.I. Mol. Kid.
(19X4) 173. 463-476
Polymorphic Transition of the Flagellar Polyhook from Escherichia coli and Salmonella typhimurium S.4ToRrT KATO. MlTSUMAS.4 OKAMOTO -4~1) SHO ASAKVRA
Institute Faculty
oj Molec,ular
Riology
of Science. Nagoya Gniversity LVagoy(l 464. ,Japnn
ISac~t~erialfagrllar polyhook fibers were reversibly transformed into a set, of helical forms depending on pH. ionic strength and temperature. Electron microscop>, \vith formalin fixation and freeze-drying was useful for observing t,hreedimrrlsionsl shapes of various polyhook helices and det,ermining their helical handedness. ,L\(lartesian plot of curvature against twist for these plyhook h&es gave a sinusoidal curve as in the case of the polymorphic forms of flagellal filament. ln the study on the polymorphism of flagellar filaments. (‘alladine (l!176,197X) and Kamlya et al. (1979) pointed out that such a relation in the polymorphic forms could be derived from the assumption that t,he subunits on the Irr;lr-longitudinal (1 I -start) helical lines should work as elastic fibers (I)rotofilaments) having two distinct states of conformation. In contrast. the ol)servc~d twist For the polyhook helices is too large to be explained by the same assumption. Instead, wca must assumtl that subunits on the strongly twisted. Ifi-start helical line should work as the co-operative prot,ofilament~.
1. Introduction The hook of’ a bacterial flagellum is a short (about 70 nm) curved rod connecting I hr long (iil)out 10 pm) flagellar filament t,o the basal body (DeT’amphilis & Atller. I!)71 ). Thcx torque produced bv the basal body is applied to the rigid flagrllar tili~ment through the hook (Berg 62 Anderson. 1973). In peritrichously flagellated lmcntrria such as Salm~onella and Escherirhia coli. the hook has been considered as A flexible joint playing an important role in organizing flagellar filaments int’o a polar bundle (Machnab, 1978). Both the hook and the flagellar filament have cy-lindrical structures. construct’ed from single prot,ein subunit’s by a process of wlf-aswmbly (Asakura et al., 1964; I)immitt & Simon, 1970: Kagawa et al.. 1976; Aizawa it al.. 1980: Kato et al., 1982). There are mutant strains that produce abnormally long hook fibers challed polyhooks (Silverman & Simon, 1972; Patterson-Delafield et cxl.. 1973; Komeda rt cd.. 1978: Suzuki & Tim), 1981). These rnutant,s carry mutations in a grnr 002 2x:~A.‘x4’f)xolK~ 11 go:3.ooN~
4(i3 :(;l
19X4
.4cwlemiv
Press
Inca.
(I~mtlor~)
I,ttl.
464
S. KATO,
M. OKAMOTO
ASD
S. ASAKURA
regulating the length of the hook, but not in the structural gene for the hook subunit protein. Thus the intact flagellar hook is presumed to be structurally identical to a segment, of the polyhook. Electron microscopic observation has shown t,hat the polyhook usually has a helical form, the amplitude and the pitch of
which
are
much
smaller
than
those
of
the
flagellar
filament.
The
helical
polyhook fibers display polymorphism (Kagawa et nl., 1979; Kutsukake et al., 1979; Aizawa & Maeda, 1980); for example. t,hey were transformed into a straight form under acidic conditions. Recently. Wagenknecht et al. (1982) reconsGtuted a three-dimensional image from electron micrographs of the straight) polyhook. Thoir results showed that the fundamental molecular architecture of t,he polyhook is similar to that of flagellar filament (Shirakihara & Wakabayashi. 1979). The flagellar filament has been shown to undergo polymorphic transition in a variety of circumstances. This phenomenon has been well-characterized by dark-field light microscopy. and explained by assuming two states in the subunit (flagellin) conformation (Asakura, 1970; Wakabayashi bz Mitsui. 1972; (‘alladine. 1975,1976,1978; Kamiya et al., 1979,1982). The question arises of whether the morphological properties of the polyhook can be explained within the cont,ext of the model of the flagellar filament. In this study we obtained information upon the helical handedness by a method of freeze-drying, and analyzed the observed forms on the basis of the assumption used t,o explain the polymorphism in t,he flagellar filament. Our results suggest tha,t the polyhook shares the basic mechanism of transformation with the flagellar filament. In other words, the transformation of a polyhook fiber can be explained as the co-operat,ive transition of rows of subunits t)hat work as elastic fibers having two discrete st,ates. However. the number of such rows appears to be 16 for the polghook in contrast to 11 for t’hc flagellar filament.
