- Email: [email protected]
Growth-saturation in vitro of Salmonella flagella
J. Mol. Biol. (1974) 86, 285-300
Growth-saturation
in vitro of Salmonella Flagella
H~ROEAZU HOTANI AND SHO ASAKURA
Department of Biophysics, Faculty of Science Kyoto University, Kyoto, Japun and
Institute of Molecular Biology, Faculty of Science Nagoya University, Nagoya, Japan (Received 12 November 1973, and in revised fmn 20 February 1974) At physiological ionic strength and pH, short fragments of Salmonella flagella (seeds) grow longer in the presence of monomeric flagellin and there exists a one-to-one correspondence between the seeds and fully grown Claments (Asakura et al., 1964). In this study it was shown that when monomer and seed derived from a preparation of flagella (strain SJ26) were mixed in a protein ratio r larger than 20, the filaments stopped growing or became inactive for a long period of time, and the average length of inactive filaments was independent of the value of r. technique The phenomenon was called growth-sc&mGm. The antibody-labelling (Asakura et al., 1968) made it possible to show that, though active filaments having equal lengths grew at various rates ranging between 0 and 0.16 ~m/min, the average value of growth rate depended little on length. On the other hand, it was found that the proportion of inactive filament in the total filament increased rapidly as the value of T was increased continuously from 0 to 10. The dependence of the proportion of inactive filament on r suggested that filaments became inactive with a probability independent of their length. The rate of inactivation (or the probability with which a flsment becomes inactive during growth by a unit length) had various values when different preparations of flagella were used as starting materials. The distribution of length for an assembly of inactive Clanrents was determined by low-magnification electron microscopy. The result could be approximated by an exponential distribution: the numberaverage length was 4.54 q and the rate of inactivation was 0.224 pm-l.
1. Introduction It is now well established that the polymerization of flagellin into flagella filaments is a self-assembly process (Ada et al., 1963; Abram & Koffler, 1964; Lowy & McDonough, 1964; Asakura et al., 1964,1966; Gerber & Noguchi, 1967; Wakabayashi et al., 1969; Hotani, 1971; Iino et al., 1972; Kuroda, 1972; Gerber et al., 1973; Kondoh BEHotani, 1974). Indeed, from a thermodynamic point of view, the process may be regarded as a simple reversible one. However, it has a kinetic feature in common with crystallization, and presumably of biological importance. For example, simple heating of Salmonella flagella at physiological ionic strength and pH gave rise to a solution of monomeric flagellin which was metastable at room temperature (Asakura et al.,
1964,1966). When the solution was seeded with short fragments of flagella, rapid 286
286
H. HOTANI
AND
S. ASAKURA
polymerization was initiated and, in a short period of time, the concentration of monomer decreased to a value approximately equal to zero. This means that the equilibrium between monomer and polymer under these conditions heavily favoured the polymeric form. It is remarkable that at a high degree of super-saturation, spontaneous nucleation rarely occurred. In the above experiment, purified flagella filaments could be shortened by sonic vibration to obtain seeds. When a seed solution was left at room temperature for a long period, the average length of shortened flagella, measured by electron microscopy, increased little, indicating that short flagella were incapable of an end-to-end association. Taking into account these circumstances, it is expected that in the presence of monomer, seeds grow into single flagella filaments and, therefore, there exists a one-to-one correspondence between the seeds and fully grown filaments. This expectation was shown to be correct in the following experiment (Asakura et al., 1964). When monomer and seed were mixed in a protein ratio r (= wt monomer/wt seed), the average length of fully grown Clanrents was (1 + r) times the average length of the added seeds, though any assembly of fully grown filaments had a broad distribution of length. The above experimental result was, however, obtained for small values of r (less than 3). A question arises at this point: if a su&iently large amount of monomer is supplied to a seed, does it grow without limit? Fujime et al. (1972a,b) have investigated this problem by measurements of quasi-elastic scattering of laser light and flow birefringence. The data obtained suggested that the average length of flagella filaments did not exceed some critical value even in the presence of monomer. The present paper reports a more detailed study of the same problem. First, it will be shown that when monomer and seed were mixed at large values of r, the overall rate of polymerization, or the rate at which the concentration of monomer decreased as a result of polymerization, decreased with time more rapidly than expected and finally reached zero, while the solution still contained a high concentration of monomer capable of rapid polymerization on the second addition of seed. Therefore, we must consider that the flagella filaments stopped growing in the presence of monomer. Hereafter, this phenomenon will be called gvw%A-aa&dion, and has been investigated by carrying out several experiments which will be described in this paper.
MaMaIs and Methods (a) Prepardon of monomer and seed 2.
&almcm&o strain 5526, which produces normal flagella with 1,2-antigen (Iino, 1961), was used for the investigation of growth-saturation. Cultivation of the organisms, the isolation and p&cation of flagella and the preparation of monomer and wed were carried out by the method described by Asakura & d. (1964) and Hotani (1971). To observe growth-satnration, mixtures of monomer and seed at large values of r had to be incubated at 26°C (optimal temp. for polymerization) for a few days. To prevent bacterial growth during this period, we used a medium (medium C) containing O-2 mg streptomycin/ml and 60 units penioillin/ml in addition to O-16 M-NaCl and O-01 r.r-phosphate bnffer (pH 643). It was shown by viscosity measurements that the overall rate of polymerization initiated at small values of r was influenced little by the addition of antibiotics. It has been found that the mininmm value of r required for observing growth-saturation varied when different preparations of flagella were used as starting materials. The reason for this remains unknown. To investigate growth-saturation by the antibody-l&belling technique (see below),
GROWTH-SATURATION
OF SALMONELLA
FLAGELLA
287
we used another strain 55870, which produces normal flagella with i-antigen (Iino, 1901). Monomer was prepared from GfIageIla by the same method as that used in the preparation 1,2-monomer. During the present study it was found that when i-monomer solutions were left at 26% for long periods of time, polymerization was spontaneously initiated in them. For this reason, we used only l,Z-flagella for the investigation of growth-saturation. (b) Kinetk
expetitnertt
of polymerizutti
Polymerization was followed by the method described by Asakura (1968). Polymerization initiated in a mixture of monomer and seed could be stopped, after any period of time, by simple dilution of the mixture with 26 vol. of cold distilled water. The diluted solution was centrifuged at 106,000 g for 1 h to sediment flagella filaments, and optical density at 278 nm (O.D.& of the supernatant solution, proportional to the concentration of monomer contained in the diluted solution, was measured (Figs 1 and 2). When the value diluted solution wae kept cold for a few hours before centrifugation, the o.D.~,~ remained unchanged. This method was useful also for observing growth-saturation and for measuring the percentage of the total monomer polymerized before growth-saturation (Table 1). (c) Antibody-labeUiw
experiment
To make clear the details of growth-saturation, it is important (1) to determine the percentage of the total filament contained in a given solution able to act a,a seed for further polymerization, and (2) to know the dependence of the growth rate of fllamenta on their length. For these purposea we used the antibody-labelling method of Asakura et al. (1988). To a solution of l,Z-flagella filament was added i-monomer, to produce heterogeneous flagella 8lament (or block copolymer), which was treated with antiserum against 1,2 or i-flagella to distinguish parts of each illament consisting of 1,2 and &-flagellins, respectively. Flagellins derived from 1,2 and i-flagella have been shown to copolymerize with little discrimination. Anti-flagella sera were prepared by the method described by Kondoh & Hotani (1974), and antigen-antibody reaction was allowed to take place by the following procedure : a drop of a block copolymer solution was applied to a grid, the excess portion was gently blotted with a long and slender filter paper, and the grid was floated with the specimen side down on a lOO-fold diluted antiserum in a small well for 6 min or longer at room temperature. Thereafter, the grid was washed with about 10 drops of distilled water to remove excess protein and the antibody-labelled block copolymer was negatively stained with 1% phosphotungetate and observed in a JEM-‘IA electron microscope at an inf3trumental magnification of 6000. (d) Meaezcre~
of le&
by low-magn@ation
electron mbroscopy
A growth-saturated sample consisted of fllamenta with various lengthi3, the maximum being longer than 30 q. To obtain the distribution of length for this sample, we ueed a IOO-mesh grid (VECO) and observed the specimens at an instrumental magnification of 1000, using an attachment, JEM-ACW, which gives wide and highly contrasted images. In addition, it W&B necessary to take 9 micrographs or more continuously with minimal overlaps. The micrograpti were printed at B-fold magnification and the prints were connected together. In general, the probability that a filament does not have its whole length within a given area increaeea with increasing Glament length. To avoid the experimental error due to this effect, we ueed the following procedure: on the connected printa was drawn a frame, each side of which was 00 mm (corresponding to 10 q) inside the edge of the connected prints. Then, almost all of the &men& crossing the frame had their whole length within the connected prints. Filaments entirely outide the frame were excluded from the investigation. Lengths of fllamenta were measured with a mapmeasurer. In one experiment, we examined the distribution of length for a sample of fully grown filaments at r = 6. In this case, single micrographs enlarged to a magnification of 26,000 were used. It has been reported that flagella filaments often associate by their enda to give the appearance of bend6 and branches (Asakura et ol., 1968,1968). Bends and branches were encountered also in this study. Lengths of filaments were measured on the basis of the rule described previously.
