure basically corresponds to crystallographic reconstruction
(cf. Section 3.3), in which the three-dimensional reconstruction is built up
from the averaged (through the crystal) single projections in the same
(which was surprising and
men. We have
raised doubts[721),that for a two-dimensional micrograph
(with spatial frequency filtering), about the same amount
of electrons are necessary as for a three-dimensional analysis with the same electron-statistical significance. In the
first case, the whole dose is applied in the taking of one
image, in the second case, it is evenly distributed over the
taking of the series of images. “Equally significant” means
that in both cases an object detail (e.9. a heavy atom
group) can be recognized, with the same ratio of signal to
noise, whereby in the first case it is assumed that it can be
discriminated due to the fanning out in the z-direction (the
direction of the optical axis) and also determined in its zthink of the obcoordinates. In order to understand
ject as being divided into a series of thin sections (having
the thickness of the z-resolution). A micrograph is made
of each section. This is obviously the optimal procedure,
because the other sections do not become impaired by the
electrons that are necessary for the imaging of one section.
Calculation shows that three-dimensional diffractometry
works as economically as does two-dimensional analysis
(or to be more precise, admittedly, only if the curvature of
the sphere of reflection can be neglected). This Gedankenalso reveals the source of the misunderstandexperiment[731
ing[?’]. Naturally, the images of the sections are more
poorly contrasted than the image of the unsliced thick object. If only the last one is to be seen, then a few electrons
suffice. However, then, no details can be seen in the twodimensional image of the object (electron noise!).
Determination of the Common Origin
A second problem concerns the phase correlation of the
structural factors of the tilted images. It would not be necessary if-as in tomography-the axis of rotation could be
rotated with the exactness of the resolution. This is not
possible in electron microscopy-the resolutions lie in the
order of magnitude of nanometers, the mechanical precisions in the order of micrometers. We worked out the procedure of cross-correlation of slightly inclined projections
for the determination of the common origin of all Fourier
section^[^^.^^], and developed this theory, first of all for the
ideal case of point atoms‘751and later for real atomsL761.
Note that it is also used for the analysis of native crystals[6sJafter translation in the reciprocal spacef7?].
Number of Images
From each picture, the structure factors on a spherical
surface in the reciprocal space can be determined (cf. Fig.
3b), which in the case of average resolutions can be approximated by their tangential plane. In three-dimensional
analysis, a discrete bundle of such surfaces (cf. Fig. 20) is
determined, between which one must interpolate in order to
obtain the continuous structural factor distribution in reciprocal space. Use of the Whittaker-Shannon interpolation
theorem shows[781that the minimum number of images is
dependent on the resolution and on the size of the object.
Our formula for the number of projections‘78Jwas confirmed by Crowther et aZ.[791.
Later, however, this problem
proved to be more complicated. These calculations[781
to the ideal case of an undisturbed three-dimensional
image point that is independent of location. Allowing for
the background disturbance increasing a little, or the
image points on the edges of the reconstruction area being
somewhat more badly resolved than in the middle, the
number of projections can be reduced by up to a factor of
2. Thus, in the Cormack procedure known from computerized tomography, which reconstructs a cylindrically
shaped body (cylinder axis identical with tilt axis), the region in the proximity of the axis is somewhat more sharply
imaged than next to the cylinder surface. We use this procedure-after exact testing of the dependency of the image
point on the location-in many of our reconstructions, because the surroundings of the object under study (the reconstruction area is always larger than the particles) are
less interesting, and with the present state of the experimental technique, a limitation of the number of images
seems to be economically necessary. This is because the
whole experiment would be ruined by one, or a few, abortive images of a series (above all in the case of drift, cf.
Figure 9b). It can be assumed that with further experimental improvements (above all, by automation), the question
of the minimum number of images will be less important.
Blind Region in Reciprocal Space
The limitation of the range of rotation in electron microscopy-because it is fundamental-is more crucial. As an
illustration, imagine a thin plate (specimen on a support)
as the object in the “tomographic grill” (Fig. 16). If this
plate stands edgewise, there is no transmission, and, in addition, mountings limit the range of angles. In electron microscopy the preparation can generally be tilted by about
f 60” away from the horizontal position, i. e. the rotation
in Figure 16 has to be replaced by a tilting of about +60”.
This has unfortunate consequences for the image point
shape, which in the ideal case should be sphere-like (as in
crystallography). From Figure 19 it can be seen that instead of a sphere, an anisotropic pattern is formed, which
shows the electron-optical resolution in the direction of the
tilting axis (Ay), perpendicular to this, but determined, not
only by the electron-optical resolution, but also by the angle increment ha (in other words, by the number of
images). Thereby, the length of the image points in the direction of the optical axis (Az) is longer by a factor n than
perpendicular to it (Ax); n depends on the angular range
(n= 1.8 when a= +60”). Ax=Ay can, of course, always be
achieved by reducing Aa, however, the elongation of Az is
always present. Undesirable, are two deep, closely neighboring side minima in the x-direction. Otherwise, however,
the background is only slightly disturbed by diffraction
ripples. Especially noteworthy is the fact that the weighting of the transfer functions with their zero positions
scarcely influences the image point shape and the background noise. After determination of the transfer function
for each picture (which can be very different), the real
image point of this reconstruction is caIculated. Figure 19b
shows one result. The cumbersome averaging by a series of
f o c ~ s s i n g s ~can
~ ~therefore
~ ~ ~ 1 be omitted in three-dimensional analysis-the averaging also works with tilted projections.
