A low-angle X-ray diffraction study of bacterial flagella

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BIOCHIMICA ET BIOPHYSICAACTA BBA 45063

A LOW-ANGLE X-RAY DIFFRACTION STUDY OF B A C T E R I A L F L A G E L L A G. SWANBECK AND B. FORSLIND Department of Medical Physics, Karolinska Institutet, Stockholm (Sweden) (Received February 28th, 1964)

SUMMARY In order to differentiate between the various proposed models for the structure of bacterial flagella, low-angle X-ray diffraction studies have been carried out on wet specimens of Proteus vulgaris. The low-angle equatorial diffraction pattern has been obtained and compared with the theoretically calculated patterns for a rod model and the double and triple helical structures according to LABAW AND MOSLEY. The comparison shows that a model comprised of helical filaments is the most likely structure. Fourier-Bessel transformation of the experimental scattering data has been performed and the radial density-distribution curve gives low values in the middle of the structure, suggesting the flagellum has a hollow center, thus favouring the triple helical form.

INTRODUCTION The structure of bacterial flagella has been studied both with electron microscopy and X-ray diffraction. The electron-microscopic studies have essentially given three different models for the structure of bacterial flagella. In some studies 1,2 the flagella of various bacterial species have been pictured as solid circular cylinders with a diameter of 120 A. LABAW AND MOSLEY3,4 have published convincing pictures showing the flagella of both Brucella bronchoseptica and a bacterium to consist of two or three filaments with a diameter of about 50 A twisted around each other giving the whole flagella a diameter of about 120 A. Similar findings have been made on flagella from Proteus vulgaris by PREUSSNER5. In sectioned material it has been shown 6 that the filaments of the flagella of Proteus vulgaris are split apart by OsO 4 fixation. In a recent study it has been claimed that the filaments consist of spherical balls 7. X-ray diffraction data of bacterial flagella have been given by ASTBURYet al.S, ~ and BEIGHTON et al. 1°. These papers have mainly described the wide-angle diffraction pattern and no registration of the diffraction pattern at low angles has been made. BERGEn has made calculations of the diffraction patterns of two models for the structure of bacterial flagella. In one model the flagella consisted of three parallel filaments and in the other model of seven parallel filaments in a hexagonal array. It is, however, difficult to evaluate these models as no experimental patterns at low angles were available. The purpose of the present study is to give data on the experimental low-angle Biochim. Biophys. Mcta, 88 (1964) 422-429

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diffraction pattern of flagella from Proteus vulgaris and to analyse the structural implications of the diffraction pattern. MATERIAL AND METHODS

The flagella used in this investigation were obtained from a strain of Proteus vulgaris, which had been grown on a liquid broth medium in a growth tank of 600 1. Detailed information on the composition of medium and growth conditions and on the separation of the flagella from the bacterial bodies has been given by ERLANDER et al. 1~. Concentration of the flagellar suspension was, however, performed b y dialyzis against cellugel and polyethylene glycol. The concentrated flagellar solution was subsequently spun for 20 rain at 40000 rev./min in a Spinco preparative (cooled) centrifuge and the resulting gel was stored at 3 ° . The preparation was examined for its content of flagella by electron microscopy. To obtain a specimen with good orientation the flagellar gel was resuspended in distilled water and subsequently spun in a special centrifuge head of aluminium at 5000 rev./min for 4-6 h continuously. This centrifuge head has a single, circular chamber along its perif'ery, the outer wall of which is shaped as a " V " (Fig. z). The rotation sets up flow gradients parallel to the perifery of the outer chamber wall and Lid

\

Centrifugotion chamber

Fig. 1. Secton t h r o u g h c e n t r i f u g e h e a d s h o w i n g close-fitting plastic lid as u s e d for o r i e n t a t i o n of t h e bacterial flagella.

