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A digital processing method for the structural analysis of lattice images of crystalloids obtained by electron microscopy
Micron and MicroscopicaActa, Vol. 14, No. 3, pp. 233 247, 1983.
0739-6260/83 $3.00+0.00 ~ 1983PergamonPressLtd.
Printed in Great Britain.
A DIGITAL PROCESSING METHOD FOR THE STRUCTURAL ANALYSIS OF LATTICE IMAGES OF CRYSTALLOIDS OBTAINED BY ELECTRON MICROSCOPY KOICHI KANAYA, NORIO BABA, CHIHARU SHINOHARA a n d MASAKO OSUMI* Kogakuin University, 1-24-2, Nishishinjuku, Shinjuku-ku, Tokyo, Japan and *Japan Women's University, Mejirodai, Bunkyo-ku, Tokyo, Japan (Received 14 January 1983; revised 24 March 1983)
Abstract--A digital processing method with the aid of a scanning densitometer system for image analysis of electron micrographs, has been applied to a microbody crystalloid containing enzymes. Some known structural features were confirmed, but the presence of unknown components were established from the subsequent diffraction patterns and reconstructed images. A model is proposed for the crystalloid possessing two facecentred lattices with a large alcohol oxidase composed of eight subunits and a small catalase component of four subunits, two of which are paired and stacked at fight angles. Index key words: electron image reconstruction, digital processing, yeast microbody crystalloids.
INTRODUCTION The optical transfer theory on the optical diffractograms of electron micrographs was originally proposed by Thon (1966) and subsequently developed by Lenz (1971), Stroke and Halioua (1973), Hanszen and Trepte (1971) and Burge et al. (1977) (see reviews: Hawkes, 1973; Saxton, 1978; MiseU, 1978; Hoppe and Mason, 1979; Mellema, 1980; Baumeister and Vogell, 1980). Based on a digital Fourier analysis, Frank et al. (1970a,b), developed a least squares method for determining the optical phase parameters from the Fourier transform. Image restoration techniques have also been discussed extensively by Erickson and Klug (1970, 1971), Frank (1973a,b), Saxton (1978), Hawkes (1980) and others. The number of biological structures studied with the aid of image processing techniques is considerable and is well documented. For recent reviews the reader is referred to Baumeister and Vogell (1980), Hawkes (1980), Saxton (1978), Shaw (1983). Closely linked to the problem of extracting information from electron micrographs of biological material is damage and structural modification to the specimen by radiation damage (Glaeser, 1971). 233
The complex scattering amplitudes mostly affecting the phase contrast images play an important role in image formation (see Zeitler and Bahr, 1959; Reimer, 1969; Kanaya and Ono, 1976).Kirkland et al. (1980), has shown that the complex image reconstructed from a defocus series of electron micrographs shows increased resolution. More recently, structural analysis by image enhancement has been applied to scanning transmission electron microscope images of tobacco mosaic virus (Kirkland et al., 1981), N e p h t y s hemoglobin (Crew and Ohtsuki, 1981) and transmission electron microscope images of a crystal lattice (Uyeda et al., 1979). In the conventional optical filtering method, the information content cannot be selected accurately and images are either disturbed by the strong background amplitude contrast, or by image effects due to strong phase variations. Following the Fourier analysis with the aperture function described by Erickson and Klug (1970), the digital processing method of Kanaya et al. (1982) has shown that the lattice images in a gold crystal representing an order of angstrom spacing can be reconstructed clearly from the diffraction spots. This digital processing method has been applied to the structural analysis of enzyme microbody crystalloids.
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K. Kanaya,N. Baba, C. Shinoharaand M. Osurni
The system consists of a scanningdensitometer of the rotating drum-type which is linked to a small computer equipped with a magnetic disk or tape memory. Within a period of 5min the system is able to scan a 1.28×1.28cm area on a raster measuring 25 x 25 lam. The optical density measurements range from 0.0D to 3.0D with 128 and 256 grey levels, where D is the density of the photographic films. The values representing transparencies on the sampling grid points in the micrographs, were recorded on a magnetic disk and subsequently converted to density values by taking logarithms. In the computer, the Fourier integral can easily be performed by a numerical integration (Cooley and Tukey, 1965). Then, by repeating inverse Fourier transforms, the lattice images of (hkl)diffraction spots selected are respectively obtained. For a pair of diffraction spots qhki obtained from crystalloids, the desired localized lattice images can be extracted using Frieders law. The defects in the lattice images are notoriously sensitive to the filter window size and its shape in the process of optical reconstruction. In digital processing, the aperture function can be used for the selection of a diffraction spot from diffractogram. The function is the unity or enhancement value inside the aperture and zero outside. By multiplying the aperture function of a diffraction spot, the desired image can be extracted. The remarkable contrast variations of reconstructed lattice images due to the scattering factor phase (Kanaya et al., 1981a,b and Kihara et al., 1981), which were first considered by Erickson and Klug (1970, 1971), have been confirmed experimentally by superimposing the individual lattice images (Kanaya et al., 1982). When based on this approach, some useful methods of digital image processing can be applied to a microbody structure observed in a biological specimen. Although the diffraction spots obtained from the Fourier transform of an image represent the regularity and symmetry of the structure, unwanted diffraction spots used for detailed observation in the desired subunit structure are often included in the diffractogram. Using the processed image obtained by the inverse Fourier transform from each diffraction pattern, it is possible to select the required diffraction and reject the unwanted spots, provided that there is sufficient independent analytical data and information based on X-ray crystallographic or biochemical studies. It is
proposed therefore, that the image contrast restoration from the required diffraction spots can be made available. During the processing, any irregularities or defects in the periodic structure may have an effect on the shape and the radius of the diffraction spots, as well as the amplitude and phase variations of the Fourier coefficients. Because variations can be immediately obtained from the numerically calculated Fourier coefficients, the enhancement of information for regularity or irregularity of the periodic structure to be analysed, is only possible in crystals similar to those described above. The use of three separate views of an object photographed in the electron microscope can provide an important method for three-dimensional image analysis. We have obtained (001), (011) and (111)-diffraction patterns from three original electron micrographs of a crystalloid microbody for the purposes of threedimensional image reconstruction in an attempt to demonstrate the precise arrangement of the unit cell structure. The detailed structure of crystalloids from the yeast Kloeckera cell when prepared by thin frozen-sections with negative staining, has demonstrated that the crystalloids are composed of a large alcohol oxidase with eight subunits (see Kato et al., 1976), also a small catalase component with four subunits arranged in similar form to the point-group symmetry 222 at the vertices of an elongated tetrahedron as previously suggested by Kislev, De Rosier and Klug (1968).
IMAGE CONTRAST FROM A CRYSTALLINE OBJECT Image contrast AI/1 from a crystalline specimen is produced by phase contrast due to interference of the coherent wave ~'das well as the amplitude contrast from an incoherent wave of AI - - = ~ d + ~ - ~,~ I
(1)
where qJdis the interfracted diffraction wave and qJiffi the dark-field term due to ionization or plasmon loss, where the transmitted wave ~bt = 1 (Kanaya et al., 1981b). In the case of small crystals which are sufficiently thin to satisfy the conditions of single scattering, the calculations apply to a perfect crystal in Bragg conditions and supported by the
A Digital ProcessingMethod for the StructuralAnalysisof LatticeImagesof Crystalloids
235
kinematical theory. For thick crystals on the other hand, the intensity of the transmitted wave varies periodically, corresponding to the intensity variation of the interfracted wave (the extinction distance ddy.). d =ddy
n=
Vc/2F(qhu),
= Sp(r)exp[2ni(r, ghk,)] dv,
(2)
where ;. is the wavelength, d the thickness equal to Mac, Ma the number of unit cells on the optical axis and the unit cell volume Vc is given by the real crystal unit cell parameters Vc=e(a x b). If we now consider the unit cell to consist of atoms or molecules of the same species, the scattering amplitude F(qhk~)relates to the elastic scattering amplitude f~(q) as a function of the generalized spatial frequency qhu=O,kt~/C,/2 and the geometrical structure factor F(hkl)
which determines the values of the scattering amplitude F(g) for an object with an electron density p(r). This possesses the property of reversibility, for a symmetrical object which consists on the basis of knowing the function F(g), we can compute p(r) from it, with aid of an inverse Fourier transform 1
[ 2 r c ( ~ + ~ + ~ ) +g,/,]
F(qhkt)=~(qhu)r(hkl);
r,hk,)=E y_expl-2,d'h + L
h~, j
\
(3)
a
(5)
(6)
whose coefficient is the structure amplitude F(qhkl)of reflections (hkl). Thus, knowing F(qal), i.e. their modulus ]F(qhu)l and cqu, by summing the above equation (6), construct the electron density distribution p(r). This is the solution of the structure, since the peaks ofp(r) give the arrangement of all atoms or molecules pj(r) according to the equation
where xj, yj and zj specify the coordinate ofjth atom of a unit cell and Cs is the spherical aberration coefficient. The characteristic angle 0hkz in the crystals is represented by the reciprical lattice vector Ig. ,l = 1/d~,, 0~, = 2/dhk:, qhu= ~ Cs~.3/dhki, p(r)= £ pj(r),6(r-rj) (7) j=l ghkl=ha*+kb*+le* where a * a = b * b = e * e = l . Therefore, the image contrast from the crystals where pj(r) is the electron density associated with satisfies the Bragg conditions, where the trans- the atom centred at r = r~. mitted wave attenuated by p2 is considered as Thus, the phase contrast of the structure in being by images can be precisely summarized from the individual harmonics with [F(q,u)[and ~hkl. The A/ = p2 2F(qhu)d_ p2 ~ d 2_ Fourier synthesis consists of superposition of V~ [ 1 P2Ndtri individual harmonics as (4)
IF(qhk,)[cos[2rr(h~q-k-~q-~)q-Othk,l
where
p~= l +
d + Ndai for d < ddy. L
c
nd = 1 + sin 2 ddy n
~
-Jr-
Ndtri for ddy n <
d
tri is the total cross-section of inelastic scattering, N the number of atoms per unit cell. The scattering amplitude F(q,u) is non-zero at the lattice point in crystals u = a/h and v = b/k. For the three-dimensional case the Fourier coefficient F(qhkt)takes the form based on the diffraction theory
(8)
each term being a plane wave of spatial density with a wavelength of du,, a normal gul and an amplitude F(qhkt)(see Vainshtein, 1981). This can be regarded as the physical embodiment of a system ofparaUel reflecting planes (hkl) in the crystal; the reflecting power--the atomic population of such a system--is expressed by IF(qhu)]. The same harmonics, being perpendicular to ghkl, can be displaced to any position along this vector and its dhktand IF(qhk:)l remain unaltered. However, this displacement can be determined exactly by the values of phase O~hk I •
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K. Kanava N. Baba, C. Shinohara and M. Osumi
The Fourier series given in equation (5), provides the three-dimensional distribution of the electron density p(r). It is also possible to construct projections of the three-dimensional distribution onto co-ordinate or any other planes.
