Microbial Predation Dynamics - ACS Symposium Series (ACS

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Microbial Predation Dynamics 1

1

M. J. BAZIN, C. CURDS , A. DAUPPE , Β. Α. OWEN, and P. T. SAUNDERS Downloaded by CHINESE UNIV OF HONG KONG on March 28, 2016 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch011

Queen Elizabeth College, Department of Microbiology, London, England W87AH

The specific growth rate of a microbial predator (λ) was found to be dependent upon the ratio of the prey (H) to predator (P) population densities rather than the prey density alone. Predatory amoebae of the cellular slime mould Dictyostelium discoideum were grown in single-stage and two -stage chemostat cultures with the gut bacterium, Escherichia coli as their source of food. Predator growth in the cultures was compared to each of three functions which have been proposed for λ . In addition to showing that λ changed with respect to H/P, the results indicated also that it depended explictly on time, so that the differential equations describing the predator-prey system are probably non-autonomous.

Quite c l e a r l y , the growth of a predator population i s i n some way dependent upon the abundance of i t s prey. The most f r e q u e n t l y c i t e d model of predator-prey dynamics i s the set o f l i n k e d , non-linear d i f f e r e n t i a l equations known as the LotkaV o l t e r r a equations ( 1 ) . This model assumes that i n the absence of predator, the prey grows e x p o n e n t i a l l y , while i n the absence of prey the predator d i e s e x p o n e n t i a l l y , and that the predator growth r a t e i s d i r e c t l y p r o p o r t i o n a l to the product o f the prey (H) and predator (P) population d e n s i t i e s . The equations a r e : H

=

Ρ

=

k

Η

-

k PH

(1)

-k Ρ

+

k PH

(2)

x

3

2

where k^ s are constants.

4

The s p e c i f i c growth r a t e of the

1

Current address: British Museum (Natural History), Cromwell Road, London SW7, England 0097-6156/83 /0207-0253$06.00/0 © 1983 American Chemical Society

Blanch et al.; Foundations of Biochemical Engineering ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

254

BIOCHEMICAL ENGINEERING

predator p o p u l a t i o n (λ) according to the model i s t h e r e f o r e d i r e c t l y p r o p o r t i o n a l to the prey d e n s i t y : λ

-

k

4

Η

(3)

Downloaded by CHINESE UNIV OF HONG KONG on March 28, 2016 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch011

In microbiology the r e l a t i o n s h i p between the s p e c i f i c growth r a t e of a m i c r o b i a l predator and i t s prey i s o f t e n expressed i n terms of the h y p e r b o l i c f u n c t i o n suggested by Monod (2) f o r the growth of b a c t e r i a on a l i m i t i n g d i s s o l v e d n u t r i e n t . Applied to prédation the f u n c t i o n i s : λ

=

λ H/(L + Η) m

(4)

where λ i s the maximum s p e c i f i c growth r a t e and L i s the c o n c e n t r a t i o n of prey s u f f i c i e n t f o r growth at s p e c i f i c r a t e V

2

·

Both the L o t k a - V o l t e r r a and the Monod functions f o r predator s p e c i f i c growth r a t e are dependent upon a s i n g l e v a r i a b l e , the c o n c e n t r a t i o n of prey organisms. A t h i r d f u n c t i o n , proposed by Contois (3) f o r b a c t e r i a l growth as an a l t e r n a t i v e to that of Monod, when a p p l i e d to predator growth takes the form: λ

=

λ Η/(LP + Η) m

(5)

In t h i s case the s p e c i f i c growth rate i s a f u n c t i o n of both prey and predator d e n s i t y . Using the c i l i a t e protozoan Tetrahymena p y r i f o r m i s as a predator and K l e b s i e l l a aerogenes as prey, Curds and Cockburn (4) found that of the three f u n c t i o n a l forms suggested f o r predator s p e c i f i c growth r a t e represented by equations (3) - ( 5 ) , the Contois equation gave the best f i t to t h e i r data. D i v i d i n g the numerator and denomenator of equation (5) by Ρ gives λ

=

λ ((H/P) / (L + H/P)) m

(5a)

showing that predator s p e c i f i c growth r a t e according to the Contois equation can be considered to be a f u n c t i o n of the r a t i o of prey to predator p o p u l a t i o n d e n s i t i e s . Using, catastrophe theory, a n a l y s i s of r e s u l t s from experiments i n which slime mould amoebae f e d on E. c o l i i n d i c a t e d that i t was t h i s r a t i o that was the c r i t i c a l v a r i a b l e i n the system 05). The goal of the research we report here was to determine whether the s p e c i f i c growth r a t e of predatory amoebae of the c e l l u l a r slime mould D i c t y o s t e l i u m discoideum feeding on the gut b a c t e r i a , E s c h e r i c h i a c o l i was dependent upon prey d e n s i t y alone or upon the r a t i o of prey to predator. Two experimental systems were employed, both based on the chemostat type of continuous c u l t u r e . A chemostat i s a continuously s t i r r e d tank r e a c t o r i n which microorganisms grow i n a homogeneous environment and are supplied with n u t r i e n t s o l u t i o n a t the same volumetric r a t e at



