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Chapter 7 Cryoelectron Tomography (CET) 555

work [C

∼ 2, if compared to liquid nitrogen studies (Fujiyoshi, 1998)].

However, the beneﬁ t of liquid helium cooling is still a subject of discus-

sion, especially for cryo-ET, where cells embedded in thick ice layers

are typically used. Unfortunately, the cryoprotection can be determined

quantitatively only by measuring the fading of the electron diffraction

patterns using 2D protein crystals. The transfer of these ﬁ ndings to

frozen-hydrated specimens of, for example, cellular structures, where

in most cases no crystalline arrays are present, remains difﬁ cult and

therefore these values can be regarded as only a rough estimate. More-

over, the experiments made at helium temperature indicate a change

in the density of the vitriﬁ ed ice (after an initial illumination of a couple

of e

−

/Å

), from a low-density amorphous phase at liquid nitrogen tem-

perature to a high-density form at liquid helium temperature, which

could be responsible for the decreased contrast observed at around 9 K

Downing, 2005; Wright, 2006).

Regarding the complexity of the biological system at hand, every

sample material will show a slightly different behavior during the

investigation at low temperatures. High amounts of sugars, for example,

either as ingredients of the buffer solution (DeCarlo et al., 1999) or the

RNA content of the macromolecules, tend to increase the acceptable

dose. Overall it can be said that electron damage at lower temperatures

induces a gradual loss of high-resolution features, much slower than

in room temperature experiments, and a reduced mass loss. However,

at “very high doses” (>500 e

−

/Å

) extensive mass loss, the formation of

bubbles, and various other dimensional changes can be seen in all

cases (Figure 7–10).

Figure 7–10. Electron dose and radiation damage shown for vitriﬁ ed samples. a) Cryo-electron micro-

graph of a ice embedded prokaryotic cell on lacey carbon ﬁ lm exposed to 50 e

−

/Å

. b) The same cell

after an exposure to 500 e

−

/Å

. The adverse effect of increased electron exposure manifest at the carbon

foil and within the cellular structure in the formation of bubbles and furthermore in the smelting of

the ice (Images courtesy of S. Nickell, MPI of Biochemistry, Martinsried, Germany).

(Heide, 1984; Schweikert et al., 2007; Plitzko et al., 2004; Comolli and

556 J.M. Plitzko and W. Baumeister

A second measure among the physical methods to improve the sta-

bility of the sample in the electron beam is the use of intermediate

voltage instruments. The ionization probability is, in a ﬁ rst-order

approximation, inversely proportional to the acceleration voltage. Thus

increasing the acceleration voltage will increase the penetration depth

and thus reduce the inﬂ uence of multiple scattering. Unfortunately,

transmission electron microscopes with, e.g., 1250 kV acceleration

voltage are huge instruments extending over almost three stories of a

regular building. The cost for the instrument and for all subsequent

resources is immense, making it almost impossible to place it in a

normal laboratory environment. Furthermore, the higher the voltage

used the lower the recorded image contrast, which is undesirable in

the case of ice-embedded biological samples, where scattering occurs

mainly from low Z-elements. Therefore, only a few high-voltage EMs

have been built and installed around the world at selected places. It is

more practical to operate EMs in the intermediate voltage range,

between 200 and 400 kV. Instruments with 300-kV guns are the most

common and they represent a good compromise in costs and resulting

performance.

A last measure to reduce the exposure to electron radiation is

the application of so-called “low-dose” acquisition schemes (Dierksen

et al., 1992; Rath and Marko, 1997; see Section 3.4.7). Only during the

time of recording electron micrographs is the electron beam allowed

to illuminate the specimen. In all other cases the beam remains blanked.

Additionally, the microscope can be preset in different states, to reduce

the amount of time needed for changing the magniﬁ cation or the

adjustment of other electron optical parameters, during the process of

screening, focusing, and ﬁ nal image acquisition. It is obvious that this

“low-dose” approach became possible only with the introduction of

computer-controlled instruments with the necessary stability and

reproducibility in the illumination system.