In the computer process, the Fourier integral has to be replaced by a numerical integration (Cooley and Tukey, 1965). 1
M-1
lqx,, q,,ml= VN j =2o
N
2 t)k
k=0
p(x, y, zO =
ky
1
where M x N equidistant point of a grid
F(qhk)= ~ F(qhu)exp(-- 2~zi l~~
(10)
in which summation is carried out over two indices h and k. The simplest case of such sections is z~=0. Hence, the factor exp[-2ni(lzJc)] in the equation is equal to 1 for I. Hence
F(qhk)= ~
F(qhkt)"
l = --co
In the calculation of equation (6) which gives the structure p(r), the determination of the Fourier series consisting of the modulus IF(qhkt)l with its phase ~hkl which are lost in the optical diffraction pattern, is an essential problem in structural analysis. DIGITIZING THE ELECTRON MICROGRAPHS A densitometer was used for digitizing the transparency of the electron micrographs. The values representing the transparency on the sampling grid points f(s x, st)= ~."fj(sx, s~) were recorded on a magnetic disk and subsequently converted to density values by taking the logarithm. The two-dimensional Fourier transform is defined by F(q~, % ) =
f(s~, sr)exp a(.
(11)
where s = (sx, sy) is the vector in real space, s is the generalized spatial co-ordinate s = I r - rjl/~C~2 3 and (qx, qy) is the vector in Fourier (or reciprocal) space q = O~CJ2. The function f(s~, sy) is in turn obtained by the inverse Fourier transform
F(qx, qy)
f(Sx, sy)= -cc
exp[ - 2ni(qxSx + %sy)] dqx dqr
The centre spot of the diffractogram is expressed by 1
M-1N-I
F(0, 0 ) = ~
~ j=0
~ f(xj, Yk)
(14)
k=O
which is used for the standard for the individual harmonics F(qhkl). For a similar array ofjth atoms, the density of diffractograms for a crystalline specimen is divided into the diffraction wave and the inelastic scattering terms
D(q)=F(qhk:)F(qhkl)+ F(q)F(q ).
(15)
According to Friedel's law in X-ray crystallography for a pair of qhkl and --qhkt, the lattice image contrast is given by the inverse Fourier transform as follows, Ig = ~ {F-l[F(qhkt)+ F ( - qhkl)] } = 2 2Fr(qhkt)" hkl
hkl
From (13) with (14), it can be calculated as follows
2 ~ ~ x/(F,(qx,, qy,.)2 +Fi(qx,. qym)2]cos l
m
[2n(~
+~ )
+ tan- '(Fi']]. \F,/J
(16)
Then, the normalized individual harmonics can be obtained as
o~
[2rti(q~sx +qfi,)] ds x dsr,
fjk = f(sx~, Srk)= f(J Asx, k Asy).
(12)
f (hk l)cos[ 2~z(hu + kv ) + c%l] F(qhkl) ' __Fi x y [(hkl)= ~ ~hkl=tan- l F,, U=--,a v =-b (17) in which O~hk i is zero (positive contrast) or n (negative contrast) according t o Frieders law. For a known orientation of the crystal, the individual phase of the Fourier series can easily be obtained from the results of positive or negative contrast of the lattice images. Whereas,
237
A Digital Processing Method for the Structural Analysisof Lattice Images of Crystaiioids the localization of lattice atoms or molecules at three-dimensional co-ordinates in a unit cell, can be analysed from the superposition of individual harmonics in which the amplitude and its phase are accurately determined by digital processing. THE STRUCTURAL ANALYSIS OF MICROBODY CRYSTALLOIDS (a) Specimen preparation and recording of the electron micrographs
spectrum in (b) and (d) unit structure of large alcohol oxidase A and small catalase B, reconstructed from 10 sets of diffraction spots qxoo, qxlo, q200, q400, q3,0, q220, qx30, q420, q330 and q240; each set has four diffraction spots. The unit structure of A and B is enhanced by filtering the dark-field image and reconstructed from the selected diffraction spots. The unit structure with a cubic phase is also confirmed from the Fourier analyses for the (011) and (lll)-diffraction patterns. Figure 2 shows the Fourier analysis of the (011)-diffraction pattern. (a) is the original micrograph, (b) its Fourier transform showing diffraction spots in the [011] orientation, (c) reconstructed image of five pairs of qloo, q200, q400, qol 1, and qo2~'spots and (d) model illustration of A and B where
The crystalloid in microbodies of the yeast Kloeckera cells grown on methanol were prepared by thin frozen sections followed by negative staining. The cells cultured on the 0"5 9/0methanol containing medium for 24-48 h were fixed with 0-5% glutaraldehyde in 0.1 M cacodylate buffer pH 7.4 and ultrathin frozen sections were obtained. The sections were then stained with a f(lO0) = 2{fa(lO0 ) -fn(lO0)} 29/0 aqueous solution of uranyl acetate and f(O1 i-) = 2{f~(O1i-) -f.(O 1i-)} examined at 100 kV in a JEM-100C electron microscope with Cs= 1.6 mm and Co= 1.8 mm /(200) = 4{fa(200 ) -f.(200 )} (Osumi and Sato, 1978). f(022) =TA(022) From the numerous micrographs recorded of microbody crystalloids, thin sections of less than f(400) = 2fa (400) about 100 nm were selected. Furthermore, the f(033) = 2fn(033) crystalloids ca. 100 nm in size of sections oriented to [001], [011] and [111] in a cubic phase which f(222)<0.02, very weak has been observed by Osumi et al. (1982b) using ~100 = 0~200 = 0~400 = 0~Oli ~0~022 ~ 0~03:~ = 0 . optical diffraction patterns, were used for the processing. Figure 3 shows the Fourier analysis for [111JThe size of the unit cell a = 22 nm is relatively diffraction orientation, (a) shows the original large when compared with a single crystal of gold micrograph at the Ell 1]-diffraction orientation, (i.e. a = 0.4 nm). Therefore, the micrographs were (c) reconstructed image of two sets of qxoi and taken with the optimum amplitude contrast at q2o~ spots and a pair of q3o~ spots, and (d) model about z = - 5 0 0 nm under-focus. Accordingly, illustration of A and B, where the phase due to defocusing and aberration in the f(lOY)=-2{fa(lOF)-fB(lOi) }, ~ , o i = n phase transfer function ? can be disregarded. R 4 ~t= ~2o~ = ~ ~,=~ rq -2~'q2-6(0)3, ~+6(0)/4q~. (18) f(202) = - 2fa(202), This is due to the spherical aberration (n/2)q 4 and the generalized defocus ~ = z/~/Cs2 and the scattering factor phase 6(0). (b) Digital processing method based on the Fourier analysis Figure 1 shows a digital processing method based on the Fourier analysis, (a) is an original micrograph ol~ a microbody crystalloid, (b) its computer generated pattern of Fourier transform showing diffraction spots in the [001] orientation, (c) dark-field image reconstructed from the incoherent component of the diffuse Fourier
f(303) = 2fB(303),
~X30~ =
7~
f(112), f(3 i2-) < 0.02,
very weak.
