LIST OF SYMBOLS FOR CHAPTER 3

η order of Bessel function / Miller index ρ density of scattering material σ density of scattering material in #-axis projection of ρ xy y, ζ Cartesian coordinates in specimen Xy Yy Ζ Cartesian coordinates in reciprocal space Ry φ9 Ζ cylindrical polar coordinates in reciprocal space F Fourier transform Gn χ complex number describing contribution of Bessel

function terms of order η to the /th layer line gntl Fourier component of scattering density

70

Chapter 3

Electron Microscopy

At the present time electron microscopy is the only method available which offers the prospect of imaging fibrous protein molecules directly. Excellent accounts of the technique are available (Heidenreich, 1964; Kay, 1965; Slayter, 1969; Cosslett, 1971; Huxley and Klug, 1971) and in the present chapter attention will be restricted to the potentialities and limitations in the study of fibrous proteins. To date, transmission electron microscopy has provided information on the morphology of protein molecules, on their mode of aggregation, and on the distribution of chemical reactivity in the molecule. The instrumental resolution of many present-day electron microscopes is about 2 A when operated under ideal conditions but a number of factors preclude the realization of this limit with proteins and other biological materials. The main difficulties relate to contrast, to radiation damage, and to dehydration.

A. CONTRAST

If a protein molecule is to be visualized, some form of contrast must be present between the image of the molecule and the image of its immediate surroundings. If the angular distributions of electrons scattered by the molecule and its surroundings are sufficiently different, adequate contrast can be introduced by inserting a limiting aperture in the back focal plane of the objective lens. In this way true amplitude contrast is obtained and when the image is accurately focused detail may be interpreted directly, except near the limit of resolution where

71

72 3. ELECTRON MICROSCOPY

lens aberrations introduce phase contrast effects (Heidenreich, 1964; Erickson and Klug, 1971; Hanszen, 1971).

Unfortunately, the differences in density and composition between different parts of an assembly of fibrous protein molecules will not, in general, be sufficient to produce a useful amplitude contrast and artificial methods of increasing the contrast between a molecule and its sur­roundings must be used. This may take the form of a selective deposition of atoms of high atomic number leading to pronounced differences between the angular distributions of the electrons in beams which emerge from different parts of the specimen. This necessity of using artificial means of enhancing contrast with the ever-present possibility of artefactual changes in the specimen is the major shortcoming of electron microscopy as applied to protein structure. A second difficulty, which is partly philosophical, is that the information obtained relates to the heavy-atom distribution and only indirectly to the protein.

Additional contrast may also be obtained by defocusing the image so that phase contrast effects are introduced. Underfocus contrast enhance­ment is employed widely in the examination of biological specimens but care is necessary to avoid the introduction of spurious detail into the image (Ruska, 1966; Thon, 1966a,b; Sjostrand, 1967; Haydon, 1968, 1969; Erickson and Klug, 1971). Erickson and Klug (1971) have made a quantitative study of the problem and formulated criteria for selecting the optimum degree of underfocus.

Another method of enhancing contrast, applicable to specimens with periodic structures, is to deflect the electron beam so that a particular diffracted beam passes along the optical axis of the microscope and to exclude the main beam by a suitably chosen objective aperture (Heiden­reich, 1964; Glaeser and Thomas, 1969). The diffracting object or objects then appear bright while the remainder of the specimen is dark. This technique of dark-field imaging is potentially valuable for studying the distribution of regular conformation in fibrous protein struc­tures.

Several methods of dark-field imaging applicable to aperiodic struc­tures have been described. The central beam of undeflected electrons may be removed by means of a "contrast stop" (Dupouy et al, 1966; Johnson and Parsons, 1969) or by tilting the beam so that the undeflected electrons do not enter the objective aperture (Heidenreich, 1964). In an alternative method an annular condenser aperture is used and the diameter of the objective aperture is chosen so as to exclude unscattered electrons (Hall, 1948; Dupouy et al, 1969; Dubochet et al, 1971).

Dark-field electron microscopy has been used to image individual biological macromolecules (Ottensmeyer, 1969; Dubochet et al, 1971)

C. SPECIMEN PREPARATION 73

but the information obtainable is severely limited by the granular background arising from inhomogeneities in the supporting membrane.

B. RADIATION DAMAGE

The damage caused to organic materials by irradiation with electrons was discussed briefly in Chapter 2 (Section A.I.c). The available evidence (Glaeser and Thomas, 1969; Stenn and Bahr, 1970) suggests that the native conformation of a protein molecule is completely destroyed under the conditions normally used to obtain transmission electron micro­graphs. The local disordering of the protein chains presumably also disrupts the local distribution of heavy-atom stains used to enhance contrast and explains why no interpretable detail is visible below a resolution of around 10-20 A.

