Interactions of Microbial Populations in Mixed Culture Situations - ACS

9

I n t e r a c t i o n s of Culture

Microbial

Populations

in

Mixed

Situations

A. G. FREDRICKSON

Downloaded by UNIV LAVAL on May 13, 2016 | http://pubs.acs.org Publication Date: January 18, 1983 | doi: 10.1021/bk-1983-0207.ch009

University of Minnesota, Department of Chemical Engineering and Materials Science, Minneapolis, MN 55455 This paper reviews the classification and dynamics of interaction between pairs of microbial populations inhabiting a common environment. A few cases of interaction between three or more populations are considered, also. The nature of the scheme of classification of interaction is described and its utility as well as its weaknesses are mentioned. Several interactions, competition for resources and feeding of one population upon another in particular, have been studied in some detail and reasonably reliable mathematical models of some simple types of these interactions are available. Other interactions have not received so much attention, however, and in some cases nothing but qualitative statements about an interaction can be made. The review is concluded with a listing of areas where research is needed to provide and improve knowledge of interspecific microbial interactions. Probably the main reason f o r the predominance of pure c u l t u r e techniques i n the fermentation i n d u s t r y i s that i n most cases the product i s a complicated, v a l u a b l e organic molecule which can be made by a s i n g l e m i c r o b i a l p o p u l a t i o n , and when we have i s o l a t e d and improved such a p o p u l a t i o n we do not want to undo the l a b o r s of the m i c r o b i o l o g i s t s and g e n e t i c i s t s by l e t t i n g i n t o our propagation apparatus other microorganisms which might compete with o r be a n t a g o n i s t i c to our producer p o p u l a t i o n , o r which might make substances which would have to be separated from the d e s i r e d product, and so on. The reasons why most fermentation technology i s pure c u l t u r e technology a r e t h e r e f o r e s i m i l a r to the reasons why our a g r i c u l t u r e tends to be monoculture of p l a n t s . Nevertheless, there a r e reasons f o r studying mixed c u l t u r e s , and I w i l l l i s t f o u r . F i r s t , c e r t a i n i n d u s t r i a l o p e r a t i o n s , notably waste d i s p o s a l s , do u t i l i z e mixed c u l t u r e s . Second, i n v a s i o n by contaminants or formation of mutants turn pure

0097-6156/83/0207-0201 $ 0 7 . 7 5 / 0 © 1983 American Chemical Society

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

BIOCHEMICAL ENGINEERING

202

c u l t u r e s i n t o mixed c u l t u r e s . T h i r d , mixed c u l t u r e s o f f e r some p o t e n t i a l advantages, such as ( i ) a b i l i t y to perform sequences of chemical transformations which no pure c u l t u r e can do, ( i i ) a b i l i t y to grow on simpler and so cheaper media, ( i i i ) a b i l i t y to continue f u n c t i o n i n g over wider ranges of environmental c o n d i t i o n s , and ( i v ) a b i l i t y to r e s i s t i n v a s i o n by contaminants. F i n a l l y , a f o u r t h reason f o r studying mixed c u l t u r e s i s that n a t u r a l systems always i n v o l v e the a c t i v i t i e s of mixed c u l t u r e s .