During the acquisition of a tilt series in electron tomography, where

typically 100–200 images are recorded, it is essential that the total

applied dose stays below a critical value, which is given by the speciﬁ c

sample at hand. Most biological materials can tolerate an exposure of

no more than 10 e

−

/Å

to 100 e

−

/Å

, at which point major changes will

have become evident in the structure of the specimen. According to

the dose-fractionation theorem (Hegerl and Hoppe, 1976), the inte-

grated dose of a conventional 2D image is likewise sufﬁ cient for a 3D

reconstruction, if the resolution and the statistical signiﬁ cance between

the two are identical. It is therefore feasible to distribute the total

applied dose among as many statistically “noisy” 2D images as possi-

ble. A total applied dose of 50 e

−

/Å

distributed among 100 2D images

over an angular range would correspond to 0.5 e

−

/Å

per image. Thus

the resulting single images will be of a very noisy quality. Depending

on the detection device utilized the statistical ﬂ uctuations from one

picture element (pixel) to another can be much greater than the inher-

ent change in image intensity from one pixel to another, i.e., the statisti-

cal ﬂ uctuations may exceed the inherent contrast. While the structure

of interest is well preserved, it is impossible to observe the structural

Chapter 7 Cryoelectron Tomography (CET) 557

detail because of the noisy quality of the image, associated with the

very low SNR. Therefore it is very important that the quality and the

performance of the detection device are sufﬁ cient to record images,

even at very low doses (see Section 3.4.5). While the radiation sensitiv-

ity of biological samples restricts the exposure to the electron beam,

the detection device fundamentally limits the resolution of the recorded

tomogram. Investigations on ice-embedded biological samples under

low-dose conditions can literally be described as “cloak-and-dagger

operations” and only by means of appropriate data acquisition schemes

and image analysis methods, i.e., tomographic methods, can the struc-

tural “secret” of the biological entity be disclosed.

3.3 Tilting Geometry

3.3.1 Single-Axis Tilting

The quality of a tomographic reconstruction is furthermore dependent

on the tilting geometry within an electron microscope. In contrast to

computer-assisted tomography (CT), tilting the specimen through the

complete angular regime of 180° within the EM is not possible. For the

collection of a single-axis tilt series, the specimen is typically tilted

around ±70° in very small increments between 0.5° and 3° and an

image of the same object area is recorded for every tilt angle. This

restricted tilt range is due to the limited spacing within the objective

lens polepieces, the slab geometry of the holder, and moreover the

planar geometry of the object itself. At higher tilt angles (e.g., ±90°) the

electron beam is blocked by the holder and eventually by the bars of

the copper grid, depending on the location of the structure within a

mesh of the grid. This angular gap can be nicely illustrated in recipro-

cal space (respectively, Fourier space), where a wedge-shaped “blind”

region is formed, the so-called “missing wedge” (Figure 7–11A).

However, the requirement for a distortion-free 3D reconstruction, all

projections of the sample over the complete tilt range (±90°) (Barnard

et al., 1992), is not fulﬁ lled, thus leading to imperfections in the recon-

structed object. There are mainly two types of distortions that can

be distinguished. First the resolution of the 3D reconstruction will be

direction dependent. The resolution parallel to the tilt axis d

will be

determined by the resolution of the instrument itself. Perpendicular to

the direction of the tilt axis, the resolution d

will be directly related to

the angular increment α

and thus to the number of projections N. The

relationship between resolution d

, increment α

, and the amount of

projections N for a spherical object with diameter D is given by the

Crowther theorem (Hoppe, 1969; Crowther et al., 1970), based on the

projection slice theorem (Radon, 1917):

=⋅π

The reconstruction of a 200 nm-thick cell (assuming that the cell is

spherical), with a resolution of 2 nm, requires 320 projections with an

angular increment of 0.6°. The Crowther expression assumes that the

N projections cover the full angular space of ±90°. Therefore the angular

558 J.M. Plitzko and W. Baumeister

gap has to be included to determine the maximum achievable resolu-

tion in a tomogram, which directly implicates the second type of dis-

tortion that can be observed in ET: features will become elongated in

the direction of the missing wedge. A spherical object, for example, a

gold bead, will be elongated in its 3D reconstruction. This elongation

can be described with the elongation factor e

, which includes the

maximum tilt angle α (Radermacher and Hoppe, 1980):