288
H. HOTANI
AND
S. ASAKURA
3. Results (a) Ouerall rate of polym.erizatk
ati growth-saturcbtion
F’igure 1 shows kinetic data obtained for polymerizations initiated in solutions containing a constant concentration of monomer (25 mg/ml) and various concentrations of seed: curves A, B and C correspond to the cases of r = 5, 30 and 60. Sinoe the scales on the abscissa for the three curves are inversely proportional to r, the curves would coincide over the whole range of the abscissa, if the rate of polymerization were directly proportional to the product of the number concentrations of monomer and polymer. However, the rate of polymerization decreased with time more rapidly as the value of c increased. When, for example, two solutions of P = 6 and 60 had an equal o.D.,,,~ value, it was expected that the average length of filamerits contained in the solution with r = 60 would be 12 times the average length of Laments contained in the other solution. Therefore, a straightforward interpretation of the results of Figure 1 is to assume that the growth rate of flaments depended on their length and decreased gradually as they grew longer. However, this possibility will be excluded later.
30 60 Timefminl
fi
FIG. 1. Rates of polymerizetions
initietad
in solutions
60 ( 120 (
oontaining
a constant
ooncentration
of
monomer end various oonoentrations of seed at 26°C. The medium used in this experiment oontained only 0.16 aa-NeC1 and O-01 M-phosphate buffer (pH 66). One ml of monomer solutions oonGning 3.0 mg protein/ml and 0.2 ml of seed solutions containing 3*0,06 and 0.26 mg protein/ ml, respeotively, were mixed to obtain 3 sets of solutions having different values of f, and the concentrations of monomer contained in eaoh set of solutions left at 26°C for verious periods of time were determined by the methods desoribed in Materiels and Methods. Initial conoentration of monomer contained in the 3 sets of solutions ~8s 2.6 mg/ml and r = 6 (aurve A), 30 (curve B) snd 60 (OUIV~ C). Ordinate, the concentration of monomer expressed in terms of O.D.srs; end 8bs&s8, time after mixing monomer and seed. Curves A, B end C should be referred to the three saales on abscissa (A), (B) end (C), respectively, which were drawn 8s being inversely proportion81 to the velue of r.
GROWTH-SATURATION
OF SALMONELLA
FLAGELLA
289
Time(h)
Or
3p
“IO
!
I 0
I 2
I 4
L 6
Fm. 2. Growth-satumtion of flagella filament in medium C at 26°C. Two ml of monomer solutions containing 3.0 mg protein/ml end 0.4 ml of seed solutions co&king 7.6, 3.0 and 0.167 mg protein/ml, respeotively, were mixed to obtain 3 sets of solution of r = 2 (curve A), 6 (curve B) and 90 (curve C), and the concentmtions of monomer contained in each set of solutions left at 26°C for verious periods were determined by the method described in Meterials and Methods. Ordinate, the concentration of monomer expressed in terms of O.D.,,,; and abscissa, time after mixing monomer and seed. Curves A and B should be referred to the lower abscisse and curve C to the upper. Curve C shows that polymerization initiated st r = 90 beceme saturated in 8bout 70 h. The experiment81 point on curve C at 91 h w&s obtained BS follows. A sample solution left for 90 h (2.4 ml tot81 vol.) was mixed with 0.4 ml of 8 fresh prep8ration of seed aontaining 7.6 mg protein/ml, and the mixture w&s left at 26°C for 1 h before the measurement of O.D.srs.
A similar experiment was carried out to follow the whole process of polymerization. Curve C in Figure 2, obtained for r = 90, shows that polymerization stopped in about 70 hours, whereas the solution left for 90 hours still contained a high concentration of monomer capable of rapid polymerization on the second addition of seed. The fmal level of O.D.87s absorbance for r = 2 (curve A) or 5 (curve B) was about O-017, which is larger than expected from the equilibration data given by Gerber et al. (1973). Indeed, when a solution containing 1.25 mg seed/ml in medium C was left at 26°C for several hours, diluted with 2.5 volumes of cold distilled water and centrifuged at 105,000 g for one hour, the supernatant fraction had sn 0.D.a78 value smaller than 0.005. Therefore, the value of 0.017 cannot correspond to the equilibrium concentration of monomer under the given conditions, It is likely that the monomer solution used contained denatured flagellin produced during he&-treatment (Asakura et al., 1964). In parallel to the above experiment, pairs of solutions of various T values were left at a given temperature for 70 and 90 hours, respectively, in order to determine the dependence on r of the saturated level of O.D.,,,. The 0.D.27s values obtained
290
H.
HOTANI
AND
S. ASAKURA
at 70 and 90 hours were equal, within experimental error, indicating that polymerization had ended or stopped within 70 hours in all casea. The averages of the two values for each pair are given in the second column of Table 1. The pair of solutions at r = co, which contained no seed, gave an 0.D.a78 value of 0*205. The third column of Table 1 gives Ao.D.,,, = O-205- o.D.~,*, which is proportional to the concen1
TABLE Growth-aaturdion
r
as rev&
by sediwbedahnb
experimeti
0.D.m
Ao.~.mst
as
0.017 0.020 0,026 O-038 O-086 o-122 o-149 0.160 0.188
O-188 O-186 0.180 0.167 0.119 O-083 O-056 0.045 0.037
2.8 10.0 14.2 17.3 18.4 19.2 17.4 17.4 17.2
1.4 4.9 7.0 8.6 9-o 9.4 8.6 8.5 8.4
2 10 16 20 30 46 60 76 90
For experimental oonditions, see Fig. 2. The given 0.D .l78 velues were averages of those obtained at 70 and 90 h after the initiation of polymerization. The everage length of the seed used wna 0.49 pm and the 0.D.278 value obtained etr = 00 was 0.206.
t Ao.D.,,, = 0.205 -
o.D.~~~.
$ Ct = 9’ (0.D.,,s/0a205)
+ 1.
8 = 0.49 a.
. OO FIG.
obtained
3. Dependence of the average from Table 1.
I 30 I
length
I 60
of Alaments
I 9f
on 7. The experimental
points
were
GROWTH-SATURATION
OF SALMONELLA
FLAGELLA
291
tration of flagellin polymerized during the experiment. The fourth column gives a = ?(dO.D.,,,/0-205) + I, which is equal to the ratio of the average length (L) of filaments produced in each solution to the average length (L). of added seeds. The preparation of seed used in this experiment was observed by electron microscopy (Plate I(a)) and it was found that (L), = 0.49 pm (Fig. 4(a)). The fifth column gives
WLength offibments measured by electron microswpy Plate I includes electron microgmphs of those samples with r = 10,20,30,60 and 90 which were used in the preceding experiment: the micrographs were taken between 70 and 90 hours after the initiation of polymerization. It will be seen that each sample consisted of filaments with various lengths. Figure 4(b) shows the distribution of length obtained for the sample with r = 10 by the method described in Materials and Methods. The average length (L) celculated from this result was 45 pm, which is approximately equal to the value of 4-9 pm given in Table 1. This agreement shows that the number of filaments contained in the solution changed little during 70 hours or more. It is clearly of interest to show growth-saturation by electron microscopy; however, it is not easy in practice. Therefore, from electron micrographs of the samples used in the experiment of Table 1, we selected filaments longer than 4.2 pm (50 mm in the electron micrograph of Plate I) and measured their length to calculate the average length of the selected filaments (Fig. 5). The results showed that in the range of r larger than 20, the average length of selected filaments was samples examined approximately constant. Presumably, the growth-saturated had similar distributions of length.
Length
crrn) b)
FIG. 4. Distributions of length determined by eleotron miorosoopy for those preparations of seed (a) and filament produced at r = 10 (b), which were used in the experiment of Tsbb 1. The total number of filaments used for (a) was 616 and that for (b) w&a 402. The broken lines denote average’lengths. 20
H.
282 ,5r--.-~~-----
HOTANI
AND ..-.
-
8. ASAKURA -
.--
.
Fm. 6. Growth-aeturation &s observed by electron miorosaopy. Filaments longer than 4.2 e were selected from eleotron micrographs of the samples used in the experiments of Table 1, and the average length of the aeleoted filaments from each aample wan determined. More than 100 filaments were wed for obtaining eaah experimental point.
(c) @moth rate and length Since any preparation of flagella filaments had a broad distribution of length, it was difEcult to determine the dependence of the growth rate of filaments on their length by conventional methods. However, the antibody-labelling method described in Materials and Methods was found to be useful for this purpose (Fig. 6). A preparation of l,2-flagella filament, obtained by mixing monomer and seed at r = 5, was allowed to grow in the presence of a large amount of i-monomer for a short period, and the product was treated with antiserum against 1,2-flagella and observed by electron microscopy (Plate II(a)). This procedure made it possible to distinguish the original 1,gpai-t of each filament from the newly added i-part. In this experiment, filaments of the type (i)-(1,2)-( i ) were not encountered: this is due to the fact that in. vitro growth of flagella filament takes place at one of the two ends (Asakura et al., 1968). From a number of electron micrographs of the antibody-labelled filament, we selected filaments having both 1,2 and i-parts and measured lengths of the two parts of each filament in the selected group. The relation between the two lengths is shown in Figure 6, which may be taken as representing length dependence of growth rate. The result shows, rather unexpectedly, that filaments having equal lengths grew at various rates ranging between 0 and 0.16 pm/minute. Possibly, this is an important feature of flagellin polymerization, though its interpretation remains unresolved. Irrespective of this circumstance, it is unlikely that the average growth rate of filaments had any meaningful dependence on their length. Indeed, the correlation coefficient, which has a value between -1 and 1 by definition, and is 0 for no correlation, is 0978 for the experimental points in Figure 6. This result is most unfavourable for the hypothesis that growth-saturation wss brought about by the mechanism of length-dependent growth rate. The distribution of length for the 1,2-part of the heterogeneous filament used in the above analysis is given in
PLATE I. Flagella filaments formed at various values of T. (a) Seed; conditions, T = 10; (c) 20; (d) 30; (e) 60; and (f) 90. For experimental Magnification 6000 x . These micrographs were used in t,he exprrimcnts
(b) filaments produced see Fig. 2 and Table of Figs 4 and 5. [.faring
at 1.
