LIST OF SYMBOLS FOR CHAPTER 2

λ wavelength V accelerating potential / atomic scattering factor for X rays fe atomic scattering factor for electrons D magnitude of reciprocal space vector t crystallite thickness Ν number of atoms in unit cell

60

Chapter 2

Electron Diffraction

Despite its potential advantages over X-ray diffraction, very little use has been made of electron diffraction in studies of conformation in fibrous proteins. Low-angle patterns have been recorded from protein specimens containing heavy atoms (Mahl and Weitsch, 1960; Murray and Ferrier, 1968; Ferrier, 1969; Glaeser and Thomas, 1969; Dobb, 1970) but these have been inferior to diffraction patterns obtained with X rays. This may be attributed to rapid deterioration of the specimen through radiation damage and it seems likely that the patterns which have been recorded are attributable to the heavy-atom framework rather than the protein.

In a recent study of the problem (Tulloch, 1971) it has been demon­strated, however, that with appropriate precautions both low- and high-angle diffraction patterns can be recorded from a wide variety of fibrous proteins without heavy-atom staining. This being so, the inherent advantages of electron diffraction, which stem mainly from the very small specimen volumes required, are likely to be increasingly exploited in future studies. In diffraction patterns obtained with X rays the arcs in fiber patterns result from the superposition of reflections from a large number of individual crystallites with a distribution of orientations. Because the irradiated volume is so much smaller in the case of electrons, an appreciable sharpening of the pattern would be expected in favorable cases and this is in fact realized (Fig. 2.1).

Excellent general accounts of the theory and technique of electron diffraction are available (Heidenreich, 1964; Vainshtein, 1964; Alderson and Halliday, 1965; Cowley, 1968; Rymer, 1970) and in the present

61

62 2. ELECTRON DIFFRACTION

FIG. 2.1. Examples of electron diffraction patterns obtained from fibrous protein specimens (Tulloch, 1971). (a) High-angle pattern obtained from a longitudinal section about 800 A in thickness cut from silk gut (Bombyx mori). (b) Tactoid of oyster muscle tropomyosin stained with uranyl acetate. The banding pattern has a period of about 380 A. (c) Low-angle pattern obtained from (b). The central diffuse scatter in the diffraction patterns is due to inelastically scattered electrons.

A. THEORY OF ELECTRON DIFFRACTION

I. INTERACTION OF ELECTRONS WITH MATTER

a. Wavelength

It is the wave character of electrons which leads to the phenomenon of electron diffraction by matter and the wavelength associated with a moving electron is a function of its velocity. For a beam accelerated through a potential Vy measured in volts, the wavelength, in angstroms, is given by

λ = 12.27(F + 0.978-10"6F2)-1 /2 (2.1)

chapter attention will be restricted to aspects that are relevant to studies of fibrous proteins.

A. THEORY OF ELECTRON DIFFRACTION 63

With an accelerating potential of 100 kV, for example, the wavelength given by Eq. (2.1) is 0.037 A. This is very much smaller than the wave­lengths commonly employed in X-ray studies and the sphere of reflec­tion (Chapter 1, Section A.I.c) has a correspondingly greater radius. The collection of diffraction data from fiber patterns is thus greatly simplified since specimen tilting (Chapter 1, Section B.IV.a) is generally unnecessary. b. Elastic and Inelastic Scattering

An electron beam is modified during its passage through a specimen by both elastic and inelastic interactions. Electrons that suffer inelastic collisions undergo a change in velocity, and energy is transferred to the specimen. The velocity change involves a change in wavelength and hence destroys the potentiality for producing interference effects with the electrons that emerge with unmodified velocities.

Electrons that only undergo elastic collisions emerge from the specimen with unmodified velocities and are capable of producing diffraction patterns similar to those obtained with monochromatic electromagnetic radiation. The inelastically scattered electrons give rise to an intense background which is concentrated in the forward direction and decreases with scattering angle (Fig. 2.1).