From the appearance of the qxoo and q~xodiffraction spots which are not present in a facecentred cube, the unit cell structure is not a halite structure in which the Bravais lattice is facecentred cubic; the basis consists of A and B separated by one-half the body diagonal of a unit cube. As an example, the simple cube lattice can be uniquely specified by (uvw)=(000) (unit cell origin). The atoms at the corners of this cell will thus contribute one-eighth of their structure and
238
K. Kanava N. Baba, C. Shinohara and M. Osumi
q
+
4
Fig. l. Digital processing of an electron micrograph from a microbody crystalloid in a Kloeckera yeast cell. (a) Area from micrograph, (b) corresponding Fourier transform showing diffraction spots in the [001] orientation, (c) reconstructed image of the incoherent component, and (d) reconstructed image from 10 sets of diffraction spots qtoo, q, to, q200, q+oo,q3 I(),q2.,o, q t30, q420, q330 and q2+o; each set has four diffraction spots.
the scattering a m p l i t u d e for the special cube crystal as s h o w n in Fig. 4 are given as b a s e d on the established c r y s t a l l o g r a p h y (Hirsch et al., 1965 ). This is as follows, for the case (a) where
A(0, 0, 0), A(½, ½, 0), A(0, ½, 0), A(0, 0, ½), B(½, 0, 0), s(½, o, ½), B(0, ½, ½), S(½, ½, ½) f a (hkl) [ 1 + e in(h + k) + eink + einl] + f B( hkl ) [ e i'h + e i'(* + +)+ ei=(k + t~ + ei,,(h + k + l)]
A(½, 0, ½),A(½, ½, ½), B(½, 0, 0), B(0, ½, 0), B(½, ½, 0), S(0, ½, ½); f A ( h k l ) [I + ei*' + ei*(h+°+ e i*(*+k +*)] + f a ( h k l ) leith + ei,k + ei,(h + k) + ei,(k + o].
(20)
F r o m (19) a n d (20), the i n d i v i d u a l diffraction spots f ( 1 0 0 ) = 2{fA(100)--fB(100)}
(19)
f ( 1 1 0 ) = 2{ fA(110)--fB(110)}
for the case (b) where A(0, 0, 0), A(0, 0, ½),
f ( 2 0 0 ) = 4{fa(200 ) +fR(200)}
(21)
A Digital Processing Method for the Structural Analysis of Lattice Images of Crystalloids
239
Fig. 2. Digital processingof an electron micrograph of a microbodycrystalloid. (a) An original micrograph, (b) corresponding Fourier transform showingdiffractionspots in the [011] orientation, (c) reconstructedimagefrom fivepairs of spots q~oo,q2oo, q,,oo,qo~i and qo2~and (d) a model showing the (01 l)-face view,including alcohol oxidaseand catalase subunits (seeFig. 10). are obtained. Accordingly, a unit structure of A and B is proposed as a combination of(a) and (b) as illustrated in Fig. 4. Figure 5 shows the unit structure of a microbody crystalloid. When based on the arrangement of such a unit structure, the Fourier harmonics of a set of individual diffraction spots are induced as follows. f(100)eos rc(u + v) x cos ~z(u- v) f ( l l 0 ) c o s 2nu x cos 2nv f(200)cos 2 n ( u + v ) x cos 2 n ( u - v )
Figure 6 shows the processed results of the unit structure, (a) is (100)-Fourier harmonics, (b) (110)-Fourier harmonics, (c) (200)-Fourier harmonics, and (d) structural image of the unit cell when reconstructed from three sets of diffraction spots; each set has four-diffraction spots. F r o m the processed results f(100)=0.1, f ( l 1 0 ) = 0 . 0 7 , and f(200)=0.38, where ~qoo=0tllO=~t2oo=0, the scattering amplitudes of A and B unit components can be determined as follows:
(22) fa(lO0) =0.15, fa(110) = 0.105, fa(200) = 0.057
which are processed in the form shown in Fig. 6. fB(lO0) = O. 1, fn(110) = 0.07, fs(200) = 0.038
(23)
240
K. Kanaya, N. Baba, C. Shinohara and M. Osumi
J Fig. 3. Digital processing applied to an electron micrograph of a microbody crystalloid. (a) An original micrograph, (b) corresponding Fourier transform showing diffraction spots in the [111] orientation, (c) reconstructed image from two sets of q~oi and q2oz and a pair of q,~o3spots, and (d) a model showing (1 ll)-face view (see Fig. 10).
wherefs(hkl) = 0.66fa(hkt) is assumed by ~ root of the molecular weight ratio of alcohol oxidase to catalase attributed to the empirical results of Osumi et al. (1982a, b). Based on the theoretical consideration, the image contrast at origin (0, 0), centre (½, ½) and mid-way point (½, 0) correspond to 3f4(100), f4(100)+fB(100) and 2.3fB(100), respectively. In the proposed model, both (210) and (300)diffraction spots disappear under the extinction condition and by a very small amount of the difference between fa(3OO)-fB(300)=0.01, respectively. If the (400)-Fourier harmonic in-
cludes the component of catalase B, the theoretical amplitude becomes less than the threshold value 0.02 i.e. 2{fa(400)--fn(400)} <0.01, then it is concluded that the (400)-Fourier harmonic together with the (220) and (310)-Fourier harmonics represent the subunit of alcohol oxidase. f(400)cos{4n(u + v)}cos{4n(u- v)}
f (220 )cos(4nu )cos(4nv ) f(310) [cos{4rr(u + v)}cos{ 2rc(u - v)} + cos{4rr(u-v)}cos{ 2rt(u + v)}] ;
(24)
A Digital Processing Method for the Structural Analysis of Lattice Images of Crystalloids
Fig. 4. A specially constructed cubic crystal model showing one-eighth of a unit cell structure for the microbody crystalloid, where wave functions of the unit cell structure are shown as follows: (a) 2{fa(lOOj-fB(lOO)}cos(2~u), 2{f,4(ll0)-fa(ll0)} cos{2n(u+v)}, 4{fA(200)+fs(200)}COS (4rtu), (b) 2{fa(OlO)--fn(OlO)}cos(2nV), 2{fA(ilO)--fB(ilO } COS{2n(U-- V)}, 4{fA(O20)+fn(O20)}COS(4nV).
(lO0)-Fourier harmonics f(100)costt(u,v)coslt(u-v)
241
Fig. 5. A unit cell structure model of a microbody crystalloid proposed as a combination of(a) and (b) in Fig. 4, where coordinates of (~, ~, ~) and (~, ~2, ~2) indicate the subunit of A and B, respectively.
(110)-Fourier harmonics f(110)cos2rtu.cos2~v
(200)-Fourier harmonics f(200)cos2rKu÷v)cos2R(u-v) Fig. 6. Processed results of the unit cell structure; (a) shows (100)-Fourier harmonics, (b) (ll0)-Fourier harmonics, (c) (200)-Fourier harmonics, and (d) structural image of the unit cell reconstructed from three sets of diffraction spots qlo0, q~ 10 and q20o; each set has four diffraction spots.
242
K. Kanaya, N. Baba, C. Shinohara and M. Osumi
(310)- Fourier harmonics
f(310) {cos4rt(u÷v) cos2rt(u-v) ÷COS211(u,v)cos411(u-v)l
Fig. 7. Processed results for the structural images of subunits, where (a) is (310)-Fourier harmonics, (b) superposition of (400)-, (220)- and (310j-Fourier harmonics, (cj superposition of (400)-, (220)-, (310)-, (330)- and (420)-Fourier harmonics and (d) superposition of (400)-, (220)-, (310)-, (310)- and (4-20)-Fourier harmonics.
where
where
f ( 4 0 0 ) = 2fA(400) = - 0.05,
a4o0 = n
f(220)=fa(220)=-O.04,
~22o =rt
f(310)=2fA(310)=--O.06,
a31o=n.
f(330) = 2fB(330) = 0.033,
f(420)=2fn(420)=-O.027,
Similarly, the (330) and (420)-Fourier harmonics represent the subunit of catalase
f (330)cos(6nu )cos(6nv ) f(420) [cos{6n(u + v ) } c o s { 2 n ( u - v)}
+cos{67r(u-v)}cos{2n(u+v)}],
(25)
~330=0 ~4zo =lr.
The structural images of the subunits as shown in Figs. 7 and 8 are very close the normalized electron density distribution when calculated on the basis of crystallographic theory. Table 1 shows the processed result for the structure of the microbody crystalloid at (001)-diffraction.
A Digital Processing Method for the Structural Analysis of Lattice Images of Crystalloids
243
(420)- Fourier harmonics f(z,20) cos6n(u+v) cos2tt(u-v)
f(~20)cos6R(u-v)cos~(u÷v) Fig. 8. Processed results showing the structural images of subunits, where (a) is (420)-Fourier harmonics, (b) superposition of (420)- and (330)-Fourier harmonics, (c) (420)-Fourier harmonics, and (d) superposition of (,~20)-and (330)-Fourier harmonics.