p. 2!1’
hATE II. Heterogeneous flagella filaments labelletl with antibody against 2,5flagella. (a) An electron micrograph used in t.hp txpwiments of Fig.; 6 and 7. r\ntibotly-labellect filament. COIIsistett of I&‘-flagellin and unlabclled filament consisted of i-flagellin. Magnificat,ion 15,000 * (b) and (c) Electron micrographs used in t,hc experiment of Fig. 8. Thcsr micrographs wcrc~ t,aken before and after incubation of a preparation of seed at. 26°C’ for 60 h. Magnificat~ion 12,~lO~l
PLATE III. Heterogonoous flagella filaments labclletl with antlbdy. Homogeneous I,Z-filammts formed at> various values of r were allowed t,o grow in t>hc:presence of i-monomrr for 6 h antl, t,hereafter, t.reatctl wit,h anti-1,2-flagella swum. (a) Sncd; (b) r = 3; (c) 6; and (cl) 10. Magnificnt.ion 15,000 x These micrographs WOI‘Cwed in t,hc>ccqwwiment of Fig. 9.
UROWTH-SATURATION’OF
SALMONELLA
FLAGELLA
293
Figure 7(a). This distribution may be compared with that for active filament contained in the 1,2-filament examined (see below). (d) lnactkvation of jihments Plate II(a) shows some homogeneous 1,2-filaments, indicating that inactive filaments, incapable of acting as nuclei for further polymerization, were contained in the given 1,2-flagella solution. In the statistical analysis of Figure 6 we used 417
I F
I
.
.
.
.
.
.
.
.
.:
.
.
:
. .
.
.
*.
:
.
.
:
.
.
:.
f
.!
.:
.
.
.
**
.
. .
.
.
. .
1.
.i
.
.
:.,.
*m
.
1..
*.
8
.
*.
. .
1..
.
. .
.
. .
:
:
:..
.I
.
.
:
:
.
.
;.
.
s
.
.
.
:.z,
:
.
.
:
.
.
.
e
:
.:.
:.
*
. .
:
.
. .
. .
i
.
.
.
.
i
,.:.
..:
. . .
.
. .
,
ii.
.
.
.
.,....
*
. .
*
. . . .
.
*
.I
.
.
.:.
e*:.
5
.
::.
.
,
I
.
.,s..:
m
.
.
. ..i..
:.i..
.:
. .
.
,
:.,!
1
.
ii
.
.l.
.
.
.
.
.
.
.
.
*.
‘I...
,..:
.
.
.
:.
e
8
. . .
. .
.
:
.
.
.
,.
. .
. .
. .
.
.
.
.
.
.
.
. .
::
.
.
.
.
.
.
.
. . . .
.
.
. .
. .
I-T-----
. .
::
.
,
. . . . .
.
.
.
.
. .
.,
:
. .
.
.
.
I
I
I
I
2
3
Length of I,P- part (pm)
!
Fro. 6. Relation between growth rata and length determined by the antibody-labelling method. Two solutions of monomer and seed (eeah oonteining 3-O mg protein/ml) were mixed at volume ratio 5: 1 and the mixture wea left at 26°C for 20 h for complete polymerixation. Then, the solution was mixed with 6 vol. of 8 solution cont.&kg 3-O mg i-monomer/ml and, after inoubation et 26°C for 5 min, the mixture waa diluted with a large volume of oold distilled water to stop the polymerization of i-flagellin. The diluted solution was mixed with antiserum against 1,2flegells and the antibody-labelled fllnment was observed by eleotron microscopy (Plate II). From a number of electron miorographa obtained, filaments having 1,2 end i-parts were selected (417 in total) end lengths of the two parts of each filament were measured. Ordinate, the length of the +art; and absoissa, the length of the 1,2-part. The reletion between the two lengths may be regarded as representing the dependewe of the growth rate of filaments on their length. Denoting the length of the 1,2-pert of a selected filament by z, and that of the i-part by y,, the correlation coefficient is given by:
where d and g denote average lengths. experiment&l points w&s 0.078.
The value of this ooefficient
c&uleted
from the given
H. HOTANI
AND
8. ASAKURA
Length (pm)
FIU. 7. (a) Distribution of length obteined for the 1,2-pert of the heterogeneous timent used in the experiment of Fig. 6. (b) Distribution of length for homogeneous 1,24lament enoountared at the same time. The total number of Clementa used wse 626. (0) The superposition of the distributions (a) and (b). The broken lines denote everage lengths.
heterogeneous filaments, while the number of homogeneous 1,2-filaments encountered at the same time was 626. A few homogeneous i-filaments also were found: however, those were excluded from the investigation. Then, the proportion A of active filament in the total filament was 0.44. Figure 7(b) shows the distribution of length for the homogeneous 1,2-filament or inactive filament. It is remarkable that the two distributions obtained for active and inactive filaments were different in type and the average length of inactive filaments was shorter than that of active filaments. This result appears to indicate that rapid interconversion of a filament between the active and inactive states never happened. Here, we assume that an active filament grows at an average rate independent of the length but suddenly becomes inactive. In connection with this assumption, it was first shown that growth is required for inactivation. In the experiment of Figure 8, parts of a preparation of I,&-seed were left at 26°C for various periods and the value of A for each part was determined by the antibody-labelling method (Plate II(b) and (c)). The result obtained shows that inactivation did not occur over the period of time examined. Next, in the experiment of Figure 9, 1,2-monomer and 1,2-seed were mixed at various values of r in a range between 0 and 10 and, after complete polymerization, the value of A for the product in each mixture was determined. The amount of i-monomer added to each preparation of 1,2-filament was equal to the amount of 1,2-seed added to 1,2-monomer in the initial step of polymerization,
GROWTH-SATURATION
-1-L
OF SAlliVONELLA
20
FLAGELLA
295
40 Time(h)
FIG. 8. Absence of inactivation when seeds were left done. Parts of a solution containing 3.0 mg I,2seed/ml were left at 26°C for various periods and each part was mixed with an equal vol. of a solution containing 3.0 mg i-monomer/ml. The mixture was left at 26°C overnight and the product was treated with antiserum against 1,2-flagella to determine the proportion A of aative filament in the total. Eaoh experimental point was obtained from more than 400 filaments.
FIQ. 9. Inaotivation of filaments depended on the extent of their growth. Parts of a solution containing 3.0 mg 1,2-seed/ml (average length 0.26 pm) were mixed with appropriate volumes of solutions containing 3.0 mg I,%-monomer/ml to give various values of z between 0 and 10, and eaoh mixture was left at 26°C overnight for oomplete polymerization. Then, each solution was mixed with an appropriate volume of a solution containing 3.0 mg i-monomer/ml to make the initial concentrations of 1,2-seed and i-monomer equal, and the mixture was left at 26°C for 6 h. The product was treated with antiserum against l,%-flagella to determine the proportion A of active filament in the total. Each experimental point was derived from more than 300 filaments.
H.
296
HCTANI
AND
8. ASAKUXA
and each mixture of l&filament and i-monomer was left at 26°C for six hours before antibody-labelling (Plate III). In this experiment also, homogeneous i-filaments were encountered, which were excluded from the statistical analysis. The results obtained show that the proportion of active filament in the total filament decreased when r or the average length of filaments increased. The smooth curve in this Figure represents : A = 0,793 exp( -0.096r). If filaments contained in each mixture of 1,2-monomer and 1,2-seed became inactive with B probability independent of their length, we have the following relation : 0*096r = Xl.(L),, where A’ is the rate of inactivation or the probability with which a filament stops growing during growth by B unit length. The seed used in the above experiment had (L), = 0.26 pm, as measured by electron microscopy. Then, we obtain A’ = 0.37 pm-‘.
15c I\
” ‘OC)5 E5 -5 P
5c )-
c
‘0 Length (pm)
J!‘ro. 10. The distribution of length obtained for an assembly of inactive filements. Monomer and seed derived from a preparation of l,%-5agella were mixed et c = 20 end the mixture (total protein 2.13x&ml) wm left et 2&W for 70 h and then observed by eleotron microaoopy. Lengths of 5lmmenta were measured by the method deaoribed in Matariala and Methods. The total num+ of 5lamenta used was 962 and the seed used had
GROWTH-SATURATION
OF S-4 LMONELLA
FLAGELLA
297
(e) Length of inactive jikzmcnd Figure 10 shows the distribution of length for filament produced in a mixture at r = 20 of monomer and seed (the average length being 0.26 pm) derived from a preparation of 1,2-flagella. Plate IV(a) shows an electron micrograph used in the statistical analysis. In a separate experiment of the type shown in Figure 3, it was found that the minimum value of r required for growth-saturation wssa about 15 when the same monomer and seed were combined. Therefore, the given distribution of length may correspond to an assembly of inactive filaments. The number-average length calculated from the distribution WIW4.64 pm, the weight-average length was 8.65 pm and the standard deviation was 4.32 pm. The smooth curve in Figure 10, which is a good approximation of the experimental result, was derived from the probability density function of the r-distribution (Lindley, 1965) : fk (L) = p+J Lkc-l exp(-AL), where A = O-224 pm-l discussed later.
and k = 1.11. The significance of the agreement will be
(f) Growth-saturation and the nature of the preparation of monomer AR has saturation materials. which led
been described repeatedly, the minimum value of r required for growthdiffered when different preparations of I,&-flagella were used as starting In the course of this study we obtained an unusual preparation of flagella to no growth-saturation within 70 hours (Fig. 11). Plate IV(b) shows very .
