Low-dose thickness measurement of glucose-embedded protein crystals by electron energy loss spectroscopy and STEM dark-field imaging

Ultramicroscopy North-Holland

ultramicroscopy

52 (1993) 157-166

Low-dose thickness measurement of glucose-embedded protein crystals by electron energy loss spectroscopy and STEM dark-field imaging Richard D. Leapman a, Jaap Brink b and Wah Chiu b a Biomedical Engineering and Instrumentation Program, National Center for Research

Resources, National Institutes of Health, Bethesda, MD 20892, USA b Verna and Marrs McLean Department of Biochemistry and The WM. Keck Center for Computational Biology, Baylor College of Medicine, One Baylor Plaza, Houston, TX 77030, USA Received

8 March

1993; in final form 2 August

1993

Electron energy loss spectroscopy and dark-field imaging in a scanning transmission electron microscope were used to determine the thickness of glucose-embedded crotoxin complex crystals. The results demonstrate the feasibility of identifying protein crystals with a thickness of half a unit cell (12.8 nm) under low-dose and low-temperature conditions. The accuracy of this method is limited by the amount of surface coating of the crystal’s embedding glucose used for preserving the high-resolution structure of the protein. The histogram of the crystal thickness distribution and the spread of the anticipated crystal thickness allow us to make an estimate of the uncertainty in the glucose layer thickness. This approach can be incorporated as part of the experimental procedure in the three-dimensional data collection for structure determination of protein crystals with variable thicknesses. The measurement can be done on areas approximately 200 nm in diameter so that crystals of suitable thickness can be pre-selected before the high-resolution data is recorded. Accurate determination of the crystal thickness will optimize the data collection efficiency by avoiding the collection and subsequent analysis of unmatchable data for the three-dimensional reconstruction.

1. Introduction

In three-dimensional structure determination of macromolecules by electron crystallography it is necessary to combine diffraction patterns and images recorded at various tilt angles [l]. In order to merge these data sets successfully all the crystals should have the same thickness. The data processing procedure for protein crystals with variable thicknesses is not a trivial task because the high resolution three-dimensional data are inevitably obtained from different crystals as governed by radiation damage. To reduce the task of matching data from crystals with the same thickness, we are developing an experimental scheme to obtain as many tilt diffraction data as possible from single crystals within the constraints of radiation damage [21. Furthermore, it is highly desir0304-3991/93/$06.00

0 1993 - Elsevier

Science

Publishers

able to characterize the crystal thickness prior to diffraction and image data collection to avoid the acquisition of a large amount of data from crystals with non-identical thicknesses, which cannot be merged. It has been shown that parallel electron energy loss spectroscopy (EELS) is useful for assessing the thickness of a beam-sensitive organic crystal [3]. Parallel detection of the energy loss spectrum in this application is essential in that it makes the most efficient use of the signal as first demonstrated experimentally by Shuman [4]. The thickness estimate can be achieved by measuring the fraction of the total transmitted electrons that do not lose energy, i.e., the zero-loss intensity [51. Results recently obtained from nparaffin crystals have shown that it is feasible to determine the number of unit cell layers under low-electron-dose conditions [3]. Our aim here is

B.V. All rights reserved

158

R.D. Leapman

et al. / EELS

thickness measurement

to investigate the EELS approach further by applying it to glucose-embedded crotoxin complex crystals typically used for the electron crystallographic analysis [6-81. We will also show how the mass thickness measurements obtained using the annular elastic dark-field signal can be adapted to map the thickness distribution of the crotoxin complex crystals. Since radiation damage can influence the reliability of the measurements, we have evaluated its effect at - 160°C.

of crotoxin crystal

for electron fluxes greater than 1000 counts per element of the spectrometer’s 1024-channel photodiode array [13]. The probe current was obtained by integrating the total signal in the lowloss spectrum and multiplying by a conversion factor of 40 incident electrons per photodiode count.

