12
Effects
of
Cell
Motility
Properties
on
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P o p u l a t i o n s in E c o s y s t e m s
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DOUGLAS A. LAUFFENBURGER University of Pennsylvania, Department of Chemical Engineering, Philadelphia, PA 19104
Because most natural ecosystems cannot r e a l l y be considered well-mixed, conclusions regarding dynamics of c e l l population growth and i n t e r a c t i o n s drawn from well-mixed, chemostat studies may not necessarily be v a l i d . Many microbial species, in f a c t , possess sophisticated movement behavioral properties by which d i s t r i b u t i o n of a population in space i s influenced by concentrations and gradients of chemicals commonly present in their environment. These chemotactic and chemokinetic properties can require s i g n i f i c a n t devotion of genetic information and sometimes s i g n i f i c a n t energy expenditure, yet are of little apparent use i n artificial well-mixed systems. However, in non-mixed environments, the e f f e c t s of chemosensory movement properties may be extremely important in determining the a b i l i t y of a species to grow, or in deciding the outcome of competitive i n t e r a c t i o n s . This paper summarizes the a v a i l a b l e experimental evidence that t h i s i s indeed the case, that movement properties can have c r u c i a l e f f e c t s in microbial ecosystems. We then present some mathematical models that help explain and predict these effects.
0097-6156/83/0207-0265 $08.00/0 © 1983 American Chemical Society
Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
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S t u d i e s o f m i c r o b i a l p o p u l a t i o n dynamics have focused p r i m a r i l y on well-mixed, macroscopically homogeneous s y s t e m s . T h i s emphasis i s e a s i l y d i s c e r n i b l e from t h e c o n t e n t s o f t h i s symposium volume. However, t h e s i t u a t i o n i n most n a t u r a l l y o c c u r i n g m i c r o b i a l systems i s f a r from i d e a l l a b o r a t o r y c o n d i t i o n s , so that understanding gained a b o u t w e l l - m i x e d s y s t e m s may n o t p r o v i d e t h e appropriate insight into ecological situations. Environments which a r e not well-mixed can allow formation o f s p a t i a l gradients o f chemical concentrat i o n s and c e l l d e n s i t i e s . Also, chemical d i f f u s i o n and c e l l m o t i l i t y ( i . e . , s e l f - p r o p e l l e d movement r e q u i r i n g energy expenditure) can replace convection a s t h e d o m i n a n t mode o f t r a n s p o r t . According to common c a t e g o r i z a t i o n , h a l f t h e o r d e r s o f b a c t e r i a c o n t a i n a t l e a s t o n e m o t i l e s p e c i e s (1), including many o f t h e commonly o c c u r i n g s p e c i e s . F u r t h e r , most m o t i l e b a c t e r i a e x h i b i t c h e m o t a x i s , w h i c h i s most s i m p l y d e f i n e d a s c e l l movement t o w a r d o r away f r o m chemicals ( 2 ) , o r a s p r e f e r e n t i a l c e l l movement t o w a r d h i g h e r o r lower c o n c e n t r a t i o n s o f a c h e m i c a l stimulus {3). A c t u a l l y , t h e r e a r e a number o f d i f f e r e n t types o f movement r e s p o n s e s w h i c h l e a d t o b e h a v i o r o f t h i s g e n e r a l d e s c r i p t i o n ( 4 ) . For peritrichously flagellated bacteria, w h i c h a p p e a r t o be t h e m o s t c o m m o n l y e n c o u n t e r e d group (and o n w h i c h t h i s p a p e r w i l l a c c o r d i n g l y f o c u s ) , k l i n o k i n e s i s ( i n which the t u r n i n g frequency o f swimming b a c t e r i a i s m o d u l a t e d b y s t i m u l u s c o n c e n t r a t i o n ) a p p e a r s t o be c l o s e s t t o o b s e r v e d b e h a v i o r ( 5 ) . T h i s i s i l l u s t r a t e d i n F i g u r e 1. In the absence o f a chemical stimulus gradient, these b a c t e r i a swim i n roughly s t r a i g h t l i n e steps c a l l e d "runs" f o r a short time (about 1 second) and t h e n s t o p and change d i r e c t i o n , o r " t u m b l e " , f o r a b o u t 1/10 s e c o n d ( 6 ) . The d i r e c t i o n c h a n g e i s p u r e l y r a n d o m , b u t t h e p r o b a b i l i t y o f tumbling i s constant d u r i n g a r u n ,so t h a t t h e r u n time d i s t r i b u t i o n i s P o i s s o n i a n ( 6 ) . T h i s movement b e h a v i o r i s t e r m e d r a n d o m m o t i l i t y . In the presence o f a g r a d i e n t , t h e d i r e c t i o n change r e m a i n s random b u t t h e t u m b l i n g p r o b a b i l i t y decreases f o r a c e l l swimming t o w a r d h i g h e r a t t r a c t a n t c o n c e n t r a t i o n s o r lower r e p e l l e n t c o n c e n t r a t i o n s (6), l e a d i n g to n e t m i g r a t i o n i n t h e d i r e c t i o n o f t h e g r a d i e n t . T h i s mechanism p r o v i d e s v e r y e f f i c i e n t response (]_) ; i n an o p t i m a l g r a d i e n t t h e n e t m i g r a t i o n v e l o c i t y i s r o u g h l y h a l f t h e l i n e a r c e l l swimming s p e e d ( 8 , 9 ) .
Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
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Cell
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RANDOM MOTILITY
CHEMOTAXIS
Figure 1. Illustration of typical movement of peritrichously flagellated bacteria. The left-handfigureshows movement of a cell in the absence of a chemical stimulus concentration gradient. The right-handfigureshows that the run length is increased when the cell moves in the direction of increasing attractant concentration, toward the top of the figure. The angles between respective runs in the two figures are identical. The increase in run length results in a greater drift in the direction of increasing attractant concentration for chemotactic movement than for random movement.
Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
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S t i m u l u s c o n c e n t r a t i o n s a r e m e a s u r e d by o c c u p a n c y o f c e l l membrane r e c e p t o r s w h i c h c a n r e v e r s i b l y b i n d stimulus molecules according to Michaelis-Menten enzyme k i n e t i c s w i t h d i s s o c i a t i o n c o n s t a n t . G r a d i e n t s a r e d e t e c t e d by a t e m p o r a l s e n s i n g m e c h a n i s m by w h i c h r e c e p t o r o c c u p a n c y o v e r t h e e n t i r e c e l l i s m o n i t o r e d d u r i n g a r u n (1Λ) . A spatial sensing m e c h a n i s m by w h i c h d i f f e r e n c e s i n r e c e p t o r o c c u p a n c y a c r o s s the c e l l l e n g t h i s measured i s i m p r a c t i c a l f o r s u c h r a p i d l y swimming c e l l s , b e c a u s e o f f a l s e a p p a r e n t g r a d i e n t s due t o c e l l m o t i o n i t s e l f (12).
A l a r g e v a r i e t y o f c h e m i c a l s c a n s e r v e as chemotactic s t i m u l i . Approximately 20 a t t r a c t a n t r e c e p t o r s a n d 10 r e p e l l e n t r e c e p t o r s h a v e b e e n i d e n t i f i e d f o r E s c h e r i c h i a c o l i and Salmonella t y p h i m u r i u m , t h e two m o s t w i d e l y - s t u d i e d s p e c i e s ( Γ 3 ) . T h e s e r e c e p t o r s a r e s p e c i f i c f o r one o r two chemicals at h i g h a f f i n i t i e s (low K ^ ) , but w i l l a l s o b i n d a range o f r e l a t e d m o l e c u l e s w i t h lower a f f i n i t y (2). Table 1 l i s t s a number o f t h e w e l l - k n o w n s t i m u l i f o r a v a r i e t y of species, although t h i s i s c e r t a i n l y i n c o m p l e t e a s new r e s p o n s e s a r e b e i n g d i s c o v e r e d almost d a i l y . I n g e n e r a l , s u b s t a n c e s b e n e f i c i a l t o an o r g a n i s m s u c h as n u t r i e n t s and o x y g e n ( i f a e r o b i c ) s e r v e as a t t r a c t a n t s w h i l e t o x i c compounds o r compounds c a u s i n g pH e x t r e m e s a c t a s r e p e l l e n t s ( 2 ) . Some a m i n o a c i d s a r e a t t r a c t a n t s and o t h e r s r e p e l l e n t s , d e p e n d i n g upon t h e s p e c i e s . A l t h o u g h t h e r e i s n o t an e x a c t correspondence between m e t a b o l i z a b l e compounds and a t t r a c t a n t s n o r b e t w e e n u n f a v o r a b l e c o m p o u n d s and r e p e l l e n t s (L4), the observed responses can g e n e r a l l y be r a t i o n a l i z e d i n t e r m s o f p a r t i c u l a r s p e c i e s b i o c h e m i c a l p a t h w a y s and by r e c o g n i t i o n o f some p u z z l i n g s t i m u l i as a n a l o g u e s o f o t h e r s t i m u l i (2). Speculation regarding a possible survival advantage o f chemotaxis i s thus not s u r p r i s