DISCUSSION By means of optical and electron diffraction methods and subsequent computer-aided simulation, Osumi et al. (1982a,b), have shown that the mierobody crystalloid is a cubic structure of the NaCI type and is composed ofan alcohol oxidase with eight subunits (molecular weight 673,000) and catalase (molecular weight 240,000) with four elongated globular subunits; two of which are paired and stacked at fight angles. However, it should be stressed that different models of eatalase have been proposed by several authors
(Valentine 1964; Home, 1965; Sund, Weber and M61bert, 1967; Spitzberg, 1969; Kislev, De Rosier and Klug, 1968; Erickson and Klug, 1970 and Veenhuis et al., 1976). Veenhuis et al. (1976) have shown that alcohol oxidase was the major enzyme present in the crystalloid microbody when the cells were grown in a methanol medium, since catalase was not integrated in the crystalloid when caused by exposure to a short-term osmotic shock procedure. In the present method, the amplitude and its phase of individual harmonies of eatalase
244
K. Kanaya, N. Baba, C Shinohara and M. Osumi Table 1. Structure of microbody crystalloid obtained by (0011-diffraction
Miller indices hkl
lnterplanar spacing dhkt (nm)
Generalized spatial frequency qhkl
100 110 200 220 310 400 330 420
22.0 15.6 11.0 7.8 6.9 5.5 5.2 4.9
0.024 0.034 0.048 0.068 0.077 0.096 0. l 0.11
~/(Cff2) = 144,
Scattering amplitude (relative value) f4(hkl) fR(hkl) O.15 O.105 0.057 0.04 0.03 0.025
Scattering phase %k~
0.1 0.07 0.038
0 0 0 n ~z
0.017 0,014
0
~/(C~2) = 76 nm
Diameter of alcohol oxidase 11 nm With eight subunits 5.5 nm
catalase four subunits with length 7.8 nm width 5.2 nm
varies when following the basic theory. Thus, the catalase component was definitely included in the crystalloid. To examine the accurate arrangement of the cubic structure, also to confirm the subunit structure, the digital processing method based on the Fourier analysis in crystallography was applied to the microbody crystalloid. The three-dimensional structure of the crystalloid (Figs. 1, 2 and 3) provides the definitive evidence for a cubic structure, as suggested by Osumi et al. (1982a,b). However, since the extinction diffraction spots (100) and (110) appear very clearly, the arrangement of the unit structure differs from the alternate structure of the NaCl-type. The precise arrangement of the alcohol oxidase and catalase is indicated more clearly as shown in Fig. 9. This shows the structural image in which the scattering amplitude and phase are exactly corrected according to the basic theory. The alcohol oxidase (Fig. 9) is composed of eight subunits of 5.5 nm dia and the catalase is composed of four elongated globular subunits, with a length of 7.8 nm and width of 5.2 nm. Furthermore, two subunits of catalase are paired and stacked at right angles, which are in good agreement with the model previously suggested by Osumi et al. (1982a,b).
Finally, detailed model of the microbody crystalloid based on our ex~riments is presented in Fig. 10, showing the positions of the components forming three layers. CONCLUSIONS First, we conclude that our studies using a digital processing method based on crystallographic Fourier analysis and the reconstruction and subsequent interpretation of structural images, was regarded as being successful for biological specimens possessing some degree of symmetry. Second, the three-dimensional arrangement of the atomic lattice or molecules can be processed from the superposition of individual harmonics in which the amplitude and its phase can be determined precisely during the processing. Third, detailed structure of the enzyme microbody crystalloids are capable of being clarified by the procedure of selecting diffraction spectra transformed from the information recorded in transmission electron microscope. Fourth, the crystatloid in the microbody of K l o e c k e r a sp. no. 2201 was shown to have a cubic structure; a = 2 2 nm, by the interpenetration of the two face-centred lattices, which is composed of a large alcohol oxidase with eight subunits,
A Digital Processing Method for the Structural Analysis of Lattice Images of Crystalloids
245
e
Fig. 9. Processed results showing the structural images where the scattering amplitude and phase are accurately corrected; (a) shows the subunit of alcohol oxidase, and (b), (c) and (d) the subunits of alcohol oxidase, also catalase where it is indicated that two subunits of catalase are paired and stacked in positions at right-angles.
5.5 nm in dia and a small catalase with four elongated globular subunits each consisting of length 7.8 nm and width 5.2 nm, two of which are paired and stacked at right angles.
Acknowledoement--Tbe authors wish to thank Prof. R. W. Home, University of East Anglia, for helpful comments and advice in connection with the preparation of this paper.
REFERENCES Baumeister, W. and Vogell, W. (eds.), 1980. Electron Microscopy at Molecular Dimensions, Springer, Berlin.
Burge, R. E., Dainty, J. C. and Scott, R. F., 1977. Optical and digital image processing in high resolution electron microscopy. Ultramicroscopy, 2: 169-178. Cooley, J. W. and Tukey, J. W., 1965. An algorithm for the machine calculation of complex Fourier series. Math. Comput., 19: 297-301. Crew, A. V. and Ohtsuki, M., 1981. Optimal scanning and image processing with the STEM. Ultramicroscopy, 7: 13-18. Erickson, H. P. and Klug, A., 1970. The Fourier transform of an electron micrograph: Effects of defocusing and aberrations, and implications of the use of under focus contrast enhancement. Bet. Bunsencdes. Phys. Chem., 74:1129-1137. Erickson, H. P. and Klug, A., 1971. Measurement and compensation of defocusing and aberrations by Fourier processing of electron micrographs. Phil. Trans. R. Soc., B261:105 118.
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K. Kanaya, N. Baba, C. Shinohara and M. Osumi
Fig. 10. A detailed model ofa microbody crystalloid where (a), (b) and (c) show the positions of the first, second and third layers forming the model (d).
Frank, J. Bussler, P. H. Langer, R. and Hoppe, W., 1970a. A computer program system for image reconstruction and its application to electron micrographs of biological objects.VII International Cong. Electron Microscopy, 1: 17-18. Frank, J., Bussler, P. H., Langer, R. and Hoppe, W., 1970b. Einige Erfahrungen mit der Rechnerischen Analyse und Synthese yon Elektronenmikroskopischen Aufnahmen hober Auflrsung. Bet. Bunsenoes. Phys. Chem., 74: 1105-1115. Frank, J., 1973a..The envelope of electron microscopic transfer functions for partially coherent illumination. Optik, 38: 519-536. Frank, J., 1973b. Computer processing of electron micrographs. In: Adv. Techn. in Biological Electron Microsc., Koehler, J.K. (ed.), Springer, New York, Heidelberg, Berlin, 215-274.