under the influence of these gradients the flagella, which are very long compared with their diameter, are oriented along the inner perifery of the centrifugation chamber and sediment to the bottom of the V-shaped cavity. To prevent evaporation (thus increasing the viscosity of the solution) the centrifuge head is equipped with a closefitting lid. After the withdrawal of the supernatant the centrifuge is run without the lid for 15 min to allow the sediment to dry, thus forming a thin transparent film which easily comes off the chamber wall. The thin flakes obtained b y this method were then trimmed into rectangles and piled on top of each other for X-ray specimens. Tests of orientation were made in a polarizing microscope. The equatorial low-angle diffraction pattern also gives a good estimation of the degree of orientation in the specimen. In order to obtain a high humidity for the specimens these were mounted in a special chamber with mica windows tight under low-pressure conditions. Low-angle diffractograms were obtained in an evacuated camera with a resolution of 450 A. The camera is pin-hole collimated according to the principle of BOLDUAN AND BEAR13 with a specimen to film distance of 12o ram. Biochim. Biophys. Acta, 88 (1964) 4 2 2 - 4 2 9

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G. SWANBECK, B. FORSLIND RESULTS

Description of the low-angle diffraction pattern The low-angle diffraction pattern of an air-dried flagellar preparation shows sharp equatorial m a x i m a at about 9 ° A_ and 45 )~, and no continuous scatter was observed. By wetting the flagellar flakes the preparation increased more than five-fold in volume, and the diffraction pattern at low angles changed considerably. For the wet preparations a continuous scatter is followed b y a distinct minimum, and a m a x i m u m at a spacing of about 70 A. Outside this m a x i m u m the scattered intensity is very low and

Fig. 2. Low-angle diffraction p a t t e r n of wet flagellar specimen. The m i n i m u m just outside the c o n t i n u o u s central scatter is clearly seen, followed b y a m a x i m u m at a b o u t 7° ~k. P a t t e r n magnified 3 x .

no further m a x i m u m is seen in the low-angle part of the equatorial pattern. The lowangle diffraction pattern of a wet preparation is illustrated in Fig. 2. A photometric tracing of the equatorial pattern is given in Fig. 3- In order to get experimental intensity data that can be compared with theoretically calculated intensity data and which m a y also be used for a Fourier-Bessel transformation, a background has to be subtracted. The estimated background is indicated in Fig. 3 and the intensity curve after subtraction of the background is given in Fig. 4- Some of the factors contributing to the background intensity are, the width of the incident beam, the intensity

\ \ \x\

I

i

20

10

O0 R • 10 . 3

lO

20

Fig. 3. P h o t o m e t r i c tracing of the diffraction p a t t e r n s h o w n in Fig. 2 giving the density along the oriented streak. The estimated b a c k g r o u n d is indicated b y the dashed line. Individual values are indicated b y dots.

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thickness of the specimen, scatter from the collimating system and scatter from the water in the specimen. We can assume that after the flagellar flakes have taken up more than five times their own volume of water, the molecular aggregates are not very regularly packed and that they therefore scatter independently. The appearance of the low-angle pattern indicates that this is the case and that the molecular aggregates are of rather uniform size. If such an aggregate is identical with a flagellum we can calculate the structure factor of one flagellum for the type of model that we are going to test and compare the calculated structure factor with the experimental diffraction pattern. Intensity

20

10

0 R. 10-3

10

20

Fig. 4- I n t e n s i t y curve of Fig. 3 after s u b t r a c t i o n of the estimated background,

Calculations of the equatorial diffraction patterns of two hypothetical models The first model we are going to test is a solid circular cylinder with a diameter of 120 A,. The intensity on the equator will then be given by

[2Jl(2~Rr)]'-' Z(R)

=

k

.

U,@r

J

where R = 2 sin 0/,t, (20 is the scattering angle and 2 is the wavelength of the radiation), r = the radius of the cylinder (in this case 60 A) and J1 (2:zRr) is a Bessel function of the first order 14. This intensity curve is illustrated in Fig. 5. The second model to be tested is a cable of two or three filaments with the diameter of 50 A, twisted around each other forming a cable with a diameter of about 12o A (illustrated in Fig. 6). To be able to calculate the diffraction pattern of this model a mathematical expression for the electron distribution has to be developed. We can describe this model approximately as a convolution of two or three coaxial helices with a radius ri~ of say 40 A and a disc with a radius rD of 25 A, perpendicular to the axis of the helices. The Fourier transform of the cable is equal to the Fourier transform of the helix multiplied by the Fourier transform of the disc 15. The Fourier transform of a continuous helix is given by COCHRAN et al.16:

F(R,%I) = Jn(2,~Rr)exp [in(~ + ~)] for the nth layer line. As we only have registered the equatorial diffraction pattern in the experimental pattern, we only need to calculate the Fourier transform for l = n ~-- o. The intensity distribution on the equator for this model will then be