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which the c u l t u r e i s harvested. The advantages of such a system for studying m i c r o b i a l predator-prey dynamics have been described p r e v i o u s l y (6), but e s s e n t i a l l y , chemostat c u l t u r e extends the period of time over which an experiment can be performed, reduces the e f f e c t of s t a t i s t i c a l f l u c t u a t i o n s and sampling e r r o r s and has w e l l - d e f i n e d parameters which can be c o n t r o l l e d by the experimenter while other aspects of the e x t e r n a l e n v i r o n ment can be kept constant. Our f i r s t experimental system c o n s i s t e d of a s i n g l e - s t a g e chemostat to which n u t r i e n t s o l u t i o n f o r the b a c t e r i a l prey was fed a t a constant r a t e and i n which the i n t e r a c t i o n between the prey and the predator took p l a c e . The equation of balance f o r the two populations can be w r i t t e n as: Ρ

-

( λ - D) Ρ

Η

=

( u - D ) H

(6)

- XJ? (7) W where D = d i l u t i o n r a t e (the r a t e of flow through the c u l t u r e v e s s e l d i v i d e d by i t s volume), u i s the s p e c i f i c growth r a t e of the prey and W i s the y i e l d of predator per u n i t of prey consumed, assumed to be constant. When slime mould amoebae and b a c t e r i a l prey are grown together i n a chemostat, the p o p u l a t i o n d e n s i t i e s of both organisms f l u c t u a t e s i n u s o i d a l l y f o r s e v e r a l days (7, 8 ) . We estimated the s p e c i f i c growth r a t e of the predator p o p u l a t i o n i n such c u l t u r e s from the slope of the curve generated by p l o t t i n g the logarithm of the predator d e n s i t y a g a i n s t time. T h i s slope i s Ρ/Ρ

=

λ - D

(8)

from which r e l a t i o n s h i p λ could be simply c a l c u l a t e d . Prey d e n s i t y was a l s o measured so that the change i n λ as a f u n c t i o n of Η and H/P could be determined. Our second experimental system c o n s i s t e d of two chemostats l i n k e d i n s e r i e s . In the f i r s t v e s s e l the b a c t e r i a l prey was allowed to come to steady s t a t e and then fed i n t o the second stage v e s s e l which contained the amoebae. As the l i m i t i n g n u t r i e n t source f o r the b a c t e r i a i s v i r t u a l l y exhausted under steady s t a t e c o n d i t i o n s , i t was assumed that no f u r t h e r growth of prey occurred i n the second v e s s e l . In the second v e s s e l the equation of balance f o r the predator i s : Ρ

=

(λ

- D ) Ρ

(9)

so that at steady s t a t e λ

=

D

(10)