2. Materials and Methods Polyhooks were prepared from mutant strains of Balmonr,lla SJW880 (Patterson-Delafield (Silverman & Simon. 197”). which produced about 5 polyhooks/cell with a maximum length of about 1 pm. We used mainly the MS1381 polghook fibers. which were usually longer than those of S,JW880. The method of isolation and purification of polyhook fibers was as described (Kato et al.. 1982).
et al.. 1973) and E. coli MS1381
(1)) Electron
niicroxcopy
Various polymorphic forms of the polyhook under different conditions were observed by electron microscopy after the specimens were fixed with 9% (v/v) formaldehyde at constant temperature. Without the fixat,ion procedure. the specimens readily changed their shape when washed with distilled water on an electron microscope grid. The time required for the fixation was about 1 h at 10°C” and d0 min at dfi”C. After the formaldehyde was the specimens were finally suspended in distilled removed by centrifugation or dialysis. water. The final concentration of protein was about 0.1 mg/ml. Essentially the same results were obtained when glutaraldehyde was used as the fixative. The fixed specimens were negatively stained with 1% (w/v) many1 acetate or l’+, (w/v) sodium phosphotungstat,e. The specimens were also freeze-dried and shadow-cast after the fixation procedure to obtain their unflattened images (R,ice ef al.. 1953). The specimens were applied to an
TRANSFORMATION
OF POI,I’HOOK
465
electron microscope grid, and quickly frozen in liquid freon. followed by sublimation of the solvent in a vacuum evaporator for about 20 min. After being shadow-cast with PtjPd at an angle of about 27”, the specimens were observed with a JEOL 1OOCelectron microscope at an instrumental magnification of 20,000 x A fraction of the fibers had long shadows. indicating that their 3-dimensional shapes were apparently preserved. We used these rrnflattened specimens for the analysis of polymorphic forms. Statistically, these freezrdried polyhook fibers had a slightly smaller pitch and amplitude than those obtained in negat,ively stained specimens. Ry comparison between negatively stained and freeze-dried images. we noted that even negatively stained images contained information on heliral handedness; the half pitch that should he on the upper side of the helix was always stained more thickly. This simple feature was useful for determining the handedness of a large number of specimens. (c) Measurements of the helical parameters of polyhook $fibrrcs In general, we selected unflattened specimens that had uniform amplitude and pitch over more than 2 wavelengths. In the case of coiled types, however. short fibers of about one wavelength were used for measurements of amplitude, Negatively stained specimens were also used t,o obtain pitches and amplitudes of helical forms wit,h small amplitudes. The measurements were performed on micrographs enlarged to a final magnification of was calibrated using tropomyosin paracrystals. which had a 100,000 x Magnification periodicity of 395 x (Cohen & Longley. 1966). (‘urvature (x) and twist (AQ) for a given polyhook helix were calculated using its pitch (p) and tliatn~trr (n): cl = q.4 - H)/(A + fl) and A@ = (4) ros- i[ (-4 * + R* - (2rrr1)2)/2AH](deg.). whrrt ‘4 = (P*+n*(n+d)*)-+.
B = (P*+7c*(D-d)*)-+
and (I is the diameter of the polyhook fiber. (d) Other methods Optical diffraction of the electron micrographs was carried out by the method of Klug & Berger (1964). Viscosity of the polyhook solution (2 mg/ml) was measured in the presence of 10 rn>rsodium phosphate buffer (pH 7.0) and 0.1 m-XaCl. using an Ostwald-type viscomrter with a flovv-time of 28 s at 25°C.