i n g . Approximately 40 g e n e s a r e d e v o t e d s p e c i f i c a l l y t o t h e c h e m o t a c t i c r e s p o n s e i n E ^ c o l i and S^ t y p h i m u r i u m (15) and a s i m i l a r number o f g e n e s may be d e v o t e d t o t h e m o t i l i t y apparatus. S u c h an i n v e s t m e n t m u s t p r o v i d e some b e n e f i t i n t h e c o m p e t i t i v e w o r l d o f m i c r o b i a l ecology. However, f u n d a m e n t a l u n d e r s t a n d i n g o f the c i r c u m s t a n c e s i n w h i c h a s i g n i f i c a n t a d v a n t a g e due t o m o t i l i t y a n d c h e m o t a x i s w i l l a c t u a l l y be p r e s e n t i s l a c k i n g , a s a r e e s t i m a t e s o f t h e m a g n i t u d e o f s u c h an advantage. This understanding i s l a c k i n g even f o r a s i n g l e s t i m u l u s , and t h e p r o b l e m b e c o m e s e v e n more complex i n any n a t u r a l e n v i r o n m e n t i n w h i c h m u l t i p l e
y
Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
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Table 1. Classification of Weil-Known Bacterial Chemotactic Responses Genus
Classes o f Attractants
Classes o f Repellents
Escherichia
sugars amino acids C>
pH extremes a l i p h a t i c alcohols
Pseudomonas
sugars amino acids nucleotides vitamins
inorganic ions pH extremes amino acids
°2 . . ammonium ions Bacillus
Salmonella
sugars amino acids °2 sugars amino acids
inorganic ions pH extremes metabolic poisons a l i p h a t i c alcohols
0„ Vibrio
amino acids
Spirillum
sugars amino acids
inorganic ions pH extremes
Rhodospirilium
nucleotides s u l f h y d r y l compounds
pH extremes poisons
Clostridium Bdellovibrio
amino acids
Proteus
sugars amino acids °2 sugars
Erwinia
inorganic acids pH extremes inorganic ions pH extremes inorganic ions pH extremes
Sarcina Serratia
sugars amino acids
inorganic ions pH extremes
0„ Bordetella Pasteurella Marine b a c t e r i a
algal culture f i l t r a t e s
heavy metals t o x i c hydrocarbons
Source: Refs. 36-38.
Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
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s t i m u l i , p r o b a b l y b o t h a t t r a c t a n t s and r e p e l l e n t s , a r e present. M u l t i p l e s i g n a l s a r e a d d i t i v e i n some s e n s e ( 1 6 ) , and p r e s u m a b l y t h e b a c t e r i a a t t e m p t t o o p t i m i z e t h e i r growth through p r e f e r e n t i a l m i g r a t i o n . F r o m an e n g i n e e r i n g p e r s p e c t i v e , t h e r e i s no q u a n t i t a t i v e b a s i s f o r p r e d i c t i o n o f the e f f e c t s o f c e l l m o t i l i t y and c h e m o t a x i s o n m i c r o b i a l p o p u l a t i o n d y n a m i c s i n a n y given s i t u a t i o n at present. T h i s paper i s devoted to r e v i e w o f the s m a l l body o f i n f o r m a t i o n a v a i l a b l e i n t h i s area at t h i s time. Experimental
Observations
T h e r e e x i s t s o n l y a s m a l l number o f p u b l i s h e d experiments p e r t a i n i n g t o the e f f e c t s o f c e l l m o t i l i t y on p o p u l a t i o n g r o w t h . A well-known m i c r o b i o l o g y t e x t g i v e s one example w i t h o u t d o c u m e n t a t i o n : the c o m p e t i t i o n b e t w e e n an a e r o t a c t i c ( i . e . , c h e m o t a c t i c a l l y a t t r a c t e d by o x y g e n ) P s e u d o m o n a s s p e c i e s a n d an i m m o t i l e A c i n e t o b a c t e r s p e c i e s , f o r o x y g e n ( 1 7 ) . When t h e g r o w t h medium i s w e l l - a e r a t e d t h e A c i n e t o b a c t e r