+⋅

−⋅

ααα

sin cos

The resolution in the third direction d

, the “depth direction,” is there-

fore further degraded to

= d

⋅ e

To provide the maximum amount of 3D information, as many projec-

tions as possible should be acquired over as wide a tilt range as pos-

Figure 7–11. The diagrams show schematically the sectors in the Fourier domain, which remain

unsampled owing to the limited tilt range (here ± 60°). a) In single-axis tilting there is a ‘missing

wedge’. b) In dual-axis tilting a ‘missing pyramid’. The artefacts resulting from the missing informa-

tion are shown below for an ideal thin-walled vesicle. In the single-axis case, the vesicle walls perpen-

dicular to the tilt axis and the poles of the vesicle are poorly represented in the reconstruction. In the

two-axis case, only the poles of the vesicle are affected by the missing information. In both cases, the

same threshold level has been applied.

Chapter 7 Cryoelectron Tomography (CET) 559

sible. In practice the molecular resolution is not limited by the Crowther

criterion but by the structural preservation of the specimen and the

signal recording and the noise (see above). Moreover, the size and the

shape of the recorded object are poorly deﬁ ned, especially in cellular

tomography, where the cellular structure itself consists of objects of

various sizes. However, it remains a useful guide for the expected reso-

lution for a 3D reconstruction.

3.3.2 Dual-Axis Tilting

To reduce the missing information space in single-axis tomography, the

acquisition of a second single-axis tilt series, where the tilt axis is

rotated in-plane by 90°, can offer some remedy. Dual-axis tilting will

reduce the “missing wedge” to a “missing pyramid” and thus increase

the amount of information up to almost 20% (Figure 7–11B). Although

the maximum resolution is not necessarily increased, the achievable

resolution is deﬁ nitely more isotropic. Moreover, structures that are

“hidden” in the single-axis case, because of their orientation relative to

the tilt axis and their location in regard to the missing wedge, will

emerge in a dual-axis acquisition scheme.

However, dual-axis tilting for cryoapplications is demanding in two

ways. First, special cryoholders have to be built, to enable the physical

90° rotation at liquid nitrogen temperatures within the EM (Nickell

et al., 2003; Gatan, Pleasanton, USA). Second, for the 3D reconstruc-

tion both tilt series have to be combined as accurately as possible,

which demands reﬁ ned alignment routines (Penczek et al., 1995;

dual-axis tilt series requires either lowering the dose further or reduc-

ing the number of projections to preserve the structure under inves-

tigation, to comply with the requirements stated above. Dual-axis tilt

cryoholders are now commercially available, which allows either a

discrete or semicontinuous in-plane rotation by 90° (Gatan, Pleasan-

ton, CA). The continuous rotation, implemented in side-entry cryohol-

ders, simpliﬁ es the “tracking” (see Section 3.5.7) at lower magniﬁ cations

of the sample during the in-plane rotation because the sample stays

inside the objective. The discrete rotation is done “outside” the objec-

tive lens system but within the vacuum of the system, making it

sometimes tedious to recenter the region of interest after the in-plane

rotation.

Despite the missing information in Fourier space (wedge or pyramid),

a more fundamental limitation in a tilting experiment within the EM

is the increasing specimen thickness at larger tilt angles. Because of

the planar (slab) geometry of the sample–holder arrangement, the

transmission path of the electrons will increase. Simple geometric cal-

culations show that the transmission path of the electrons for a speci-

men initially 100 nm thick will double at 60° (200 nm), almost triple at

70° (290 nm), and the projected thickness will be increased more than

ﬁ ve times at 80° (590 nm). Thus at very high tilt angles the image con-

trast is dramatically reduced because of the increase in multiple scat-

tering. For specimens with an initial thickness of more than 500 nm the

projected thickness at high tilt angles would even prevent the trans-

Mastronarde, 1997; Nickell et al., 2007). It is clear that acquisition of a

560 J.M. Plitzko and W. Baumeister

mission of electrons in commonly used 300 kV instruments! However,

to preserve the contrast at even higher tilts for imaging thick speci-

mens such as vitriﬁ ed cells, which can easily reach dimensions of a

couple of hundred nanometers, energy ﬁ ltering can offer some remedy

(see Section 3.4.6).