.
.
/
/
.
-
.
/;i
/ ./
l
/ /
I
I
30
60
90
Fxo. 11. Relation between average length and r derived from en unusual preparation of 1,2flagella. For experiments1 aonditiona and procedure see Fig. 2. The experimental points were obtained et 70 h sfter the initiation of polymerization. The seed used has, = 0.33 pm.
II. HOTANI
298
AND
S. ASAKURA
long filaments produced at r = 90. It is unlikely that polymerization continued as a result of spontaneous nucleation or the formation of new filaments. We named the above preparation of flagella slow (or s) and that used in the experiment of Figure 10 fast(or f)and examined which factor in the combination of monomer and seed was responsible for slowness in growth-saturation (Table 2). From f and Alagella were prepared monomers and seeds (each containing 3-O mg protein/ml) and they were mixed at r = ti in all combinations. Each mixture was left at 26°C overnight for complete polymerization and then mixed with l/6 volume of a solution containing 3-O mg i-monomer/ml. The mixture was left at 26°C for several hours and treated with antiserum against i-flagella to determine the value of A for each preparation of 1,2-filament. The f-seed had (L),, = 034 pm and the s-seed had (L)O = 0.33 pm. To obtain the initial value of A, each preparation of seed was mixed with an equal volume of a solution containing 3.0 mg i-monomer/ml and the mixture was left at 26°C for several hours, followed by the treatment with anti-i-flagella serum. The results obtained are given in the third column of Table 2. The fourth TABLET Rates of inactivations when monomers and seeds derived from fast and slow preparations of jhgelb were combined Monomer
Seed
f f” 8
;
8
8
o = 0.34
A
AoIA
h’t (pm-l)
0.686 0*809 0.366 0.642 0.624 0.726
1.88 1.49 1.10 1.12
0.37 0.24 0.06 0.07
pm for f-seed and 0.33 pm for s-seed. t I\’ = h (Ao/AYW~>o.
column A,/A givea the ratio of the initial value of A to the final value for each combination of monomer and seed. Assuming that in each combination, filaments became inactive at a rate A’ independent of their length, ln(A,/A)
= 5x’(L),.
The value of A’ calculated from the above relation is given in the last column of Table 2. The result shows that slowness in growth-saturation was due to the nature of the preparation of monomer. 4. Discussion On the basis of the experimental results obtained in this study, we shall discuss a model of inactivation. The model assumes (1) that during polymerization, a failure may happen by which a monomer is incorporated in a filament in an incorrect manner ; (2,) that this failure occurs, independently of the previous one, with a probability independent of the length of Lament, and (3) that a filament stops growing or
GROWTH-SATURATION
OF SALMONELLA
FLAGELLA
299
becomes inactive when a certain number of failures have been accumulated along the length of it. In addition, we assume, for simplicity, that filaments start growing from iniinitesimal length. Then, the model predicts that the distribution of length for an assembly of inactive filaments may be given by the probability density function of the r-distribution given in equation (l), where k denotes the number of failures required for inactivation and h denotes the rate of failure (or the probability that a filament meets a failure during growth by a unit length). The two parameters may be related to average length (L) and standard deviation u as follows (Lindley, 1966) : x = (L)/u~
and
k = (L)2/oa.
(2)
An assembly of inactive filaments has been shown to have (L) = 464 pm and ~7= 4.32 pm (Fig. 10). Putting these values in equation (2), we have X = 0.224 Pm -I and k = l-11. Moreover, equation (1) with these values of A and k fitted the experimental result closely. However, it must be noted that in this fitting, an incorrect assumption was involved that filaments grew from infinitesimal length. Presumably, one failure was enough for a filament to become inactive, that is, k = I. Then, equation (1) is reduced to an exponential distribution. In the dist& bution of Figure 10, the ratio of the weight-average length of filaments to the numberaverage was l-91, which is approximately equal to 2, the value required for any exponential distribution. Kawamura & Maruyama (1970) have found that F-act& in equilibrium with G-actin, has an exponential distribution of length. This result may be interpreted on the basis ,of an equilibrium theory presented by Flory (1957) and Oosawa & Kasai (1962). However, this theory can not be applied to the present case: When k = 1, the rate of failure is equal to the rate of inactivation and equation (2) is reduced to X = l/(L). Therefore, the value of X estimated from the data given in Table 1 is about O-12 pm-l. From Figure 10 we obtained h = 0.224 pm-l, while X = 0.37 pm -I for the combination of f-monomer and f-seed in Table 2. The reason for this disagreement remains unknown. According to a model of Salmonella flagella presented by O’Brien & Bennett (1972), a flagellum contains 2200 monomers in I pm of length. Taking into account this value and assuming that h = O-2 pm-l, one failure happens,. on average, when 11,000 monomers polymerize on to the end of each filament. At present, the mechanism of inactivation remains unresolved. Our preparations of monomer might have contained a substance which tightly associates to the ends of flagella filaments and prevents the further polymerization of monomer. The substance might be an impurity other than flagellin or partially denatured flagellin. We are now investigating the factor (or factors) controlling the rate of inactivation. Figure 7(a) shows that the distribution of length for active filament may be approximated by a Poisson distribution. This feature may be interpreted on the basis of the theory presented by Oosawa (1970) : he predicted that polymerization initiated in the presence of nuclei gives rise to a Poisson distribution of length. To explain the distribution of Figure 7(b), let us assume, for simplicity, that in the presence of any concentration of monomer, active filaments grow at a constant rate. Then, inactive filaments, which have been produced before the active filaments grow to length X, have the following distribution of length : f(L) = h exp(--hL) = 0
for L $ X, for L > X.
300
H.
HOTANI
AND
S. ASAKURA
Qualitatively, Figure 7(b) seems to satisfy this distribution. If any assembly of flagella filaments has a distribution of length possessing a peak at a finite length, the peak may be attributed to active filaments contained in the assembly (Fig. 7(c)). Iino (1969) has found that flagella attached to living bacteria (ad&) have a Poisson distribution of length, the most frequent length being about 10 pm. Such a distribution of length can not come from inactivation. From our point of view, most of the intact flagella appear to be still active. In addition, Iino (1969) has described how the average growth rate of intact flagella became smaller as their length increased. This flnding disagrees with the result given in Figure 6. The disagreement is likely to show that there exists a large difference in mechanism between in viva and in w&c polymerization of flagellin. We thank Professor T. Iino for generous gifts of S&none& strains. We are greatly indebted to Dr G. Eguchi for electron microscopy and to Dr S. Muramatsu for the preparations of antisera. Computations were performed using FACOM 230-60 in the Data Processing Centre, Kyoto University. REFERENCES Abram, D. & Koffler, H. (1964). J. Mo2. B&d. B, 168-185. Ada, G. L., Nossal, G. J. V., Pye, J. & Abbot, A. (1963). Nature (London), 199, 1257-1259. Asakura, S. (1968). J. Mol. Bid. 35, 237-239. Asakura, S., Eguchi, G. & Iino, T. (1964). J. MoZ. Bid 10, 42-56. Asakura, S., Eguchi, G. &z Iino, T. (1968). J. Mol. Bid. 16, 302316. Asakura, S., Eguchi, G. & Iino, T. (1968). J. Mol. Bid. 35, 227-236. Flory, P. J. (1957). Prinoipls of Polymer Olumiedry, Cornell University Press, Indiana. Fujime, S., Hada, Y., Usami, T., Maruyama, M. & Asakura, S. (1972~). Biochim. Bkphya. Acta, 278, 685-688. Fujime, S., Maruyama, M. & Asakura, 8. (197%). J. Mol. Bid. 68, 347-359. Gerber, B. R. & Noguchi, H. (1967). J. Mol. B&L 26, 197-210. Gerber, B. R., Asakura, S. & Oosawa, F. (1973). J. Mol. B&L 74, 467-487. Hotani, H. (1971). J. Mol. Bid. 57, 575-687. Iino, T. (1961). #en&x, 46, 1465-1469. Iino, T. (1969). J. Cen. Mic.robiol. 56, 227-239. Iino, T., Suzuki, H. & Yamaguchi, S. (1972). Nature New Bial. 237, 238-240. Kawamura, M. & Maruyama, K. (1970). J. Biochem. 67, 437-457. Kondoh, H. & Hotani, H. (1974). B&him. Biophv. Acta, 336, 117-139. Kuroda, H. (1972). B&him. Bbphya. Ada, 285, 253-268. Viewpoint, Lindley, D. V. (1966). Introdudkm. to ProbabWy and St&&&a from Bag&an Cambridge University Press, London. Lowy, J. & MaDonough, M. W. (1964). No&re (Loladon), ter, 125-127. O’Brien, E. J. &z Bennett, P. M. (1972). J. Mol. Bid. 70, 133-162. Oosawa, F. (1970). J. Theo*. Bid. 27, 69-86. Oosawa, F. & Kasai, M. (1962). J. Mol. Bid. 4, 19-21. Wakabayashi, K., Hotani, H. BEAsakura, S. (1969). B&him. Btiphy8. Acta, 175, 195-203.