3 Results (a) Trnnsfornbation
of polyhook jbers
Polyhook fibers from E. coli M81381 were able to adopt several different helical forms under different environmental conditions. As described in Ma,terials and Slethods, the fixat’ion procedure was necessary to observe these forms, because unfixed polyhook tibers readily changed their shape when washed on an electron microscope grid with solutions of different compositions. Figures 1 and 2 show rrpresent,ative forms of the polyhook fibers. We classified them roughly into four groups: normal. (aoiled, left-handed and straight types. First. a normal type (Fig. 1(a)) appeared over a wide range of conditions around neutral pH and room t’emperature. Almost all the fibers assume this type in Figure l(a). The normal
lil(:. 1. Electron micrographs of various polo.-morphic forms assumed hy the pol~hook fibc‘lx. wimvns were fixed with 9?{, formaldehyde. and neg:ativrly stained with lo, uranyl acetate ((a). ( h). (a) Xormal type found in 50 mwphosphate bui 53 ;tnd ((1)) or (e) I “T,&sodium phosphotungstate. -I 74)) at 25°C’; (b) coiled types in 50 mwcitric ircid buffer (pH 34) at 20°C’; (c) left-handed types ; in mMr-glycine HCI buffer (pH 2.7) at 4°C’; (d) Irft- handed types in 10 mu-phosphate buffer (pH 7.0) at buffrv (pH 7.0) and WI M-NaU at 1°C. The Ihar ‘: and (e) straight tgpv in 10 mu-phosphate msent.s 400 nm.
TKANSFORMATIOS
OF
POLYHOOK
lM-4
S. KATO.
11. OKAMOTO
.4X1) S. ASAKUKA
type was found to be the right-handed helix using the freeze-drying method (Fig. 2(a)). Secondly. coiled t,ypes occurred under acidic conditions, and had much smaller pitches than the normal type (Fig. l(b)), This group appeared to cAont)ain both right’- and lefthanded helices (Fig. 2(b)). Under these conditions. most of t’he long polyhook fibers showed more or less entangled forms, making it almost impossible to measure their pitchrs precisely. The third group. left-handed t’ypes, appeared under conditions of slightly more acidic pH or lower temperature than where the coiled types appeared (Fig. I(c). (d) and 2(c)). This group cont,ained a series of left-handed helices wit,h small amplitude as well as a lefthanded type having just the same pitch and amplitude as those of the righthanded normal type. Finally. we obtained a straight type under conditions of extremely acidic pH or low temperat,urr (Fig. 1 (e)). Table 1 and Figure 3 summarize the characteristics of the four polymorphic groups. As pH or temperature was lowered, there appeared forms more twisted in the left-handed sense: i.e. in the order of normal. coiled and left-handed types. Hence WC inferred that the above straight t.ype has a left-handed twist, (see scbction (b). below). llnder intermediate conditions, polyhook solutions wpre always mixtures of several polymorphic* forms. When the ionic strength was increased. the normal and the st’raight types appeared more frequently. For examplt. on lowering the temperature. polyhook fibers were transformed from thv normal into the left-handed type in t ht. t)resencae of 10 rnsr-phosphatc~ buffer (pH 74). \i\‘hen 0.1 M-NaC’l was present, however, they were t’ransformed from the normal int’o the straight type without passing through the stat’e of left-handed hrlicrx
\‘iscometry was used to examine the dynamic properties of the normal-to \vas lowered. a sharp rise in straight t.ransformation (Fig. 4). \Vh en the t,rmperature sl>e(bitic viscosity was observed, which should reflect the conformational change of plyhook fibers. The end-to-end distance of a polyhook fiber is increased about 1.5.fold upon transformation from the normal into the straight type. The t.ransformation occurred within a narrow range of temperature, as compared with thr similar t,ransformat,ion phenomenon of t,he flagellar filament (Hasegawa et (11.. 198%). This sharp change in viscosity indicat,es t’hat a large enthalpy change
Type Normal (‘oiled Left-handed: Straight
(‘onditionst
I’itch (nm)
Ihmetrr
(ml)
Handrdn~ss Right Right,. Left Lrft
SD, not determined. i Solutions contained 50 mwplyc*ine H(‘1 buffrr or 50 rnwphthalak huffcar for pH 2 to 4. citric acid buffer for pH 3 to 6, phosphate buffer or Tris H(‘I hufkr for pH 6 to 9. 1 Forms with larger pitches had larpw arrrptitutlrs.
TRANSFORMATIOS
-Hi’)
OF POLYHOOK
Normal
FIG. X. A diagram to show the conditions where the 4 polymorphic groups occurred. A few forms under alkaline appeared simultanrously in rather broad regions near the boundaries. Transformation (,onditiorrs
has not heen examined
extensively.