3.4 Instrumentation and Automation

Among the keys to the successful investigation of biological structures

at cryotemperatures and especially for the application of cryo-ET are

certainly the transmission electron microscope (TEM), the preparation

of the specimens (see Section 3.1), and sophisticated acquisition and

automation procedures (see Section 3.4.7). We therefore have dedicated

one section of this chapter to the equipment and the technical improve-

ments made, and to a description of the necessary technical require-

ments for 3D structural analysis with the EM.

3.4.1 Acceleration Voltage and Emission

TEMs are now operated typically in an acceleration voltage regime

between 100 and 1250 kV. With increasing voltage the penetration depth

of the electrons increases, allowing us to image samples a couple of

micrometers thick; at the same time the inelastic cross section is

reduced, thus directly resulting in a longer resistance against beam

damage (Wilson et al., 1992; Martone et al., 1999, 2000; O’Toole et al.,

1999). However, high-voltage EMs are less frequently used for biologi-

cal studies, mainly because of the decreased image contrast due to the

reduced cross section. The gain in penetration power is limited, because

the elastic σ

as well as the inelastic cross section σ

are in a good

approximation proportional to 1/β

(Scherzer, 1970), where β is the

ratio of electron velocity to the velocity of light (β = v/c). Thus, increas-

ing the acceleration voltage from 100 to 300 kV results in an improve-

ment of a factor of 2, while an additional increase from 300 kV to 1.2 MV

will result in only a 1.5 times increase (Koster et al., 1997). As men-

tioned earlier, it is more practical to operate EMs in the intermediate

voltage range, between 200 and 300 kV, because this represents a good

compromise in cost and resulting performance and, additionally, EMs

are available in combination with FEGs.

FEGs were implemented in the late 1980s. Compared to thermionic

emitters FEGs possess several advantages, notably a very small energy

spread, usually in the range of ∼0.8 eV, combined with an increased

brightness. Both properties lead to an improved envelope of the CTF,

since the increased temporal and spatial coherence reduces the

damping of the envelope function (Frank, 1973). This is especially

advantageous for ET of ice-embedded specimens at intermediate

resolution (∼1–2 nm) because a relatively large defocus (several micro-

meters) can be selected without sacriﬁ cing good contrast transfer. FEG

instruments at 200 and 300 kV are today’s “workhorses” in many dif-

ferent laboratories from life and material sciences. But LaB

120-kV

systems are widespread as well and are adequate whenever high

resolution is not of major interest, e.g., for sample screening and

assessment.

Chapter 7 Cryoelectron Tomography (CET) 561

3.4.2 Electron Optics

Like regular light microscopes the EM is built up from three major lens

systems: the condenser, the objective, and the projective lenses.

The performance of these electromagnetic lenses almost exclusively

determines the quality of the recorded image. Most important are the

properties of the objective lens system, likewise known from light

microscopy, especially the value of C

, the spherical aberration coefﬁ -

cient. The objective lens inﬂ uences the transfer of electrons, and

together with the illumination system (FEG or LaB

) and the chosen

focus, is described by the CTF.

The opening in the center of the objective lens system, where the

electron beam passes, affects the magnitude of C

. In simple terms, the

bigger this gap the higher C

, the higher the contrast, but the lower

the resulting resolution. However, the sample holder with the speci-

men is located inside the objective lens system and therefore the gap

dimensions cannot be too small. In particular, to tilt the holder, e.g., for

an angular acquisition, a considerable amount of space is required to

allow tilts to higher angles, or the sample holder has to be designed in

a way to enable tilting even within very small gaps (Fischione Instru-

ments, Inc., Export, PA; Gatan, Inc., Pleasanton, CA). The objective lens

spacing in current EM systems is in the range of a couple of millime-

ters, thus resulting in C

values from 0.7 mm (lowest) up to 6 mm

(highest). For life science applications typically objectives with a C

of ∼2 mm are used, because they offer enough space for tilting the

specimen and at the same time the possibility of recording high-

resolution images.

Ongoing instrumental improvements include, for example, the use

of C

correctors, which, especially in materials science, already revealed

new possibilities and real image improvement (Haider et al., 1998;

Lentzen et al., 2002; Jia et al., 2003; Freitag et al., 2005). However, in

biological EM we have to cope with very weak scatterers and so, for

reasonable image contrast, we have to defocus in the range of a couple

of micrometers even for very thin objects. Since this low-frequency

information is essential for cryo-EM investigations, the advantage of

correction is almost canceled (Plitzko et al., 2005). However, there is

reason to believe that C

correctors might be beneﬁ cial for biological

EM and especially cryo-EM if used in combination with phase plates

(Unwin, 1972; Danev and Nagayama, 2001; Majorovits and Schroeder,

2002; Lentzen, 2004; Marko, 2004).