The loss of native conformation is accompanied by the disappearance of the high-angle diffraction pattern, which thus provides a useful check on the extent of radiation damage. It has been shown (Tulloch, 1971) that under favorable conditions electron micrographs can be obtained with preservation of the high-angle pattern and in these cases the detail can be interpreted in terms of the native conformation. An incidental advantage of routine monitoring of the high-angle diffraction pattern is that damage due to fixation, staining, or sectioning can also be detected.

Radiation damage can be reduced by the use of image intensifiers but with currently available equipment some loss of resolution is usually entailed.

C. SPECIMEN PREPARATION

Methods available for the preparation of specimens for transmission electron microscopy include sectioning (Glauert and Phillips, 1965; Sjostrand, 1967), mechanical disintegration, and various means of mounting particulate specimens (Bradley, 1965b; Slayter, 1969; Dubochet et al., 1971). Enhancement of contrast can be achieved by shadow casting and positive or negative staining with heavy atoms (Bradley, 1965c; Glauert, 1965; Home, 1956a,b; Slayter, 1969).

Shadow casting provides an important means of studying the morphology of individual molecules but the resolution attainable is limited by the grain size of the evaporated metal. With present methods this places a limitation of about 20 A on this technique. A further limitation is due to surface irregularities in the supporting film but these may be overcome, albeit with some difficulty, by the use of a

74 3. ELECTRON MICROSCOPY

shadow-transfer technique devised by Hall (1956). Particles to be examined are applied as aerosols to freshly cleaved mica, which is extremely smooth, and the shadowed film is transferred to a supporting medium.

Staining for negative contrast also provides information about the morphology of molecules and aggregates of molecules and has proved particularly valuable in the study of filamentous structures from muscle (Huxley, 1963; Moore et al, 1970) and from keratins (Whitmore, 1972). Under suitable conditions the granularity in the stain can be reduced to a very low level and background due to inhomogeneities in the supporting film becomes noticeable. This can be eliminated by using perforated carbon films (Huxley and Zubay, 1960).

Shadow casting and the use of negative contrast have proved to be useful methods of investigating the morphology of fibrous protein molecules and assemblies. Positive staining, as a probe of the detailed internal structure of protein molecules, has proved, except in certain isolated cases, to be largely unsuccessful. This appears to be due to the difficulty of attaching sufficient concentrations of heavy atoms to produce significant contrast. Silver, mercury, and uranyl salts, osmium tetroxide, and phosphotungstates have all been used as positive stains for various fibrous proteins but the precise nature of the binding mechanism is unknown and it seems likely that part of the observed effect may be due to negative rather than positive contrast effects.

D. INTERPRETATION OF MICROGRAPHS

Much of the value of electron microscopy as a tool for the investigation of the structure of fibrous proteins depends upon the interpretation of fine detail in the image and a discussion of the many factors involved would be beyond the scope of the present treatment. Estimates of the resolution attainable in practice with biological specimens vary from 10 to 20 A and valuable accounts of the requirements for realizing this limit have been given by Heidenreich (1964), Ruska (1966), and Hay don (1968, 1969).

The information contained in an electron micrograph can frequently be transformed into a more useful form by means of optical or computer processing and useful reviews have been given by Klug (1971), Nathan (1971), Home and Markham (1972), Klug and Crowther (1972), Lake (1972a), Ottensmeyer et al (1972) and Thompson (1972). Aspects of inter­pretation that are of special interest in the study of fibrous proteins are discussed in the following sections.

D. INTERPRETATION OF MICROGRAPHS 75

I. LINEAR MEASUREMENTS

The accuracy of length measurement attainable using the electron microscope is extremely poor due to the combination of a number of factors. Instrumental calibration is difficult and an accuracy of ± 5 % is probably all that is generally achieved. In addition, specimen dimensions undergo changes during fixation, embedding, staining, and irradiation. These changes may be small but their direction and magnitude cannot be assessed without reference to some other technique such as X-ray diffraction. Measurements of dimensions based on shadow casting are also subject to systematic errors which must be determined empirically (Hall, 1960; Slayter, 1969). Rowe and Rowe (1970) have considered the relationship between the distribution of shadow shapes and the shape of the shadowed object.

II. PARAMETERS OF PERIODIC STRUCTURES

Klug and Berger (1964) pointed out that the optical diffraction pattern of an electron micrograph provides a convenient means of analyzing periodicities in the image. These patterns can readily be obtained using an optical diffractometer and the procedure is described in Chapter 4. By means of the theory outlined in Chapter 1 the optical diffraction pattern can be used to identify the line or space group to which the periodic structure belongs and to estimate the values of the helical or unit cell parameters (see, for example, Klug and Berger, 1964; Hitchborn and Hills, 1967; Miller, 1968; Markham, 1968; Berger, 1969; Sternlieb and Berger, 1969; Burton, 1970; Lake and Slayter, 1970; Moore et aL, 1970; Champness, 1971; Mikhailov, 1971).