0.25 -
-*e-.-e 0.
P \
0.20-
la
_ apl
l
0
I
5
I
I
IO
15
20
Temperature
(“Cl
I
FIG. 4. Reversible thermal transition in the sprcific viscosity (q+,,) of the polyhook solution. was measured after the temperature was lowered (0) or raised (0). For experimental cwlditions. see Matrrials and Methods. 1.iscwsity
acacompanies
t.hr transformation.
(~lei~~~l>- denlonstratd
by
irt(~Wi~sing
The
revrrsihility
of the
anti
subscylucxntly
(ircrpasjng
transformation the
was
tprnpprattlrca.
More detailed thermodynamic2 studies on the transformation are now in progress. The above observations were carried out using polyhooks from E. coli MSl4XI with decreasing pH or temperaturr, In the chase of A’almonrZZu S,JW:XXO polyhooks, pol~morphic~ forms appeared with helical parameters similar to those of E. co/i polq’hooks. though the opt’imal conditions for the respectjive types were slightly diffbent. In addition, elect,ron micrograph s of E. coli and &zlmonrlln st’raight types gave rise to almost identic4 optical diffrac+on pat’terns (Fig. 5). Thus all of thr, polymorphic forms seem t’o be common t)o E. c-ok and &honrkx.
Two-state models based on t,he arrangement and co-operative caonformational cahange of subunits were able t,o explain the occurrence of the various polymorphic forms of flagellar filaments (Asakura. 1970: (lalladine. 1975.1976,1978; Kamiya it crl.. 1979). These models involved two fundamental assumpt,ions. (1) There is a particular set of longitudinal rows of subunits. one of which traces t’hr innermost or the outermost line on the surface of a helical flagellar filament. (In a helical rod having a radius of rod r and a mean radius of helix H, t,he outermost and the innermost. lines are such that t,hey arc in contact with the surface of cylinders having radii RS r and K-r. rrspec+ively. For details. see Lowy & Spencer (1968).) (2) Each longitudinal row of subunits can assume two stable configurations on the environmental conditions. For convenience. we (R or I,), depending designat,e here such a row of subunits as a “protofilament”. Calladine (1976) pointed out that, if Hooke’s law could he applied to those protofilaments, thr curvature should he a sine function of the number of R or I, rows (the definition of
TKAXSFOKMATION
OF
POLE’HOOK
I
25
50
curvature and twist is present,ed in Materials and Methods). Actually. the observed polymorphic forms of flagellar filaments were discretely distributed on a sinusoidal curve in the curvature/twist plot. LVagenknecht, rt al. (1982) showed that the packing pattern of subunits in the Snlrr~~n&r straight polyhook resembles that in the flagellar filament. In the light of t,his structural similarit,y between the polyhook and t)he flagellar filament. it is interesting to examine whether the transformation of the polyhook can be taxplained by the two-state model as described above. A necessary condition for a t\\~o-state model to be applied to the polyhook is that the curvature/twist plot for t hr. polymorphic forms shows a sinusoidal curve. Thus we plott’ed the curvature and twist for the individual polyhook fibers (Fig. 6). The plot suggests that there is a sirnpk sinusoidal relation between caurvature and twist of the polymorphic forms. as in the case of the flagellar filament. This result indicates that the assumption of elastic protofilaments having two st’ates could explain the observed fia;itures of the polyhook transformation. However. it is inconsistent with the assumption that the polymorphic3 forms of the polyhook were not distributed discretely on the curvature/twist plot. because the assumption allows a polyhook fiber to adopt only a definite number of polymorphic forms. This discrepancy has not bt~l explained, although it could be due to the deformation of helical forms
lil’
S. KATO,
31. OKAMOTO
ANT) S. ASAKI‘KA
through the preparation of microscope specaimens andjor the thermal fluctuation. Figure 6 provides information on the subunit arrangement in a straight type, in which all the protofilaments have an identical cwnfiguration. The value of t,wist at the interswtion on the abscissa should represent the inclination to t)he fiber axis of the rows of subunits working as prototilaments in the straight polyhook ((Calladine, 1976). Since the sinusoidal (urvv has two such intersections* with opposit’r signs, two kinds of straight typrs are expected to exist.. which havp prot,ofilament,s twisted in opposite sense. In the case of the flagellar filament. two kinds of straight t ypes have actually hern found. as predicted hy the wrvatury twist plot (Kamiya ct nl.. 1979). The straight polyhook found at, extrrmely acidic, pH values or Ion trmperaturr