Angew. Chem. Int. Ed. Engl. 22 (1983) 454-485
ing. The negative minima have totally disappeared. The
image geometry is, however, more complicated than with
simple tilting on a single axis (Fig. 19) but should be controllable. Because of this surprisingly convenient form of
image point, experiments to replace the flat support foils
used in electron microscopy by needles (whiskers)1801,and
Fig. 19. Image point problems in three-dimensional electron microscopy. Because of finite resolution, an image point is always an extended object, in the
ideal case in two dimensions with circular symmetry, in three dimensions
(crystallography) with spherical symmetry. The limited range of tilting angle
of goniometers is the reason for the asymmetry and the anisotropy. On tilting
about an axis, the three-dimensional reconstruction body can be thought of
as being divided into a series of layers perpendicular to the tilting axis (yaxis), which are arranged at intervals equal to the y-resolution (Ay). a) Imaging of the image point in the x,z-plane on tilting between 60” and - 54”,
ideal weight function, contour lines <O dashed, contour line spacing 6%
(above the density +303/o the contour line spacing increases to 8%). Image
point height normalized to 1; background noise well under 10% with the exception of two neighboring side minima. These effect a certain deformation
of the reconstructions in the x-direction (cf. test calculations [81c]). Important is that the side minima can only influence the immediate surroundings
of the image points, and thus, large falsifications of the total reconstruction
are impossible. Naturally, astigmatic distortions have to be taken into consideration when interpreting the analyses. On overlapping of reproducible,
equally orientated structures, (with different directions of the tilting axis) the
influence of the negative minima largely averages out, whilst the anisotropy
along z remains. Unfortunately, an averaging of differently orientated particles (which could produce an almost spherically symmetrical averaged
image point) meets with difficulties, owing to orientation effects, at least with
current preparation procedures. b) Same image point as in a), but calculated
with the aid of experimental transfer functions. Note the surprisingly large
similarity to a), which makes the averaging of the influences of spatial frequency gaps according to [26, 271 unnecessary. By weighting the transfer
functions, however, the image point height is reduced by about 25%(non-optimal contrast transfer with respect to the hypothetical ideal case (error-free
microscope and Zernike plate)).
Does this strongly anisotropic image point suffice? Our
situation is similar to that of a person with an astigmatic
eye. If the resolution in the direction of the lengthened
image point is sufficient, he is able to read; deformations
in the other directions are then only slightly disturbing.
For application in electron microscopy, this means that Az
should be the same size as the required resolution (i.e.
about 2 nm with stained biological structures). This is not
difficult to achieve, since the electron microscopic resolution is always rather high in the case of individual structures. The granulation is always seen, so to speak, in the
heavy atom glass, which is not interesting in itself (if its
laws are not to be studied), but which helps to reach a sufficient z-resolution. For this reason, we usually work with
a Ax range of about 1 nm. As test calculations have shown,
the negative, closely neighboring minima only disturb the
nearest surroundings with very steep edges, (they produce
a kind of Fresnel fringe); these fringes, and the randomness of the structure in the directions of sharper reproduction, must be “overlooked”. Figure 20 systematically
shows the whole reconstruction procedure.
The disturbance by negative minima can be totally eliminated with “conical tilting”[491using special reconstruction
procedures[78b1.Figure 21 shows an image point which is
rotationally symmetrical and which already seems to be
lengthened by only n = 1.4 in the z-direction with 45” tiltAngew. Chem. In!. Ed. Engl. 22 (1983) 456-485
DF FA ‘p
fCormack/Smi th 1
Fig. 20. Flow diagram of a reconstruction on tilting about one axis. A: Occupation of the reciprocal space with Fourier sections; the coordinates x*, y*.
Z * are parallel to the coordinates x, y, z in the real space, central sections
(corresponding to the projections in the real space) are drawn in the tilting
angle range of -54” to +60° at angular increments of 6” (projected along
y*). Note the “blind” region in the reciprocal space, which is not filled with
sections and therefore causes the anisotropies of the image point as discussed in Figure 19. B: Block of micrographs, which are measured in the automatic densitometer C (after testing in the light diffractometer M, which
gives the light diffractograms N). From these (semi-quantitative) and from
the densitometer data, the parameters 0 (defocussing, axial astigmatism) are
obtained for the correction of the structure factors (transfer functions P). In
step D, this correction (two-dimensional image reconstruction, also called
image restoration) is made. In the next step, the determination of the common origin of all projections (and hence that of the three-dimensional body)
is accomplished. The last step is the actual three-dimensional synthesis (sections G).
thus to reach a kind of “rotating molecule method” with
spherical image points, were stopped. In spite of indisputable theoretical advantages, this would have meant a
changing of the whole technique of specimen preparation
in electron microscopy. Three-dimensional microscopy
should, however, be “seamlessly” coupled to conventional
Fig. 21. Image point by conical tilting, If the primary beam is guided onto the
surface of a cone, which corresponds to circular tomography in geometry (cf.