Growth-saturation
in vitro of Salmonella Flagella
H~ROEAZU HOTANI AND SHO ASAKURA
Department of Biophysics, Faculty of Science Kyoto University, Kyoto, Japun and
Institute of Molecular Biology, Faculty of Science Nagoya University, Nagoya, Japan (Received 12 November 1973, and in revised fmn 20 February 1974) At physiological ionic strength and pH, short fragments of Salmonella flagella (seeds) grow longer in the presence of monomeric flagellin and there exists a one-to-one correspondence between the seeds and fully grown Claments (Asakura et al., 1964). In this study it was shown that when monomer and seed derived from a preparation of flagella (strain SJ26) were mixed in a protein ratio r larger than 20, the filaments stopped growing or became inactive for a long period of time, and the average length of inactive filaments was independent of the value of r. technique The phenomenon was called growth-sc&mGm. The antibody-labelling (Asakura et al., 1968) made it possible to show that, though active filaments having equal lengths grew at various rates ranging between 0 and 0.16 ~m/min, the average value of growth rate depended little on length. On the other hand, it was found that the proportion of inactive filament in the total filament increased rapidly as the value of T was increased continuously from 0 to 10. The dependence of the proportion of inactive filament on r suggested that filaments became inactive with a probability independent of their length. The rate of inactivation (or the probability with which a flsment becomes inactive during growth by a unit length) had various values when different preparations of flagella were used as starting materials. The distribution of length for an assembly of inactive Clanrents was determined by low-magnification electron microscopy. The result could be approximated by an exponential distribution: the numberaverage length was 4.54 q and the rate of inactivation was 0.224 pm-l.
1. Introduction It is now well established that the polymerization of flagellin into flagella filaments is a self-assembly process (Ada et al., 1963; Abram & Koffler, 1964; Lowy & McDonough, 1964; Asakura et al., 1964,1966; Gerber & Noguchi, 1967; Wakabayashi et al., 1969; Hotani, 1971; Iino et al., 1972; Kuroda, 1972; Gerber et al., 1973; Kondoh BEHotani, 1974). Indeed, from a thermodynamic point of view, the process may be regarded as a simple reversible one. However, it has a kinetic feature in common with crystallization, and presumably of biological importance. For example, simple heating of Salmonella flagella at physiological ionic strength and pH gave rise to a solution of monomeric flagellin which was metastable at room temperature (Asakura et al.,
1964,1966). When the solution was seeded with short fragments of flagella, rapid 286
286
H. HOTANI
AND
S. ASAKURA
polymerization was initiated and, in a short period of time, the concentration of monomer decreased to a value approximately equal to zero. This means that the equilibrium between monomer and polymer under these conditions heavily favoured the polymeric form. It is remarkable that at a high degree of super-saturation, spontaneous nucleation rarely occurred. In the above experiment, purified flagella filaments could be shortened by sonic vibration to obtain seeds. When a seed solution was left at room temperature for a long period, the average length of shortened flagella, measured by electron microscopy, increased little, indicating that short flagella were incapable of an end-to-end association. Taking into account these circumstances, it is expected that in the presence of monomer, seeds grow into single flagella filaments and, therefore, there exists a one-to-one correspondence between the seeds and fully grown filaments. This expectation was shown to be correct in the following experiment (Asakura et al., 1964). When monomer and seed were mixed in a protein ratio r (= wt monomer/wt seed), the average length of fully grown Clanrents was (1 + r) times the average length of the added seeds, though any assembly of fully grown filaments had a broad distribution of length. The above experimental result was, however, obtained for small values of r (less than 3). A question arises at this point: if a su&iently large amount of monomer is supplied to a seed, does it grow without limit? Fujime et al. (1972a,b) have investigated this problem by measurements of quasi-elastic scattering of laser light and flow birefringence. The data obtained suggested that the average length of flagella filaments did not exceed some critical value even in the presence of monomer. The present paper reports a more detailed study of the same problem. First, it will be shown that when monomer and seed were mixed at large values of r, the overall rate of polymerization, or the rate at which the concentration of monomer decreased as a result of polymerization, decreased with time more rapidly than expected and finally reached zero, while the solution still contained a high concentration of monomer capable of rapid polymerization on the second addition of seed. Therefore, we must consider that the flagella filaments stopped growing in the presence of monomer. Hereafter, this phenomenon will be called gvw%A-aa&dion, and has been investigated by carrying out several experiments which will be described in this paper.
MaMaIs and Methods (a) Prepardon of monomer and seed 2.
&almcm&o strain 5526, which produces normal flagella with 1,2-antigen (Iino, 1961), was used for the investigation of growth-saturation. Cultivation of the organisms, the isolation and p&cation of flagella and the preparation of monomer and wed were carried out by the method described by Asakura & d. (1964) and Hotani (1971). To observe growth-satnration, mixtures of monomer and seed at large values of r had to be incubated at 26°C (optimal temp. for polymerization) for a few days. To prevent bacterial growth during this period, we used a medium (medium C) containing O-2 mg streptomycin/ml and 60 units penioillin/ml in addition to O-16 M-NaCl and O-01 r.r-phosphate bnffer (pH 643). It was shown by viscosity measurements that the overall rate of polymerization initiated at small values of r was influenced little by the addition of antibiotics. It has been found that the mininmm value of r required for observing growth-saturation varied when different preparations of flagella were used as starting materials. The reason for this remains unknown. To investigate growth-saturation by the antibody-l&belling technique (see below),
GROWTH-SATURATION
OF SALMONELLA
FLAGELLA
287
we used another strain 55870, which produces normal flagella with i-antigen (Iino, 1901). Monomer was prepared from GfIageIla by the same method as that used in the preparation 1,2-monomer. During the present study it was found that when i-monomer solutions were left at 26% for long periods of time, polymerization was spontaneously initiated in them. For this reason, we used only l,Z-flagella for the investigation of growth-saturation. (b) Kinetk
expetitnertt
of polymerizutti
Polymerization was followed by the method described by Asakura (1968). Polymerization initiated in a mixture of monomer and seed could be stopped, after any period of time, by simple dilution of the mixture with 26 vol. of cold distilled water. The diluted solution was centrifuged at 106,000 g for 1 h to sediment flagella filaments, and optical density at 278 nm (O.D.& of the supernatant solution, proportional to the concentration of monomer contained in the diluted solution, was measured (Figs 1 and 2). When the value diluted solution wae kept cold for a few hours before centrifugation, the o.D.~,~ remained unchanged. This method was useful also for observing growth-saturation and for measuring the percentage of the total monomer polymerized before growth-saturation (Table 1). (c) Antibody-labeUiw
experiment
To make clear the details of growth-saturation, it is important (1) to determine the percentage of the total filament contained in a given solution able to act a,a seed for further polymerization, and (2) to know the dependence of the growth rate of fllamenta on their length. For these purposea we used the antibody-labelling method of Asakura et al. (1988). To a solution of l,Z-flagella filament was added i-monomer, to produce heterogeneous flagella 8lament (or block copolymer), which was treated with antiserum against 1,2 or i-flagella to distinguish parts of each illament consisting of 1,2 and &-flagellins, respectively. Flagellins derived from 1,2 and i-flagella have been shown to copolymerize with little discrimination. Anti-flagella sera were prepared by the method described by Kondoh & Hotani (1974), and antigen-antibody reaction was allowed to take place by the following procedure : a drop of a block copolymer solution was applied to a grid, the excess portion was gently blotted with a long and slender filter paper, and the grid was floated with the specimen side down on a lOO-fold diluted antiserum in a small well for 6 min or longer at room temperature. Thereafter, the grid was washed with about 10 drops of distilled water to remove excess protein and the antibody-labelled block copolymer was negatively stained with 1% phosphotungetate and observed in a JEM-‘IA electron microscope at an inf3trumental magnification of 6000. (d) Meaezcre~
of le&
by low-magn@ation
electron mbroscopy
A growth-saturated sample consisted of fllamenta with various lengthi3, the maximum being longer than 30 q. To obtain the distribution of length for this sample, we ueed a IOO-mesh grid (VECO) and observed the specimens at an instrumental magnification of 1000, using an attachment, JEM-ACW, which gives wide and highly contrasted images. In addition, it W&B necessary to take 9 micrographs or more continuously with minimal overlaps. The micrograpti were printed at B-fold magnification and the prints were connected together. In general, the probability that a filament does not have its whole length within a given area increaeea with increasing Glament length. To avoid the experimental error due to this effect, we ueed the following procedure: on the connected printa was drawn a frame, each side of which was 00 mm (corresponding to 10 q) inside the edge of the connected prints. Then, almost all of the &men& crossing the frame had their whole length within the connected prints. Filaments entirely outide the frame were excluded from the investigation. Lengths of fllamenta were measured with a mapmeasurer. In one experiment, we examined the distribution of length for a sample of fully grown filaments at r = 6. In this case, single micrographs enlarged to a magnification of 26,000 were used. It has been reported that flagella filaments often associate by their enda to give the appearance of bend6 and branches (Asakura et ol., 1968,1968). Bends and branches were encountered also in this study. Lengths of filaments were measured on the basis of the rule described previously.
