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Bacteria and their flagella
344
B I O C H I M I C A E T B I O P H Y S I C A ACTA
Short Communications Bacteria and their flagella F l a g e l l a are difficult to observe on living b a c t e r i a for t h e y have extreme, ly small d i a m e t e r s t. U n d e r an electron microscope, however, t h e y a p p e a r to be m a d e u p of v e r y fine filaments of m a c r o m o l e c u l a r dimensions which are t w i s t e d t o g e t h e r in ropelike s t r u c t u r e s 2 4. H o w flagella are utilized b y b a c t e r i a has been d e b a t e d over t h e y e a r s since t h e y were first seen on fixed a n d s t a i n e d p r e p a r a t i o n s . Flagella g e n e r a l l y are found on motile b a c t e r i a l cells a n d when cells are in motion the flagella, w h e n seen, also a p p e a r to be in motion. The c i r c u m s t a n t i a l evidence is strong for the belief t h a t flagella are organs of locomotion ~,~. On the o t h e r hand, there is some indication t h a t t h e y reduce the forward speed because of viscous d r a g G. I t has been difficult to conceive the ultrafine flagellar filaments themselves to be sufficiently c o m p l e x in s t r u c t u r e to s u p p o r t inetabolic or other processes for p r o d u c i n g energy-rich molecules a n d at the same time to convert the released energy to kinetic e n e r g y of locomotion. Some i n v e s t i g a t o r s h a v e suggested t h a t the source of energy is n o t the flagellum b u t the b a c t e r i a l cell itself. I t is a s s u m e d t h a t the b a c t e r i u m r a t h e r leisurely snaps the flage!lmn as a whip, or coils a n d uncoils it at different rates, t h u s propelling itself forward. U n f o r t u n a t e l y , this suggestion also meets with difficulties. B e c a u s e of viscous d r a g the flagellum would be unable to s u p p o r t a wave, c e r t a i n l y not one of u n i f o r m a m p l i t u d e ~1. The base end would need to c o n t i n u a l l y execute to a n d fro d i s p l a c e m e n t s equal to the a m p l i t u d e of the m l d u l a t i o n s on the flagellum a n d even then the motion would be d a m p e d out so r a p i d l y t h a t there would be no a p p a r e n t waveform. A piece of flagellum with an initial speed of 3 ° iz/sec in water, for example, would come to rest within a distance of less t h a n i m/x. A t h i r d group of i n v e s t i g a t o r s u n d e r the leadership of PUPER have suggested t h a t b a c t e r i a l locomotion is accomplished b y the sinuous m o v e m e n t s of the b a c t e r i u m itself a n d t h a t the flagella are really trails of m a t e r i a l s sloughed off a slime l a y e r 7. In o t h e r words, the flagella serve neither as organs nor as propellers for l o c o m o t i o n ; t h e y are s i m p l y inactive appendages. As p o i n t e d out b y Ho[TwIx K aN t~ VAN ITV;RSON'~, however, the electron-microscopic o b s e r v a t i o n s suggest t h a t the high degree of u n i f o r m i t y in cross-section a n d th~ a t t a c h m e n t of the flagellum to the cell are not consistent with this picture. In this note we suggest t h a t some means of stabilization is needed b y a b a c t e r i u m if it is to undergo long range t r a n s l a t o r y motions a n d t h a t flagella m a y well serve as such stabilizers. T r a n s l a t i o n a l B r o w n i a n motion c o m m o n l y is observed a m o n g bacteria, for t h e y are small enough to reveal the effects of fluctuations in the i m p a c t s of molecules of the growth m e d i u m . In essence, the b a c t e r i a are large "molecules" in t h e r m a l agitation. P e r h a p s not so well known is the p h e n o m e n o n of r o t a t i o n a l Brownian motion. An equation for the m e a n - s q u a r e angle of r o t a t i o n for a spherical particle was d e r i v e d b y E~Nsxt,;ix s a n d e x p e r i m e n t a l l y veritied b y PERRIN 9. A similar e q u a t i o n m a y be Biochim. t~iophys.