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BIOCHEMICAL

ENGINEERING


By feeding b a c t e r i a to the predator p o p u l a t i o n at d i f f e r e n t d i l u t i o n r a t e s and measuring the steady state prey d e n s i t y i n the second v e s s e l i t i s therefore p o s s i b l e to r e l a t e λ and Η to each other. Methods E s c h e r i c h i a c o l i B/r and D i c t y o s t e l i u m discoideum NC4 were maintained r o u t i n e l y and grown i n s i n g l e - s t a t e chemostat c u l t u r e as described p r e v i o u s l y ( 8 ) . The outflow of chemostat c u l t u r e s was passed along the same l i n e as e x p e l l e d a i r and by t h i s means was forced i n t o tubes r e s t i n g i n a r e f r i g e r a t e d f r a c t i o n c o l l e c t o r . F r a c t i o n s were c o l l e c t e d at hourly i n t e r v a l s . For two-stage continuous c u l t u r e , the f i r s t stage v e s s e l had a maximum c a p a c i t y of 1 L while the v e s s e l used f o r the second stage had a maximum c a p a c i t y of e i t h e r 1 L or 500 cm-*, depending upon the volume appropriate to a p a r t i c u l a r experiment. The v e s s e l s were f i t t e d with f l a t , flanged l i d s each bearing f i v e access p o r t s . Both v e s s e l s were mixed by means of magnetic s t i r r e r s and immersed i n water maintained at 25°. F i l t e r s t e r i l i s e d a i r was supplied to both stages and the flow of n u t r i e n t to the f i r s t v e s s e l and the flow from the f i r s t to the second v e s s e l was regulated by p e r i s t a l t i c pumps. Two-stage chemostat experiments were performed by i n o c u l a t i n g the f i r s t v e s s e l with I>» c o l i and i n c u b a t i n g with the flow on u n t i l the system came to steady s t a t e . This was considered to have occurred when no s i g n i f i c a n t change i n the t u r b i d i t y of the e f f l u e n t c e l l suspension could be detected. At t h i s time the second v e s s e l was f i l l e d with c u l t u r e from the f i r s t and i n o c u l a t e d with a suspension of D. discoideum spores. The c u l t u r e i n the second v e s s e l was incubated under batch c o n d i t i o n s f o r about 48 h during which time the spores germinated to form amoebae. Flow from the f i r s t v e s s e l to the second was then i n i t i a t e d and the amoebae c u l t u r e d on a continuous b a s i s . Samples were taken d i r e c t l y from the culture vessels for analysis. The c e l l number d e n s i t i e s of the b a c t e r i a and the amoebae i n both systems was measured on a C o u l t e r Counter (Coulter E l e c t r o n i c s L t d . , Harpenden, England). Mean c e l l volumes were estimated using a C o u l t e r C1000 Channelyzer. A 30 um diameter aperture was used f o r the b a c t e r i a and a 50 um aperture f o r the amoebae. Samples were suspended e i t h e r i n c u l t u r e medium or "Isoton" (Coulter E l e c t r o n i c s Ltd) immediately p r i o r to c o u n t i n g . Biomass was estimated e i t h e r i n terms of biovolume, the product of the mean c e l l volume and the number of c e l l s present, or, f o r b a c t e r i a l biomass where appropriate, as t u r b i d i t y at 560 nm. Within the range of readings made there i s a l i n e a r r e l a t i o n s h i p between c e l l volume d e n s i t y and t u r b i d i t y at 560 nm f o r E. c o l i . Sing-estage continuous c u l t u r e data was smoothed by the method of cubic s p l i n e s using Nottingham Algorithms Routine E02AAF. A l l computations were performed on a CDC 6600 d i g i t a l computer.


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Results Single-stage chemostat c u l t u r e . The s i n g l e stage chemostat system represents a food chain i n which glucose i s converted to b a c t e r i a l biomass which, i n turn, i s converted to amoebal biomass. As glucose i s measured on a weight per u n i t volume b a s i s i t i s appropriate that the other dependent v a r i a b l e s of the system, H and P, be measured i n the same terms, i . e . biomass per u n i t volume. The number d e n s i t i e s of the prey and predator populations would be appropriate u n i t s provided that the average mass per b a c t e r i a l or amoebal c e l l remained constant. Results of a t y p i c a l s i n g l e stage experiment are shown i n Figure 1. The change i n the mean c e l l volume (MCV) of each species i n d i c a t e s q u i t e c l e a r l y that c e l l mass does not remain constant. Therefore, we have used the biovolume d e n s i t y , the product of the number d e n s i t y and MCV, as estimates of H and Ρ i n our a n a l y s i s of the data. That considerable d i f f e r e n c e s e x i s t between the system i n terms of numbers and biovolumes i s shown by i n s p e c t i n g phase p l a n t p l o t s of our r e s u l t s . There were constfucted using smoothed data to p l o t predator d e n s i t y against prey d e n s i t y . Figure 2 shows the r e s u l t s obtained when number d e n s i t i e s were used. An i n t e r dependence between the two v a r i a b l e s i s not r e a d i l y apparent. On the otherhand, as shown i n F i g u r e 3, when biovolume d e n s i t i e s were used a more r e a d i l y interprétable r e l a t i o n s h i p emerges. I t i s c l e a r from the t r a j e c t o r y i n phase space that the system damps slowly at f i r s t and then moves r a p i d l y towards an e q u i l i b r i u m value. Figure 4 shows the change i n P/P as a f u n c t i o n o f t i m e , c a l c u l a t e d from smoothed data, and Figure 5 i s a p l o t of P/P against Η constructed from the data i n Figure 4. β