C l a s s i f i c a t i o n of population

interactions

When s e v e r a l populations of microorganisms i n h a b i t a common a b i o t i c environment they w i l l almost i n v a r i a b l y i n t e r a c t with one another. Attempts to construct t h e o r i e s of the dynamics of such s y s t e m s — t h a t i s , to construct t h e o r i e s which w i l l p r e d i c t how the systems evolve i n time—must be based therefore on knowledge of what i n t e r a c t i o n s occur and on the k i n e t i c s of such i n t e r a c t i o n s . Hence, the r e s t of what I have to say w i l l focus on what i s known about i n t e r a c t i o n s i n simple mixed c u l t u r e systems. Economy of d i s c u s s i o n makes i t necessary to devise some scheme f o r naming m i c r o b i a l i n t e r a c t i o n s . In a d d i t i o n , development and use of such a scheme w i l l help organize our t h i n k i n g on the subject and w i l l even suggest research that should be done. A l l schemes of naming i n t e r a c t i o n s that I have seen are based on naming i n t e r a c t i o n s between p a i r s of populations. This i s p e r f e c t l y understandable, s i n c e a p a i r of populations i s the sim p l e s t u n i t of b i o l o g i c a l o r g a n i z a t i o n that can e x h i b i t i n t e r a c t i o n s other then i n t r a s p e c i f i c ones. However, the use of the b a s i s named leads to some d i f f i c u l t i e s when we consider systems with three or more populations, as w i l l be explained s h o r t l y . The scheme of naming i n t e r a c t i o n s between a p a i r of popula t i o n s , say A and B, u s u a l l y adopted by e c o l o g i s t s i s based on the q u a l i t a t i v e e f f e c t s that the presence of A has on Β as w e l l as on the e f f e c t s that Β has on A. I f the presence of A stimulates the growth of Β somehow, then A i s s a i d to have a p o s i t i v e e f f e c t on Β whereas A i s s a i d to have a negative e f f e c t on Β i f the presence of A represses or slows the growth of B. Nothing i s s a i d about the p r e c i s e means by which one population a f f e c t s the other, and thus, by t h i s scheme, q u i t e d i f f e r e n t mechanisms of i n t e r a c t i o n w i l l be c l a s s i f i e d i n the same way; t h i s i s not altogether undesirable, of course. A t y p i c a l scheme of such c l a s s i f i c a t i o n i s given by Odum (1).



9.

FREDRICKSON

Interactions

of Microbial

Populations

203

I am going to r e t a i n the foregoing scheme, but i n a d d i t i o n , as I have suggested elsewhere ( 2 ) , the scheme w i l l be combined with another that names i n t e r a c t i o n s as d i r e c t or i n d i r e c t . D i r e c t i n t e r a c t i o n s are those f o r which p h y s i c a l contact of i n d i v i d u a l organisms from the two d i f f e r e n t populations i s a necessary part of the i n t e r a c t i o n . I n d i r e c t i n t e r a c t i o n s r e q u i r e no such contact, but r a t h e r are those i n t e r a c t i o n s which occur when changes i n the a b i o t i c environment produced by the a c t i v i t i e s of one p o p u l a t i o n a f f e c t the growth r a t e of the other, and v i c e v e r s a . D i r e c t i n t e r a c t i o n s are thus p h y s i c a l i n nature, whereas i n d i r e c t i n t e r a c t i o n s are chemical i n nature. The scheme of naming b i n a r y i n t e r a c t i o n s based on these two s e t s of c r i t e r i a i s shown i n F i g u r e 1. T h i s f i g u r e i s l a r g e l y s e l f explanatory and most of the names used are f a m i l i a r , although not every e c o l o g i s t would attach the exact same meaning to s e v e r a l of them that the f i g u r e does. For example, some e c o l o g i s t s use antagonism to r e f e r to any i n t e r a c t i o n that has a negative e f f e c t but i n the f i g u r e , antagonism means that each member of the p a i r exerts a negative e f f e c t on the other. In two cases, however, I have used words which are new or d e v i a t e from common usage. The i n t e r a c t i o n which r e s u l t s when population Β grows on products of l y s i s of c e l l s of p o p u l a t i o n A, the l y s i s being caused by exoenzymes released by p o p u l a t i o n B, i s c a l l e d e c c r i n o l y s i s . T h i s i s a word which I got from d i s c u s s i o n s with C. Takoudis, S. Pavlou, and R. A r i s . E c c r i n o l y s i s i s t y p i f i e d by the i n t e r a c t i o n of myxobacteria with c e r t a i n other b a c t e r i a ; see, e. g., K a i s e r ejt a l . (3). The word which d e v i a t e s from common usage i s feeding, which i s here used i n preference to prédation. Prédation has connotations of hunting and one-on-one a c t i o n which do not c h a r a c t e r i z e a l l of the i n t e r a c t i o n s that I c a l l f e e d i n g . I agree that feeding i s too general a word to be used as F i g u r e 1 uses i t , and I hope that someone can suggest a b e t t e r word to replace i t . Very o f t e n the i n t e r a c t i o n between a p a i r of populations w i l l be more complicated than any one of the i n t e r a c t i o n s named and described i n F i g u r e 1. When we are confronted with such s i t u a t i o n s , i t seems best not to t r y to invent new words to desc r i b e them but r a t h e r to s t a t e what combination of the i n t e r a c t i o n s of F i g u r e 1 are i n v o l v e d . For example, consider a s i t u a t i o n where a by-product of the metabolism of one population acts as a growth f a c t o r f o r a second p o p u l a t i o n , and where the two populations consume a common s u b s t r a t e to supply t h e i r needs f o r carbon and a v a i l a b l e energy. The i n t e r a c t i o n between the populations i s n e i t h e r commensalism nor competition, but we do not invent a new word to d e s c r i b e i t ; i n s t e a d , we say that i t i s commensalism p l u s competition. When the i n t e r a c t i o n between two populations i s f u l l y described by j u s t one of the items l i s t e d i n F i g u r e 1, i t i s convenient to emphasize that f a c t by saying that the i n t e r a c t i o n i s pure.