The cross sections of atoms for elastic and inelastic scattering are of the same order of magnitude and both decrease with increasing accelerating potential. It is generally believed that the ratio of elastic to inelastic cross section increases with increasing accelerating potential, so that the proportion of diffuse scatter is reduced as the potential is increased (Heidenreich, 1964).

The ratio of elastically to inelastically scattered electrons emerging from a specimen depends on the accelerating potential and on the nature and thickness of the specimen. An illustrative example is shown in Fig. 2.2 (Crick and Misell, 1971), where the calculated ratios at 100 kV for simulated protein specimens of different thicknesses are compared. The proportion of elastically scattered electrons rises to a maximum at a thickness of about 750 A and then decreases slowly with increasing thickness. In contrast the proportion of inelastically scattered electrons shows a monotonic increase with thickness. The maximum in the curve for elastic scattering is very broad and a specimen with half the optimum thickness gives 0.83 of the maximum yield. When specimen thickness can be controlled accurately there are advantages in working at thick­nesses somewhat less than that for the maximum yield of elastically scattered electrons, since a significant improvement in the elastic/inelas­tic ratio (Fig. 2.2) can be obtained with very little sacrifice in yield.

64 2. ELECTRON DIFFRACTION

1.0

500 1000 1500 2000

ο Thickness (A)

FIG. 2.2. Comparison of the proportions of elastically and inelastically scattered electrons from a carbon specimen irradiated with 100-keV electrons. Calculated for a density of 1.3 g c m

-3 from the data given by Crick and Misell (1971).

The nature of the background produced by inelastically scattered electrons varies with specimen thickness as the half-width of the angular distribution increases with increasing specimen thickness (Crick and Misell, 1971).

c. Radiation Damage

The cross sections of atoms for inelastic scattering of electrons are several orders of magnitude greater than those for X rays and structural changes take place very rapidly in organic materials under the usual conditions of observation in the electron microscope (Stenn and Bahr, 1970). In addition to damage by heating, the electron bombardment induces ionization and radical formation and these are believed to be the chief causes of structural changes within the specimen. According to Breedlove and Trammell (1970) the cross section for ionization decreases less rapidly with accelerating potential than the cross section for elastic scattering. It might be concluded that a reduction in acceler­ating potential would enable more useful information to be obtained from a specimen before it was destroyed. According to other authors,

A. THEORY OF ELECTRON DIFFRACTION 65

however, the reverse is true (Kobayashi and Sakaoku, 1965; Thomas et al, 1970; Parsons, 1970).

Quantitative measurements on poly(ethylene) show that the lattice spacings in this material change as the radiation dose increases (Fischer, 1964) and similar effects are to be expected in other polymers. Insofar as heating is involved in structural changes during irradiation, the provision of facilities for cooling the specimen should prolong the useful life of the specimen (Watanabe et al, 1960; Tulloch, 1971).

II. ELASTIC SCATTERING

a. Atomic Scattering Factors

The periodic distribution of electrical potential in a crystal produces diffraction effects in the elastically scattered electrons which are super­ficially similar to those produced by the electron density distribution on a beam of X rays (Chapter 1, Section A.I).

For most purposes a point-atom approximation is sufficient and an atomic scattering factor for electrons / e is used which is related to the atomic scattering factor / f o r X rays by the expression (MacGillavry and Rieck, 1962)

fe(D) = 0.095736[Z - /(Z))]/D2, D Φ 0 (2.2)

where D is the magnitude of the reciprocal space vector D (Chapter 1, Section A.I.c) and Ζ is the atomic number. This expression applies to neutral, isolated atoms and considerable changes in the effective value of fe are brought about, particularly for small values of D, by ionization and chemical bonding. Values of / e have been tabulated by Doyle and Turner (1968). The modifications to fe that result from chemical bonding have been investigated by Harada and Kashiwase (1962).