should have left,-handed protofilaments. judging from the positive correlation Iwtwwn increasing left-handed t\vist and decreasing pH or temperaturr. The inclination of thra protofilamrnt of this straight type is predicted t’o t)r about 50” from the value of twist at thv Jr+-hand irtt~rrswtion in Figure 6. So far we have not found anothr,r straight type t.hat show-s an optical diffraction pat’tern different from that of the ahow straight type. Tn the helical lattice of the subunits packing in thct straight polyhciok. therr are swcral prominrnt lattice lines that trace adjacent subunits: f f-start. S-start and B-start lattice lines (Fig. 7). However, these latticy lines do not) have the inclination of 50”. The only c:andidatc for the prototilament is the 1B-start lattiw line. whicoh 16-start
TRANSFORMATIOS
OF POLYHOOti
47%
has left-handed twist and inclines at an angle close to 50” to the fiber axis. Thus. if the two-state model is applied to explain the polyhook polymorphism. the co-operative strand should be on the l&start helical line. Our model of the polyhook is as follows: subunits on the I&start lattice line. G-hich run parallel t’o the innermost or the outermost line of each polymorphic2 f’orm. undergo a stepwise conformational change between two states depending on the environmental conditions. To make t,he free energy of the polyhook structure minimal. I he protofilaments having the same configuration should tend to be calustered (Calladine, 1976). Therefore, this model predicts that. maximally. 17 polymorphic forms (including two straight types) are present. According to the above assumptions, protofilaments should greatly shorten or lengthen upon transformation to bring about a large change in curvature. For example. the coiled type has the curvature of about 70?,,. which implies that the length of the outermost line on the surface of the helical cylinder is twice as long AS that of the innermost line. Thus the difference in length between the two (-onfigurations of protofilaments seems t)o be large enough to be detected b> measuring the mean contour length of the polyhook fibers in different polymorphic forms. Preliminary measurement showed that the cont,our length was reduced by only 81:, upon the straight-to-normal transformation, The absence of marked shortening of the polyhook fiber is consistent with the assumption that the prototilaments (16start lattice lines) in the straight) type take the longer configuration and the short’ening of protofilaments is cancelled by their decreased inc*linat,ion to the fiber axis upon transformation,
4. Discussion We have described several polymorphic forms of polyhook and presented a plausible explanation for t’heir occurrence. applying the basic features of the twostate model of t)he flagellar filament (Calladine. 19i5,1976,1978; Kamiya rt al.. 1979). The rnodels for these two flagellar struct’ures share the assumption that elastic protofilaments (co-operative strands of subunits) run parallel to the innermost or outermost line of each polymorphic form. However. in spite of their similarity in the packing pattern of subunits, the lattice line that is assumed to Lvork as a protofilament is diRerent: the 16start lattice line in the polyhook and the 1 l-start in the flagellar filament. Therefore there may be a mismatrh &xt\ve(xn the hook and the fiagellar filament with respect to t’he lattice line along which the co-operative interaction takes place. Considering the significant difference between these two structures in curvature and in the predicted arrangement of co-operative subunits, they should be quite different in the mode of subunit interaction and conformational change although similar allosteric mechanisms might work upon their transformation. The present data may contain some systematic errors such as are c,aused h> deformation of polyhook helices through the preparat’ion for electron microscop>,. Therefore. our int,erpretation of the transformation of the polyhook may not be c~ompletel?; conclusive. However, even if the data in Figure 6 have an error of as much as %I(%, of t’he maximal values of curvature and twist’, the polymorphic
171
S. KATO. MI. OKAMOTO AND S. ASAKUKL4