204


Effect of presence of Β on growth rate of A

-

—

—

—

—

Ο

—


Effect of presence of A on growth rate of Β

-

Ο

+

ο

+

•

•

+

-

+

+

-

Name of Qualifying remarks interaction Negative effects caused by COMPETITION removal of resources ANTAGONISM Negative effects caused by production of toxins or inhibitors AMENSALISM Negative effects caused by production of lytic agents; ECCRINOLYSIS positive effects caused by solubilization of biomass Positive effect caused by production by Β (host) of a stimulus for growth of A (commensal) or by removal COMMENSALISM by Β of an inhibitor for growth of A See remarks for Commensalism. Also presence of both PROTO populations not necessary COOPERATION for growth of both See remarks for Commensalism. Also presence of both MUTUALISM populations is necessary for growth of either

Β feeds on A

The parasite (B) penetrates the body of its host (A) and + therein converts the host's biomaterial or activities into its own A and Β are in physical contact; • (or perhaps Ο ) interaction highly specific Competition for space

-

FEEDING INCLUDES PREDATION AND SUSPENSIONFEEDING

PARASITISM

SYMBIOSIS CROWDING

Figure 1. Scheme of classification of binary population interactions. The roles of A and Β may be reversed. Top, indirect interactions; bottom, direct interactions.


9.