3. Results 3.1. EELS measurements

2. Experimental

methods

and analysis

Crotoxin complex was purified and crystallized as previously described [6]. Specimens were prepared by placing a suspension of crotoxin complex crystals mixed with a 1% glucose solution on a holey carbon support film on 3 mm copper grids covered with a thin carbon film. The grids were blotted and allowed to dry before transferring them to a VG Microscopes HB501 scanning transmission electron microscope (STEM) equipped with a field-emission source and operating at an accelerating voltage of 100 kV [9]. The specimens were cooled to - 160°C in order to minimize radiation damage and were searched at an electron dose rate of < 0.1 e nme2 ss’ (= 10-3 e A-2 s-1 > in the dark-field mode at an electron-optical magnification of 5000 X . Selected images of 512 X 512 pixels that contained thin crystals were recorded with a probe current of - 1 pA. The YAG annular dark-field detector collected scattering angles from approximately 20 to 60 mrad. Single pulses originating from an optically coupled photomultiplier were discriminated, amplified and fed into a fast counter. Images were acquired with a 486 IBM PC-compatible computer [lo] and subsequently transferred to an Apple Macintosh II for processing with the image analysis program, IMAGE [ill. EELS spectra were acquired by means of a Gatan model 666 parallel-detection spectrometer especially modified for ultra-high vacuum compatibility with the HB501 STEM [12], and were processed with the Gatan EL/P program also running on the Apple Macintosh II. The detective quantum efficiency has been shown to exceed 0.1

The crotoxin complex has a molecular weight of 24000 Da and forms tetragonal crystals containing eight molecules per unit cell [6]. The unit cell parameters are a = b = 3.88 nm, and c = 25.6 nm, giving a dry protein density of 0.828 g/cm’ and a mass per unit area of 12750 Da/nm’ for a crystal one unit cell thick. A low-magnification dark-field STEM micrograph of typical glucoseembedded crotoxin complex crystals with different thicknesses is shown in fig. la, which was recorded at a dose of - 10 e/rim’. In addition to glucose being incorporated into the crotoxin complex a thin surface coating of glucose is also likely to surround the crystal, as indicated in the schematic cross sectional diagram in fig. lb. Variations in this surface layer are expected to result in some uncertainties in the crystal thickness determination. EELS spectra were collected at a resolution of around 0.6 eV from 0.5 pm diameter regions and also from the neighboring supporting carbon film as illustrated in fig. 2. Usually, more than one spectrum was obtained from a single crystal and each of these was recorded with a dose of less than lo2 e/nm2. The spectra are dominated by a broad plasmon maximum at - 24 eV; weak peaks at - 6.5 eV were also evident which could be attributed to rr + r* transitions in the protein. The specimen thickness can be determined from the electron energy loss spectrum by measuring the fraction of the transmitted electrons that have not suffered any inelastic scattering [3,14]. If I, is the integrated zero-loss intensity intensity in the and Itot is the total integrated energy loss spectrum, then the specimen thick-

R.D. Leapman

et al. / EELS

thickness measurement

of crotoxin crystal

159

Fig. 1. (a) Dark-field STEM micrograph of glucose-embedded crotoxin complex crystals recorded at 100 keV beam energy with electron dose of y lo2 e/nm2; (b) schematic cross-sectional diagram of specimen showing crystal (C) embedded in glucose (G) supported on carbon film (F).

ness, mean

t, is given in terms free path, hi, by,

t/4 = Wt,,/Zz).

of the

total

inelastic

(1)

The inelastic mean free path can be expressed in terms of the inelastic scattering cross section per molecule, ci, (2)

with 12 the number of molecules per unit volume. It can also be written in terms of the crystal density, p, and the cross section per unit mass, vi/m,

as,

Ai= [p(a,/m)]

-‘.

(3)

Based on an analysis of over one hundred protein crystals [15], the solvent content of cro-

160

R.D. Leapman et al. / EELS thickness measurement

6 S S a, u.

of crotoxin

14

-

12

-

10

;

8t 64

-

2

-

0

f. 0

..I h

toxin complex crystals is likely to be in the range of 40%-50% [6]. If we assume that the embedded crotoxin complex crystals contain 40% glucose by weight, then the crystal has a total density of p = 1.38 g/cm”. Taking previous calculations of the cross section per unit mass of 1.11 X lo-” nm2/Da and 1.08 X lop5 nm2/Da for protein and glucose, respectively, based on optical data and dielectric theory [14,161, we obtain a value of Aj = 109 f 10 nm for the inelastic mean free path in glucose-embedded crotoxin complex crystals at 100 keV beam energy. It has been observed that the crotoxin complex crystal may be formed with different thicknesses with the thinnest possible being 6.4 nm, corresponding to a l/4 unit cell [61. One can therefore expect to see crystal thicknesses at integral multiples of t/Ai of 0.06 (equivalent to l/4 unit cell) if no additional thickness is being contributed from the embedding glucose. A total of 97 measurements of t/A, obtained from 28 glucose-embedded crotoxin complex crystals are presented as a histogram in fig. 3. These crystals were selected according to their appearance of being thin in the dark-field search mode. it is seen from the histogram that 60% of the crystals have a thickness less than or equal to one unit cell with the data falling into two main peaks. This may reflect a tendency for formation