:1~ta, 4 2 (190o) 344 345
345
SHORT COMMUNICATIONS
deduced for the rotation of a small cylinder about a transverse axis through its center. It is ~ = 24 kTt/:zrll a, where k is the Boltzmann constant, T is the absolute temperature, ~] is the coefficient of viscosity of the medium, l is the length of the cylinder, and t is the time interval between observations of the angle 0 through which the sphere rotates. It must be understood t h a t O~ represents the resultant mean-square angular displacement due to a very large n u m b e r of nudges from impacts of the substrate molecules. In all observations on rotational Brownian motion, however, the projection of the angle on a fixed plane is measured, so t h a t the foregoing equation should be divided b y 3 in applying it to experimental data. Consider a rod-like bacterium 1. 5/x long and o.5 tx in diameter in a medium at a temperature of 27 °. Set ~] equal to I cpoise, t to I sec and k to 1.38. IO -16 erg/°. Then the ratio of the mean-square angle of rotation about a transverse axis to the time intorval for observations equals 24 ;4 1.38 ;,( IO -16 y, 300 :,( o.oi x (1.5) 3 ~ lO -12 or 9.3 radians2 sec. On the average, therefore, the bacterium would rotate t h r o u g h approximately I75 °, almost a complete about face, during a I-see time interval. Thus locomotion in a given direction long enough to measure the speed, or even to allow the bacterium to go anywhere, is practically impossible unless provision is made to reduce the effects of rotational Brownian motion. A flagellum or flagellar tress several tens of /, long would prevent undue rotations; in effect, it would act as a stabilizer for the bacterium. If the over-all length is increased b y a factor of IO the root-meansquare angle is reduced b y a factor of I/3O. REICHERT'S observations that, by and large, small bacteria have longer flagella than large bacteria 1° support this hypothesis.
Da;'tmouth Collage, Hanover N.H. (U.S.A.)
ALLEN L.
KING
1 (;. ](NAYSI, Eleme~zts o/ Bacterial Cytology, 2 n d ed., I t h a c a , C o n a s t o c k , 195 t. 2 ~l. P. STARR AND R. C. \¥ILLIAMS, J. Bacteriol., 63 (i952) 7Ol. :~ ] . \V. I~ABAVVAND ~r. M..'~OSLEY, Biochim. Biophys. Hcta, 16 (1954) 325; 17 (~955) 322. 4 [ Vv'. SMITH, Biochim. Biophys. dcta, I 5 (19.54) 20. 5 A. L. HOUWlNK AND \V. VAN ITERSON, Biochim. Biophys. :Iota, 5 (195o) IO. 6 C. C. I4RINTON, A. BUZZELL AND M. A. LAUFFER, Biochim. Biophys. dcta, 15 (1954) 533. 7 _\. PIJPER, J. Pathol. Bacleriol., 47 (1938) I ; 58 (1946 ) 325. s A. EINSTEIN, d n n . Phys., 17 (19o5) 549; 19 (19o6) 371. 9 j 1~. PERRIN, ~4toms, t r a n s l a t e d b y D. L. HAMSIICK, C o n s t a b l e , L o n d o n , 192o. 10 1.£. REICHERT, Zentr. Bakteriol. Parasite~zh., l Origi., 51 ([9o9) 14. 11 I£. E . MACHIN, J. Experimental Biol., 35 (I958) 796.