predominate, thus showing s u p e r i o r g r o w t h k i n e t i c s on t h e r a t e - l i m i t i n g s u b s t r a t e (presumably oxygen) s i n c e c e l l m o t i l i t y i s a p p a r e n t l y irrelevant. But i n a non-mixed c u l t u r e the Pseudomonas p r e d o m i n a t e . The c h e m o t a c t i c a b i l i t y of the Pseudomonas s p e c i e s p r o v i d e s , i n t h i s s i t u a t i o n , enough o f a b e n e f i t t o overcome i t s growth k i n e t i c inferiority. The f i r s t l i t e r a t u r e r e p o r t i n t h i s a r e a was by S m i t h a n d D o e t s c h (]J*) , who s t u d i e d c o m p e t i t i o n b e t w e e n a e r o t a c t i c P s e u d o m o n a s f l u o r e s c e n s and an i m m o t i l e m u t a n t s t r a i n o f t h e same s p e c i e s , f o r o x y g e n (see Figure 2 ). In a e r a t e d mixed c u l t u r e b o t h s t r a i n s g r e w t o a r o u g h l y 1:1 r a t i o o v e r a 2 4 - h o u r p e r i o d i n d i c a t i n g t h a t t h e i r g r o w t h k i n e t i c p r o p e r t i e s were i d e n t i c a l as e x p e c t e d . In n o n - a e r a t e d media, the a e r o t a c t i c s t r a i n outgrew the mutant t o a f i n a l ratio o f o v e r 10:1 a f t e r 24 h o u r s . U n f o r t u n a t e l y , the a u t h o r s c r e d i t e d m o t i l i t y per se f o r t h i s a d v a n t a g e , e v e n t h o u g h i t i s not c l e a r whether random m o t i l i t y without chemotaxis i s n e c e s s a r i l y always b e n e f i c i a l . In the c o u r s e o f s t u d y i n g t h e r o l e o f f i m b r i a e i n b a c t e r i a l g r o w t h , O l d and D u g u i d l o o k e d a t c o m p e t i t i o n f o r o x y g e n b e t w e e n two n o n f i m b r i a t e s t r a i n s o f Salmonella typhimurium: one a e r o t a c t i c and one immotile (_19) (see Table 2 ) . In a e r o b i c shaken b r o t h , t h e a e r o t a c t i c s t r a i n m u l t i p l i e d by a f a c t o r o f 46 w i t h i n 48 h o u r s , w h i l e t h e i m m o t i l e s t r a i n m u l t i p l i e d by a f a c t o r o f 52. Again the growth k i n e t i c
Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
12.
LAUFFENBURGER
Cell
Time (hr)
211
Motility
Time (hr)
Figure 2. Multiplication of aerotactic (O) and immotile (Φ) strains of Pseudo monas fluorescens in two different experiments, each in aerated mixed culture (left) and nonaerated mixed culture (right). Reproduced, with permission, from Ref. 18. Copyright 1969, Society for General Microbiology.
Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
2.
0.15 2.91 3.00 2.94
0.15 0.38 0.55 0.69
0.19 0.35 0.46 0.48 0.66 1.41
0.16 3.27 3.48 3.61
0.16 0.37 0.71 1.84
typhimurium
Society
94 6,900 3,800 4,900
94 380 500 540
65 270 195 86 105 190
130 4,200 4,600 4,700
130 530 380 1,030
Challenged bacteria
f o r Microbiology.
0.00024 0.016 0.011 0.011
0.00024 0.00080 0.0016 4.5
0.00017 0.00080 4.8 74 185 450
0.00033 0.0012 0.0029 0.0093
0.00033 0.0053 165 880
Challenging bacteria
Viable Count (10 bacteria)/ml o f
1970, A m e r i c a n
0 6 24 48
Aerobic shaken broth
Copyright
0 6 24 48
0 6 24 48 72 96
0 6 24 48
Aerobic s t a t i c broth
Aerobic s t a t i c broth
Aeiobic shaken broth
Aerobic s t a t i c broth
Conditions o f Growth
Amt of Growth
Strains of Salmonella
Time o f Incubation hr 0 6 24 48
of P a i r s of Variant
f r o m R e f e r e n c e 19.
S6353, fim f l a
S6351, fim f l a
Reproduced w i t h p e r m i s s i o n
S6355, fim f l a
+
S6351, fim f l a
+
S6358, f i m f l a
S6352, fim f l a
Challenged (rha-)
i n Mixed C u l t u r e s
Challenging (rha+)
Growth
COMPETING STRAINS
Table
W
9
-J to
12.