I(R) = k [Jo(2:rtRrH) L

2Jl (2yERr.D)]2 2:TTR~"D

J

Biochim. Biophys. Acta, 88 (1964) 422 429

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G. S W A N B E C K ,

B. F O R S L I N D

The numerical values of this function have been calculated with the help of a digital c o m p u t e r for rD = 25 )t and rH --~ 25, 30, 35, 4 ° and 45 A. I n Fig. 7 I(R) for rH = 4 ° A is plotted. As we are analysing the equatorial pattern only, it is not possible to get a n y information on the pitch of the coiled filaments in the flagellum. W h a t we are really testing is which model has the correct average density distribution along a radius running perpendicular from the axis of the flagellum. Intensity

/

(/

10

20

l)/

30 R. 10-3

Fig. 5. Equatorial scattering curve of solid cylinder of radius 6o .3,_.

Fig. 6. One length of period of a flagellum with three filaments according to Model II. The meaning of rD and ri~ are indicated in the figure.

Comparison between experimental and calculated patterns B y comparing the calculated patterns in Figs. 5 and 7 with the experimental p a t t e r n (Fig. 4) one can see t h a t neither of the two models tested, is unreasonable. However, the absence of m a x i m a in the low-angle part of the pattern outside the 7o-• peak favors the second model. It m a y thus be concluded that the second model is largely compatible with the experimental pattern. However, there are discrepancies, as can readily be observed. The fact t h a t the low-angle pattern consists of two maxima, the zero-order m a x i m u m and the first-order m a x i m u m , makes it possible to assign the phases. The zero-order m a x i m u m must have a positive sign and the first-order m a x i m u m m u s t have a negative sign. These are the signs obtained for the structure amplitude of the second model. Of the other three possible combinations of signs two will gave negative densities and the third an unreasonable density distribution.

Calculation of the radial density distribution W h e n the phases are known for the equatorial m a x i m a the radial density dis-

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tribution can be calculated with a Fourier-Bessel transformation (cf. FRANKLIN"AND HOLMES17) according to the following formula o0

p(r) = k ~oRF(R)Jo(2:zRr)dR

where p(r) is the radial density distribution and

F(R) is the amplitude of the scattered radiation. Because of the difficulty in measuring the scattered intensity at very low angles an extrapolation has to be made. The scattered amplitude inside the first 2Jl(2:~Rr)/2xRr given such

minimum is represented by the corresponding part of Intensity

Fig. 7- E q u a t o r i a l scattering curve for a cable of three f i l a m e n t s t w i s t e d a r o u n d each other. Note the a l m o s t complete d a m p i n g of the curve outside the first m a x i m u m .

10

20

~

3'0-""-

R. 10 - 3

I

It

30

60 P

Fig. 8. Cross section of a flagellum according to Model I I after the refinement described in the text.

Fig. 9. Fourier-13esse] t r a n s f o r m a t i o n giving the radial density-distribution curves for the flagella (full line) and the corresponding curve of Model I I (dashed line).

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G. SWANBECK, B. FORSLIND

a weight, t h a t no n e g a t i v e values of p(r) are o b t a i n e d . The curve of p(r) t h u s o b t a i n e d is i l l u s t r a t e d in Fig. 9 (solid line). F r o m this curve we m a y d r a w the conclusion t h a t there is a hole in the center of the flagellum. This indicates s t r o n g l y t h a t the flagellum is n o t a t w o - s t a n d cable of filaments, b u t r a t h e r a t h r e e - s t a n d cable. To get a b e t t e r u n d e r s t a n d i n g of the m e a n i n g of the discrepancies between the e x p e r i m e n t a l p a t t e r n a n d the calculated p a t t e r n of Fig. 7 we c a l c u l a t e d t h e r a d i a l d e n s i t y d i s t r i b u t i o n for the second m o d e l in a refined form. W e m a y assume t h a t the filaments have a circular cross section. As the filaments are t w i s t e d a r o u n d each o t h e r in the flagellum m a k i n g an angle of a b o u t 45 ° w i t h the axis of the flagellum, the filaments will a p p e a r as ellipses in a cross section of a flagellum. I n Fig. 8 such a cross section is shown. W e h a v e allowed a d i s t a n c e of a b o u t IO A between the filam e n t s which is the m i n i m u m distance, t h a t can be expected, b e t w e e n the b a c k b o n e s of the p r o t e i n chains in one filament a n d the b a c k b o n e s of t h e p r o t e i n chains in a n e i g h b o u r i n g filament. If we f u r t h e r assume t h a t the d e n s i t y d i s t r i b u t i o n in the filament is fairly even, we can easily calculate the c o r r e s p o n d i n g r a d i a l d e n s i t y dist r i b u t i o n , which is i l l u s t r a t e d w i t h a d a s h e d line in Fig. 9. W e see t h a t the discrepancies b e t w e e n t h e two curves in Fig. 9 are r a t h e r small. The m a i n difference is the tail of the e x p e r i m e n t a l curve for large values of r. This t a i l m a y i n d i c a t e t h a t a small p a r t of t h e filaments are s i t u a t e d at larger distances from the flagellar axis. This m i g h t be caused b v strain in the flagellum. DISCUSSION