Glaeser, R. M., 1971. Limitations to significant information in biological electron microscopy as a result of radiation damage. Ultrastruct. Res., 36: 466. Hanszen, K. J. and Trepte, L., 1971. Der Einfluss yon Energiebreite der Strahlelektronen auf Kontrastfibertragnng und Aufl6sung des Elektronenmikroskops. Optik, 32: 514-538. Hawkes, P. W. (ed.), 1973. Image Processing and Computeraided Desion in Electron Optics, Academic Press, London. Hawkes, P. W. (ed.), 1980. Computer Processin0 of Electron Microscope Images, Springer, Berlin, Heidelberg, New York. Hirsch, P., Howie, A., Nicholson, R. B., Pashley, O. W. and Wbelan, M. J., 1965. Electron Microscopy of Thin Crystals, Robert E. Krieger, Malabar, Florida. Hoppe, W. and Mason, R. (eds.), 1979. Unconventional electron microscopy for molecular structure deter-
A Digital Processing Method for the Structural Analysis of Lattice Images of Crystalloids ruination. In: Advances in Structure Research by Diffraction Methods, 7:1-225. Home, R. W., 1965. Application of negative staining methods to quantitative electron microscopy. Lab. Invest., 14: 1054-1068. Kanaya, K. and Ono, S., 1976. Consistent theory of electron scattering with atoms in electron microscopes. J. Phys. D: Appl. Phys., 9:161--174. Kanaya, K. Kihara, H. and Ishigaki, F., 1981a. Measurement of the scattering factor phase and the spherical and astigmatic constants from diffractograms of electron micrographs. Micron, 12: 105-121. Kanaya, K., Baba, N. and Takamiya, K., 1981b. Computeraided reconstruction of the image contrast of atom clusters from diffractograms of electron micrographs. Micron, 12: 353-364. Kanaya, K., Baba, N., Shino, M., Takamiya, K. and Oikawa, T., 1982. Digital processing of lattice images from a diffraction spot selected in diffractograms of electron micrographs. Micron, 13: 205-219. Kato, N., Omori, Y., Tani, Y. and Ogata, K., 1976. Alcohol oxidase of Kloeckera sp. and Hansenula polymorpha. Catalytic properties and subunit structure. Eur. J. Biochem., 64: 341-350. Kihara, H., Nakatani, T. and Kanaya, K., 1981. Further improved measurement of the angular dependence of complex scattering factor phase and the aberration coefficient as well as the partial coherence angle from diffractograms of electron micrographs. Kogakuin Rep., 50: 178-192. Kirkland, E. J., Siegel, B. M., Uyeda, N. and Fujiyoshi, Y., 1980. Digital reconstruction of bright field phase contrast images from high resolution electron micrographs. UItramicroscopy, 5: 479-503. Kirkland, E. J., Freeman, W. T., Ohtsuki, M., Issacson, M. S. and Siegel, B. M., 1981. Computer image processing of STEM images of tobacco mosaic virus. Ultromicroscopy, 6: 367-376. Kislev, N. A. De Rosier, D. J. and Klug, A., 1968. Structure of the tubes of catalase; Analysis of electron micrographs by optical filtering. J. Mol. Biol., 35: 561-566. Lenz, F. A., 1971. Transfer of image information and phase contrast. In: Electron Microscopy in Material Science, Vaidr6, U. (ed.), Academic Press, New York and London, 541-569. Mellema, J. E., 1980. Computer reconstruction of regular biological objects, Computer processing of electron microscopic images. In: Topics in Current Physics, Hawkes, P. W. (ed.), Springer, Berlin, 89-126. Misell, D. L., 1978. Image analysis, enhancement and Interpretation. In: Practical Methods in Electron
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Microscopy, Glauert, A.M. (ed.), North-Holland, Amsterdam, Vol. 7, 91-103. Osumi, M. and Sato, M., 1978. Further studies on the localization of catalase in yeast microbodies by ultrathin frozen sectioning. J. Electron Microsc., 27: 127-136. Osumi, M. Nagano, M., Sato, M., Imai, M. and Yamada, N., 1982a. The three-dimensional structure of the composite crystal in the Kloeckera microbody. Jap. Women's Univ. J., 29: 163-176. Osumi, M., Nagano, M., Yamada, N., Hosoi, J. and Yanagida, M., 1982b. Three-dimensional structure of the crystalloid in the microbody of Kloeckera sp. : Composite crystal model. J. Bact., 151: 376-383. Reimer, L., 1969. Elektronenoptischer Phasenkontrast. II Berechnung mit Komplexen Atomstreuamplituden f'tir Atome und Atomgruppen. Z. Natur., 24a: 377-389. Saxton, W. O., 1978. Computer Techniques for Imoge Processin0 in Electron Microscopy, Academic Press, New York. Shaw, P. J., 1983. 2-dimensional and 3-dimensional reconstruction in electron microscopy. In: Computino in Biology, Barratt, A. and Gieson, G. (eds.), Elsevier-North-Holland, Amsterdam. Spitzberg, C. L., 1969. Dissociation and reassociation of catalase of erythrocytes of man. Biophysics, 11: 766-771. Stroke, G. W. and Halioua, M., 1973. Image improvement in high resolution electron microscopy with coherent illumination using holographic image-deblurring deconvolution III. Optik, 37: 249-264. Sund, H., Weber, K. and M61bert, E., 1967. Dissoziation der Rinderleber-Katalase in ihre Untereinheiten. Eur. J. Biochem., 1: 400-410. Thon, F., 1966. Zur Defokussierungs-Abhanglgkeit des Phasenkontrastes bei Elektronen Mikroskopischen Abbiidung. Z. Naturf., 21a: 476-478. Uyeda, N., Kobayashi, K., Ishizuka, K. and Fujiyoshi, Y., 1979. High voltage electron microscopy for image discrimination of consistent atoms in crystals and molecules. Proc. 57 Novel Symm., LidingiS, Sweden, 47-61. Vainshtein, B. K., 1981. Symmetry of Crystals. Methods of structural Crystallography. In" Modern Crystallography I, Springer, Berlin, Heidelberg, New York, 22-26. Valentine, R. C., 1964. Sub-unit of the catalase molecule seen by electron microscopy. Nature, 204: 1262-1264. Veenhuis, M., van Dijken, J. P. and Harder, W., 1976. Cytochemical studies on the localization of methanol oxidase and other oxidases in peroxisomes of methanolgrown Hansenula polymorpha. Archs. Microbiol., 111: 123-135. Zeitler, E. and Bahr, G. F., 1959. Contributions to quantitative electron microscopy. J. appl. Phys., 30: 940-944.
0739-6260/83 $3.00+0.00 ~ 1983PergamonPressLtd.
Printed in Great Britain.
A DIGITAL PROCESSING METHOD FOR THE STRUCTURAL ANALYSIS OF LATTICE IMAGES OF CRYSTALLOIDS OBTAINED BY ELECTRON MICROSCOPY KOICHI KANAYA, NORIO BABA, CHIHARU SHINOHARA a n d MASAKO OSUMI* Kogakuin University, 1-24-2, Nishishinjuku, Shinjuku-ku, Tokyo, Japan and *Japan Women's University, Mejirodai, Bunkyo-ku, Tokyo, Japan (Received 14 January 1983; revised 24 March 1983)
Abstract--A digital processing method with the aid of a scanning densitometer system for image analysis of electron micrographs, has been applied to a microbody crystalloid containing enzymes. Some known structural features were confirmed, but the presence of unknown components were established from the subsequent diffraction patterns and reconstructed images. A model is proposed for the crystalloid possessing two facecentred lattices with a large alcohol oxidase composed of eight subunits and a small catalase component of four subunits, two of which are paired and stacked at fight angles. Index key words: electron image reconstruction, digital processing, yeast microbody crystalloids.
INTRODUCTION The optical transfer theory on the optical diffractograms of electron micrographs was originally proposed by Thon (1966) and subsequently developed by Lenz (1971), Stroke and Halioua (1973), Hanszen and Trepte (1971) and Burge et al. (1977) (see reviews: Hawkes, 1973; Saxton, 1978; MiseU, 1978; Hoppe and Mason, 1979; Mellema, 1980; Baumeister and Vogell, 1980). Based on a digital Fourier analysis, Frank et al. (1970a,b), developed a least squares method for determining the optical phase parameters from the Fourier transform. Image restoration techniques have also been discussed extensively by Erickson and Klug (1970, 1971), Frank (1973a,b), Saxton (1978), Hawkes (1980) and others. The number of biological structures studied with the aid of image processing techniques is considerable and is well documented. For recent reviews the reader is referred to Baumeister and Vogell (1980), Hawkes (1980), Saxton (1978), Shaw (1983). Closely linked to the problem of extracting information from electron micrographs of biological material is damage and structural modification to the specimen by radiation damage (Glaeser, 1971). 233
The complex scattering amplitudes mostly affecting the phase contrast images play an important role in image formation (see Zeitler and Bahr, 1959; Reimer, 1969; Kanaya and Ono, 1976).Kirkland et al. (1980), has shown that the complex image reconstructed from a defocus series of electron micrographs shows increased resolution. More recently, structural analysis by image enhancement has been applied to scanning transmission electron microscope images of tobacco mosaic virus (Kirkland et al., 1981), N e p h t y s hemoglobin (Crew and Ohtsuki, 1981) and transmission electron microscope images of a crystal lattice (Uyeda et al., 1979). In the conventional optical filtering method, the information content cannot be selected accurately and images are either disturbed by the strong background amplitude contrast, or by image effects due to strong phase variations. Following the Fourier analysis with the aperture function described by Erickson and Klug (1970), the digital processing method of Kanaya et al. (1982) has shown that the lattice images in a gold crystal representing an order of angstrom spacing can be reconstructed clearly from the diffraction spots. This digital processing method has been applied to the structural analysis of enzyme microbody crystalloids.