288
H. HOTANI
AND
S. ASAKURA
3. Results (a) Ouerall rate of polym.erizatk
ati growth-saturcbtion
F’igure 1 shows kinetic data obtained for polymerizations initiated in solutions containing a constant concentration of monomer (25 mg/ml) and various concentrations of seed: curves A, B and C correspond to the cases of r = 5, 30 and 60. Sinoe the scales on the abscissa for the three curves are inversely proportional to r, the curves would coincide over the whole range of the abscissa, if the rate of polymerization were directly proportional to the product of the number concentrations of monomer and polymer. However, the rate of polymerization decreased with time more rapidly as the value of c increased. When, for example, two solutions of P = 6 and 60 had an equal o.D.,,,~ value, it was expected that the average length of filamerits contained in the solution with r = 60 would be 12 times the average length of Laments contained in the other solution. Therefore, a straightforward interpretation of the results of Figure 1 is to assume that the growth rate of flaments depended on their length and decreased gradually as they grew longer. However, this possibility will be excluded later.
30 60 Timefminl
fi
FIG. 1. Rates of polymerizetions
initietad
in solutions
60 ( 120 (
oontaining
a constant
ooncentration
of
monomer end various oonoentrations of seed at 26°C. The medium used in this experiment oontained only 0.16 aa-NeC1 and O-01 M-phosphate buffer (pH 66). One ml of monomer solutions oonGning 3.0 mg protein/ml and 0.2 ml of seed solutions containing 3*0,06 and 0.26 mg protein/ ml, respeotively, were mixed to obtain 3 sets of solutions having different values of f, and the concentrations of monomer contained in eaoh set of solutions left at 26°C for verious periods of time were determined by the methods desoribed in Materiels and Methods. Initial conoentration of monomer contained in the 3 sets of solutions ~8s 2.6 mg/ml and r = 6 (aurve A), 30 (curve B) snd 60 (OUIV~ C). Ordinate, the concentration of monomer expressed in terms of O.D.srs; end 8bs&s8, time after mixing monomer and seed. Curves A, B end C should be referred to the three saales on abscissa (A), (B) end (C), respectively, which were drawn 8s being inversely proportion81 to the velue of r.
GROWTH-SATURATION
OF SALMONELLA
FLAGELLA
289
Time(h)
Or
3p
“IO
!
I 0
I 2
I 4
L 6
Fm. 2. Growth-satumtion of flagella filament in medium C at 26°C. Two ml of monomer solutions containing 3.0 mg protein/ml end 0.4 ml of seed solutions co&king 7.6, 3.0 and 0.167 mg protein/ml, respeotively, were mixed to obtain 3 sets of solution of r = 2 (curve A), 6 (curve B) and 90 (curve C), and the concentmtions of monomer contained in each set of solutions left at 26°C for verious periods were determined by the method described in Meterials and Methods. Ordinate, the concentration of monomer expressed in terms of O.D.,,,; and abscissa, time after mixing monomer and seed. Curves A and B should be referred to the lower abscisse and curve C to the upper. Curve C shows that polymerization initiated st r = 90 beceme saturated in 8bout 70 h. The experiment81 point on curve C at 91 h w&s obtained BS follows. A sample solution left for 90 h (2.4 ml tot81 vol.) was mixed with 0.4 ml of 8 fresh prep8ration of seed aontaining 7.6 mg protein/ml, and the mixture w&s left at 26°C for 1 h before the measurement of O.D.srs.
A similar experiment was carried out to follow the whole process of polymerization. Curve C in Figure 2, obtained for r = 90, shows that polymerization stopped in about 70 hours, whereas the solution left for 90 hours still contained a high concentration of monomer capable of rapid polymerization on the second addition of seed. The fmal level of O.D.87s absorbance for r = 2 (curve A) or 5 (curve B) was about O-017, which is larger than expected from the equilibration data given by Gerber et al. (1973). Indeed, when a solution containing 1.25 mg seed/ml in medium C was left at 26°C for several hours, diluted with 2.5 volumes of cold distilled water and centrifuged at 105,000 g for one hour, the supernatant fraction had sn 0.D.a78 value smaller than 0.005. Therefore, the value of 0.017 cannot correspond to the equilibrium concentration of monomer under the given conditions, It is likely that the monomer solution used contained denatured flagellin produced during he&-treatment (Asakura et al., 1964). In parallel to the above experiment, pairs of solutions of various T values were left at a given temperature for 70 and 90 hours, respectively, in order to determine the dependence on r of the saturated level of O.D.,,,. The 0.D.27s values obtained
290
H.
HOTANI
AND
S. ASAKURA
at 70 and 90 hours were equal, within experimental error, indicating that polymerization had ended or stopped within 70 hours in all casea. The averages of the two values for each pair are given in the second column of Table 1. The pair of solutions at r = co, which contained no seed, gave an 0.D.a78 value of 0*205. The third column of Table 1 gives Ao.D.,,, = O-205- o.D.~,*, which is proportional to the concen1
TABLE Growth-aaturdion
r
as rev&
by sediwbedahnb
experimeti
0.D.m
Ao.~.mst
as
0.017 0.020 0,026 O-038 O-086 o-122 o-149 0.160 0.188
O-188 O-186 0.180 0.167 0.119 O-083 O-056 0.045 0.037
2.8 10.0 14.2 17.3 18.4 19.2 17.4 17.4 17.2
1.4 4.9 7.0 8.6 9-o 9.4 8.6 8.5 8.4
2 10 16 20 30 46 60 76 90
For experimental oonditions, see Fig. 2. The given 0.D .l78 velues were averages of those obtained at 70 and 90 h after the initiation of polymerization. The everage length of the seed used wna 0.49 pm and the 0.D.278 value obtained etr = 00 was 0.206.
t Ao.D.,,, = 0.205 -
o.D.~~~.
$ Ct = 9’ (0.D.,,s/0a205)
+ 1.
8
. OO FIG.
obtained
3. Dependence of the average from Table 1.
I 30 I
length
I 60
of Alaments
I 9f
on 7. The experimental
points
were
GROWTH-SATURATION
OF SALMONELLA
FLAGELLA
291
tration of flagellin polymerized during the experiment. The fourth column gives a = ?(dO.D.,,,/0-205) + I, which is equal to the ratio of the average length (L) of filaments produced in each solution to the average length (L). of added seeds. The preparation of seed used in this experiment was observed by electron microscopy (Plate I(a)) and it was found that (L), = 0.49 pm (Fig. 4(a)). The fifth column gives
WLength offibments measured by electron microswpy Plate I includes electron microgmphs of those samples with r = 10,20,30,60 and 90 which were used in the preceding experiment: the micrographs were taken between 70 and 90 hours after the initiation of polymerization. It will be seen that each sample consisted of filaments with various lengths. Figure 4(b) shows the distribution of length obtained for the sample with r = 10 by the method described in Materials and Methods. The average length (L) celculated from this result was 45 pm, which is approximately equal to the value of 4-9 pm given in Table 1. This agreement shows that the number of filaments contained in the solution changed little during 70 hours or more. It is clearly of interest to show growth-saturation by electron microscopy; however, it is not easy in practice. Therefore, from electron micrographs of the samples used in the experiment of Table 1, we selected filaments longer than 4.2 pm (50 mm in the electron micrograph of Plate I) and measured their length to calculate the average length of the selected filaments (Fig. 5). The results showed that in the range of r larger than 20, the average length of selected filaments was samples examined approximately constant. Presumably, the growth-saturated had similar distributions of length.
Length
crrn) b)
FIG. 4. Distributions of length determined by eleotron miorosoopy for those preparations of seed (a) and filament produced at r = 10 (b), which were used in the experiment of Tsbb 1. The total number of filaments used for (a) was 616 and that for (b) w&a 402. The broken lines denote average’lengths. 20
H.
282 ,5r--.-~~-----
HOTANI
AND ..-.
-
8. ASAKURA -
.--
.
Fm. 6. Growth-aeturation &s observed by electron miorosaopy. Filaments longer than 4.2 e were selected from eleotron micrographs of the samples used in the experiments of Table 1, and the average length of the aeleoted filaments from each aample wan determined. More than 100 filaments were wed for obtaining eaah experimental point.
(c) @moth rate and length Since any preparation of flagella filaments had a broad distribution of length, it was difEcult to determine the dependence of the growth rate of filaments on their length by conventional methods. However, the antibody-labelling method described in Materials and Methods was found to be useful for this purpose (Fig. 6). A preparation of l,2-flagella filament, obtained by mixing monomer and seed at r = 5, was allowed to grow in the presence of a large amount of i-monomer for a short period, and the product was treated with antiserum against 1,2-flagella and observed by electron microscopy (Plate II(a)). This procedure made it possible to distinguish the original 1,gpai-t of each filament from the newly added i-part. In this experiment, filaments of the type (i)-(1,2)-( i ) were not encountered: this is due to the fact that in. vitro growth of flagella filament takes place at one of the two ends (Asakura et al., 1968). From a number of electron micrographs of the antibody-labelled filament, we selected filaments having both 1,2 and i-parts and measured lengths of the two parts of each filament in the selected group. The relation between the two lengths is shown in Figure 6, which may be taken as representing length dependence of growth rate. The result shows, rather unexpectedly, that filaments having equal lengths grew at various rates ranging between 0 and 0.16 pm/minute. Possibly, this is an important feature of flagellin polymerization, though its interpretation remains unresolved. Irrespective of this circumstance, it is unlikely that the average growth rate of filaments had any meaningful dependence on their length. Indeed, the correlation coefficient, which has a value between -1 and 1 by definition, and is 0 for no correlation, is 0978 for the experimental points in Figure 6. This result is most unfavourable for the hypothesis that growth-saturation wss brought about by the mechanism of length-dependent growth rate. The distribution of length for the 1,2-part of the heterogeneous filament used in the above analysis is given in
PLATE I. Flagella filaments formed at various values of T. (a) Seed; conditions, T = 10; (c) 20; (d) 30; (e) 60; and (f) 90. For experimental Magnification 6000 x . These micrographs were used in t,he exprrimcnts
(b) filaments produced see Fig. 2 and Table of Figs 4 and 5. [.faring
at 1.