Two-stage chemostat c u l t u r e . In the two-stage continuous c u l t u r e system, steady s t a t e i n the second v e s s e l which contained the amoebal p o p u l a t i o n took more than two weeks to achieve. Steady s t a t e was accompanied by considerable clumping of the c e l l s i n d i c a t i n g , p o s s i b l y , that the slime mould amoebae were aggregating. T h i s c o n d i t i o n was r e l i e v e d only s l i g h t l y by i n c r e a s i n g the concentration of EDTA i n the medium from 0.65 mM to 0.8 mM. Both the amount of time r e q u i r e d to reach steady s t a t e and the tendency of the amoebae to form clumps of c e l l s once steady s t a t e has been reached made c o l l e c t i n g s u f f i c i e n t data to c h a r a c t e r i s e the system with respect to the amoebal s p e c i f i c growth r a t e d i f f i c u l t . Therefore, steady-state data was augmented with estimates made near to steady s t a t e and r e s u l t s recorded i n terms of the s p e c i f i c r a t e or prédation, Φ = -fi/P + D ^ - I ^ ) /Ρ, which i s d i r e c t l y p r o p o r t i o n a l to predator s p e c i f i c growth r a t e i f the y i e l d , W, i s constant. The s p e c i f i c r a t e of prédation was estimated by applying the f o l l o w i n g c a l c u l a t i o n : Φ =

D (Η

χ

-

H )/P 2

(11)


258

BIOCHEMICAL

ENGINEERING

7

io E


Ε ο

ο

Mo» ë

w 10-

Φ

I °% .·/··

Φ

1

β

ο°;°ο·β

ν

%

1

o

o

100.2

φ O

E < 100

200

300

TIME (h) Figure L Change in mean cell volume and number density of D . discoideum amoebae and Ε . coli grown together in single-stage chemostat culture.



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Dynamics

1

Smoothed prey number density ml"

Figure 2. Phase plane plot of predator and prey number densities. Data from a single stage chemostat culture of D . discoideum and E . coli were smoothed by the method of cubic splines, and the smoothed data were used to construct this figure. The arrows indicate the direction of increasing time.



260


1

Smoothed prey biovolume density (μηι ml') Figure 3. Phase plane plot of predator and prey densities constructed as for Figure 2, using biovolume density as the coordinates. The arrows indicate the direction of increasing time.


BAZIN ET A L .

11.

Microbial

Prédation

261

Dynamics

008

i\ A

ooH


s o

ooH

o φ υ Φ α ^

Λ • •

f

Λ · ·

:

· ·

· ·

/ ·

\ - \/

\ \

m S

w

v

y -004H

0

1 l I

50

250

200

100 150 Time ( h )

Figure 4. Change in the specific rate of change of D. discoideum in a single-stage chemostat as a function of time. Values were obtained from smoothed data. The specific growth rate of the amoebae is obtained by adding the dilution rate of the culture (0.065 h' ) to the values on the ordinate. 1

0.08 h

ο

σ

0.04

-0.04

-D

6.0

7.0

8.0

Log prey population density Figure 5. Specific rate of change of predator in a single-stage chemostat culture as a function of prey density. The specific growth rate of the predator is the sum of the specific rate of change and the dilution rate (0.065 h' ). 1