..~, h

1kJ-k 0.1

Energy Loss (eV)

Fig. 2. Parallel EELS spectra from 500 nm diameter area of glucose-embedded crotoxin complex crystal (labeled as A) and carbon support film (labeled as B) recorded at electron dose of - 10’ e/nm2. Zero-loss peak is off scale to show plasmon more clearly. Dashed line shows extrapolation of zero-loss peak. This crystal had thickness t = 0.23 hi after correction for supporting carbon film, which has thickness of - 7 nm.

crystal

0.2

0.3

0.4

0.5

Relative Thickness

(ffh,)

.,.. i

0.6

Fig. 3. Histogram of 97 EELS thickness determinations of twenty eight thin glucose-embedded crotoxin complex crystals in terms of t/A,.

of crystals with thicknesses at half-unit-cell increments which is also evident from the values of t/hi listed in table 1. The remaining values of t/Ai corresponded to crystals with thicknesses in the range 3/2 to 5/2 unit cells. The observation that the peaks are not distributed distinctly at integral multiples of t/hi of 0.06 can be explained by the variable amount of embedding glucose coating the crystals. In fig. 3 the smallest observed t/A, value is 0.12 suggesting a glucose coating thickness of 6 nm if the thinnest crystal had a thickness of l/4 unit cell. Alternatively, these measured values can be interpreted as cor-

Table 1 Frequency of thickness measurements lying in ranges of t/h, corresponding to different numbers of “quarter unit cells” for 28 crotoxin crystals after correction for carbon support film Thickness (“quarter unit cells”)

Range

of

0.06-O. 12 0.12-0.18 0.18-0.24 0.24-0.30 0.30-0.36 0.36-0.42 0.42-0.48 0.48-0.54 0.54-0.60 0.60-0.66

t/hi

Frequency

(0) 28

(8) 24 (7) 4 (1) 11 (3) 9

Odd-multiples of quarter unit cells are shown in parentheses. It is assumed that the glucose coating ranges in thickness from zero to t/h, = 0.06.

R.D. Leapman et al. / EELS thickness measurement

responding to crystals of half a unit cell thickness with a negligible glucose surface coating. A rough value for the glucose thickness can be estimated as t/Ai = 0.05 from the observed widths of the peaks in the histogram. The frequency of occurrence of crystals at intervals of t/Ai = 0.06 (l/4 unit cell) can be extracted from fig. 3 and is summarized in the right-hand column of table 1. In this tabulation, we. have assumed that the thickness of glucose surface coating can range from t/h, = 0 to 0.06 for all crystals. In order to assess the effect of radiation damage on the thickness measurements we have obtained EELS spectra as a function of electron dose from crystals cooled down to - 160°C. The electron dose on the specimen was controlled by varying the dose rate and the duration of the exposure. The dose rate was varied by changing the size of the rastered area on the specimen and at low magnification the probe was defocused to N 50 nm to ensure uniform irradiation of the scanned area. Since the dose rate used was less than lo3 e nm-* s-i, we did not expect that the damage would be dose rate dependent in accordance with previously studied biological systems [17,18]. After correction for the carbon film, which was estimated to be 8 f 1 nm assuming a Ai for carbon of 100 nm, the fractional decrease in thickness was determined as a function of irradiation exposure (fig. 4). The mass loss at high dose reaches a value of approximately 40% asymptotically with a l/e damage dose of about 2 x lo4 e/nm2. An exponential curve with this decay constant fits the experimental measurements and is also consistent with the fractional decrease in dark-field intensity with increasing dose. This critical dose, associated here with mass loss, is larger than that required for obtaining high-resolution structural data, which is typically < lo3 e/rim2 [19]. Apparently degradation of the structure occurs at a lower dose than is the case for loss of protein mass [17]. This result is consistent with the statistical treatment of low-dose EELS spectra recorded with parallel detection from nparaffin crystals [3]. In order to have sufficient statistics in the spectrum and minimal mass loss at a recording dose of N lo3 e/rim*, it is reasonable to expect that one can obtain a thickness