p. 2!1’
hATE II. Heterogeneous flagella filaments labelletl with antibody against 2,5flagella. (a) An electron micrograph used in t.hp txpwiments of Fig.; 6 and 7. r\ntibotly-labellect filament. COIIsistett of I&‘-flagellin and unlabclled filament consisted of i-flagellin. Magnificat,ion 15,000 * (b) and (c) Electron micrographs used in t,hc experiment of Fig. 8. Thcsr micrographs wcrc~ t,aken before and after incubation of a preparation of seed at. 26°C’ for 60 h. Magnificat~ion 12,~lO~l
PLATE III. Heterogonoous flagella filaments labclletl with antlbdy. Homogeneous I,Z-filammts formed at> various values of r were allowed t,o grow in t>hc:presence of i-monomrr for 6 h antl, t,hereafter, t.reatctl wit,h anti-1,2-flagella swum. (a) Sncd; (b) r = 3; (c) 6; and (cl) 10. Magnificnt.ion 15,000 x These micrographs WOI‘Cwed in t,hc>ccqwwiment of Fig. 9.
UROWTH-SATURATION’OF
SALMONELLA
FLAGELLA
293
Figure 7(a). This distribution may be compared with that for active filament contained in the 1,2-filament examined (see below). (d) lnactkvation of jihments Plate II(a) shows some homogeneous 1,2-filaments, indicating that inactive filaments, incapable of acting as nuclei for further polymerization, were contained in the given 1,2-flagella solution. In the statistical analysis of Figure 6 we used 417
I F
I
.
.
.
.
.
.
.
.
.:
.
.
:
. .
.
.
*.
:
.
.
:
.
.
:.
f
.!
.:
.
.
.
**
.
. .
.
.
. .
1.
.i
.
.
:.,.
*m
.
1..
*.
8
.
*.
. .
1..
.
. .
.
. .
:
:
:..
.I
.
.
:
:
.
.
;.
.
s
.
.
.
:.z,
:
.
.
:
.
.
.
e
:
.:.
:.
*
. .
:
.
. .
. .
i
.
.
.
.
i
,.:.
..:
. . .
.
. .
,
ii.
.
.
.
.,....
*
. .
*
. . . .
.
*
.I
.
.
.:.
e*:.
5
.
::.
.
,
I
.
.,s..:
m
.
.
. ..i..
:.i..
.:
. .
.
,
:.,!
1
.
ii
.
.l.
.
.
.
.
.
.
.
.
*.
‘I...
,..:
.
.
.
:.
e
8
. . .
. .
.
:
.
.
.
,.
. .
. .
. .
.
.
.
.
.
.
.
. .
::
.
.
.
.
.
.
.
. . . .
.
.
. .
. .
I-T-----
. .
::
.
,
. . . . .
.
.
.
.
. .
.,
:
. .
.
.
.
I
I
I
I
2
3
Length of I,P- part (pm)
!
Fro. 6. Relation between growth rata and length determined by the antibody-labelling method. Two solutions of monomer and seed (eeah oonteining 3-O mg protein/ml) were mixed at volume ratio 5: 1 and the mixture wea left at 26°C for 20 h for complete polymerixation. Then, the solution was mixed with 6 vol. of 8 solution cont.&kg 3-O mg i-monomer/ml and, after inoubation et 26°C for 5 min, the mixture waa diluted with a large volume of oold distilled water to stop the polymerization of i-flagellin. The diluted solution was mixed with antiserum against 1,2flegells and the antibody-labelled fllnment was observed by eleotron microscopy (Plate II). From a number of electron miorographa obtained, filaments having 1,2 end i-parts were selected (417 in total) end lengths of the two parts of each filament were measured. Ordinate, the length of the +art; and absoissa, the length of the 1,2-part. The reletion between the two lengths may be regarded as representing the dependewe of the growth rate of filaments on their length. Denoting the length of the 1,2-pert of a selected filament by z, and that of the i-part by y,, the correlation coefficient is given by:
where d and g denote average lengths. experiment&l points w&s 0.078.
The value of this ooefficient
c&uleted
from the given
H. HOTANI
AND
8. ASAKURA
Length (pm)
FIU. 7. (a) Distribution of length obteined for the 1,2-pert of the heterogeneous timent used in the experiment of Fig. 6. (b) Distribution of length for homogeneous 1,24lament enoountared at the same time. The total number of Clementa used wse 626. (0) The superposition of the distributions (a) and (b). The broken lines denote everage lengths.
heterogeneous filaments, while the number of homogeneous 1,2-filaments encountered at the same time was 626. A few homogeneous i-filaments also were found: however, those were excluded from the investigation. Then, the proportion A of active filament in the total filament was 0.44. Figure 7(b) shows the distribution of length for the homogeneous 1,2-filament or inactive filament. It is remarkable that the two distributions obtained for active and inactive filaments were different in type and the average length of inactive filaments was shorter than that of active filaments. This result appears to indicate that rapid interconversion of a filament between the active and inactive states never happened. Here, we assume that an active filament grows at an average rate independent of the length but suddenly becomes inactive. In connection with this assumption, it was first shown that growth is required for inactivation. In the experiment of Figure 8, parts of a preparation of I,&-seed were left at 26°C for various periods and the value of A for each part was determined by the antibody-labelling method (Plate II(b) and (c)). The result obtained shows that inactivation did not occur over the period of time examined. Next, in the experiment of Figure 9, 1,2-monomer and 1,2-seed were mixed at various values of r in a range between 0 and 10 and, after complete polymerization, the value of A for the product in each mixture was determined. The amount of i-monomer added to each preparation of 1,2-filament was equal to the amount of 1,2-seed added to 1,2-monomer in the initial step of polymerization,
GROWTH-SATURATION
-1-L
OF SAlliVONELLA
20
FLAGELLA
295
40 Time(h)
FIG. 8. Absence of inactivation when seeds were left done. Parts of a solution containing 3.0 mg I,2seed/ml were left at 26°C for various periods and each part was mixed with an equal vol. of a solution containing 3.0 mg i-monomer/ml. The mixture was left at 26°C overnight and the product was treated with antiserum against 1,2-flagella to determine the proportion A of aative filament in the total. Eaoh experimental point was obtained from more than 400 filaments.
FIQ. 9. Inaotivation of filaments depended on the extent of their growth. Parts of a solution containing 3.0 mg 1,2-seed/ml (average length 0.26 pm) were mixed with appropriate volumes of solutions containing 3.0 mg I,%-monomer/ml to give various values of z between 0 and 10, and eaoh mixture was left at 26°C overnight for oomplete polymerization. Then, each solution was mixed with an appropriate volume of a solution containing 3.0 mg i-monomer/ml to make the initial concentrations of 1,2-seed and i-monomer equal, and the mixture was left at 26°C for 6 h. The product was treated with antiserum against l,%-flagella to determine the proportion A of active filament in the total. Each experimental point was derived from more than 300 filaments.
H.
296
HCTANI
AND
8. ASAKUXA
and each mixture of l&filament and i-monomer was left at 26°C for six hours before antibody-labelling (Plate III). In this experiment also, homogeneous i-filaments were encountered, which were excluded from the statistical analysis. The results obtained show that the proportion of active filament in the total filament decreased when r or the average length of filaments increased. The smooth curve in this Figure represents : A = 0,793 exp( -0.096r). If filaments contained in each mixture of 1,2-monomer and 1,2-seed became inactive with B probability independent of their length, we have the following relation : 0*096r = Xl.(L),, where A’ is the rate of inactivation or the probability with which a filament stops growing during growth by B unit length. The seed used in the above experiment had (L), = 0.26 pm, as measured by electron microscopy. Then, we obtain A’ = 0.37 pm-‘.
15c I\
” ‘OC)5 E5 -5 P
5c )-
c
‘0 Length (pm)
J!‘ro. 10. The distribution of length obtained for an assembly of inactive filements. Monomer and seed derived from a preparation of l,%-5agella were mixed et c = 20 end the mixture (total protein 2.13x&ml) wm left et 2&W for 70 h and then observed by eleotron microaoopy. Lengths of 5lmmenta were measured by the method deaoribed in Matariala and Methods. The total num+ of 5lamenta used was 962 and the seed used had
GROWTH-SATURATION
OF S-4 LMONELLA
FLAGELLA
297
(e) Length of inactive jikzmcnd Figure 10 shows the distribution of length for filament produced in a mixture at r = 20 of monomer and seed (the average length being 0.26 pm) derived from a preparation of 1,2-flagella. Plate IV(a) shows an electron micrograph used in the statistical analysis. In a separate experiment of the type shown in Figure 3, it was found that the minimum value of r required for growth-saturation wssa about 15 when the same monomer and seed were combined. Therefore, the given distribution of length may correspond to an assembly of inactive filaments. The number-average length calculated from the distribution WIW4.64 pm, the weight-average length was 8.65 pm and the standard deviation was 4.32 pm. The smooth curve in Figure 10, which is a good approximation of the experimental result, was derived from the probability density function of the r-distribution (Lindley, 1965) : fk (L) = p+J Lkc-l exp(-AL), where A = O-224 pm-l discussed later.
and k = 1.11. The significance of the agreement will be
(f) Growth-saturation and the nature of the preparation of monomer AR has saturation materials. which led
been described repeatedly, the minimum value of r required for growthdiffered when different preparations of I,&-flagella were used as starting In the course of this study we obtained an unusual preparation of flagella to no growth-saturation within 70 hours (Fig. 11). Plate IV(b) shows very .