For values of D < 0.5 A - 1 the values of/ e for C, N, and Ο atoms are in reverse order to the factors for X rays. Also, the disparity between the scattering factors for Η atoms and those for C, N, and Ο atoms is less marked than for X rays. When computing the Fourier transform of the electron density distribution of model structures for comparison with observed X-ray patterns the contribution of Η atoms is usually ignored, but when computing the Fourier transform of the electrical potential the Η atoms cannot be ignored.

b. The Kinematic Approximation

In Chapter 1 X-ray diffraction was interpreted on the basis of a single-scattering approximation in which it was assumed that a scattered beam could pass through the crystallite without further interaction. The

66 2. ELECTRON DIFFRACTION

cross section of atoms for X-ray scattering with λ ~ 1.5 A and the dimensions of crystallites in molecular crystals are such that this approxi­mation is usually valid, but this is not generally true for electron diffrac­tion. The cross section of atoms for elastic scattering of electrons is sufficiently great that multiple scattering must be taken into account. The intensity distribution in the diffraction pattern of a material in which appreciable multiple scattering has occurred within a single crystallite is virtually uninterpretable in the case of unit cells as large as those found in fibrous proteins and it is only when diffraction patterns are obtained under conditions where the effects of multiple scattering may be neglected that they are likely to be of value for structure analysis. Under these conditions the so-called kinematic approximation is valid and the interpretation of intensities closely follows that given for X rays in Chapter 1 except that p(d) represents electrical potential rather than electron density (Vainshtein, 1964).

The prediction of the conditions under which the kinematic theory of scattering is valid is extremely difficult. According to Vainshtein (1964) an estimate of the value of the crystallite dimension parallel to the beam at which the kinematic approximation breaks down, in the case of unstained biological materials, is given by

t ~ 10 VN/X (2.3)

where Ν is the number of atoms in the unit cell and λ is given by Eq. (2.1). The transition from kinematic to dynamic scattering with increasing crystallite size is not uniform over the diffraction pattern and occurs first at low angles. From Eq. (2.3) it follows that an increase in acceler­ating potential or an increase in complexity of the structure favors kinematic scattering.

The complexity of fibrous protein structures and their poor crystal-Unity favor kinematic scattering and it is likely that the approximation will be valid in many cases for these materials. However, the expression given in Eq. (2.3), which is based on a gross oversimplification of the problem, can only be regarded as yielding an order of magnitude for the thickness at which the kinematic approximation breaks down.

B. E X P E R I M E N T A L T E C H N I Q U E S

I . DIFFRACTION EQUIPMENT

Most modern electron microscopes provide facilities for electron diffraction studies but the requirements for recording the fine detail

Β. EXPERIMENTAL TECHNIQUES 67

present in the rather weak diffraction patterns yielded by fibrous proteins are fairly stringent, and desirable features of the microscope are summarized in the present section.

The optimum specimen thickness with regard to the yield of elas­tically scattered electrons (Fig. 2.2) increases with accelerating potential. Provision for operation up to 100 kV or greater facilitates the preparation of specimens of optimum thickness over areas several microns square.

Various electron optical arrangements have been used for diffraction studies and their relative merits have been discussed by Ferrier (1969). The most generally useful method for fibrous proteins is the selected-area microdiffraction mode in which provision is made for visual selec­tion of the specimen area to be irradiated. The area is usually delineated by means of an aperture in the object plane of the intermediate lens. The selection of the area must of course be performed at very low intensity to avoid, as far as possible, damage to the specimen. Photo­graphic recording of the image of the irradiated area for survey purposes presents no problems since this may be done subsequent to the recording of the diffraction pattern.

In order to provide adequate separation of orders in specimens with axial periods up to about 1000 A, an effective camera length of several meters is required when operating at 100 kV. A goniometer stage is required to tilt the specimen so as to bring the required portion of reciprocal space into the reflecting position (Chapter 1, Section A.I.c), and facilities must be provided to orient the specimen relative to aniso-diametric selecting apertures.

Since specimen heating plays some part in radiation damage (Stenn and Bahr, 1970), a specimen cooling device may be advantageous but the extent of reduction in damage which may be achieved by this method has not been evaluated quantitatively.