FREDRiCKSON

Interactions

of

Microbial

Populations

205


In a system i n h a b i t e d by ρ d i f f e r e n t populations, there i s a p o s s i b i l i t y f o r p!/2!(p-2)! b i n a r y i n t e r a c t i o n s to occur. A q u a n t i t a t i v e understanding of the dynamics of each of these i n t e r a c t i o n s i s necessary but not s u f f i c i e n t f o r a q u a n t i t a t i v e understanding of the dynamics of the whole system. Insufficiency may be demonstrated by c o n s i d e r i n g as an example the feeding of a s i n g l e protozoan population on two b a c t e r i a l populations which compete f o r a common resource. C l e a r l y , study of the two i n d i v i d u a l food chains i n v o l v e d here w i l l not allow us to p r e d i c t the behavior of the three-population system, because u n t i l the p r o t o zoans are a c t u a l l y presented with the choice of the two kinds of b a c t e r i a , we w i l l not know whether and to what extent the p r o t o zoans w i l l e x e r c i s e preference i n t h e i r uptake of food. D i s c u s s i o n of the i n t e r a c t i o n s I w i l l now d i s c u s s these v a r i o u s i n t e r a c t i o n s i n turn, beginning with the i n d i r e c t or chemical ones; the p r i n c i p a l o b j e c t s of the d i s c u s s i o n w i l l be to summarize the s t a t e of know ledge about each and to p o i n t out research that needs to be done on each. Competition. Probably the m a j o r i t y of s t u d i e s of competition that have been published have d e a l t with what has been c a l l e d pure and simple competition ^4). In t h i s type of competition, there i s only one resource whose a v a i l a b i l i t y or c o n c e n t r a t i o n a f f e c t s the growth r a t e of a competitor p o p u l a t i o n , t h i s resource i s the same f o r both competitors i n the i n t e r a c t i o n , and the growth r a t e s are not a f f e c t e d by changes i n the concentrations of other substances present i n the common environment. Pure and simple competition has a strong tendency to r e s u l t i n the e x c l u s i o n of one of the competitors, and v a r i o u s attempts to formulate a competitive e x c l u s i o n p r i n c i p l e have appeared i n the l i t e r a t u r e . One such f o r m u l a t i o n , which i s supported by many experiments as w e l l as by the p r e d i c t i o n s of mathematical models, i s that pure and simple competitors w i l l not c o e x i s t i n d e f i n i t e l y i n a system that i s s p a t i a l l y homogeneous and that i s s u b j e c t to t i m e - i n v a r i a n t e x t e r n a l i n f l u e n c e s . For example, the p r e d i c t i o n i s that pure and simple competitors w i l l not c o e x i s t i n a w e l l mixed chemostat having a v a n i s h i n g l y s m a l l surface-to-volume r a t i o (so that the s p a t i a l heterogeneity due to the presence of the chemostat w a l l s i s n e g l i g i b l e ) i f the d i l u t i o n r a t e and temperature of the chemostat, the composition of feed to the chemostat, e t c . , are a l l independent of time. Moreover, the p r e d i c t i o n i s that not only w i l l the competitors not c o e x i s t i n a steady s t a t e i n such a system but that they w i l l not even c o e x i s t i n a p e r p e t u a l l y t r a n s i e n t s t a t e , such as sustained o s c i l l a t i o n s of t h e i r population d e n s i t i e s ; see F r e d r i c k s o n and Stephanopoulos (4) f o r a d i s c u s s i o n of the l i t e r a t u r e on these p o i n t s .