Fig. 15 and [49]), then, with a modified reconstruction program [78bI, an
image point can be derived, which is, however, lengthened in the z-direction,
but which appears circular in the x,y-plane (think of the figure as being rotated about the z-axis perpendicular to the plane of the paper) and produces
no negative minima. If, therefore, the z-resolution Az is properly chosen,
then no more problems arise on interpretation than when a spherical image
point (diameter Az) would be present-the anisotropy actually produces a
“reducing” of the image point (in the x,y-direction). Notice, however, that in
certain “pathological” occupations of the reciprocal space with structure factors (in which these lie mostly in the non-measured blind region of the reciprocal space), difficulties can arise. With asymmetrical structures, such difficulties are hardly to be expected.
3.5. Use of Three-Dimensional Electron Microscopy in
the Structural Investigation of Ribosomes
With a resolution of 2 nm, smaller biomolecular particles-for example, the TMV protein, phage proteins, coat
proteins of spherical virus molecules, bacteriorhodopsin,
etc. (molecular weights of the order of 20000)-also show
only a few details in three-dimensional analysis (number
of image points of the order of 10). The situation is different if (asymmetrical) particles with molecular weights of
several millions are being studied-structures are obtained
which, even with this low resolution, show the complexity
of smaller proteins (resolution 0.2-0.3 nm; more than
1000 image points). Clearly, these are cases in which projections will have to remain uninterpretable.
The first real three-dimensional analysis of an electronmicroscopic object was published in 1974[*’].As shown in
Section 3.2.3, difficulties might be encountered in investigations with the production of the projections by symmetry operations. The first three-dimensional crystal structure
analysis (for which these limitations, with exception of the
averaging of similar objects, do not apply) was published
in 1975‘651.In collaboration with Lynen el al. in Munich,
we studied the structure of fatty acid synthetase of yeast
( M r z 2 . 3 x 106)[811.
At that time, our experimental technique was not perfected (a= f 45 Aa = loo), and also the
total dose was higher than that required for recording the
micrographs (no minimal dose technique). Later, stimulated by work on label triangulation methods (cf. 1691), we
turned to the structure analysis of ribosomes (ribosomes of
E. coli, M,=2.1 x lo6). It was no accident that the first investigations in this new field of individual analysis were
not carried out on real aperiodic structures”’, but on chemO,
ically reproducible, although very large, particles, which
could in theory also have been investigated using crystallographic methods. The identical chemical structures enable
comparison of the reaction products-dependent on preparation conditions such as orientation towards the support foil, etc. Further, in the case of the ribosomes, the
strong ionic character of the protein-RNA complex is interesting, which also leads to the assumption of staining of
structural details in the inner particle (positive staining).
Above all, however, ribosomes are molecular structures
which are biologically very important, occur in all forms of
life, and through which the synthesis of proteins takes
place. They are not only highly differentiated in their (totally asymmetric) structure, but are also highly differentiated in their function. Depending on the cell (prokaryote,
eukaryote) and functional assignment (cytoplasm, mitochondria), they can show large differences (e.g . in molecular size and form), but-especially as sequence analysis of
RNA strands have shown-are closely related to one another. In the last few years ribosomes, especially from E.
coli, have been intensively investigated chemically; today,
for example, practically all the sequences of the approximately 50 (different) ribosomal proteins are known. Characteristic is the capability of the ribosome, after its segregation into the single proteins and nucleic acid strands, to
aggregate back into intact and active ribosomes, a capability which is utilized in the label triangulation investigations
for the determination of the native protein topology (see
1691). The ribosomes are easily divided into two subunits of
different sizes; 30s and 50s subunits[*] for prokaryotes,
40s and 60s subunits for eukaryotes. It is obvious that
these subunits should next of all be investigated separately.
3.5.1. Conventional Electron Microscopy of Ribosomes
Because of the size of the particles, and their relative stability toward preparation procedures with staining, they
were investigated electron microscopically fairly early
on-actually, they were discovered in this way. But, however, there is hardly any other object with which the limits
of conventional electron microscopy are made so drastically clear than with ribosomes-in spite of, or perhaps because of the ingenious experiments to characterize structural details immunologically or with other labels.
It was not only due to their size, but also to the complete
lack of symmetry, that-in contrast to the somewhat
equally sized spherical viruses (with which the ribosomal
particles were first of all compared)-no structural laws
could be found, and in the best case, only the outlines of
the particles could be recognized. The surroundings and
the particles are covered with a general granulation
(“structural noise”) (cf. Figures 22 and 23). Only a short
while ago, (long after the beginning of our analyses) were
defined structures inside the particles revealed, by the averaging of micrographs of equally oriented particle^[^^^^^^,
[*] Exceptions are investigations on the analysis of the action of complement
on vesicles [9I], and preliminary high resolution investigations on amorphous carbon 1921.
[*] Classification according to the sedimentation constant in the ultracentri-
Angew. Chem. Int. Ed. Engl.
22 (1983) 456-485
which, as projections of thick bodies, can tell us little“].
Even the seemingly simple problem of the determination
of the shape found no satisfactory solution. Three-dimensional bodies were tentatively “invented”, which-projected in different directions-should explain the different
molecular images appearing in the micrographs. In a way,
this is a primitive form of the three-dimensional analysis of
projections; however the number of projections is extremely low (of the order of 5 ) , and their respective angles
are unknown. Furthermore, it is fully unknown, whether
structural changes are associated with the different orientations of the specimen. It is understandable that in different laboratories, different models were found.