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Motility
273
p r o p e r t i e s appeared n e a r l y the same. In a e r o b i c s t a t i c b r o t h , however, the a e r o t a c t i c s t r a i n m u l t i p l i e d by a f a c t o r o f 18,000 i n 48 hours w h i l e the immotile s t r a i n m u l t i p l i e d by a f a c t o r o f 6. Interp r e t a t i o n o f t h i s c a s e i s not s t r a i g h t f o r w a r d , t h o u g h , because p e l l i c l e f o r m a t i o n was noted a f t e r 24 h o u r s , c o m p l i c a t i n g the s i t u a t i o n . More r e c e n t l y , P i l g r a m and W i l l i a m s s t u d i e d a s l i g h t l y d i f f e r e n t c a s e — c o m p e t i t i o n between c h e m o t a c t i c P r o t e u s m i r a b i l i s and a nonchemotactic but randomly m o t i l e mutant o f the s p e c i e s (20) (see F i g u r e s 3 and 4 ) . In both pure and mixed c u l t u r e s o f p e r i o d i c a l l y a g i t a t e d amino a c i d b r o t h , the two s t r a i n s grew t o a 1:1 r a t i o a f t e r 14 h o u r s . On the o t h e r hand, i n both pure and mixed c u l t u r e s o f s e m i s o l i d agar the r a t i o o f c h e m o t a c t i c to randomly m o t i l e s t r a i n s was g r e a t e r than 5:1 a f t e r 14 h o u r s . The f i n a l e x p e r i m e n t a l r e p o r t s were by F r é t e r et_ al. (21, 22, 2 3 ) , who s t u d i e d growth o f V i b r i o c h o l e r a e i n mouse and r a b b i t l a r g e i n t e s t i n e (see Figure 5 and Table 3. Here t h r e e s t r a i n s were compared: the c h e m o t a c t i c w i l d t y p e , an immotile mutant s t r a i n , and a nonchemotactic but randomly m o t i l e mutant strain. In w e l l - s t i r r e d c o n t i n u o u s flow c u l t u r e , a l l t h r e e s t r a i n s grew i n p r o p o r t i o n . In the i n t e s t i n a l l o o p s , the nonchemotactic s t r a i n was r a p i d l y d i s p l a c e d by the c h e m o t a c t i c w i l d t y p e . Most i n t e r e s t i n g l y , i n another experiment the randomly m o t i l e s t r a i n was a l s o r a p i d l y d i s p l a c e d by the immotile s t r a i n . A p p a r e n t l y , i n t h i s s i t u a t i o n at l e a s t , m o t i l i t y w i t h o u t chemot a x i s was a l i a b i l i t y f o r the c e l l s . It i s e v i d e n t t h a t t h e o r e t i c a l a n a l y s i s o f m o t i l i t y and chemotaxis i s n e c e s s a r y i n o r d e r t o p r o v i d e q u a n t i t a t i v e i n t e r p r e t a t i o n o f these r e s u l t s , and even q u a l i t a t i v e e x p l a n a t i o n o f the l a s t , perhaps c o u n t e r - i n t u i t i v e , o b s e r v a t i o n by F r é t e r et al_. This w i l l be the c o n c e r n o f the next s e c t i o n o f t h i s p a p e r . But i s i m p o r t a n t to emphasize at t h i s p o i n t t h a t the e x p e r i m e n t a l r e s u l t s c i t e d here demonstrate t h a t the e f f e c t s o f c e l l movement p r o p e r t i e s can c l e a r l y be s i g n i f i c a n t , and even dominant, i n d e t e r m i n i n g the c o m p e t i t i v e a b i l i t i e s o f b a c t e r i a l p o p u l a t i o n s i n nonmixed e n v i r o n m e n t s . Theoretical
Analyses
E a r l y attempts at t h e o r e t i c a l a n a l y s i s o f the e f f e c t s o f c e l l m o t i l i t y on p o p u l a t i o n growth c e n t e r e d on uptake o f n u t r i e n t by a s i n g l e c e l l i n a medium o f i n f i n i t e e x t e n t (12, 24, 25, 2 6 ) . These a n a l y s e s have
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6
J8
10
12
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Hours
6
8 10
12
H 2L
Hours Figure 3. Growth of pure cultures of chemotactic (O) and nonchemotactic ( O strains of Proteus mirabilis in periodically shaken amino acid broth (top) and soft-agar amino acid medium (bottom). Reproduced, with permission, from Ref. 20. Copyright 1976, National Research Council of Canada.
Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
12.
LAUFFENBURGER
Cell
Motility
ο
I
1
ι
ι
ι
ι
ι
0
2
4
6
8
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Hours Figure 4. Growth of mixed cultures of chemotactic (O) and nonchemotactic ( Q ) strains of Proteus mirabilis in periodically shaken amino acid broth (top) and soft-agar amino acid medium (bottom). Reproduced, with permission, from Ref. 20. Copyright 1976, National Research Council of Canada.
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BIOCHEMICAL
276
c
ENGINEERING
100 η
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1 a r e m e r e l y extrapolations. N u m e r i c a l c o m p u t a t i o n s h a v e shown t h e p e r t u r b a t i o n r e s u l t s t o be a c c u r a t e up t o a t l e a s t 6 = 1.1, however ( 3 1 ) . An i n t e r e s t i n g i n f e r e n c e w h i c h c a n be d r a w n f r o m F i g u r e 12 i s t h a t t h e r e i s a minimum v a l u e o f 6 that m u s t be e x c e e d e d i n o r d e r f o r m o t i l i t y t o c o n f e r an advantage i n t h i s c o n f i n e d growth s i t u a t i o n . I f λ r e p r e s e n t s t h e B r o w n i a n m o t i o n c o e f f i c i e n t f o r an 2
1
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LAUFFENBURGER
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Motility
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Figure 9. Plot of dimensionless total steady state bacterial density vs. 8 for single chemotactic populations. Extrapolations of perturbation computations beyond 8 = 1 shown ( ). Asymptotic values for δ = 0 shown (- · - · -).
Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
12.
LAUFFENBURGER
Figure 10.
Cell
Motility
285
Typical steady state profiles of dimensionless bacterial density, v.
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i m m o t i l e s p e c i e s (_33) , t h e n a c h e m o t a c t i c s p e c i e s m u s t have a l a r g e r v a l u e , say λ > λι. By i t s e l f t h i s w o u l d y i e l d a s m a l l e r v a l u e o f B. Increasing 6 from 0 i n c r e a s e s B, and t h e r e w i l l be a c r i t i c a l v a l u e , 6*, a t w h i c h Β f o r λ2 and 6 b e c o m e s e q u a l t o Β f o r λ O n l y f o r 6>6* w i l l t h e c h e m o t a c t i c s t r a i n o u t g r o w t h e immotile s t r a i n . Thus, s p e c u l a t i o n t h a t a m o t i l e c h e m o t a c t i c s t r a i n s h o u l d a l w a y s be s u p e r i o r t o an immotile s t r a i n i s not n e c e s s a r i l y t r u e . T h e s e s i n g l e p o p u l a t i o n r e s u l t s s u g g e s t some i m p o r t a n t i m p l i c a t i o n s f o r c o m p e t i t i o n b e t w e e n two o r more p o p u l a t i o n s g r o w i n g t o g e t h e r o n a s i n g l e r a t e limiting nutrient. I f one s p e c i e s h a s s u p e r i o r g r o w t h k i n e t i c p r o p e r t i e s but t h e o t h e r has s u p e r i o r m o t i l i t y p r o p e r t i e s , we m i g h t e x p e c t c o e x i s t e n c e t o o c c u r . A n a l y s i s o f t h e t h i r d c a s e , c o m p e t i t i o n b e t w e e n two r a n d o m l y m o t i l e p o p u l a t i o n s , shows t h a t t h i s i s i n d e e d possible. T h e r e a r e now a c t u a l l y t h r e e p e r m i s s i b l e steady s t a t e s : 1) c o e x i s t e n c e , 2) s p e c i e s 1 o n l y , a n d 3) s p e c i e s 2 o n l y . For sake o f c l a r i t y , l e t the two s p e c i e s have i d e n t i c a l p r o p e r t i e s e x c e p t t h a t ki > k2« Then s p e c i e s 1 w i l l have a g r e a t e r growth rate at a l l n u t r i e n t concentrations. In a d d i t i o n , the t h r e s h o l d c o n c e n t r a t i o n f o r net growth o f s p e c i e s 2 must be g r e a t e r t h a n t h a t o f s p e c i e s 1; i . e . , c i * We c a n i m m e d i a t e l y see t h a t a n e c e s s a r y c o n d i t i o n f o r coexistence i s that ω * · The v a l u e s o f ω f o r e a c h s p e c i e s a r e d e t e r m i n e d by t h e same e q u a t i o n a s i n t h e s i n g l e p o p u l a t i o n c a s e , u n a f f e c t e d by t h e p r e s e n c e o f the other s p e c i e s . We c a n , t h e r e f o r e , move d i r e c t l y to a g r a p h i c a l d e s c r i p t i o n o f the steadys t a t e behavior f o r our c o m p e t i t i o n model. F i g u r e 11 shows i s o c l i n e s o f ω i n t h e p l a n e o f (κ,λ) v a l u e s . If we s p e c i f y v a l u e s λ χ and κι f o r p o p u l a t i o n 1, t h i s y i e l d s a value for ωι. We c a n t h e n immediately d i s c o v e r t h e p e r m i s s i b l e s t e a d y - s t a t e s f o r any s p e c i e s 2 with parameter values λ and κ (see Figure 1 2 ) . If κ < K o n l y s p e c i e s 1 can s u r v i v e , u n l e s s λ2 i s such t h a t o)2 > ω — which would a l l o w c o e x i s t e n c e . If κ > Κ χ , o n l y s p e c i e s 2 can s u r v i v e , u n l e s s λ is s u c h t h a t α)2 < ω ι , w h i c h a g a i n a l l o w s c o e x i s t e n c e . S o , t h e c o m p e t i t i o n o u t c o m e c a n be p r e d i c t e d f r o m t h e s i n g l e p o p u l a t i o n r e s u l t s , w i t h one m i n o r modification. Remember t h a t t h e ω c r i t e r i o n i s o n l y a necessary condition for coexistence. I t turns out t h a t a s e c o n d , s l i g h t l y more r e s t r i c t i v e c o n d i t i o n i s a l s o r e q u i r e d , t o e n s u r e t h a t t h e c e l l d e n s i t i e s and n u t r i e n t c o n c e n t r a t i o n r e m a i n p o s i t i v e e v e r y w h e r e (3JL) . The d i f f e r e n c e b e t w e e n t h e two c o n d i t i o n s i s s m a l l 2
1 #
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Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
2
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LAUFFENBURGER
Figure 11.