234
K. Kanaya,N. Baba, C. Shinoharaand M. Osurni
The system consists of a scanningdensitometer of the rotating drum-type which is linked to a small computer equipped with a magnetic disk or tape memory. Within a period of 5min the system is able to scan a 1.28×1.28cm area on a raster measuring 25 x 25 lam. The optical density measurements range from 0.0D to 3.0D with 128 and 256 grey levels, where D is the density of the photographic films. The values representing transparencies on the sampling grid points in the micrographs, were recorded on a magnetic disk and subsequently converted to density values by taking logarithms. In the computer, the Fourier integral can easily be performed by a numerical integration (Cooley and Tukey, 1965). Then, by repeating inverse Fourier transforms, the lattice images of (hkl)diffraction spots selected are respectively obtained. For a pair of diffraction spots qhki obtained from crystalloids, the desired localized lattice images can be extracted using Frieders law. The defects in the lattice images are notoriously sensitive to the filter window size and its shape in the process of optical reconstruction. In digital processing, the aperture function can be used for the selection of a diffraction spot from diffractogram. The function is the unity or enhancement value inside the aperture and zero outside. By multiplying the aperture function of a diffraction spot, the desired image can be extracted. The remarkable contrast variations of reconstructed lattice images due to the scattering factor phase (Kanaya et al., 1981a,b and Kihara et al., 1981), which were first considered by Erickson and Klug (1970, 1971), have been confirmed experimentally by superimposing the individual lattice images (Kanaya et al., 1982). When based on this approach, some useful methods of digital image processing can be applied to a microbody structure observed in a biological specimen. Although the diffraction spots obtained from the Fourier transform of an image represent the regularity and symmetry of the structure, unwanted diffraction spots used for detailed observation in the desired subunit structure are often included in the diffractogram. Using the processed image obtained by the inverse Fourier transform from each diffraction pattern, it is possible to select the required diffraction and reject the unwanted spots, provided that there is sufficient independent analytical data and information based on X-ray crystallographic or biochemical studies. It is
proposed therefore, that the image contrast restoration from the required diffraction spots can be made available. During the processing, any irregularities or defects in the periodic structure may have an effect on the shape and the radius of the diffraction spots, as well as the amplitude and phase variations of the Fourier coefficients. Because variations can be immediately obtained from the numerically calculated Fourier coefficients, the enhancement of information for regularity or irregularity of the periodic structure to be analysed, is only possible in crystals similar to those described above. The use of three separate views of an object photographed in the electron microscope can provide an important method for three-dimensional image analysis. We have obtained (001), (011) and (111)-diffraction patterns from three original electron micrographs of a crystalloid microbody for the purposes of threedimensional image reconstruction in an attempt to demonstrate the precise arrangement of the unit cell structure. The detailed structure of crystalloids from the yeast Kloeckera cell when prepared by thin frozen-sections with negative staining, has demonstrated that the crystalloids are composed of a large alcohol oxidase with eight subunits (see Kato et al., 1976), also a small catalase component with four subunits arranged in similar form to the point-group symmetry 222 at the vertices of an elongated tetrahedron as previously suggested by Kislev, De Rosier and Klug (1968).
IMAGE CONTRAST FROM A CRYSTALLINE OBJECT Image contrast AI/1 from a crystalline specimen is produced by phase contrast due to interference of the coherent wave ~'das well as the amplitude contrast from an incoherent wave of AI - - = ~ d + ~ - ~,~ I
(1)
where qJdis the interfracted diffraction wave and qJiffi the dark-field term due to ionization or plasmon loss, where the transmitted wave ~bt = 1 (Kanaya et al., 1981b). In the case of small crystals which are sufficiently thin to satisfy the conditions of single scattering, the calculations apply to a perfect crystal in Bragg conditions and supported by the
A Digital ProcessingMethod for the StructuralAnalysisof LatticeImagesof Crystalloids
235
kinematical theory. For thick crystals on the other hand, the intensity of the transmitted wave varies periodically, corresponding to the intensity variation of the interfracted wave (the extinction distance ddy.). d =ddy
n=
Vc/2F(qhu),
= Sp(r)exp[2ni(r, ghk,)] dv,
(2)
where ;. is the wavelength, d the thickness equal to Mac, Ma the number of unit cells on the optical axis and the unit cell volume Vc is given by the real crystal unit cell parameters Vc=e(a x b). If we now consider the unit cell to consist of atoms or molecules of the same species, the scattering amplitude F(qhk~)relates to the elastic scattering amplitude f~(q) as a function of the generalized spatial frequency qhu=O,kt~/C,/2 and the geometrical structure factor F(hkl)
which determines the values of the scattering amplitude F(g) for an object with an electron density p(r). This possesses the property of reversibility, for a symmetrical object which consists on the basis of knowing the function F(g), we can compute p(r) from it, with aid of an inverse Fourier transform 1
[ 2 r c ( ~ + ~ + ~ ) +g,/,]
F(qhkt)=~(qhu)r(hkl);
r,hk,)=E y_expl-2,d'h + L
h~, j
\
(3)
a
(5)
(6)
whose coefficient is the structure amplitude F(qhkl)of reflections (hkl). Thus, knowing F(qal), i.e. their modulus ]F(qhu)l and cqu, by summing the above equation (6), construct the electron density distribution p(r). This is the solution of the structure, since the peaks ofp(r) give the arrangement of all atoms or molecules pj(r) according to the equation
where xj, yj and zj specify the coordinate ofjth atom of a unit cell and Cs is the spherical aberration coefficient. The characteristic angle 0hkz in the crystals is represented by the reciprical lattice vector Ig. ,l = 1/d~,, 0~, = 2/dhk:, qhu= ~ Cs~.3/dhki, p(r)= £ pj(r),6(r-rj) (7) j=l ghkl=ha*+kb*+le* where a * a = b * b = e * e = l . Therefore, the image contrast from the crystals where pj(r) is the electron density associated with satisfies the Bragg conditions, where the trans- the atom centred at r = r~. mitted wave attenuated by p2 is considered as Thus, the phase contrast of the structure in being by images can be precisely summarized from the individual harmonics with [F(q,u)[and ~hkl. The A/ = p2 2F(qhu)d_ p2 ~ d 2_ Fourier synthesis consists of superposition of V~ [ 1 P2Ndtri individual harmonics as (4)
IF(qhk,)[cos[2rr(h~q-k-~q-~)q-Othk,l
where
p~= l +
d + Ndai for d < ddy. L
c
nd = 1 + sin 2 ddy n
~
-Jr-
Ndtri for ddy n <
d
tri is the total cross-section of inelastic scattering, N the number of atoms per unit cell. The scattering amplitude F(q,u) is non-zero at the lattice point in crystals u = a/h and v = b/k. For the three-dimensional case the Fourier coefficient F(qhkt)takes the form based on the diffraction theory
(8)
each term being a plane wave of spatial density with a wavelength of du,, a normal gul and an amplitude F(qhkt)(see Vainshtein, 1981). This can be regarded as the physical embodiment of a system ofparaUel reflecting planes (hkl) in the crystal; the reflecting power--the atomic population of such a system--is expressed by IF(qhu)]. The same harmonics, being perpendicular to ghkl, can be displaced to any position along this vector and its dhktand IF(qhk:)l remain unaltered. However, this displacement can be determined exactly by the values of phase O~hk I •
236
K. Kanava N. Baba, C. Shinohara and M. Osumi
The Fourier series given in equation (5), provides the three-dimensional distribution of the electron density p(r). It is also possible to construct projections of the three-dimensional distribution onto co-ordinate or any other planes.
In the computer process, the Fourier integral has to be replaced by a numerical integration (Cooley and Tukey, 1965). 1
M-1
lqx,, q,,ml= VN j =2o
N
2 t)k
k=0
p(x, y, zO =
ky
1
where M x N equidistant point of a grid
F(qhk)= ~ F(qhu)exp(-- 2~zi l~~
(10)
in which summation is carried out over two indices h and k. The simplest case of such sections is z~=0. Hence, the factor exp[-2ni(lzJc)] in the equation is equal to 1 for I. Hence
F(qhk)= ~
F(qhkt)"
l = --co
In the calculation of equation (6) which gives the structure p(r), the determination of the Fourier series consisting of the modulus IF(qhkt)l with its phase ~hkl which are lost in the optical diffraction pattern, is an essential problem in structural analysis. DIGITIZING THE ELECTRON MICROGRAPHS A densitometer was used for digitizing the transparency of the electron micrographs. The values representing the transparency on the sampling grid points f(s x, st)= ~."fj(sx, s~) were recorded on a magnetic disk and subsequently converted to density values by taking the logarithm. The two-dimensional Fourier transform is defined by F(q~, % ) =
f(s~, sr)exp a(.
(11)
where s = (sx, sy) is the vector in real space, s is the generalized spatial co-ordinate s = I r - rjl/~C~2 3 and (qx, qy) is the vector in Fourier (or reciprocal) space q = O~CJ2. The function f(s~, sy) is in turn obtained by the inverse Fourier transform
F(qx, qy)
f(Sx, sy)= -cc
exp[ - 2ni(qxSx + %sy)] dqx dqr
The centre spot of the diffractogram is expressed by 1
M-1N-I
F(0, 0 ) = ~
~ j=0
~ f(xj, Yk)
(14)
k=O
which is used for the standard for the individual harmonics F(qhkl). For a similar array ofjth atoms, the density of diffractograms for a crystalline specimen is divided into the diffraction wave and the inelastic scattering terms
D(q)=F(qhk:)F(qhkl)+ F(q)F(q ).
(15)
According to Friedel's law in X-ray crystallography for a pair of qhkl and --qhkt, the lattice image contrast is given by the inverse Fourier transform as follows, Ig = ~ {F-l[F(qhkt)+ F ( - qhkl)] } = 2 2Fr(qhkt)" hkl
hkl
From (13) with (14), it can be calculated as follows
2 ~ ~ x/(F,(qx,, qy,.)2 +Fi(qx,. qym)2]cos l
m
[2n(~
+~ )
+ tan- '(Fi']]. \F,/J
(16)
Then, the normalized individual harmonics can be obtained as
o~
[2rti(q~sx +qfi,)] ds x dsr,
fjk = f(sx~, Srk)= f(J Asx, k Asy).