Fig. 22. One of the 21 micrographs (0” tilt) from the +60” to -60” series of
micrographs (-60” micrograph discarded due to drift) taken at angular increments of 6”: ribosomal 50s subunits from E. coli without L7 and L12
stalks. Enlargement of 79300, mean defocussing Az=827 nm, axial defocussing difference dz= 386 nm, dose=7 x 10’ e/nm2. Reconstructed particles
marked, direction of the tilting axis drawn in.
3.5.2. Three-DimensionalAnatysis of Stained Ribosomal
The large experimental expenditure in the case of these
specimens‘”] makes it necessary to limit the analysis to a
few particles. With today’s priority of averaging methods
in electron microscopy, this would seem to imply a severe
limitation, but this is not true. On comparing structures (in
the general sense) not only the number of structures, but
also the number of structural details are important. A classic example is the “fingerprint” of criminology. Even a
comparison of two fingerprints is enough to prove the
identity. In the case of the three-dimensional analysis of ribosomes, the number of characteristic details is especially
large (corresponding to the volume of the particle), and
thus the information content of the analysis is considerable. Of course, it is necessary to choose a high enough radiation dose so that the electron statistical significance suf[*I The experimental averaging in 1821 agrees very well with the projection
of our 3-D model.
We thank Dr. M. Stiiffler-Meilicke. Max-Planck-Institut fur Molekulare
Genetik, Berlin, for the preparation of ribosomal particles and ribosomes from E. coli.
Angew. Chem. Int.
Ed. Engl. 22 (1983) 456-485
fices for significant recognition of the details. We work
with doses o f about 1.5 x lo5 e/nm2-this is a factor of
about lo3 more than in the analysis of native crystals. The
results, similarly as in crystallography, can be represented
quantitatively in contour maps of the single sections. We
chose the contour line distance in such a way that it corresponds to the double or triple amount of the electron statistical standard deviation-differences
between reconstructions of different particles are therefore certainly not
noise, but are produced chemically (and radiation chemically). To prove that no significant changes occur during a
series, we expose a “radiation damage series”, under the
same conditions but without tilting (at another site on the
specimen). The mathematical measure of the similarity of
two images is the cross correlation coefficient Ck[*].
We test
the constancy of the images in the radiation damage series
with cross correlation, visual examination, and by calculating the difference. Of course, the organic substance is totally destroyed, even on recording the first micrograph-its
skeleton, however, is very stable against further radiation;
the reconstruction procedures average out smaller changes
(as the theory shows). However, with a dose of about 10’
e/nm’, recrystallization of the contrasting material slowly
therefore, this dose should not be exceeded to
any great extent. Since our experiments are done under
minimal dose conditions, no further loading occurs
through adjustment processes.
Our reconstructions~8s1
were done on uranyl salt-stained
30s and 50s subunits of E. coli in different orientations.
3-5 particles were investigated in each orientation. A simple trick enables us to avoid having to do separate tilting
series for each particle. On choosing the proper preparation conditions, relatively many particle projections are
imaged (about 500) on a micrograph (magnification about
80000). These micrographs show different “shapes”,
whose differences are explained by different orientations
and by influences of specimen preparation. Often, shapes
occur which are especially characteristic and similar in
outline, which the electron microscopist-as already mentioned-interprets as different projections of a three-dimensional body. In the literature, they are referred to by
different names-e. g. asymmetric and symmetric forms
with 30s subunits, kidney and crown forms with 50s subunits. In the tilting series, approximately the same number
of ribosomes are imaged on each micrograph of the series,
so that the three-dimensional preparation under study is
actually a population of ribosomes. Subsequently, the single particle pictures to be reconstructed are chosen, and
measured in an automatic densitometer. Note the immense
information capacity of the photoplate, which will make it
difficult to replace it electronically. With the 20 pm scanning raster (diameter of the probe on the specimen 0.25 nm
Ck= C , , / ~ - C l isZ the magnitude of the cross-correlation maximum, CI1and C22are the magnitudes of the autocorrelation maxima of
the structures compared. With the supposition that the cross correlation
maximum lies in the zero position (i.e. that both images were exactly in
line, by correlation), then CI2equals the integral over the products of the
densities of both images. C , , and CZ2correspond to the integral over the
square of the densities o f the single images. When both images are the
same, C, = I ; with different images C , decreases. With two random structures, Ck= 0.
47 7
Fig. 23. Gallery of all "kidneys" studied, of the series a= +60° to - 54", Aa(r=6",with their respective light diffractograms. Designation, from left to right: RID,
RIC, RIE, RIF, R I H (cf. Fig. 22).
Angew. Chem. Int. Ed. Engl. 22 (1983) 486-488
with an enlargement of 80000[’]), which we mostly used, a
6 x 9 cm2 photoplate contains 13.5 x lo6 image elements, a
series with 20 pictures 2.7 x 10’ image elements! From this
information, only a very small fraction is used. With higher
tilting angles the defocussing in the preparation changes to
a large extent. This does not matter, since it is determined
by calculation, and corrected. For the same reason, it is
also immaterial whether the focus on the reference position (with which it is adjusted and which is at a distance of
several micrometers from the picture position) varies
somewhat, due to mechanical inexactness or because of
the not completely planar specimen surface.