Received March 28th, 196o Biochim. Biophys. Acta, 42 (196o) 3 4 4 - 3 4 5
Masked condition of ionic residues in collagen Physico-chemical studies on collagen have emphasized the importance of hydrogen bonds in the structure. However, the state of the ionized residues in this protein is still obscure, although there is evidence, from electron microscopy t h a t they m a y have a special orientation in the fibril 1. Also, analysis of titration curves reveals unusual behavior in that there is slight reactivity over the range p H 6-1o, and a low alkali-neutralizing capacity compared to the content of basic amino acids 2. This and other evidence mentioned b y GUSTAVSON suggests the existence of salt-like Biochim. Biophys. d cta, 42 (196o) 3 4 5 - 3 4 S
B I O C H I M I C A E T B I O P H Y S I C A ACTA
Short Communications Bacteria and their flagella F l a g e l l a are difficult to observe on living b a c t e r i a for t h e y have extreme, ly small d i a m e t e r s t. U n d e r an electron microscope, however, t h e y a p p e a r to be m a d e u p of v e r y fine filaments of m a c r o m o l e c u l a r dimensions which are t w i s t e d t o g e t h e r in ropelike s t r u c t u r e s 2 4. H o w flagella are utilized b y b a c t e r i a has been d e b a t e d over t h e y e a r s since t h e y were first seen on fixed a n d s t a i n e d p r e p a r a t i o n s . Flagella g e n e r a l l y are found on motile b a c t e r i a l cells a n d when cells are in motion the flagella, w h e n seen, also a p p e a r to be in motion. The c i r c u m s t a n t i a l evidence is strong for the belief t h a t flagella are organs of locomotion ~,~. On the o t h e r hand, there is some indication t h a t t h e y reduce the forward speed because of viscous d r a g G. I t has been difficult to conceive the ultrafine flagellar filaments themselves to be sufficiently c o m p l e x in s t r u c t u r e to s u p p o r t inetabolic or other processes for p r o d u c i n g energy-rich molecules a n d at the same time to convert the released energy to kinetic e n e r g y of locomotion. Some i n v e s t i g a t o r s h a v e suggested t h a t the source of energy is n o t the flagellum b u t the b a c t e r i a l cell itself. I t is a s s u m e d t h a t the b a c t e r i u m r a t h e r leisurely snaps the flage!lmn as a whip, or coils a n d uncoils it at different rates, t h u s propelling itself forward. U n f o r t u n a t e l y , this suggestion also meets with difficulties. B e c a u s e of viscous d r a g the flagellum would be unable to s u p p o r t a wave, c e r t a i n l y not one of u n i f o r m a m p l i t u d e ~1. The base end would need to c o n t i n u a l l y execute to a n d fro d i s p l a c e m e n t s equal to the a m p l i t u d e of the m l d u l a t i o n s on the flagellum a n d even then the motion would be d a m p e d out so r a p i d l y t h a t there would be no a p p a r e n t waveform. A piece of flagellum with an initial speed of 3 ° iz/sec in water, for example, would come to rest within a distance of less t h a n i m/x. A t h i r d group of i n v e s t i g a t o r s u n d e r the leadership of PUPER have suggested t h a t b a c t e r i a l locomotion is accomplished b y the sinuous m o v e m e n t s of the b a c t e r i u m itself a n d t h a t the flagella are really trails of m a t e r i a l s sloughed off a slime l a y e r 7. In o t h e r words, the flagella serve neither as organs nor as propellers for l o c o m o t i o n ; t h e y are s i m p l y inactive appendages. As p o i n t e d out b y Ho[TwIx K aN t~ VAN ITV;RSON'~, however, the electron-microscopic o b s e r v a t i o n s suggest t h a t the high degree of u n i f o r m i t y in cross-section a n d th~ a t t a c h m e n t of the flagellum to the cell are not consistent with this picture. In this note we suggest t h a t some means of stabilization is needed b y a b a c t e r i u m if it is to undergo long range t r a n s l a t o r y motions a n d t h a t flagella m a y well serve as such stabilizers. T r a n s l a t i o n a l B r o w n i a n motion c o m m o n l y is observed a m o n g bacteria, for t h e y are small enough to reveal the effects of fluctuations in the i m p a c t s of molecules of the growth m e d i u m . In essence, the b a c t e r i a are large "molecules" in t h e r m a l agitation. P e r h a p s not so well known is the p h e n o m e n o n of r o t a t i o n a l Brownian motion. An equation for the m e a n - s q u a r e angle of r o t a t i o n for a spherical particle was d e r i v e d b y E~Nsxt,;ix s a n d e x p e r i m e n t a l l y veritied b y PERRIN 9. A similar e q u a t i o n m a y be Biochim. t~iophys.