Another important fact is the change in the direction and angle of

the tilting axis at different magniﬁ cations due to a rotation of the image

within the electron optics of the microscope. Previously this change

was obvious at every magniﬁ cation step. It is now partly compensated

by so-called “rotation-free lens series,” which guarantee an almost

“ﬁ xed” (in angle and direction) tilt axis in distinct magniﬁ cation ranges.

This is crucial, especially in low-dose acquisition schemes, where a fast

transition and reproducible change between states (see Section 3.4.7)

and sample areas at different magniﬁ cations are necessary, e.g., in

dual-axis experiments to reposition the area of interest after the in-

plane rotation.

562 J.M. Plitzko and W. Baumeister

3.4.3 Tilting Device: Goniometer Tilt Stage

As already mentioned, tilting the holder inside the microscope is a

fundamental requirement for ET. The tilting device, normally located

outside the EM column, is called the goniometer tilt stage and in some

instances the “compustage,” because of its power to be controlled by

computers. However, tilting is now done in an exclusively mechanical

way, thus resulting in a major practical difﬁ culty: the mechanical

imperfections and the inability to set the eucentric height of the speci-

men precisely. The eucentric plane is normal to the optic axis; this way

a point on the optic axis should not move laterally when tilted around

the holder axis. As a result, specimens can experience signiﬁ cant shifts

in the x, y, and z directions during the course of angular acquisition.

Shifts in the z direction cause severe focus changes, and in an uncor-

rected case, complicate the 3D reconstruction or even render a recon-

struction meaningless.

Typically, side entry holders are used—at the rear part of which a

small Dewar for liquid nitrogen is located (Figure 7–12). The Dewar is

connected to a temperature conduction rod, transferring the tempera-

ture of ∼180°C to the specimen mounted at the outermost end of the

holder tip. The cryoholder, almost 30 cm in length, is tilted by the goni-

ometer around its vertical axis. It is easy to imagine that tilting must

be very inaccurate. Especially at high tilt angles above ±45° imprecise

tilting will add up to displacements in the micrometer range. However,

at a resolution of 10 Å a tolerable deviation would be in the range of 3 Å,

thus resulting in a discrepancy of three to four orders of magnitude

between the desired resolution and the actual precision of the tilting

device. The best current stages can tilt and move the sample within an

accuracy of 0.5 µm. To partially compensate for the still large displace-

ments, automation is mandatory during the acquisition of a tilt series

composed typically out of 100 micrographs. Therefore sophisticated

acquisition and correction schemes have been developed, to keep the

feature of interest at all times focused and centered (see Section 3.4.7).

Figure 7–12. Photographs of a standard side entry cryo-holder (Model 626 Gatan, Pleasanton, CA,

USA). a) The holder is almost 30 cm in length and equipped with a nitrogen dewar in the back. b)

Images of the tip of the holder with open (top) and closed ‘shutter’ (bottom). The stationary cryoshield

(‘shutter’) protects the grid from mechanical damage and from frost accumulation during transfer

from the specimen loading workstation (not shown) into the TEM.

Chapter 7 Cryoelectron Tomography (CET) 563

Developments have already been made to test and implement piezo-

controlled stages into the EM environment to allow nanopositioning

in the order of ∼1 nm, which might enable accuracy during tomo-

graphic acquisition to be improved dramatically (Lengweiler et al.,

2004; JEOL Ltd., Tokyo, Japan).

3.4.4 Cooling System

Since all investigations in cryo-EM have to be made under cryo condi-

tions, i.e., under constant cooling with liquid nitrogen, special holders

and/or special cryostages have to be designed. Typically, side entry

holders are used—ﬁ tted with a small Dewar for liquid nitrogen (Gatan

Inc., Pleasanton, CA). The requirements for mechanical and tempera-

ture stability are severe and it is quite clear that the dimensions of the

holder tip must be smaller than the polepiece gap of the objective.