Figure 22 shows a 0” micrograph taken from a series of
21 micrographs of a population of 50s subunits stained
with uranyl formate (z-resolution 2 nm), which were isolated in such a way that two of the 34 proteins of the subunit (L7 and L12) were split off. These proteins-closely
related in their chemical structure, and present in up to 4
copies-are located, as comparative conventional analyses
had shown, in a lateral rod-shaped protrusion (stalk) of the
subunit. We have investigated subunits with and without
the stalk, in parallel, since we were interested in how this
chemical operation influences the inner structure of the
subunit. As already mentioned, artificial and natural modifications of the structure of the ribosomes of different
kinds are characteristic of ribosome chemistry-we are
dealing here with a simple model case. In the micrograph,
the chosen particles of two orientations are marked (kidneys RIC, R l D , RlE, RIF, RlH, crowns RIA, RlG, RlI,
RlK). Figure 23 shows a gallery of all micrographs of 5
chosen kidneys, in a tilt series, together with their light diffractograms. The micrographs show such strong, and such
random differences, that the experimental evidence could
almost be regarded as being obscure. But this is incorrect-on the contrary, it is remarkable how exactly electron optics “draw”, if lens aberrations are corrected. The
micrograph can perhaps be compared with projections of
fruits which are dug up from moist and loamy earth and
seem like accidentally formed clumps of earth, but which
are highly ordered within.
Generally, it can be said that particles in the same orientation have structures which differ a little in detail (different staining and radiation influences), but which are surprisingly reproducible in their general proportions. They
can also be superimposed to give a well resolved average
structure, whereby, however, a correlation of the slightly
different orientations becomes necessary by laborious
three-dimensional correlation procedures. By way of contrast, the structures of differently orientated particles show
large differences; the first suspicion, that the particles flatten strongly by surface forces on drying, has fortunately
not been confirmed (see also [“l). The staining material
forms a ring around the particles (cf., e.g.. Fig. 24); with
thick specimens, in particular, (e.g . oriented in edgewise
positions) the staining intensity inside the particle varies
(‘1 From Fourier principles, the scanning elements may maximally have half
the diameter of the resolution elements. With the scanning calibration,
pictures with a resolution of up to 0.5 nm can therefore be worked with,
so that adequate certainty is ensured with the necessary reconstruction resolution of about 1.0 nm (in the x, y plane).
Angew. Chem. Inf. Ed. Engl. 22 (1983) 456-485
Fig. 24. “Looking around the corner” in three-dimensional electron microscopy. With a three-dimensional body, projections can be calculated in any
direction, which can also correspond to micrographs which would not be accessible due to the imaging geometry. A projection of the “kidney” averaged
from RlC, RID, RlE, R I F (cf. Fig. 22) in the direction of the y-axis is
shown: a) positive regions, b) negative regions. Note: in a) a general decrease
in contrast from the middle plane to above and below, which corresponds to
the decrease in contrast in the layers. However, the bordering of the particles
above and below can be seen, since the differently structured foils above and
below the particles already average themselves out (the projections of the
foils appear with lower contrast); in b) primarily the projection of the ringshaped contrast middle region is conspicuous. The particle area seems “more
positive” than the surroundings, due to the normalization, which equates the
total integral from the positive densities with the integral o f the negative densities.
from above to below. The middle layers are the most
strongly stained. All particles show contrasted channel-like
regions inside-the assumption arises that, at least for the
largest part, positively stained RNA is being dealt with.
Note that in the reconstruction the areas of high scattering
density are negatively depicted. Because of the normalization (phase contrast!), areas with weak scattering ability
seem positive in all reconstructions, whereby positive maxima correspond to areas with especially low scattering ability. Up to now we have investigated the 50s subunit more
precisely, since with its compactness, drastic changes of
form are not likely to appear-in the case of the 30s subunit we see evidence for not inconsiderable orientation-dependent changes of shape.
Naturally, it is not possible to present all the details of
these complicated investigations in a progress report. Figure 25 shows a section through 4 contrasted 50s particles
in crown form (after correlation of the orientation). For
sake of clarity, only the contour lines of the non-contrasted
structure are represented- the channel-like contrasted
structures therefore appear white. To facilitate the comparison, common negative areas are depicted with “guiding”
dots-they are also contained in the mid-structural section
AV2. After correlation, the three-dimensional cross-correlation coefficients lie between 0.25 and 0.3. Actually, their
values are surprisingly low, considering the really pronounced similarities in Figure 25. The reason for this lies
in the great sensitivity of the cross-correlation coefficients
towards a11 individual changes. We can try, however, using
principles of pattern recognition, to mark out and compare
the fundamental structural information-in this case, the
special channel-like staining. Here, two steps can be distinguished. In the first step, the same overall structure is demanded (no distortion is allowed); however, the abstraction from details such as, for example, intensity and struc479
Fig. 25. Analysis of the crown form of ribosomal 50s particles (without stalks). The reconstruction body is a cylinder (extension
along the tilting axis (y)) with a diameter of D=23.8 nm and a length of L=23.8 nm. It is divided into cubic scanning elements
of edge length D/64=0.37 nm. The resolution is Ax = 1.3 nm, Az =2.0 nm; AYequals the mean electron optical resolution, which
varies in the micrographs between 0.7 and 1.0 nm (as a standard value we assume that Ay= 1 nm). The reconstruction body can
be cut into layers in any orientation and, for example, 64 x,y-layers are obtained perpendicular to the optical axis (z-axis). For
comparison, however, the single particles must be three-dimensionally correlated with one another in respect to location and
orientation. In all layers, the comparison shows surprisingly strong similarities. As examples, the most central sections (No. 32)
of the “crowns” RIA, RIG, RII, R I K (cf. Fig. 22) are shown. As already made clear in Figure 24, negative areas correspond to
structural elements with high scattering ability, especially with contrasted structures. The use of the zero line for characterization
of the separation of weakly contrasted structures (light atomic structures, positive) from strongly contrasted structures (heavy
atomic structures) is somewhat arbitrary. For clarity, the contour lines in the negative areas are not shown. To facilitate comparison, the common negative regions of the single particles are marked by guiding dots. The averaged structure AV2 has practically
the same resolution (only small distortion of the particles) and now shows even more clearly the channel-like negative regions; in
addition, beneath section 32 of AV2, the section 32 of a “model” of the structure of AV2 is shown, which is produced by occupation of the negative regions with points at a distance of 2 nm. If this model is imaged with a resolution of 2 nm, tube-like objects
emerge, since neighboring point images blend with each other (see picture). Note that in the model, the contrasted areas are positively marked (not negative as in the contour line charts!). Analogous models of the single particles have cross-correlation coef7
respect to each other (instead of 0.25-0.3).