The p r e s e n t s t u d y s t r o n g l y s u p p o r t s the conception t h a t the flagella of Proteus wdgaris consist of three filaments with a d i a m e t e r of a b o u t 5o A t w i s t e d a r o u n d each other. Two models, the t w o - s t r a n d cable of filaments a n d the s m o o t h cylinder of a d i a m e t e r of 12o.~, can b o t h be e x c l u d e d as n o n - c o m p a t i b l e w i t h the X - r a y low-angle e q u a t o r i a l s c a t t e r i n g d a t a . The same is true to an even larger e x t e n t for the m o d e l s w i t h three parallel filaments or w i t h seven parallel filaments, the s c a t t e r i n g curves of which have been c a l c u l a t e d b y BURGE 11. The r a d i a l d e n s i t y d i s t r i b u t i o n curve shows t h a t there is a hole in the center of the flagellum. The d i a m e t e r of this hole is e s t i m a t e d to be b e t w e e n IO a n d 2o A, a n d t h u s t h e r e is r o o m for small molecules, b u t w h e t h e r or n o t p h o s p h o t u n g s t i c acid can p e n e t r a t e this region is uncertain. As the flagella c o n t a i n no s u l f h y d r y l groups 18, an i s o m o r p h o u s r e p l a c e m e n t as a c h i e v e d in the case of tobacco mosaic virus 1~ is difficult to m a k e . The tail of the e x p e r i m e n t a l r a d i a l d e n s i t y d i s t r i b u t i o n curve for large values of r is p r o b a b l y due to s t r a i n as was m e n t i o n e d above. I n the electron m i c r o g r a p h s one can see a wa\~ness of the flagella with a p e r i o d of a b o u t 2/x. If one measures the tilt angle of the filaments in different p a r t s of the w a v y flagella one finds t h a t this angle varies. Tile l a t t e r p r o p e r t i e s are p r o b a b l y the u l t r a s t r u c t u r a l m a n i f e s t a t i o n s of strain in the flagella. I t has been p o i n t e d out b y MERCER ~9 t h a t for c,-keratin the microfibril w i t h a d i a m e t e r of 5o 7o A is a basic s t r u c t u r a l unit. I t is i n t e r e s t i n g to note t h a t b a c t e r i a l flagella w i t h an a m i n o acid c o m p o s i t i o n different from t h a t of c~-keratin also form a v e r y similar s t r u c t u r a l unit, the filament, w i t h a d i a m e t e r of 5 ° A. I t seems as if c~-helices in fibrous p r o t e i n s aggregate into a fibril with a circular cross section a n d

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a diameter of about 5 ° A. It is probable that the factors determining the shape of the filaments or microfibrils and limiting their diameter are inherent in the a-helical structure itself and are not primarily dependent on the amino acid sequence. One mechanism which may determine or limit the size and shape of such fibrillar aggregates has been presented in connection with the proposal of a new model for the structure of a-keratin2°, 21. ACKNOWLEDGEMENTS

We are indebted to Dr. B. LUNDBERG at the Computer division of our department for the help with calculations of the theoretical scattering curves. We are also much indebted to Prof. G. HEDt~N and Dr. K. PALMSTIERNA at the Department of Bacteriology, Karolinska Institutet, and their staff members for helping us with the culturing of the bacteria and the isolation of the flagella.

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