Moreover, special cryoshields have to be installed to guarantee

contamination-free investigations. They are seated next to the tip of

the holder inside the microscope and connected to the cooling trap of

the microscope for constant cooling with liquid nitrogen.

Side-entry cryoholders are routinely used, but recently stages incor-

porating the cooling system within the electron microscope have been

designed (“Polara” Tecnai F30 by FEI Company, Eindhoven, Nether-

lands, and Jeol 3200FSC by JEOL Ltd., Tokyo, Japan). By including the

cooling system for the sample holder into the microscope the mechani-

cal stability and the temperature stability of the holder are improved

enormously, and additionally these systems allow cooling to very low

temperatures, even to liquid helium temperature (∼10 K). Furthermore

the temperature can be kept stable over longer time periods; instead

of hours in the side-entry case, days or even weeks are now possible.

Moreover the stages designed for these cooling systems can hold

several samples, unlike the side-entry holder where only one individ-

ual sample can be mounted at a time (Figure 7–13). Additionally, pro-

totypes have been developed and tested holding up to 100 different

samples, to enable high-throughput applications in the future (Gatan

Inc., Pleasanton, CA). The exchange of samples is faster and the transfer

of the samples to the microscope is done under vacuum conditions, to

minimize the chance of contamination.

3.4.5 Detector

Temperature and mechanical stability of the stages, holders, and goni-

ometers as well as the overall performance of the electron optics are

crucial for high-resolution data acquisition, however, the quality of the

detector system used is of vital importance, especially in cryoapplica-

tions under low-dose conditions (Downing and Hendrickson, 1999;

Fan and Ellisman, 2000). Previously photographic plates were utilized,

making a fast assessment of the collected data impossible; however,

today microscopes are equipped with TV rate systems and digital

cameras (Krivanek and Mooney, 1993; Faruqi and Subramanian, 2000),

so-called CCD cameras (Janesick, 2001). With the help of the CCD

camera it is possible to easily calculate online the Fourier transforma-

tion of the image, for example, to determine the focus or to readjust the

microscope, e.g., astigmatism and coma correction. In principle they

564 J.M. Plitzko and W. Baumeister

are built up from a scintillator (either a single crystal or a polycrystal-

line coating), “decelerating” the electrons and thus creating photons

by cathodoluminescence. The scintillator is coupled to a ﬁ ber optic

array, which will transfer the light optical signal to the CCD sensor,

which is built up from a series of metal oxide semiconductor (MOS)

capacitors, where the light induces the creation of electron hole pairs

in the active area.

CCD cameras are now available in dimensions between 1024 × 1024

and 4096 × 4096 pixels with a pixel size ranging from 15 to 30 µm. Thus

they are still smaller than the typical photographic plate dimensions

(∼10,000 × 8000 pixels assuming a pixel size of 10 µm for a typical plate).

However, CCDs possess an excellent linearity and a large dynamic

range [i.e., ratio between maximum signal and the root mean square

(RMS) of the noise level]. Because of the excellent linearity the intensity

distribution of the recorded image is directly proportional to the

number of primary electrons hitting the detection device. However, the

lateral resolution is worse than in photographic plates, because of the

signal spreading within the whole CCD assembly. This spreading is

mainly caused by multiple light scattering of the photons created and

by electron backscattering within the scintillator. Thus a point-like

input signal produces an output that is spread over several pixels of

the CCD chip. In real space this will result in a “blurring” of the

recorded image, which is similar to a Gaussian smoothing of the image.

In Fourier space it can be observed as a damping of the high spatial

frequencies. The extent of this spread can be quantitatively analyzed

by inspection of the modulation transfer function (MTF), which is the

Fourier transform of the point spread function (PSF), to measure the

spatial frequency response (Weickenmeier et al., 1995; Ruijter, 1995).

Figure 7–13. Multispec-

imen chamber and car-

tridges for the Polara

Te c n a i F3 0 (F EI c om p a ny,

lands). a) The multi-

allows the storage of up

to 6 samples, which are

samples are clamped or

screwed into cartridges

(insets) and the transfer

is done under cryo- and

vacuum conditions.

Eindhoven, The Nether-

specimen chamber

nary cryoshields. b) The

of the complete system

all protected by statio-