ficients of ~ 0 . with
ture in the stained areas or in the region of the light atom
structure is required. The guiding dot concept offers a possibility for this. If guiding dots are arranged at the approximate resolution distance in the negative regions in each
single structure, then on Fourier mapping with 1.5 nm resolution (at which the dots become ~meared‘”~),a tube-like
model of the contrasted structure is obtained. Figure 25
(AV2) shows one section. The models obtained from the
different structures can be correlated with each other, and
a (three-dimensional) correlation coefficient between 0.6
and 0.7 is obtained-a clear indication of how analogous
the structures of the single particles really are. However, it
should be noted that the simplest method of model building (if no large distortions are present) would actually be
an averaging of sufficient single structures-this procedure, however, is very laborious.
Exactly the same analysis was carried out on 50s subunits with the L7, L12 stalk. It can only be referred to as
surprising, how exactly the average structure of four subunits with “stalk” AV3 is in agreement with the average
structure without “stalk” AV2 (Fig. 26)-the correlation
coefficient C, is about 0.5. As Figure 26 shows, the struc-
ture AV4 averaged from AV2 and AV3 (the stalk was cut
out by calculation in these comparisons) is now only a little different from AV2 and AV3. The chemical splitting of
the stalk therefore does not touch the rest of the structure
at all. Incidentally, these two analyses can be interpreted
as an excellent consistency test for the method. We are
concerned with chemically different, electron microscopically different preparations, and-last but not least-analyses in very different defocussing ranges“]. During the
next analysis steps attempts were made to compare
“crowns” and “kidneys” with each other. For the calculations, the tube models were taken because they have a reciprocal space that is filled equally (without blind regions)an important requirement for a good correlation with large
angular differences. The correlation converges very well;
however, only a cross-correlation coefficient of Ck=0.26
could be reached, a clear sign of how much the specimen
[‘I The second analysis was carried out near to the Scherzer focus. The associated decrease in the lower spatial frequencies led to a lowering of the
general contrast of the images.
Angew. Chem. Int. Ed. EngL 22 (1983) 456-485
Fig. 26. Comparison of the average structures of each of four 50s subunits “without L7 and L12 stalks” (AV2) and “with L7 and
L12 stalks” (AV3) (Sections Nos. 36). In AV3, the stalk is mathematically cut off. The reconstruction body of AV3 was later reduced to the size of the reconstruction body of AV2; the correlation coefficient between AV2 and AV3 is =OS. The structure
AV4 averaged from AV2 and AV3 is very similar to AV2 and AV3.
Fig. 27. a) Comparison of the models of the 50s subunit (crown orientation) without stalk [photographed from above (1) and from below (2))
and the 50s subunit (crown orientation) with stalk [photographed from above (4) and from below ( 5 ) ] ; comparison of the model of the
“crown” [without stalk (3)] with the “kidney” [without stalk (6)].Because of the low contrast of the most upper and lower layers, these are not
shown in the model of the kidney. The small and large black points indicate areas where channels penetrate the surface. Regions marked by
large black points correspond to regions in which the RNA, according to earlier conventional pictures (with marking using respective effectors), comes to the surface. b) Schematic representation of the mutual orientations of “kidney” and “crown” (average structures AVI and
AV2, see Figures 25 and 26). AVI shows the orientation of the foil; on turning about the longitudinal axis by 90”,AVl’is obtained. The longitudinal axis of AVI’is tilted by 35” towards the longitudinal axis of AV2. Areas lying above and below are not easily recognizable in the only
weakly contrasted “kidney”, and so have not been shown in the model.
preparation conditions influence the structure. As already
mentioned, one should not speak of the structure of the ribosomes, but of reaction product structures. However, in
spite of this the general deformation is so low that the
shape can be derived from the combination of both results.
Angew. Chem. Int. Ed. Engl. 22 (1983) 456-485
With a reconstruction of crown or kidney alone, the particle borders only partially on the staining material, so that
the determination at the bottom (in respect to the support
foil) and with sandwich preparations (as in our case) at the
top gives difficulties (Fig. 27).