161

of crotoxin crystal

5

10

Dose(104e/rim*) Fig. 4. Fractional mass-loss of glucose-embedded crotoxin complex crystals at - 160°C as function of electron dose. At high electron dose of approximately 2 X lo4 e/nm’ up to = 40% mass loss occurs. Open circles are EELS measurements and solid circles are dark-field measurements.

measurement in diameter.

from a crystal area of 0.1-0.2 pm

3.2. Dark-field measurements It is well established that elastic scattering can also provide a precise means for determining specimen mass [20,21]. There are several ways in which the elastic data can be recorded. One approach is simply to measure the attenuation of the transmitted beam. This method is most suitable for thicker specimens where there is a large difference between the incident and unscattered intensities [22]. In an alternative approach, the scattered dark-field signal can be measured. This can be achieved most efficiently in the STEM [231, which has been applied successfully to mapping the weights of macromolecules [24]. Absolute mass measurements with the dark-field detector, however, requires knowledge of the incident beam current and the exact collection geometry of the detector. In practice, the dark-field mass calibration can most easily be performed by employing a standard. For example, tobacco mosaic virus particles are commonly used in STEM molecular weight measurements [24]. Thus, if we know the mass of one feature in a dark-field image we also know the masses of all the other features. In the present application we have used

R.D. Leapman et al. / EELS thickness measurement of crotoxin crystal

162

the concurrent EELS thickness measurement to provide this mass calibration. For very thin specimens the dark-field signal is directly proportional to the thickness, but for the multiple unit cell layers of the crotoxin complex crystal considered here, this assumption is not quite valid. If the elastic mean free path is A,, then the dark-field intensity, I, is given by, I =A[1 - exp( -t/A.)],

(4)

where A is a constant. The dark-field intensity can also be expressed as a function of the EELS relative thickness parameter, t/hi, I =A[1

- exp( -kt/Ai)],

(5)

where k = hi/A, is the ratio of inelastic to elastic mean free paths. In fig. 5 we plot experimental measurements of the variation of I with t/hi for a number of glucose-embedded crotoxin complex

Relatwe Thickness

(t/h,)

Fig. 5. Plot of dark-field counts obtained from glucose-embedded crotoxin complex crystals as function of relative specimen thickness (t/Ai) at 100 keV beam energy showing departure from linearity for crystal thicknesses greater than 1.5 unit cells (t/h, > 0.36).

crystals. The theoretical curve which is obtained by assuming a k-value of 0.56 for protein [25,261 agrees well with the experimental data. This good

d 0

Fig. 6. Dark-field images and intensity histograms of glucose-embedded crotoxin complex crystals recorded at an electron dose < 10’ e/rim’; (a) area containing crystals with 0.5, 1.5 and 2 unit cells, (b) area containing crystals with thicknesses equivalent to 2.5 and 3.5 unit cells. Cc, d) Histogram peak assignments fin half-unit cells) corresponding to images of (a and b) are made from EELS calibration and after correction for non-linearity of dark-field signal (see table 2).

163

R.D. Leapman et al. / EELS thickness measurement of crotoxin crystal Table 2 Comparison of thickness determination by inelastic calibrated with EELS measurements in the crystals Area

t/Ai

Image 1 Carbon film Crystal 1 Crystal 2 Crystal 3

0.077 0.171 0.425 0.576

Image 2 Film Crystal 4 Crystal 5

0.072 + 0.005 0.680 f 0.005 0.875 f 0.005

a) b, ‘) d,

+ f f f

0.005 0.005 0.005 0.005

and elastic indicated)

scattering

in two images

of crotoxin

crystals

(dark-field

No. half unit cells from EELS

DF signal a) (arbitrary units)

Corrected (arbitrary

0 1 c, 3 4

12.1*0.1 27.2+0.2 52.5 f 0.2 65.2 k 0.2

12.4&0.1 28.9 k 0.2 59.4 f 0.2 76.3 + 0.2

0 1.03 2.94 4 d,

0 5 7

8.2kO.l 60.4+0.2 73.9+0.2

8.4kO.l 72.6 + 0.2 93.5 + 0.2

0 5.28 7 d’