Cell
Motility
Sample plot of curves of constant ω in plane of (Χ, λ).
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Figure 12. Illustration of predicted results for competition between two randomly motile populations with identical properties except for Κ and λ.
Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
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for t y p i c a l parameter v a l u e s , however, so t h a t g i v e n the a p p r o x i m a t i o n i n v o l v e d i n the model i t s e l f , we n e e d n o t be t o o c o n c e r n e d w i t h i t . When t h e c e l l d e n s i t i e s a r e c o m p u t e d f o r a c o e x i s t e n c e s t a t e , t h e s p e c i e s w i t h s m a l l e r k c a n grow to a g r e a t e r p o p u l a t i o n s i z e than the s p e c i e s w i t h l a r g e r k, i f i t s m o t i l i t y p r o p e r t i e s a r e s u f f i c i e n t l y superior. T h i s g i v e s an e x p l a n a t i o n t o t h e r e s u l t c i t e d by S t a n i e r e t a l (1_7) . S i m i l a r r e s u l t s a r e e x p e c t e d when c h e m o t a x i s i s present i n competing p o p u l a t i o n s , although the a n a l y s i s has not y e t been c a r r i e d o u t . Chapman (5) f o r m u l a t e d a m o d e l f o r c o m p e t i t i o n o f two chemotactic s p e c i e s i n a t r a v e l i n g band, which p r e d i c t e d t h a t superior chemotaxis could allow a species with i n f e r i o r growth r a t e c o n s t a n t to exclude the other species. T h i s r e s u l t i s c o n s i s t e n t w i t h our e x p e c t a t i o n s ; the model, however, i s r a t h e r e m p i r i c a l . Conclusions R e v i e w o f t h e l i t e r a t u r e r e v e a l s a s m a l l number o f e x p e r i m e n t s t h a t show t h a t c e l l m o t i l i t y p r o p e r t i e s c a n h a v e d r a m a t i c e f f e c t s o n p o p u l a t i o n g r o w t h and c o m p e t i t i o n i n non-mixed systems. Simple mathematical models have been d e v e l o p e d w h i c h p r o v i d e q u a l i t a t i v e e x p l a n a t i o n f o r a l l t h e o b s e r v e d p h e n o m e n a , and yield q u a n t i t a t i v e p r e d i c t i o n of the magnitude of e f f e c t s w h i c h m i g h t be e x p e c t e d i n a v a r i e t y o f s i t u a t i o n s . Ac k nowledgme n t s T h i s work h a s b e e n p a r t i a l l y s u p p o r t e d by NSF C h e m i c a l and B i o c h e m i c a l P r o c e s s e s Program G r a n t CPE80-06701. D.A.L. w o u l d a l s o l i k e t o t h a n k P a t Thompson f o r t y p i n g t h i s m a n u s c r i p t and R e n a t e S c h u l t z f o r many o f t h e f i g u r e s .
L i t e r a t u r e Cited 1.
Breed, R. S.; Murray, E . D. G . ; Smith, N. R. "Bergey's Manual of Determinative Bacteriology"; Williams and w i l k i n s : Baltimore, 7th e d i t i o n , 1957.
2.
Koshland, Jr., D. E. "Bacterial Chemotaxis as a Model Behavioral System"; Raven Press: New York, 1980.
Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
290
BIOCHEMICAL ENGINEERING
3.
Lauffenburger, D. A. "Effects of M o t i l i t y and Chemotaxis in C e l l Population Dynamical Systems"; PhD Thesis, University of Minnesota, 1979.
4·
Fraenkel, G. S.; Gunn, D. L . "The Orientation of Animals"; Dover: New York, 1961.
5.
Chapman, P. A. "Chemotaxis of Bacteria"; PhD Thesis, University of Minnesota, 1973.
6.
Berg, H. C.; Brown, D. A. Nature 1972, 239, 500-504.
7.
Macnab, R. M . ; Koshland, Jr., D. E . J. Mechanochem. C e l l M o t i l . 1973, 2, 141-148.