48 1
3.5.3. The Structure of the Uranyl-Contrasted
50s Ribosomal Subunit from E. eoli in Crown Form
From our investigations it is clear that the 50s particle
is especially well imaged structurally, in its crown form. It
lies flat on the base, is well stained, and is easily distinguishable against the staining material. Further, an averaged
structure of 8 particles (AV3) is present, and experiments
have shown that changes in the inner structure of preparations with and without stalk are negligably small. Since the
“accidental” structures of the support foil already averaged out well on the averaging of 8 particles“’, the demarcation “below” and “above” can be well recognized (even
though their confirmation by the kidney structure is very
valuable). Cross-correlation coefficients can then be calculated in different averaging combinations, which agree
well with the statistical expectations. Of particular interest
is the cross-correlation coefficient with the (extrapolated)
averaging structure from “infinitely” many particles,
which is so large with C, = 0.8, that only small differences
are to be expected with respect to the structure, determined
from an infinite number of particles. This means, however,
that practically the same results occur as with a hypothetical “crystal”. The tilt of the particles with respect to the 2direction (about 3-4”) is also considered, which cannot
be corrected in crystal analysis. Figure 28 shows the complete structure of the averaged particles.
3.5.4. Radiation Damage in Ribosomal Particles
In a further analysis, we were more closely concerned
with the problem of the influence of the radiatiodggl.We
had produced a tilting series of 30s subunits with a 3 angular increment, which actually consisted of two 6” series
tilted against one another by 3”. With this it was possible
not only to carry out a reconstruction of larger areas or
with higher resolution, but also to compare both 6” series
(after correction of the tilting), in order to study the influence of the radiation[”’. However, the radiation load of
the second series was much larger than we would normally
tolerate. Actually, a comparison shows changes, the crosscorrelation coefficient has the order of magnitude Ck= 0.7.
The reconstructions show, that on comparison of the tine
details, care must be taken; migration of heavy atoms occurs on irradiation[*]. It is important (and actually to be expected) that the general proportions do not change-disI*]
If the cross-correlation Coefficient for two particles equals Ckand the assumption is made that the particles are only disturbed by “white noise”
(no changing of the general proportions) then the correlation coefficients
can be calculated between the average structure from nl particles, and the
average structure from n2 particles:
If n2 equals infinity, then it follows that
= l / Z
(I thank Dr. R . Henderson, Cambridge, for the reference to these statistical relationships). The quasistatistical behavior was tested by calculation
of different experimental averagings.
tortions are therefore surely caused largely by the specimen preparation. Note, incidentally, that even with this
overloading of radiation the similarity of both structures of
the same particle, which have been loaded differently with
radiation, is larger than with two different particles of the
same orientation.
3.5.5. Pattern Recognition with Consideration of Distortions
These experiments prove that ribosomal 50s particles in
crown form (the same applies for the kidney form) show
the general structural relations-otherwise, on averaging, a
drastic reduction of the resolution would have to occur.
They also explain the jump of the cross-correlation coefficients between single particles, from about 0.25 to about
0.7, if pattern recognition of the first kind (no distortions)
is made (cf. Fig. 25). Of particular value are those results
for the investigations of aperiodic structures, with which
averaging is not possible-it is to be expected that the result can be interpreted in a topologically meaningful way.
The analysis of the 30s structure in different orientations
should become interesting with such kinds of topologically
smoothed models, because the analysis of crowns and kidneys already show clear topological differences. Then, pattern recognition procedures of the second kind have to be
worked out, which-somewhat in analogy to the comparison of different types of handwriting-tolerate distortions,
too. Then, simple averaging processes do not suffice any
4. Outlook
The problems of ribosomal analysis made it especially
clear how valuable the further development of the methods
are (if possible, with automation). What is really interesting is the function. Structural analyses have no use in
themselves but should lead to an understanding of the ribosomal “protein factory”. Therefore, we do not believe
that a single analysis of a native crystal-as important as it
would naturally be-would offer very much for an understanding of ribosomal function. Reactions have to be carried out, and reaction products with small and large partners have to be investigated. Only a born optimist would
hope that all the reaction products would be crystallizabfe.
Actually, conventional ribosomal microscopy already
shows us the way. The reaction products are studied not
only with the preparation reagents, but also with many effectors, The not very helpful two-dimensional methods
have only to be repiaced by three-dimensional analysis. It
is by no means self-evident that the “dirty” ribosomal
“dumplings” have shown defined and reproducible structures on the inside in spite of crude preparation and irraI**]
The total dose after the first series was 9.6 x lo4 e/nm*, after the second
series 20.1 x lo4 e/nm2. But note that in the first case the effective dose
for the imaging is only half as great as the total dose (this applies to all
series without preirradiation), since the partial images come from particles irradiated for different times (in the first picture, actually from
unirradiated particles) (average load 4.3 x lo4 e/nm2). With the second
series this load is about three times as great as in the first series
(14.7 x lo4 e/nm2), because of the pre-irradiation.