forms will still be regarded as being distributed on a sinusoidal curve with the maximal twist of between 40” and 60” in the curvature/twist plot. The conclusion t.hat the l&start lattice line works as a protofilament is supported by the fact that t’his line has t,he lowest starting number among all the latt’ice lines having lefthanded inclination of between 40” and 60”. The maxima1 value of curvature in various polymorphic forms suggests that the longest protofilaments in a polyhook fiber should be about twice as long as the shortest ones. This suggests that polyhook subunits must undergo a very large conformational changr upon t’ransformation. However, the actual magnitude of the c*onformational change of subunits depends on the radial position of the actual interac%ion sit.rk between subunits. Our model postulates that the subunit interaction takes place surface at thp ver) of the polyhook cylinder (radius = 10 ntn). merely as a matter of conveniencae. The acltual int’ernction radius rnust be much smaller, judging from a deep groove along the (i-start latt,ice lint, seen in the three-dimensional image oft he straight polyhook (Wagcnknecht it r/l.. 19X1,1982). Tf we assumr a smaller intjerac+ion radius. the calculated values of caurvaturct and twist will be reduced. Thus. it, is likely that) curvature and t)wist for cba<*hpolymorphic form arc overestimated in Figure 6. However. the variation in interaction radius does not affect. t.he main features of our model; for example. whtln t’h(l interaction radius is assumed to be 5 nm. curvature and twist for the polymorphic forms st,ill k eep their sinusoidal relation. though the maxima,1 curvat)urcl and t.wist, are reduced to 35’&, and 31”, resprctively. Sinchtb the angle of tilt of’ a hrliral family in th(> surface latt’icr (Fig. 7) depends on its radius. tjhr angle of tilt for th(l l&start helicrs is also decreased by t,he same amount Thus. t hc Anglo of tilt for thch l&start helicars agrees with thaw maxitnal twist predicted from t)hrh gross helical structurrs, irrespective of the assumption on thr interaction radius. lti flagcallar filaments, a co-operat,ive strand (11 &art lattice line) tracars an arra) of adjoining subunits. In cont,rast,, in the ease of the polyhook it is unlikely. as judged from the surface lattice given in Figure 7, that subunits on the l&tart latt,ice line st,rongly interact with one an()t) because there is a large interval between them. However, we should notfl that, the direct interaction is not Ilccessarily required for a special row of subunits to behave co-operatively. but that surrounding subunits could mediate, the co-operat)ive interaction. Figure fj predicted thr exist,rncp of t,hvo straight types: one is right-handed and the other left,-handed. We havt) found straight) fbrms under t’wo different csonditions: (1 ) at pH values lower than 2.5 (Kagawa uf nl., 1979). and (2) at lo\\ temperature and neutral pH. The straight, forms appearing under these sets of according to their optical diffraction c*onditions were structurally equivalent pat,terns and all regarded as t,he left-handed type (see Results). We have not been able to find a right-handed straight type. In t,he case of flagellar filaments. a filament from a given strain was unable to be transformed into all of the r)olymorphic* forms no matter how widely the environmental conditions were varied. lCvidenc:e for t,he exist,encr of two straight types of the flagellar filament was first obtained after appropriate mut~ant strains were discovered (O’Brien 8: I3r~nnrt.t. 1972; Kondoh oi Yanagida, 197.5: Kamiya it a,/.; 1979,19X0.1982). Tt) is
TRANSFORhIA’TIOS
OF I’OL~HOOK
47.i
likely that. the polyhook specimens used in this study are incapable of being iransformed into a right-handed straight t’ype. Probably we need to isolatfk appropriate mutant strains to study the characteristics of such a right-handed si raight type. As a bac*terial flagellum is usually rotated in the counter-clockwise direction when viewed from the distal end, the mechanical torque is transmitted to the proximal hook so as to cancel its right-handed twist. Macnab B Ornston (19’77) and Hotani (198%) observed by dark-field microscopy that. when mechanical torque was applied to a flagellar filamentj through viscous drag, the filament was transformed into it helical form that had opposite handedness to the initial form. transfcjrmed. since the t,orsional force is ‘I%(~ hook also may bo mechanically st rongrst at the basal portion in a rotating flagellum. N’e presume t)hat rnrc4~anic~al transformation of the proximal hook occurs accompanying the tiayrllar rotation and such polymorphic transformation plays a role in bundling iil\tl unbundling of t)he flagellar filarnerrts in a swimming l)actcrinm. \Vr thank I)r S. Yamaguchi and Professor 11. Simon for t’he gift of bacterial strains. I)r R. Kamiya for criticaal irading of the manusvript~. and MS E. Oh~alwShioi for twhnical itssistanw
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47fi
S. KATO.
MM.OKAJIOTO
ANI) S.
ASAKYK.-\
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