II. SPECIMEN PREPARATION

Methods of preparing fibrous protein specimens for examination by electron diffraction are essentially similar to those used for transmission electron microscopy (Chapter 3) except that additional precautions must usually be observed if the native conformation is to be preserved. Provided that suitable embedding methods can be devised, it has been found (Tulloch, 1971) that the most generally useful method is sec­tioning (Glauert and Phillips, 1965) while in suitable cases mechanical cleavage and disintegration may be used. Care is needed when ultrasonic disintegration is used in order to avoid cellulosic contamination (Mill-

68 2. ELECTRON DIFFRACTION

ward, 1969). Other methods, which have been used with synthetic polypeptides, include the preparation of collapsed surface films (Mal­colm, 1968a,c, 1970) and thin single crystals (Keith et aL, 1969a,b; Padden et aL, 1969) and the stretching of cast films (Parsons and Martius, 1964; Vainshtein and Tatarinova, 1967a).

In order to avoid scattering by a supporting medium, it is convenient to use perforated plastic films (Fukami and Adachi, 1965; Bradley, 1965a) in which the hole sizes are a few microns in diameter.

As with other biological materials, the crystallinity of fibrous proteins is usually adversely affected by drying and the dehydration which occurs in the electron microscope is thus undesirable. Various attempts have been made to overcome this problem by the use of special chambers in which a moist environment can be maintained around the specimen (Stoyanova and Mikhailovskii, 1959; Dupouy et aL, 1960; Parsons, 1968, 1970). These have not so far been used routinely and the advantage gained must be weighed against the added specimen damage caused by reaction with radicals created by the interaction between the electron beam and the water.

III. PROCESSING OF OBSERVED DATA

The processing of photographically recorded electron diffraction patterns follows similar lines to those for X-ray diffraction patterns (Chapter 1). The response of photographic emulsions to electrons is such that optical density is proportional to exposure over a useful range (Valentine, 1966) but multiple exposures are usually necessary to encompass the wide range of intensities present in a single diffraction pattern.

The effective camera length is usually determined experimentally by recording the diffraction pattern of a calibrating substance (Alderson and Halliday, 1965; Ferrier, 1969). Sometimes it is convenient to evapo­rate a material such as gold or thallous chloride directly on to the specimen. The image of the specimen and the image of the diffraction pattern are rotated about the beam by different amounts during the imaging process and if they are to be correlated the extent of this differ­ence must also be determined experimentally.

As mentioned earlier, the inelastically scattered electrons give rise to a background which decreases with increasing scattering angle. This is particularly troublesome when intensity measurements are to be made in a radial direction as the required profile is superimposed on a rapidly varying background.

C. SUMMARY 69

C. SUMMARY

Electron diffraction studies have considerable potential in the deter­mination of conformation in fibrous proteins. The main advantage over X-ray diffraction is the very much greater atomic scattering cross section so that the optimum thickness for specimens is of the order of a few hundred angstroms with 100-keV electrons. Coupled with the fact that selected areas of about 0.001 X 0.001 mm at the specimen can be used, the possibility arises of obtaining much higher degrees of orientation over volumes of these dimensions, with a corresponding improvement in the resolution of fine detail in the diffraction pattern. Other advantages are the very short photographic exposures required and the large radius of the sphere of reflection. Dynamical effects, which generally complicate the interpretation of intensities in electron diffrac­tion patterns, are unlikely to be troublesome in the case of most fibrous protein specimens. When extensive crystallites of considerable perfection are encountered, for example, in certain insect silks (Chapter 13), condi­tions must be chosen to reduce dynamical effects to a minimum.

The main difficulties to be overcome relate to the very rapid destruc­tion of conformation which occurs during irradiation. The development of high-resolution image intensifiers should materially assist in this regard. The requirements for specimen preparation are more stringent than with X-ray diffraction because the background due to inelastically scattered electrons increases with specimen thickness and soon becomes objectionably strong. The development of energy analyzers capable of simultaneous two-dimensional operation would be of assistance in over­coming this problem. The presently available raster-scan analyzers are of limited value due to the relatively large dose of radiation received by the specimen during the scanning process.