206


F u r t h e r a n a l y s i s of pure and simple competition suggests that populations which so compete can c o e x i s t i f two s e t s of c o n d i t i o n s are s a t i s f i e d . F i r s t , the dependence of the growth r a t e s of the populations on the c o n c e n t r a t i o n of the l i m i t i n g resource must be such that there i s a range (or set of ranges) of concentration which causes the f i r s t population to grow f a s t e r than the second, and another range (or set of ranges) of concentration which causes the second population to grow f a s t e r than the f i r s t . If one population grows f a s t e r than the other at a l l concentrations of the l i m i t i n g resource, coexistence seems never to be p o s s i b l e . Second, the environment must be e i t h e r s p a t i a l l y or temporally heterogeneous, and heterogeneous i n such a way that i t favors the growth of one population here (now) and of the other population there (then). S p a t i a l heterogeneity can be imposed on a system, as f o r example, by using two chemostats with i n t e r s t a g e flows (5) and temporal heterogeneity can be imposed on a s i n g l e chemostat by p e r i o d i c v a r i a t i o n of d i l u t i o n r a t e , feed composition, e t c . , as studied by many workers (6-11). Analyses of the competition equations used by the foregoing workers shows that so long as s p a t i a l homogeneity i s imposed on systems, as by mixing i n a chemostat, temporal heterogeneity i s not generated by the a c t i v i t i e s of pure and simple competitors, so that temporal heterogeneity must be imposed from outside the system (12,13). Now the competition equations j u s t r e f e r r e d to are based on the hypothesis that we are d e a l i n g with a resource that i s not self-renewing; that i s , which i s e i t h e r a n o n - l i v i n g substance or a b i o l o g i c a l resource which f o r some reason or other i s not growing and reproducing. When t h i s hypothesis i s changed, and one assumes that the resource competed f o r i s capable of s e l f - r e n e w a l , i t appears that the competitive e x c l u s i o n p r i n c i p l e s t a t e d above i s no longer true. Some years ago A. L. Koch (14) published computer simulations of s i t u a t i o n s i n which two predator populations competed purely and simply f o r one prey p o p u l a t i o n . Koch's simulations showed these three populations c o e x i s t i n g i n what appeared to be l i m i t c y c l e s , a c l e a r v i o l a t i o n of the competitive e x c l u s i o n p r i n c i p l e stated above, but s i n c e h i s s i m u l a t i o n s were based on LotkaV o l t e r r a type equations whch I consider to be q u i t e i n a p p r o p r i a t e for m i c r o b i a l p o p u l a t i o n s , I disregarded h i s r e s u l t s and d i d not see t h e i r s i g n i f i c a n c e . S i m i l a r r e s u l t s published by Hsu et a l . (15,16) were disregarded f o r the same reason. However, P. Waltman of the U n i v e r s i t y of Iowa r e c e n t l y pointed out to me i n a personal communication that even when L o t k a - V o l t e r r a concepts are discarded e n t i r e l y and Monod's model i s used f o r a l l growth r a t e s , the r e s u l t i n g competition equations f o r two predators and one prey seem to have l i m i t c y c l e s o l u t i o n s f o r c e r t a i n c o n d i t i o n s of o p e r a t i o n . Mr. B a s i l B a l t z i s has found that use of a s o - c a l l e d m u l t i p l e s a t u r a t i o n model f o r the predators, which seems to be more appropriate than Monod's model f o r protozoans at any r a t e (17), and of Monod's model f o r the prey, a l s o leads to p r e d i c t i o n



9.