Elliott et aL (1968b) have described the use of a convolution camera (Hosemann and Bagchi, 1962) for the analysis of periodicities in electron micrographs. The camera produces a Patterson-like function and thus in general complicates rather than simplifies interpretation of periodici­ties. It was claimed that the convolution camera was capable of revealing periodicities which could not be detected by the optical diffraction method of Klug and Berger (1964).

III. IMAGE AVERAGING

Electron micrographs of regular structures such as helices or crystals are in general poor representations of the original material, due, first, to various types of distortion introduced during the preparation and recording of the image and, second, to a combination of irregular staining and various types of damage which causes originally like volumes to be modified in a random fashion. These random differences

76 3. ELECTRON MICROSCOPY

can be regarded as noise and McLachlan (1958) pointed out that by combining a number of images of originally like volumes, reinforcement of genuine detail would occur while the noise would tend to average out.

This principle has been applied to micrographs of a variety of bio­logical materials (Fraser et al.y 1962b; Markham et al.y 1963, 1964; Valentine, 1964; Hitchborn and Hills, 1967; Labaw and Rossmann, 1969; Burton, 1970; Fraser and Millward, 1970; Erickson and Klug, 1971).

Markham et al. (1963) have described a method of averaging applicable to objects with rotational symmetry, and this was later elaborated by Crowther and Amos (1971). The method is useful when the symmetry is known, but attempts to determine the symmetry by this means are fraught with difficulty (Agrawal et al.y 1965; Norman, 1966; Frisch, 1969; Friedman, 1970).

When translational periodicities are present in a micrograph an averaged image of the repeating unit can be obtained by superposing a number of images (McLachlan, 1958). In the procedure described by Markham et al. (1964) a mechanical device was used to photograph an electron micrograph. Multiple exposures were made on a single sheet of film and the micrograph was translated a distance equal to the period between each exposure. The method is laborious, however, and requires an independent series of experiments to determine the direction and magnitude of the periodicity. Warren and Hicks (1971) have described an alternative method, employing multiple light sources, that enables the averaged image to be viewed directly.

Finch et al. (1967) showed that a reduction in noise in micrographs of periodic objects could be obtained by filtering the optical diffraction pattern of the micrograph, and techniques for obtaining a number of different types of averaged image by this means have been described by Fraser and Millward (1970). The advantages of the optical diffraction method are its flexibility and the fact that the magnitude and directions of periodicities do not need to be determined explicitly. Techniques used to obtain and filter optical diffraction patterns of electron micro­graphs are described in Chapter 4.

Although optical processing of images is simple, it is difficult to make it completely quantitative and the technique is gradually being replaced by exact numerical processing of digitized data obtained from the micrograph with a scanning microdensitometer. An important advantage of the latter method is that both the magnitude and the phase of the Fourier transform are readily available. The phase information is particularly valuable for assessing the degree of preservation of sym­metric structures and for locating symmetry axes (Finch and Klug, 1971; Klug, 1971).

D. INTERPRETATION OF MICROGRAPHS 77

IV. THREE-DIMENSIONAL RECONSTRUCTION

The depth of field in the electron microscope is such that all the axial levels in the specimen are in focus at the final image and the super­position of detail at various levels complicates interpretation. With filaments having helical symmetry some resolution of the detail at the upper and lower levels can be obtained by filtering an optical diffraction pattern of the micrograph (Klug and DeRosier, 1966). The method is based on the fact that when a discontinuous helix is projected onto a plane parallel to its axis the distribution of projected points in the vicinity of the projected axis resembles that of two superimposed two-dimensional lattices, one corresponding to the "front" of the helix and the other corresponding to the "back" of the helix. If the helical param­eters of the filament are known, the (—η, I) plot (Fig. 1.14) can be used to predict regions in the optical diffraction pattern which contain contributions primarily from, say, the "front" of the filament. If these are isolated by filtering and are recombined using the methods outlined in Chapter 4, the resulting image will be freed from overlapping detail originating from the "back" of the filament.

Although this type of image processing has proved useful in a number of instances (Klug and DeRosier, 1966; Kiselev et aL, 1968; Kiselev and Klug, 1969), the method is open to the criticism that subjective decisions are required, and an incorrect choice of helical parameters produces an erroneous result which is not readily recognizable as such.

A more sophisticated and objective method, capable of providing a complete three-dimensional reconstruction of the scattering density in a specimen, has been described by DeRosier and Klug (1968). The method exploits the fact that a transmission electron micrograph is essentially a projection of the scattering density in the direction of the optical axis of the microscope. A series of such projections, obtained with varying orientations of the specimen, contains information about the three-dimensional distribution of scattering density and two methods for extracting this information have been described.