:1~ta, 4 2 (190o) 344 345
345
SHORT COMMUNICATIONS
deduced for the rotation of a small cylinder about a transverse axis through its center. It is ~ = 24 kTt/:zrll a, where k is the Boltzmann constant, T is the absolute temperature, ~] is the coefficient of viscosity of the medium, l is the length of the cylinder, and t is the time interval between observations of the angle 0 through which the sphere rotates. It must be understood t h a t O~ represents the resultant mean-square angular displacement due to a very large n u m b e r of nudges from impacts of the substrate molecules. In all observations on rotational Brownian motion, however, the projection of the angle on a fixed plane is measured, so t h a t the foregoing equation should be divided b y 3 in applying it to experimental data. Consider a rod-like bacterium 1. 5/x long and o.5 tx in diameter in a medium at a temperature of 27 °. Set ~] equal to I cpoise, t to I sec and k to 1.38. IO -16 erg/°. Then the ratio of the mean-square angle of rotation about a transverse axis to the time intorval for observations equals 24 ;4 1.38 ;,( IO -16 y, 300 :,( o.oi x (1.5) 3 ~ lO -12 or 9.3 radians2 sec. On the average, therefore, the bacterium would rotate t h r o u g h approximately I75 °, almost a complete about face, during a I-see time interval. Thus locomotion in a given direction long enough to measure the speed, or even to allow the bacterium to go anywhere, is practically impossible unless provision is made to reduce the effects of rotational Brownian motion. A flagellum or flagellar tress several tens of /, long would prevent undue rotations; in effect, it would act as a stabilizer for the bacterium. If the over-all length is increased b y a factor of IO the root-meansquare angle is reduced b y a factor of I/3O. REICHERT'S observations that, by and large, small bacteria have longer flagella than large bacteria 1° support this hypothesis.
Da;'tmouth Collage, Hanover N.H. (U.S.A.)
ALLEN L.
KING
1 (;. ](NAYSI, Eleme~zts o/ Bacterial Cytology, 2 n d ed., I t h a c a , C o n a s t o c k , 195 t. 2 ~l. P. STARR AND R. C. \¥ILLIAMS, J. Bacteriol., 63 (i952) 7Ol. :~ ] . \V. I~ABAVVAND ~r. M..'~OSLEY, Biochim. Biophys. Hcta, 16 (1954) 325; 17 (~955) 322. 4 [ Vv'. SMITH, Biochim. Biophys. dcta, I 5 (19.54) 20. 5 A. L. HOUWlNK AND \V. VAN ITERSON, Biochim. Biophys. :Iota, 5 (195o) IO. 6 C. C. I4RINTON, A. BUZZELL AND M. A. LAUFFER, Biochim. Biophys. dcta, 15 (1954) 533. 7 _\. PIJPER, J. Pathol. Bacleriol., 47 (1938) I ; 58 (1946 ) 325. s A. EINSTEIN, d n n . Phys., 17 (19o5) 549; 19 (19o6) 371. 9 j 1~. PERRIN, ~4toms, t r a n s l a t e d b y D. L. HAMSIICK, C o n s t a b l e , L o n d o n , 192o. 10 1.£. REICHERT, Zentr. Bakteriol. Parasite~zh., l Origi., 51 ([9o9) 14. 11 I£. E . MACHIN, J. Experimental Biol., 35 (I958) 796.
Received March 28th, 196o Biochim. Biophys. Acta, 42 (196o) 3 4 4 - 3 4 5
Masked condition of ionic residues in collagen Physico-chemical studies on collagen have emphasized the importance of hydrogen bonds in the structure. However, the state of the ionized residues in this protein is still obscure, although there is evidence, from electron microscopy t h a t they m a y have a special orientation in the fibril 1. Also, analysis of titration curves reveals unusual behavior in that there is slight reactivity over the range p H 6-1o, and a low alkali-neutralizing capacity compared to the content of basic amino acids 2. This and other evidence mentioned b y GUSTAVSON suggests the existence of salt-like Biochim. Biophys. d cta, 42 (196o) 3 4 5 - 3 4 S