FREDRICKSON

Interactions

of Microbial

Populations

207

of coexistence of the three p o p u l s t i o n s i n what appear to be l i m i t c y c l e s . Hence, i t i s not the p a r t i c u l a r growth model that makes the d i f f e r e n c e here; r a t h e r , i t i s the presence of the a d d i t i o n a l t r o p h i c l e v e l that allows competing predators to c o e x i s t . I t seems i n t u i t i v e l y evident that a necessary c o n d i t i o n f o r coexistence ( i n a l i m i t c y c l e ) of two feeding populations that compete purely and simply f o r a growing and reproducing food popul a t i o n i s that there must be a range (or s e t of ranges) of food c o n c e n t r a t i o n f o r which the f i r s t feeder grows f a s t e r than the second and another range (or s e t of ranges) of food c o n c e n t r a t i o n f o r which the second feeder grows f a s t e r than the f i r s t . I f this i s so, then what appears t o be happening i n these three-population systems i s that the a c t i v i t i e s of the populations c r e a t e temporal heterogeneity o f the environment even when none i s imposed from without, and when t h i s heterogeneity f a v o r s i n succession growth of f i r s t one feeder and then the other, coexistence i n c y c l e s of p o p u l a t i o n d e n s i t y w i l l i n some cases be p o s s i b l e . The p r e d i c t i o n s of these recent modeling s t u d i e s should be tested by experimental research. T h i s could be done by observing, say, the competition of two protozoan populations, which do not feed on each other, f o r a s i n g l e , growing b a c t e r i a l p o p u l a t i o n i n a chemostat. In a d d i t i o n , modeling and mathematical analyses of other s i t u a t i o n s where competition ends a food chain might be rewarding. An example might be a system where two populations compete f o r a growth f a c t o r which i s r e l e a s e d i n t o the environment by the a c t i v i t i e s of a host p o p u l a t i o n . T h i s would not be expected to produce coexistence of the competitors i f the i n t e r a c t i o n of each with the host was pure commensalism, but i f the competitors a l s o d i d something that i n f l u e n c e d the host p o p u l a t i o n , coexistence i n l i m i t c y c l e s might be p o s s i b l e . F i n a l l y , these recent r e s u l t s suggest that f u r t h e r examination o f pure and simple competition f o r a resource that does not renew i t s e l f might be profitable. I t should be remembered i n t h i s connection that experimental devices l i k e the chemostat impose s p a t i a l homogeneity on competition systems. I f we d i d not impose homogeneity by mixing, i s i t p o s s i b l e that the a c t i v i t i e s of the populations could create s p a t i a l heterogeneity even where none i s imposed? I f t h i s i s p o s s i b l e , could i t allow pure and simple competitors to c o e x i s t ? I think that P r o f . Lauffenberger has been working on questions l i k e t h i s , and I hope that he w i l l provide us with some answers today. There are s e v e r a l other p o i n t s about competition that I would l i k e t o make b e f o r e going on to other kinds of i n t e r a c t i o n . Comp e t i t i o n between populations i n c e r t a i n environments might be p u r e — 1 . e., the only i n t e r a c t i o n between the p o p u l a t i o n s — b u t i t might not be simple because the concentrations of two o r more n u t r i e n t s competed f o r may a f f e c t the growth r a t e s of the populations. " N u t r i e n t s " as used here means chemicals not produced by the competing populations o r by others present, so there i s no question here of competition f o r self-renewing resources. In n u t r i e n t - p o o r environments, the concentrations of s e v e r a l



208


substances which are complementary resources ( f u l f i l l d i f f e r e n t needs i n the c e l l u l a r economies) may become r a t e - l i m i t i n g whereas i n complex, n u t r i e n t - r i c h environments, the concentrations of s e v e r a l substances which are s u b s t i t u t a b l e resources ( f u l f i l l the same need i n the c e l l u l a r economies) may become r a t e - l i m i t i n g . Many mathematical models of s i t u a t i o n s l i k e the foregoing have been published; see (6, 18-25). Analyses of these models suggests that pure but not simple competition should o f t e n r e s u l t i n coexistence of competitors, even i n systems i n which s p a t i a l homogeneity of the environment i s imposed and f o r which a l l e x t e r n a l i n f l u e n c e s are t i m e - i n v a r i a n t . Experimental data of Yoon e£ a l . (22) on competition of B a c i l l u s cereus and Candida t r o p i c a l i s f o r the s u b s t i t u t a b l e resources glucose and f r u c t o s e show that coexistence i n a chemostat i s indeed p o s s i b l e here. Experimental t e s t i n g of model p r e d i c t i o n s i n s i t u a t i o n s of elementary but not simple competition i s q u i t e important, because the models used are n e c e s s a r i l y those f o r m u l t i p l e s u b s t r a t e l i m i t a t i o n of growth, and a l l such models have low c r e d i b i l i t y , i n my o p i n i o n . Another form of elementary but not simple competition i s what has been c a l l e d (4) p a r t i a l competition. In t h i s , two populations compete f o r a resource whose a v a i l a b i l i t y a f f e c t s both t h e i r growth r a t e s , but i n a d d i t i o n , the growth r a t e of one of the popul a t i o n s , at l e a s t , i s also a f f e c t e d by the c o n c e n t r a t i o n of a substance which i s exempt from competition, e i t h e r because i t i s a resource which only one of the populations can use, or because i t i s a substance that i s not used by e i t h e r population but nevert h e l e s s exerts an e f f e c t , say of a u t o i n h i b i t i o n , on the growth r a t e of one of them. G o t t s c h a l ejt a l . (26) have provided an elegant experimental example of the former s i t u a t i o n with t h e i r mixotroph-obligate heterotroph system fed on a combination of acetate and t h i o s u l f a t e ; coexistence of these populations i n a chemostat occurred even though the populations competed f o r acetate. A s i m i l a r example i s given by Laanbroek et_ a l . (27). De F r e i t a s and F r e d r i c k s o n (28) Tiave analyzed mathematical models of s i t u a t i o n s of the l a t t e r type, and these show that the production of a u t o i n h i b i t o r s can allow c o m p e t i t o r s — p a r t i a l comp e t i t o r s — t o c o e x i s t . F i n a l l y , Miura et a l . (29) have analyzed a mathematical model of a s i t u a t i o n where p a r t i a l competition f o r a resource i s coupled with commensalism; again, coexistence i s pred i c t e d to be p o s s i b l e . Broad as w e l l as deep knowledge of microb i a l n u t r i t i o n and physiology are probably n e c e s s i t i e s f o r c r e a t i n g s u c c e s s f u l experimental systems of p a r t i a l competition, and one hopes that more poeple having such knowledge w i l l attempt to apply i t i n the d i r e c t i o n noted. The l a s t thing that I want to say about competition i s that i t might be rewarding to consider models of i t that take i n t o account some of the n o n - i d e a l f a c t o r s that f r e q u e n t l y complicate growth of microorganisms. By n o n - i d e a l f a c t o r s I mean such things as the occurrence of maintenance, v a r i a b i l i t y of biomass y i e l d , time l a g of metabolic process r a t e s i n response to changes i n