DF signal b, units)

signal was

No. half unit cells from DF

Abbreviation: DF = dark-field. Non-linearity of dark-field signal was corrected by means of eq. (6). Some mass-loss due to higher dose in this area. Dark-field images were calibrated from EELS t/hi measurements in these areas.

match confirms that it is indeed necessary to make a correction for non-linearity of the darkfield signal for specimen thicknesses larger than _ 30 nm. From eq. (5) we can obtain a corrected darkfield signal that is proportional to the specimen thickness if we calibrate by measuring the relative thickness tca,/Ai of a given feature in the image with a pixel intensity Ical. The choice of feature for the calibration is arbitrary but there is some advantage in selecting a thicker crystal (two or three unit cells) to minimize the fractional error in t/Ai. The corrected dark-field signal, I’, is given by, Z’=Z_, ln[(l -aZ/l,,,))‘]/~,

(6)

first processed by nearest-neighbor smoothing, and the intensity histograms in figs. 6c and 6d were obtained as indicated for the regions shown in figs. 6a and 6b. EELS measurements of t/hi from these indicated regions yield thicknesses of 2 unit cells and 3.5 unit cells, respectively (see table 2). The pixel intensities associated with the different peaks were then corrected for non-linearity of the dark-field signal so that assignment of the crystal thicknesses could be made. As is evident in table 2 the thicknesses obtained from the dark-field images are in agreement with the values obtained from the EELS measurements.

4. Discussion

where a = 1 - exp( - kt,,,/hi)

.

The thickness of glucose-embedded crotoxin complex crystals was obtained by quantifying image arrays of 512 X 512 pixels recorded at low dose, as shown for two typical specimen areas (figs. 6a and 6b). Quantification is most easily achieved by generating intensity histograms and by using EELS measurements as a calibration in order to assign the peaks in the intensity histogram in terms of the number of half unit cells (figs. 6c and 6d). The 512 X 512-pixel images were

Protein electron crystallography has allowed the visualization of the polypeptide backbone [27]. Crotoxin complex is one of several soluble proteins that have been crystallized and found to diffract beyond 0.2 nm [6,7,28]. Its structure has not yet been solved because of a number of relatively difficult technical problems such as choice of embedding medium with respect to the specimen flatness, crystal thickness variation, structural motif variation across a large patch of crystal, sampling requirements for three-dimensional data collection and choice of data collec-

164

R.D. Leapman et al. / EELS thickness measurement

tion strategies. Some of these problems have been identified and gradually overcome [8,29-311. In this investigation, we address the problem of how to determine the thickness of the glucoseembedded crotoxin complex crystal in conjunction with the other electron crystallographic measurements, so that we can confidently merge three-dimensional data from different crystals. A preferred procedure would involve pre-screening the crystals in terms of their thickness prior to the data collection in order to avoid the acquisition of a large amount of data that would not be immediately useful for computer reconstruction. Our previous observations have shown that the crotoxin complex crystals have different thicknesses, but a given crystal generally has a uniform thickness [61. Since crystals are usually 2 pm or longer on edge as shown in fig. 1, it is reasonable to sacrifice a small region (e.g. 0.2 X 0.2 pm2) of the crystal for the thickness measurement before collecting image or diffraction data. It is well known that EELS provides a highly sensitive and reliable technique for thickness determination and here we have demonstrated that it can adequately characterize the glucose-embedded crotoxin complex crystals under the low-dose condition. By considering the crystal parameters and the scattering cross sections, we have been able to estimate the inelastic mean free path of the glucose-embedded crotoxin complex crystal as 109 nm for a beam energy of 100 keV. Though this value is not based on a direct experimental measurement, its accuracy should be better than 10%. This value allowed us to make numerical calculation of the crystal’s thickness from the EELS measurements by means of eq. (1). Since the counting statistics in the EELS spectrum are sufficiently high even in our low-dose condition, the measurement errors should not exceed a few percent [3]. The greatest source of error in this determination lies in the uncertain amount of the surface coating and/or protein-embedding glucose. However, in our measurements, we have observed the spread in t/h, from the expected values to be around 0.05 (fig. 3) which happens to be equivalent to a quarter unit cell of the crystal. Therefore, although we cannot precisely assign the crystal thickness to the nearest quarter unit