262



where H and H^ are the p o p u l a t i o n d e n s i t i e s o f the b a c t e r i a l prey i n the f i r s t and second stages of the continuous c u l t u r e system r e s p e c t i v e l y and D i s the d i l u t i o n r a t e of the second stage v e s s e l . For the purposes o f t h i s c a l c u l a t i o n , b a c t e r i a l d e n s i t y was estimated i n terms of t u r b i d i t y at 560 nm and i t was assumed that the c o n t r i b u t i o n by the amoebal p o p u l a t i o n i n the second v e s s e l at t h i s wavelength was n e g l i g i b l e . The change i n Φ as a f u n c t i o n of steady s t a t e prey d e n s i t y i s shown i n Figure 6. Discussion The three models we tested our experimental r e s u l t s against are given i n equations (3), (4) and ( 5 ) . The L o t k a l V o l t e r r a equations p r e d i c t a l i n e a r r e l a t i o n s h i p between predator s p e c i f i c growth r a t e (or the s p e c i f i c rate of prédation) and prey d e n s i t y ; when λ i s p l o t t e d against Η according to the Monod f u n c t i o n , the f a m i l i a r rectangular hyperbola i s generated. A h y p e r b o l i c r e l a t i o n s h i p between λ and H/P i s p r e d i c t e d by the Contois expression. Figures 5 and 6 show the way i n which λ changes as a f u n c t i o n of prey d e n s i t y taken from s i n g l e - and double-stage chemostat c u l t u r e s r e s p e c t i v e l y . In n e i t h e r case do the r e l a t i o n s h i p s i n d i c a t e d i n equations (3) and ( 4 ) , a s t r a i g h t l i n e and a rectangular hyperbola, become apparent! Figure 7 shows λ p l o t t e d against the r a t i o of prey to predator, H/P, c a l c u l a t e d from data from the two-stage experiment. Quite c l e a r l y , t h i s r e l a t i o n s h i p can be i n t e r p r e t e d i n terms of equation ( 5 ) . Figure 8 shows a s i m i l a r p l o t using data from s i n g l e - s t a g e experiments. Here i t seems that a family of rectangular hyperbola are represented with H/P as the independent v a r i a b l e and with λ and L of equation (5) decreasing with time. I t appears, t h e r e f o r e , that the s p e c i f i c growth r a t e of the amoebal predator i s dependent not j u s t on H, but upon the r a t i o of prey to predator present. The mechanism with which the amoebae are able to c o n t r o l t h e i r growth r a t e i n t h i s way i s , of course, not known. We have suggested (5) that f o l i c a c i d , which i s secreted by the b a c t e r i a and i s , t h e r e f o r e , a f u n c t i o n of the prey population d e n s i t y , might be i n a c t i v a t e d by the amoebae so that i t s concentration depends a l s o on the d e n s i t y of predator present. This indeed appears to be the case as reported by Pan and Wurster (9). I t i s conceivable, t h e r e f o r e , that the concentration of f o l i c a c i d i n the media might serve to regulate the rate of growth of the predator population. Furthermore, the r e s u l t s i n d i c a t e that the s p e c i f i c growth rate might depend e x p l i c i t l y on time. I f such i s the case then the d i f f e r e n t i a l equations d e s c r i b i n g the dynamics of the system are non-autonomous with time appearing on the r i g h t hand side of the equals s i g n and not autonomous as are the L o t k a - V o l t e r r a equations and the vast majority of equations that have been suggested f o r d e s c r i b i n g m i c r o b i a l predator-prey i n t e r a c t i o n s .


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263


2

0.2

0.1

0.3

Prey density Figure 6. Data from a two-stage chemostat system showing the change in the specific feeding rate of D . discoideum in the second stage as a function of E . coli density. The specific feeding rate is directly proportional to specific growth rate providing that the yield of predator produced per unit of prey consumed is constant. Prey density is measured in terms of absorbance at 560 nm in the second-stage vessel. Specific feeding rate was calculated as the product of the difference in turbidity between the cultures in the two vessels and the dilution rate, divided by the prey biovolume density. The units on the ordinate are therefore absorbance at 560 nm/mL culture h' μm~ . 1

3

6h

-6 4

Q.

10 20 Prey/predator ratio

30

Figure 7. Specific feeding rate plotted against the ratio of prey to predator in the second vessel, estimated in terms of absorbance at 560 nm divided by the predator biovolume density (μ/η mL ). Other conditions as in Figure 6. ζ

1



264

0.08 h

•

0.04 h

• Downloaded by CHINESE UNIV OF HONG KONG on March 28, 2016 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch011

0

.·.·*.

· · ·*··.

··

#

»

h

£ -0.04 ν..·. LÎ!_

0.8

0.9 1.0 l.l 1.2 Ratio of prey t o predator population densities

Figure 8. Specific rate of change of the predator population in a single-stage chemostat culture, plotted as a fraction of the ratio of prey to predator biovolume densities. The dilution rate of the culture was 0.065 h' . 1

Acknowledgments T h i s r e s e a r c h was supported by the U.K. N a t u r a l Environmental Research C o u n c i l and an SRC CASE

studentship.

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9.

Curds, C.R.; Bazin, M.J. "Advances in Aquatic Microbiology"; Droop, M.R.; Jannasch, H.W., Ed.; Academic: London, 1977; Vol. 1, p. 115. Monod, J . Ann. Inst. Pasteur 1950, 79, 390. Contois, D.E. J . Gen. Microbiol. 1959, 21, 40. Curds, C.R.; Cockburn, A. J . Gen. Microbiol. 1968, 54, 343. Bazin, M.J.; Saunders, P.T. Nature 1978, 275, 52-54. Bazin, M.J.; Rapa, V.; Saunders, P.T. "Ecological Stability"; Usher, M.B.; Williamson, M.E., Ed; Chapman and Hall: London, 1974; p. 159. Tsuchiya, H.M.; Drake, J . F . ; Jost, J . F . ; Fredrickson, A.G. J . Bacteriol. 1972, 100, 1147-1153. Dent, V . E . ; Bazin, M.J.; Saunders, P.T. Arch. Microbiol. 1976, 109, 187-194. Pan, P.; Wurster, B. J . Bacteriol. 1978, 955-959.

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June 29, 1982


Microbial Predation Dynamics - ACS Symposium Series (ACS

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