Angew. Chem. Int. Ed. Engl. 22 (1983) 456-485
Fig. 28. Almost an “artificial crystal” of the uranyl stained 50s subunit in the crown orientation. The reproducibility of the single particles (dose about
10’ e/nm2) is so excellent that even an averaging of 8 particles yields a correlation coefficient for the (hypothetical) “crystal structure” of C,= 0.8. Averaging of a further arbitrary number of particles would not change the model in any major way. Representation of the structure in 64 layers in the
distance of 0.4 nm; the even-numbered layers from 14 to 52 are imaged (zero line dashed, positive areas with solid lines, negative areas shown with
dots). Positive (negative) contour lines form weak (strong) scattering regions, high positive maxima therefore correspond to especially weakly scattering parts of the structure. The contour line spacing is arbitrary, but the structure corresponds, to a good approximation, to the distribution of potential
in the particles distorted by the influence of the image point. Resolution in the z-direction cu. 2 nm, in the x,y-plane 1.0 to 1.5 nm. Characteristics:
contrasting of different strengths in the single layers, strongest in the middle layers. The particles extend from about layer 20 to layer 46. From layer 22
to layer 44,guiding dots at a spacing of about 2 nm (in the channels) are marked in the negative regions. Their imaging in the 2 nm resolution yields a
tube-like model structure (see Fig. 25). The bottom side of the subunit is relatively planar, with a relatively narrow groove, which does not, however,
cut through the whole particle. Note the strong contrasting in the groove. The more complicated channel structure on the inside, which should correspond, for the greater part, to the ribosomal RNA, is more weakly contrasted. However, one has to be careful on interpretation, since artefacts of
staining can appear (staining variability stronger than radiation-induced variability!). Investigations by other preparative methods are yet to be camed
out. The structure shows several penetration points of the stained channels (A to N) to the surface, whereby according to results with conventional labeling microscopy, C should correspond to the 3‘end of the 23s RNA and G to the 3’ end of the 5s RNA. Note, too, the highly differentiated surface,
which borders the particles and the negative contrasting material.
Angew. Chem. Int. Ed. Engl. 22 (1983) 456-485
diation. They could have been disturbed much more
strongly-even then, it would have been a significant result
that would have had to be accepted.
But, naturally, it is also desirable to study individual organic structures without the “corset” of heavy atom staining. We believe that in this case, investigations at low temperatures (liquid helium) would help further. At room temperature the real structural catastrophies actually develop
secondarily. Bonds become broken, large and small fragments are formed. The small fragments try to break free,
and finally, after a mass reduction of about 40%, a skeleton
remains, which perhaps (given luck) can still show some
relation to the native structure-we do not know.
The experimentally proven advantage of cryomicroscopy is that no mass reduction occurs. We can assume that
on the whole, the low molecular fragments keep their
place, hence, the spatial architecture should survive. At the
moment, there is little sense in speculating on what really
happens. Perhaps the idea of trace structure analysis
(cf. [&I) can be used, and extrapolated to the native original
state. But one can certainly experiment along these lines,
since it is now possible to build high-resolution cryomicroscopes (cf. [231).
A microscope ideal for cryomicroscopy would be one in
which the relative change of direction is produced electronically by the tilting of the primary beam (instead of
tilting the specimen). In this way, no location errors occur,
which necessitate a further determination of the common
origin. This is of importance with low radiation doses, with
which the present correlation methods may fail. Serious
proposals have already been put forward herecg9),and attempts have actually been made at their realization[901.
The enhancement of the resolution down to the atomic
limit has not yet been mentioned-it goes almost without
saying that this will have to be attempted. As this report
tries to demonstrate, if the newly-developed field emission
guns are used, then experimental methodology is no longer
the limiting factor. Admittedly, a great deal of preparative
chemistry (not only in the biological field) remains to be
learnt. However, atomic resolution must be coupled with
three-dimensional analysis. Matter is “porous”, only in
three dimensions-and only then can one also use structural limitations in the analysis, as we had suggested some
Cross-checking in the chemical “sense”
(bond lengths and angles) will facilitate the analysis.
Finally, a remark for contemplation: It is the strong interaction between atoms and electrons which (in principle)
enables the determination of the position of an atom by
the scattering of electrons, in an incredibly short time.
Centuries of measuring time would be needed to reach the
same goal with X-rays. Thus, a great deal of experimental
information is obtainable in a very short time-in contrast
the volume of experimental data obtainable by using even
the most sophisticated X-ray or neutron diffraction analysis is tiny. However, its accomplishment is only possible
with very effective computers. Phase-determining electron
diffractometry is a real child of our computer age.
The long period of 20 years, covered in this report, makes
it impossible to thank all my co-workers personally. More
than 50 diploma and doctoral theses concern our work car484
ried out in the field of electron microscopy-from instrumental techniques to informational theoretical contributions. I
therefore ask to be pardoned if I o n b mention a few collaborators of the last few years: E. Demm. B. Grill, R . Guckenberger, H . Hebert (Cuest from the Karolinska Institute,
Stockholm), R . Hegerl, U. Jakubowski, V. Knauer, G. Nutzel, H . Uttf, H . R . Tietz, I). Typke. With the construction of
an He-cryornicroscope,work will be possible in an important
part of the subject in our laboratory. I thank Dr. I . Dietrich
and her co-workers (Siemens AG, Munich)for their collaboration. I also wish to thank the Deutsche Forschungsgemeinschaji and the Fonds der Chemischen Industrie for financial
Received: January 18, 1983 [A 455 IE]
German version: Angew. Chem. 95 (1983) 465
Translated by K . Duffy and Dr M . Tropschug, Martinsried (Germany)
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