ofcrotoxin

crystal

cell, we can confidently determine it to the nearest half unit cell. Since protein crystals are radiation sensitive, their mass thickness may be affected by beam damage. We conducted all our measurements at low temperature, i.e. - 160°C to minimize the damage effects [18]. The results from the damage series showed that the electron dose used to record EELS spectra or dark-field images is well below the critical dose normally associated with fading of diffraction spots (fig. 4). The radiation phenomena were also consistent with those observed previously in other biological systems studied at low temperature. Although our current feasibility study was performed in the dedicated STEM, such measurements could also be made in the conventional TEM. The electron energy loss spectra would then be collected in the so-called “image mode” with an image of the crystal at the spectrometer entrance aperture rather than a diffraction pattern as in the case of the STEM. The crystal to be analyzed could either be selected by the spectrometer entrance aperture situated just below the microscope viewing screen or by a low-intensity beam focused on the specimen. The alternative procedure for determining the crystal thickness by annular dark-field STEM imaging has the important advantage of providing fast two-dimensional mapping of the crystal thickness with minimal radiation exposure of the specimen. However, some means of calibrating the intensities and correcting for non-linearities must be employed. We have shown how such corrections can be achieved by EELS measurements in selected areas of the specimen. Application of the darkfield imaging in the present context would, of course, require the TEM to be equipped with a STEM accessory.

5. Conclusion Electron energy loss spectroscopy and darkfield imaging provide useful methods for determining the thickness of glucose-embedded crotoxin complex crystals which have a c axis unit cell spacing of 25.6 nm. Such information is im-

R.D. Leapman et al. / EELS thickness measurement of crotoxin crystal

portant for deciding which crystals are suitable for data collection and for merging with data obtained from other crystals in the process of a high-resolution structure determination. Despite some spread in measurements from the same crystal thickness due to a variation in the glucose layer, it is possible to deduce the crystal thickness with an uncertainty within a quarter unit cell. We are very much encouraged with the present results demonstrating the feasibility of identifying crystals as thin as a half unit cell. Since our strategic plan is to determine the structure of the crotoxin complex from the most commonly found thin crystals, the half unit cell crystal is the most suited for the high-resolution structural studies. This particular crystal thickness will minimize the number of tilt pictures and therefore the concern of multiple scattering. In practice, we will coordinate the data from the thickness measurement of a crystal with the symmetry properties derived from the electron diffraction intensities of the same crystal in the untilted position. Both these measurements will help to alleviate the crystal thickness uncertainty and allow the effort to be concentrated on other technical aspects of this project. Electron crystallographic studies are performed in the transmission electron microscope rather than in the STEM that is employed in the present work. Recent results using a 1024 X 1024pixel slow-scan CCD (charge couple device) camera have shown the feasibility of recording more than 100 electron diffraction patterns from a single crystal of glucose-embedded crotoxin complex in a high-resolution 400 keV cryomicroscope [2]. To measure the crystal thickness by EELS it would therefore be desirable to incorporate an electron energy loss spectrometer combined with a large-array slow-scan CCD camera [32] in such an intermediate voltage electron cryomicroscope. In this arrangement the camera serves as a twodimensional parallel detector for spectroscopic measurements and also as an electronic recording device for high-resolution energy-filtered images. The inelastic mean free path increases approximately three-fold as the beam energy is raised from 100 to 400 keV so that a quarter unit cell of crotoxin complex has a t/h, value of only 0.02.

165

Under these conditions the high intensity of the zero-loss peak relative to the plasmon would necessitate spectral deconvolution by the detector point spread function to remove the zero-loss tail produced by spreading of electrons and light in the scintillator [33]. After this correction is applied sufficient signal should still be available to measure the crotoxin crystal thickness with an uncertainty of a quarter unit cell. Acknowledgments