8.
Macnab, R. M. In "Biological Regulation and Development", v o l . 2; R. Goldberger, e d . ; Plenum Press: New York, 1980, pp. 377-412.
9.
Dahlquist,
J.
F . W.; E l w e l l , R. Α . ; Lovely, P. S.
Supramol. S t r u c t .
1976, 4, 329-342.
10.
A d l e r , J. Science 1969, 166, 1588-1597.
11.
Macnab, R. M . ; Koshland, Jr., D. E . Proc. N a t l . Acad. S c i . USA 1972, 69, 2509-2512. Berg, H. C.; P u r c e l l , E . M. Biophys. J. 1977, 20, 193-219.
12. 13.
Hazelbauer, G. L.; Parkinson, J. S. In "Receptors and Recognition: Microbial Interactions"; J. R e i s s i g , e d . ; Chapman and Wall: London, 1977; pp. 60-80.
14.
A d l e r , J. Annu. Rev. Biochem. 1975, 44, 341-356.
15.
DeFranco, A. T.; Parkinson, J. S.; Koshland, D. E . J. B a c t e r i a l 1979, 139, 107-114.
16.
Tsang, N . ; Macnab, R. Μ., Koshland, Science 1973, 181, 60-63.
Jr.,
Jr.,
D. E .
17.
Stanier, R . ; Adelberg, E.; Ingraham, J. "The Microbial World"; P r e n t i c e - H a l l : Englewood Cliffs, New Jersey, 1976. 18.
Smith, J. L.; Doetsch, 1969, 55, 379-391.
R. N. J. Gen. M i c r o b i o l .
Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
12.
LAUFFENBURGER
291
Cell Motility
19.
O l d , D. C., Duguid, J. P. J. B a c t e r i o l . 103, 447-456.
20.
Pilgram, W. R.; Williams, F. D. Can. J. M i c r o b i o l . 1976, 22, 1771-1773.
21.
F r e t e r , R.; A l l w e i s s , B . ; O'Brien, P. C. M . ; Halstead, S. A. In "Proceedings of the 13th Joint Conference on Cholera", U.S. - Japan Cooperative Medical Sciences Program; U.S. Govt. Printing O f f i c e , Washington, D . C . ; pp. 153-181.
22.
F r e t e r , R.; O'Brien, P. C. M . ; Halstead, S. A. Adv. Exp. Med. B i o l . 1978, 107, 429-437.
23.
F r e t e r , R.; O'Brien, P. C. M . ; Macsai, M. S. Am. J. C l i n . Nutr. 1979, 32, 128-132.
24.
Carlson, F . D. In "Spermatozoan M o t i l i t y " ; D. W. Bishop, ed.; AAAS Publication No. 72: Washington, D. C., 1962.
25.
Koch, A. L . Adv. Microb. P h y s i o l .
1971,
1970,
6,
147-217. 26.
Brunn, P. O. J. Biomech. Eng. 1981,
103,
27.
P u r c e l l , Ε. M. Am. J. Physics 1977,
45,
28.
Lauffenburger, D. Α . ; A r i s , R.; K e l l e r , Κ. H. Microb. E c o l . 1981, 7, 207-227. Lauffenburger, D. Α . ; A r i s , R.; K e l l e r , Κ. H. Biophys. J . (submitted for p u b l i c a t i o n ) .
29.
32-37. 3-11.
30.
Lauffenburger, D. Α . ; Calcagno, B. Biotech. Bioeng. (submitted for p u b l i c a t i o n ) .
31.
Calcagno, B. "Analysis of Steady-State Growth and Competition of Motile B a c t e r i a l Popula tions in Non-mixed Environments", M.S. Thesis, University of Pennsylvania, 1981.
32.
K e l l e r , E . F.; Segel, L . A. J. Theor. B i o l . 30, 225-234.
33.
Segel, L . Α . ; Chet, I . ; Henis, Y. J. Gen. M i c r o b i o l . 1977, 98, 329-337.
Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.
1971,
292 34.
BIOCHEMICAL ENGINEERING
Segel, L . A.; Jackson, J. L . J. Mechanochem. C e l l M o t i l . 1973, 2, 25-34.
35.
Holz, M . ; Chan, S. Biophys. J. 1979, 26, 243-262.
36.
Barrachini, O.; S h e r r i s , J. C. J. Path. Bact. 1959, 77, 565-574. Seymour, F . W. K . ; Doetsch, R. N. J. Gen. M i c r o b i o l . 1973, 78, 287-296.
37. 38.
Chet, I . ; M i t c h e l l , R. Annu. Rev. M i c r o b i o l . 1976, 30, 221-239.
RECEIVED
June 1, 1982
Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.