In the so-called algebraic reconstruction technique (Gordon et aL, 1970; Frieder and Herman, 1971; Herman and Rowland, 1971) optical density data from projections taken over a limited range of angles are used to construct a set of linear equations involving the scattering power at a grid of points throughout the specimen. These equations are then used as a basis for reconstructing the three-dimensional distribution of scattering power. The reliability of the result is difficult to assess (Crowther and Klug, 1971) and for the present, at least, methods based on a completely representative series of projections (Crowther et aL,

78 3. ELECTRON MICROSCOPY

1970a,b; DeRosier and Moore, 1970; Crowther, 1971; Gilbert, 1972a,b) would appear to be more generally useful.

The algebraic reconstruction method relates the optical density data directly to the distribution of scattering density but the inversion property of the Fourier transform (Chapter 1, Section A.I.f) can usefully be employed in this procedure (DeRosier and Klug, 1968). If the scattering density ρ in an object is referred to a set of Cartesian coordi­nates x, yy and ζ with the χ axis parallel to the optical axis of the micro­scope, the projected density a(yy z)y which can be derived from a transmission micrograph, is given by

σ( yy *) = j p(x> yyz) dx (3.1)

The Fourier transform of the object (Chapter 1, Section A.I.g) is given by

F(Xy YyZ)= j jj P(xy yy z) exp[2m(Xx + Yy + Zz)] dx dy dz (3.2) object

and it follows from Eq. (3.1) that

F(0y YyZ)= jj a(yy z) exp[2wi(Fv + Zz)] dy dz (3.3) projection

Thus the value of the Fourier transform over the plane X = 0 can be evaluated by numerical integration from the χ axis projection by means of Eq. (3.3).

Each different projection of the object yields information about a plane in the Fourier transform which passes through the point X = Υ = Ζ = 0 (a central section) and by a suitable choice of the number and directions of different projections the Fourier transform can be mapped to any required degree of accuracy (Crowther et al.y 1970a,b). The density of scattering matter at any point in the object is then given by

P(xy yy z) = J J J F{Xy Yy Ζ) β χ ρ [ - 2 π ί ( Λ * + Yy + Zz)] dX dY dZ transform /n . x

(3.4)

In practice Eq. (3.4) is replaced by a summation over a series of elements of constant volume 8V =8X8Y8Z and the appropriate value of F must be obtained by interpolation from the measured point values.

In the case of helical structures a single micrograph contains a series of projections of the repeating unit at equispaced azimuths around the

Ε. SUMMARY 79

helix axis and such structures are particularly suited to the technique of three-dimensional reconstruction. A simplified procedure can be used (DeRosier and Moore, 1970) based on the theory of diffraction by helices (Chapter 1, Section A.III.d). If only one Bessel function contrib­utes to each layer line in the Fourier transform of a helix, Eq. (1.30) becomes

F(R, φ, l/c) = GnJ(R) exp[ffi(0 + \π)} (3.5)

where GnJ is defined in Eq. (1.31). Application of Eq. (3.3) yields information about the Fourier transform

over the half-planes φ = 0 (Y > 0) and φ = π (Υ < 0) and two estimates of GnJ can be obtained given by

Gntl(R) = F(Ry 0, l/c) exp( - ιηπ/2) (3.6)

Gntl(R) = F(Ry π , l/c) exp(iwr/2) (3.7)

The reconstruction is performed by using the inverse Fourier-Bessel transformation (Klug et al.y 1958)

p(ry φ,ζ) =Σ gn,i(r) exp{*[w<£ - (Inlz/c)]} (3.8)

ι

where

gn,i(r) = 2π j Gntl(R) ]n{l7rRr)R dR (3.9) layer line

This method has been applied successfully to the reconstruction of F-actin filaments (Chapter 15). The resolution attainable is limited by the restriction that measurements of F must be limited to a range of R for which only one Bessel function contributes to each layer line. Gilbert (1972a,b) has described an equivalent "direct" method, and Lake (1972b) has extended the Fourier method to sectioned helical structures.

E. SUMMARY

At present the method of transmission electron microscopy cannot be applied directly to fibrous protein specimens because the contrast between different portions of the specimen is too low. A second limitation is the very rapid deterioration of the specimen due to damage by the electron beam. A number of means are available for increasing specimen contrast by the addition of heavy atoms. In certain cases the heavy-atom

80 3. ELECTRON MICROSCOPY

deposits are sufficiently stable to the electron beam for micrographs to be recorded, even though the protein is disorganized. When used in conjunction with image-averaging and three-dimensional reconstruction techniques micrographs so obtained provide information about the morphology and the mode of aggregation of fibrous proteins.

The accuracy of the method with respect to the measurement of linear dimensions is inherently low and the presently achieved resolution (of the heavy-atom deposits) is probably only about 10 A even in the most favorable cases.