We would like to thank J.A. Hunt for developing the digital imaging software system that was used in this work. This research has been supported partially by grant RR02250 from the National Institutes of Health and by the W.M. Keck Foundation. References [ll L.A. Amos, R. Henderson and P.N.T. Unwin, Prog. Biophys. Mol. Biol. 39 (1982) 183. [2] J. Brink and W. Chiu, in: Proc. 10th Eur. Congr. on Electron Microscopy, Granada, Spain, Eds. L. MegiasMegias, M.I. Rodriguez-Garcia, A. Rios and J.M. Aria (Seer. Publ. Universidad de Granada, Granada, 1992) p. 15. [3] P. Rez, W. Chiu, J.K. Weiss and J. Brink, J. Microsc. Res. Tech. 21 (1992) 166. [4] H. Shuman, Ultramicroscopy 6 (1981) 163. [5] R.F. Egerton, Electron Energy Loss Spectroscopy in the Electron Microscope (Plenum Press, New York, 1986) p. 229. [61 T.-W. Jeng and W. Chiu, J. Mol. Biol. 164 (1983) 329. [7] T.-W. Jeng, W. Chiu, F. Zemlin and E. Zeitler, J. Mol. Biol. 175 (1984) 93. [81 J. Brink, W. Chiu and M. Dougherty, Ultramicroscopy 46 (1992) 229. [9] R.D. Leapman and S.B. Andrews, J. Microscopy 161 (1991) 3. [lo] J.A. Hunt and D.B. Williams, Ultramicroscopy 38 (1991) 47. [ill R.R. O’Neill, L.U. Mitchell, C.R. Merril and W.S. Rasband, Appl. Theor. Electrophoresis 1 (1989) 163. 1121 O.L. Krivanek, C.C. Ahn and R.B. Keeney, Ultramicroscopy 22 (1987) 103. [13] O.L. Krivanek, J.H. Paterson and H.R. Poppa, in: Proc. 47th Annual EMSA Meeting, Ed. G.W. Bailey (San Francisco Press, San Francisco, 1989) p. 410. [14] R.D. Leapman, C.E. Fiori and C.R. Swyt, J. Microscopy 133 (1984) 239.

166

R.D. Leapman et al. / EELS thickness measurement

[15] B.W. Matthews, J. Mol. Biol. 33 (1968) 491. [16] J.C. Ashley and M.W. Williams, Radiat. Res. 81 (19801 364. [17] MS. Isaacson, in: Principles and Techniques of Electron Microscopy, Ed. M.A. Hayat (Van Nostrand-Reinhold, New York, 1977) p. 1. [18] M.K. Lamvik, J. Microscopy 161 (19911 171. [19] T.-W. Jeng and W. Chiu, J. Microscopy 136 (1984) 35. [20] J.P. Langmore, J. Wall and MS. Isaacson, Optik 38 (1973) 335. [21] J.P. Langmore and M.F. Smith, Ultramicroscopy 46 (1992) 349. [22] B.P. Halloran and R.G. Kirk, in: Microbeam Analysis in Biology, Eds. C.P. Lechene and R.R. Warner (Academic Press, New York, 1979) p. 571. [23] A.V. Crewe and J. Wall, J. Mol. Biol. 48 (1970) 375. [24] J.S. Wall and J.F. Hainfeld, Annual Rev. Biophys. Biophys. Chem. 15 (19861 355. [25] C. Colliex, C. Jeanguillaume and C. Mary, J. Ultrastruct. Res. 88 (1984) 177.

of crotoxin crystal

[26] R. Reichelt and A. Engel, Ultramicroscopy 19 (1986) 43. [27] R. Henderson, J.M. Baldwin, T.A. Ceska, F. Zemlin, E. Beckmann and K.H. Downing, J. Mol. Biol. 213 (19901 899. [28] W. Chiu, Annual Rev. Biophys. Biomol. Struct. 22 (19931 233. [29] J. Frank, W. Chiu and L. Degn, Ultramicroscopy 26 (1988) 345. [30] B.V.V. Prasad, L.L. Degn, T.-W. Jeng and W. Chiu, Ultramicroscopy 33 (1990) 281. [31] W. Chiu, J. Brink, T. Soejima and M.F. Schmid, in: Proc. 50th Annual EMSA Meeting, Boston, Eds. G.W. Bailey, J. Bentley and J.A. Small (San Francisco Press, San Francisco, 1992) p. 1054. [32] A.J. Gubbens and O.L. Krivanek, in: Proc. 50th Annual EMSA Meeting, Boston, Eds. G.W. Bailey, J. Bentley and J.A. Small (San Francisco Press, San Francisco, 1992) p. 1570. [33] R.F. Egerton, Y.-Y. Yang and S.C. Cheng, Ultramicroscopy 48 (1993) 239.