.
.
/
/
.
-
.
/;i
/ ./
l
/ /
I
I
30
60
90
Fxo. 11. Relation between average length and r derived from en unusual preparation of 1,2flagella. For experiments1 aonditiona and procedure see Fig. 2. The experimental points were obtained et 70 h sfter the initiation of polymerization. The seed used has
II. HOTANI
298
AND
S. ASAKURA
long filaments produced at r = 90. It is unlikely that polymerization continued as a result of spontaneous nucleation or the formation of new filaments. We named the above preparation of flagella slow (or s) and that used in the experiment of Figure 10 fast(or f)and examined which factor in the combination of monomer and seed was responsible for slowness in growth-saturation (Table 2). From f and Alagella were prepared monomers and seeds (each containing 3-O mg protein/ml) and they were mixed at r = ti in all combinations. Each mixture was left at 26°C overnight for complete polymerization and then mixed with l/6 volume of a solution containing 3-O mg i-monomer/ml. The mixture was left at 26°C for several hours and treated with antiserum against i-flagella to determine the value of A for each preparation of 1,2-filament. The f-seed had (L),, = 034 pm and the s-seed had (L)O = 0.33 pm. To obtain the initial value of A, each preparation of seed was mixed with an equal volume of a solution containing 3.0 mg i-monomer/ml and the mixture was left at 26°C for several hours, followed by the treatment with anti-i-flagella serum. The results obtained are given in the third column of Table 2. The fourth TABLET Rates of inactivations when monomers and seeds derived from fast and slow preparations of jhgelb were combined Monomer
Seed
f f” 8
;
8
8
A
AoIA
h’t (pm-l)
0.686 0*809 0.366 0.642 0.624 0.726
1.88 1.49 1.10 1.12
0.37 0.24 0.06 0.07
pm for f-seed and 0.33 pm for s-seed. t I\’ = h (Ao/AYW~>o.
column A,/A givea the ratio of the initial value of A to the final value for each combination of monomer and seed. Assuming that in each combination, filaments became inactive at a rate A’ independent of their length, ln(A,/A)
= 5x’(L),.
The value of A’ calculated from the above relation is given in the last column of Table 2. The result shows that slowness in growth-saturation was due to the nature of the preparation of monomer. 4. Discussion On the basis of the experimental results obtained in this study, we shall discuss a model of inactivation. The model assumes (1) that during polymerization, a failure may happen by which a monomer is incorporated in a filament in an incorrect manner ; (2,) that this failure occurs, independently of the previous one, with a probability independent of the length of Lament, and (3) that a filament stops growing or
GROWTH-SATURATION
OF SALMONELLA
FLAGELLA
299
becomes inactive when a certain number of failures have been accumulated along the length of it. In addition, we assume, for simplicity, that filaments start growing from iniinitesimal length. Then, the model predicts that the distribution of length for an assembly of inactive filaments may be given by the probability density function of the r-distribution given in equation (l), where k denotes the number of failures required for inactivation and h denotes the rate of failure (or the probability that a filament meets a failure during growth by a unit length). The two parameters may be related to average length (L) and standard deviation u as follows (Lindley, 1966) : x = (L)/u~
and
k = (L)2/oa.
(2)
An assembly of inactive filaments has been shown to have (L) = 464 pm and ~7= 4.32 pm (Fig. 10). Putting these values in equation (2), we have X = 0.224 Pm -I and k = l-11. Moreover, equation (1) with these values of A and k fitted the experimental result closely. However, it must be noted that in this fitting, an incorrect assumption was involved that filaments grew from infinitesimal length. Presumably, one failure was enough for a filament to become inactive, that is, k = I. Then, equation (1) is reduced to an exponential distribution. In the dist& bution of Figure 10, the ratio of the weight-average length of filaments to the numberaverage was l-91, which is approximately equal to 2, the value required for any exponential distribution. Kawamura & Maruyama (1970) have found that F-act& in equilibrium with G-actin, has an exponential distribution of length. This result may be interpreted on the basis ,of an equilibrium theory presented by Flory (1957) and Oosawa & Kasai (1962). However, this theory can not be applied to the present case: When k = 1, the rate of failure is equal to the rate of inactivation and equation (2) is reduced to X = l/(L). Therefore, the value of X estimated from the data given in Table 1 is about O-12 pm-l. From Figure 10 we obtained h = 0.224 pm-l, while X = 0.37 pm -I for the combination of f-monomer and f-seed in Table 2. The reason for this disagreement remains unknown. According to a model of Salmonella flagella presented by O’Brien & Bennett (1972), a flagellum contains 2200 monomers in I pm of length. Taking into account this value and assuming that h = O-2 pm-l, one failure happens,. on average, when 11,000 monomers polymerize on to the end of each filament. At present, the mechanism of inactivation remains unresolved. Our preparations of monomer might have contained a substance which tightly associates to the ends of flagella filaments and prevents the further polymerization of monomer. The substance might be an impurity other than flagellin or partially denatured flagellin. We are now investigating the factor (or factors) controlling the rate of inactivation. Figure 7(a) shows that the distribution of length for active filament may be approximated by a Poisson distribution. This feature may be interpreted on the basis of the theory presented by Oosawa (1970) : he predicted that polymerization initiated in the presence of nuclei gives rise to a Poisson distribution of length. To explain the distribution of Figure 7(b), let us assume, for simplicity, that in the presence of any concentration of monomer, active filaments grow at a constant rate. Then, inactive filaments, which have been produced before the active filaments grow to length X, have the following distribution of length : f(L) = h exp(--hL) = 0
for L $ X, for L > X.
300
H.
HOTANI
AND
S. ASAKURA
Qualitatively, Figure 7(b) seems to satisfy this distribution. If any assembly of flagella filaments has a distribution of length possessing a peak at a finite length, the peak may be attributed to active filaments contained in the assembly (Fig. 7(c)). Iino (1969) has found that flagella attached to living bacteria (ad&) have a Poisson distribution of length, the most frequent length being about 10 pm. Such a distribution of length can not come from inactivation. From our point of view, most of the intact flagella appear to be still active. In addition, Iino (1969) has described how the average growth rate of intact flagella became smaller as their length increased. This flnding disagrees with the result given in Figure 6. The disagreement is likely to show that there exists a large difference in mechanism between in viva and in w&c polymerization of flagellin. We thank Professor T. Iino for generous gifts of S&none& strains. We are greatly indebted to Dr G. Eguchi for electron microscopy and to Dr S. Muramatsu for the preparations of antisera. Computations were performed using FACOM 230-60 in the Data Processing Centre, Kyoto University. REFERENCES Abram, D. & Koffler, H. (1964). J. Mo2. B&d. B, 168-185. Ada, G. L., Nossal, G. J. V., Pye, J. & Abbot, A. (1963). Nature (London), 199, 1257-1259. Asakura, S. (1968). J. Mol. Bid. 35, 237-239. Asakura, S., Eguchi, G. & Iino, T. (1964). J. MoZ. Bid 10, 42-56. Asakura, S., Eguchi, G. &z Iino, T. (1968). J. Mol. Bid. 16, 302316. Asakura, S., Eguchi, G. & Iino, T. (1968). J. Mol. Bid. 35, 227-236. Flory, P. J. (1957). Prinoipls of Polymer Olumiedry, Cornell University Press, Indiana. Fujime, S., Hada, Y., Usami, T., Maruyama, M. & Asakura, S. (1972~). Biochim. Bkphya. Acta, 278, 685-688. Fujime, S., Maruyama, M. & Asakura, 8. (197%). J. Mol. Bid. 68, 347-359. Gerber, B. R. & Noguchi, H. (1967). J. Mol. B&L 26, 197-210. Gerber, B. R., Asakura, S. & Oosawa, F. (1973). J. Mol. B&L 74, 467-487. Hotani, H. (1971). J. Mol. Bid. 57, 575-687. Iino, T. (1961). #en&x, 46, 1465-1469. Iino, T. (1969). J. Cen. Mic.robiol. 56, 227-239. Iino, T., Suzuki, H. & Yamaguchi, S. (1972). Nature New Bial. 237, 238-240. Kawamura, M. & Maruyama, K. (1970). J. Biochem. 67, 437-457. Kondoh, H. & Hotani, H. (1974). B&him. Biophv. Acta, 336, 117-139. Kuroda, H. (1972). B&him. Bbphya. Ada, 285, 253-268. Viewpoint, Lindley, D. V. (1966). Introdudkm. to ProbabWy and St&&&a from Bag&an Cambridge University Press, London. Lowy, J. & MaDonough, M. W. (1964). No&re (Loladon), ter, 125-127. O’Brien, E. J. &z Bennett, P. M. (1972). J. Mol. Bid. 70, 133-162. Oosawa, F. (1970). J. Theo*. Bid. 27, 69-86. Oosawa, F. & Kasai, M. (1962). J. Mol. Bid. 4, 19-21. Wakabayashi, K., Hotani, H. BEAsakura, S. (1969). B&him. Btiphy8. Acta, 175, 195-203.