(12)
f (hk l)cos[ 2~z(hu + kv ) + c%l] F(qhkl) ' __Fi x y [(hkl)= ~ ~hkl=tan- l F,, U=--,a v =-b (17) in which O~hk i is zero (positive contrast) or n (negative contrast) according t o Frieders law. For a known orientation of the crystal, the individual phase of the Fourier series can easily be obtained from the results of positive or negative contrast of the lattice images. Whereas,
237
A Digital Processing Method for the Structural Analysisof Lattice Images of Crystaiioids the localization of lattice atoms or molecules at three-dimensional co-ordinates in a unit cell, can be analysed from the superposition of individual harmonics in which the amplitude and its phase are accurately determined by digital processing. THE STRUCTURAL ANALYSIS OF MICROBODY CRYSTALLOIDS (a) Specimen preparation and recording of the electron micrographs
spectrum in (b) and (d) unit structure of large alcohol oxidase A and small catalase B, reconstructed from 10 sets of diffraction spots qxoo, qxlo, q200, q400, q3,0, q220, qx30, q420, q330 and q240; each set has four diffraction spots. The unit structure of A and B is enhanced by filtering the dark-field image and reconstructed from the selected diffraction spots. The unit structure with a cubic phase is also confirmed from the Fourier analyses for the (011) and (lll)-diffraction patterns. Figure 2 shows the Fourier analysis of the (011)-diffraction pattern. (a) is the original micrograph, (b) its Fourier transform showing diffraction spots in the [011] orientation, (c) reconstructed image of five pairs of qloo, q200, q400, qol 1, and qo2~'spots and (d) model illustration of A and B where
The crystalloid in microbodies of the yeast Kloeckera cells grown on methanol were prepared by thin frozen sections followed by negative staining. The cells cultured on the 0"5 9/0methanol containing medium for 24-48 h were fixed with 0-5% glutaraldehyde in 0.1 M cacodylate buffer pH 7.4 and ultrathin frozen sections were obtained. The sections were then stained with a f(lO0) = 2{fa(lO0 ) -fn(lO0)} 29/0 aqueous solution of uranyl acetate and f(O1 i-) = 2{f~(O1i-) -f.(O 1i-)} examined at 100 kV in a JEM-100C electron microscope with Cs= 1.6 mm and Co= 1.8 mm /(200) = 4{fa(200 ) -f.(200 )} (Osumi and Sato, 1978). f(022) =TA(022) From the numerous micrographs recorded of microbody crystalloids, thin sections of less than f(400) = 2fa (400) about 100 nm were selected. Furthermore, the f(033) = 2fn(033) crystalloids ca. 100 nm in size of sections oriented to [001], [011] and [111] in a cubic phase which f(222)<0.02, very weak has been observed by Osumi et al. (1982b) using ~100 = 0~200 = 0~400 = 0~Oli ~0~022 ~ 0~03:~ = 0 . optical diffraction patterns, were used for the processing. Figure 3 shows the Fourier analysis for [111JThe size of the unit cell a = 22 nm is relatively diffraction orientation, (a) shows the original large when compared with a single crystal of gold micrograph at the Ell 1]-diffraction orientation, (i.e. a = 0.4 nm). Therefore, the micrographs were (c) reconstructed image of two sets of qxoi and taken with the optimum amplitude contrast at q2o~ spots and a pair of q3o~ spots, and (d) model about z = - 5 0 0 nm under-focus. Accordingly, illustration of A and B, where the phase due to defocusing and aberration in the f(lOY)=-2{fa(lOF)-fB(lOi) }, ~ , o i = n phase transfer function ? can be disregarded. R 4 ~t= ~2o~ = ~ ~,=~ rq -2~'q2-6(0)3, ~+6(0)/4q~. (18) f(202) = - 2fa(202), This is due to the spherical aberration (n/2)q 4 and the generalized defocus ~ = z/~/Cs2 and the scattering factor phase 6(0). (b) Digital processing method based on the Fourier analysis Figure 1 shows a digital processing method based on the Fourier analysis, (a) is an original micrograph ol~ a microbody crystalloid, (b) its computer generated pattern of Fourier transform showing diffraction spots in the [001] orientation, (c) dark-field image reconstructed from the incoherent component of the diffuse Fourier
f(303) = 2fB(303),
~X30~ =
7~
f(112), f(3 i2-) < 0.02,
very weak.
From the appearance of the qxoo and q~xodiffraction spots which are not present in a facecentred cube, the unit cell structure is not a halite structure in which the Bravais lattice is facecentred cubic; the basis consists of A and B separated by one-half the body diagonal of a unit cube. As an example, the simple cube lattice can be uniquely specified by (uvw)=(000) (unit cell origin). The atoms at the corners of this cell will thus contribute one-eighth of their structure and
238
K. Kanava N. Baba, C. Shinohara and M. Osumi
q
+
4
Fig. l. Digital processing of an electron micrograph from a microbody crystalloid in a Kloeckera yeast cell. (a) Area from micrograph, (b) corresponding Fourier transform showing diffraction spots in the [001] orientation, (c) reconstructed image of the incoherent component, and (d) reconstructed image from 10 sets of diffraction spots qtoo, q, to, q200, q+oo,q3 I(),q2.,o, q t30, q420, q330 and q2+o; each set has four diffraction spots.
the scattering a m p l i t u d e for the special cube crystal as s h o w n in Fig. 4 are given as b a s e d on the established c r y s t a l l o g r a p h y (Hirsch et al., 1965 ). This is as follows, for the case (a) where
A(0, 0, 0), A(½, ½, 0), A(0, ½, 0), A(0, 0, ½), B(½, 0, 0), s(½, o, ½), B(0, ½, ½), S(½, ½, ½) f a (hkl) [ 1 + e in(h + k) + eink + einl] + f B( hkl ) [ e i'h + e i'(* + +)+ ei=(k + t~ + ei,,(h + k + l)]
A(½, 0, ½),A(½, ½, ½), B(½, 0, 0), B(0, ½, 0), B(½, ½, 0), S(0, ½, ½); f A ( h k l ) [I + ei*' + ei*(h+°+ e i*(*+k +*)] + f a ( h k l ) leith + ei,k + ei,(h + k) + ei,(k + o].
(20)
F r o m (19) a n d (20), the i n d i v i d u a l diffraction spots f ( 1 0 0 ) = 2{fA(100)--fB(100)}
(19)
f ( 1 1 0 ) = 2{ fA(110)--fB(110)}
for the case (b) where A(0, 0, 0), A(0, 0, ½),
f ( 2 0 0 ) = 4{fa(200 ) +fR(200)}
(21)
A Digital Processing Method for the Structural Analysis of Lattice Images of Crystalloids
239
Fig. 2. Digital processingof an electron micrograph of a microbodycrystalloid. (a) An original micrograph, (b) corresponding Fourier transform showingdiffractionspots in the [011] orientation, (c) reconstructedimagefrom fivepairs of spots q~oo,q2oo, q,,oo,qo~i and qo2~and (d) a model showing the (01 l)-face view,including alcohol oxidaseand catalase subunits (seeFig. 10). are obtained. Accordingly, a unit structure of A and B is proposed as a combination of(a) and (b) as illustrated in Fig. 4. Figure 5 shows the unit structure of a microbody crystalloid. When based on the arrangement of such a unit structure, the Fourier harmonics of a set of individual diffraction spots are induced as follows. f(100)eos rc(u + v) x cos ~z(u- v) f ( l l 0 ) c o s 2nu x cos 2nv f(200)cos 2 n ( u + v ) x cos 2 n ( u - v )
Figure 6 shows the processed results of the unit structure, (a) is (100)-Fourier harmonics, (b) (110)-Fourier harmonics, (c) (200)-Fourier harmonics, and (d) structural image of the unit cell when reconstructed from three sets of diffraction spots; each set has four-diffraction spots. F r o m the processed results f(100)=0.1, f ( l 1 0 ) = 0 . 0 7 , and f(200)=0.38, where ~qoo=0tllO=~t2oo=0, the scattering amplitudes of A and B unit components can be determined as follows:
(22) fa(lO0) =0.15, fa(110) = 0.105, fa(200) = 0.057
which are processed in the form shown in Fig. 6. fB(lO0) = O. 1, fn(110) = 0.07, fs(200) = 0.038
(23)
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K. Kanaya, N. Baba, C. Shinohara and M. Osumi
J Fig. 3. Digital processing applied to an electron micrograph of a microbody crystalloid. (a) An original micrograph, (b) corresponding Fourier transform showing diffraction spots in the [111] orientation, (c) reconstructed image from two sets of q~oi and q2oz and a pair of q,~o3spots, and (d) a model showing (1 ll)-face view (see Fig. 10).
wherefs(hkl) = 0.66fa(hkt) is assumed by ~ root of the molecular weight ratio of alcohol oxidase to catalase attributed to the empirical results of Osumi et al. (1982a, b). Based on the theoretical consideration, the image contrast at origin (0, 0), centre (½, ½) and mid-way point (½, 0) correspond to 3f4(100), f4(100)+fB(100) and 2.3fB(100), respectively. In the proposed model, both (210) and (300)diffraction spots disappear under the extinction condition and by a very small amount of the difference between fa(3OO)-fB(300)=0.01, respectively. If the (400)-Fourier harmonic in-
cludes the component of catalase B, the theoretical amplitude becomes less than the threshold value 0.02 i.e. 2{fa(400)--fn(400)} <0.01, then it is concluded that the (400)-Fourier harmonic together with the (220) and (310)-Fourier harmonics represent the subunit of alcohol oxidase. f(400)cos{4n(u + v)}cos{4n(u- v)}
f (220 )cos(4nu )cos(4nv ) f(310) [cos{4rr(u + v)}cos{ 2rc(u - v)} + cos{4rr(u-v)}cos{ 2rt(u + v)}] ;
(24)
A Digital Processing Method for the Structural Analysis of Lattice Images of Crystalloids
Fig. 4. A specially constructed cubic crystal model showing one-eighth of a unit cell structure for the microbody crystalloid, where wave functions of the unit cell structure are shown as follows: (a) 2{fa(lOOj-fB(lOO)}cos(2~u), 2{f,4(ll0)-fa(ll0)} cos{2n(u+v)}, 4{fA(200)+fs(200)}COS (4rtu), (b) 2{fa(OlO)--fn(OlO)}cos(2nV), 2{fA(ilO)--fB(ilO } COS{2n(U-- V)}, 4{fA(O20)+fn(O20)}COS(4nV).
(lO0)-Fourier harmonics f(100)costt(u,v)coslt(u-v)
241
Fig. 5. A unit cell structure model of a microbody crystalloid proposed as a combination of(a) and (b) in Fig. 4, where coordinates of (~, ~, ~) and (~, ~2, ~2) indicate the subunit of A and B, respectively.
(110)-Fourier harmonics f(110)cos2rtu.cos2~v
(200)-Fourier harmonics f(200)cos2rKu÷v)cos2R(u-v) Fig. 6. Processed results of the unit cell structure; (a) shows (100)-Fourier harmonics, (b) (ll0)-Fourier harmonics, (c) (200)-Fourier harmonics, and (d) structural image of the unit cell reconstructed from three sets of diffraction spots qlo0, q~ 10 and q20o; each set has four diffraction spots.
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K. Kanaya, N. Baba, C. Shinohara and M. Osumi
(310)- Fourier harmonics
f(310) {cos4rt(u÷v) cos2rt(u-v) ÷COS211(u,v)cos411(u-v)l
Fig. 7. Processed results for the structural images of subunits, where (a) is (310)-Fourier harmonics, (b) superposition of (400)-, (220)- and (310j-Fourier harmonics, (cj superposition of (400)-, (220)-, (310)-, (330)- and (420)-Fourier harmonics and (d) superposition of (400)-, (220)-, (310)-, (310)- and (4-20)-Fourier harmonics.
where
where
f ( 4 0 0 ) = 2fA(400) = - 0.05,
a4o0 = n
f(220)=fa(220)=-O.04,
~22o =rt
f(310)=2fA(310)=--O.06,
a31o=n.
f(330) = 2fB(330) = 0.033,
f(420)=2fn(420)=-O.027,
Similarly, the (330) and (420)-Fourier harmonics represent the subunit of catalase
f (330)cos(6nu )cos(6nv ) f(420) [cos{6n(u + v ) } c o s { 2 n ( u - v)}
+cos{67r(u-v)}cos{2n(u+v)}],
(25)
~330=0 ~4zo =lr.
The structural images of the subunits as shown in Figs. 7 and 8 are very close the normalized electron density distribution when calculated on the basis of crystallographic theory. Table 1 shows the processed result for the structure of the microbody crystalloid at (001)-diffraction.
A Digital Processing Method for the Structural Analysis of Lattice Images of Crystalloids
243
(420)- Fourier harmonics f(z,20) cos6n(u+v) cos2tt(u-v)
f(~20)cos6R(u-v)cos~(u÷v) Fig. 8. Processed results showing the structural images of subunits, where (a) is (420)-Fourier harmonics, (b) superposition of (420)- and (330)-Fourier harmonics, (c) (420)-Fourier harmonics, and (d) superposition of (,~20)-and (330)-Fourier harmonics.
DISCUSSION By means of optical and electron diffraction methods and subsequent computer-aided simulation, Osumi et al. (1982a,b), have shown that the mierobody crystalloid is a cubic structure of the NaCI type and is composed ofan alcohol oxidase with eight subunits (molecular weight 673,000) and catalase (molecular weight 240,000) with four elongated globular subunits; two of which are paired and stacked at fight angles. However, it should be stressed that different models of eatalase have been proposed by several authors
(Valentine 1964; Home, 1965; Sund, Weber and M61bert, 1967; Spitzberg, 1969; Kislev, De Rosier and Klug, 1968; Erickson and Klug, 1970 and Veenhuis et al., 1976). Veenhuis et al. (1976) have shown that alcohol oxidase was the major enzyme present in the crystalloid microbody when the cells were grown in a methanol medium, since catalase was not integrated in the crystalloid when caused by exposure to a short-term osmotic shock procedure. In the present method, the amplitude and its phase of individual harmonies of eatalase
244
K. Kanaya, N. Baba, C Shinohara and M. Osumi Table 1. Structure of microbody crystalloid obtained by (0011-diffraction
Miller indices hkl
lnterplanar spacing dhkt (nm)
Generalized spatial frequency qhkl
100 110 200 220 310 400 330 420
22.0 15.6 11.0 7.8 6.9 5.5 5.2 4.9
0.024 0.034 0.048 0.068 0.077 0.096 0. l 0.11
~/(Cff2) = 144,
Scattering amplitude (relative value) f4(hkl) fR(hkl) O.15 O.105 0.057 0.04 0.03 0.025
Scattering phase %k~
0.1 0.07 0.038
0 0 0 n ~z
0.017 0,014
0
~/(C~2) = 76 nm
Diameter of alcohol oxidase 11 nm With eight subunits 5.5 nm
catalase four subunits with length 7.8 nm width 5.2 nm
varies when following the basic theory. Thus, the catalase component was definitely included in the crystalloid. To examine the accurate arrangement of the cubic structure, also to confirm the subunit structure, the digital processing method based on the Fourier analysis in crystallography was applied to the microbody crystalloid. The three-dimensional structure of the crystalloid (Figs. 1, 2 and 3) provides the definitive evidence for a cubic structure, as suggested by Osumi et al. (1982a,b). However, since the extinction diffraction spots (100) and (110) appear very clearly, the arrangement of the unit structure differs from the alternate structure of the NaCl-type. The precise arrangement of the alcohol oxidase and catalase is indicated more clearly as shown in Fig. 9. This shows the structural image in which the scattering amplitude and phase are exactly corrected according to the basic theory. The alcohol oxidase (Fig. 9) is composed of eight subunits of 5.5 nm dia and the catalase is composed of four elongated globular subunits, with a length of 7.8 nm and width of 5.2 nm. Furthermore, two subunits of catalase are paired and stacked at right angles, which are in good agreement with the model previously suggested by Osumi et al. (1982a,b).
Finally, detailed model of the microbody crystalloid based on our ex~riments is presented in Fig. 10, showing the positions of the components forming three layers. CONCLUSIONS First, we conclude that our studies using a digital processing method based on crystallographic Fourier analysis and the reconstruction and subsequent interpretation of structural images, was regarded as being successful for biological specimens possessing some degree of symmetry. Second, the three-dimensional arrangement of the atomic lattice or molecules can be processed from the superposition of individual harmonics in which the amplitude and its phase can be determined precisely during the processing. Third, detailed structure of the enzyme microbody crystalloids are capable of being clarified by the procedure of selecting diffraction spectra transformed from the information recorded in transmission electron microscope. Fourth, the crystatloid in the microbody of K l o e c k e r a sp. no. 2201 was shown to have a cubic structure; a = 2 2 nm, by the interpenetration of the two face-centred lattices, which is composed of a large alcohol oxidase with eight subunits,
A Digital Processing Method for the Structural Analysis of Lattice Images of Crystalloids
245
e
Fig. 9. Processed results showing the structural images where the scattering amplitude and phase are accurately corrected; (a) shows the subunit of alcohol oxidase, and (b), (c) and (d) the subunits of alcohol oxidase, also catalase where it is indicated that two subunits of catalase are paired and stacked in positions at right-angles.
5.5 nm in dia and a small catalase with four elongated globular subunits each consisting of length 7.8 nm and width 5.2 nm, two of which are paired and stacked at right angles.
Acknowledoement--Tbe authors wish to thank Prof. R. W. Home, University of East Anglia, for helpful comments and advice in connection with the preparation of this paper.
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