9.

FREDRiCKSON

Interactions

of Microbial

Populations

209

environmental c o n d i t i o n s , and so on. These things are u s u a l l y ignored i n mathematical models of competition, but i t seems p o s s i b l e that t h e i r occurrence could have strong e f f e c t s on the r e s u l t s of competition. F o r example, Alexander (30) mentions that c a p a c i t y of a population t o s y n t h e s i z e and s t o r e reserve foods when e x t e r n a l food i s abundant and then to use the s t o r e d food when the e x t e r n a l supply dwindles i s l i k e l y to be an important aspect of a p o p u l a t i o n s s competitive a b i l i t y . The experiments of van Gemerden (31) on competition of purple s u l f u r b a c t e r i a grown i n a chemostat subjected to a regimen of a l t e r n a t i n g l i g h t and dark seem to v e r i f y Alexander's suggestion. Wilder et a l . (32) have considered r e c e n t l y a model of competition i n which time lags of metabolic response were accounted f o r . But a s i d e from these examples, I do not know of other papers which consider the e f f e c t s that n o n - i d e a l phenomena might have on competitive s i t u a t i o n s . Mathematical models that we might make f o r such s i t u a t i o n s undoubt e d l y would not have high c r e d i b i l i t y , but they might make i n t e r e s t i n g p r e d i c t i o n s which could then be tested experimentally.


f

Amensalism and antagonism. A computerized l i t e r a t u r e search on these i n t e r a c t i o n s w i l l produce a l a r g e number of r e f e r e n c e s , a f a c t which i n d i c a t e s that the importance of these i n t e r a c t i o n s i s recognized widely. However, examination of the references produced w i l l show that very l i t t l e mathematical modeling work or experimental work that i s h e l p f u l i n c o n s t r u c t i n g such models has been done. The most important reason f o r t h i s i s probably that models o f amensalism and antagonism have to be based on models f o r the k i n e t i c s of production and a c t i o n of i n h i b i t o r s and t o x i n s , and current models f o r the k i n e t i c s of these processes are not of high c r e d i b i l i t y . B e t t e r models could, no doubt, be constructed from data from experiments on systems e x h i b i t i n g amensal o r a n t a g o n i s t i c i n t e r a c t i o n s , but the best remedy f o r the d i f f i c u l t y noted i s the performance of a u t e c o l o g i c a l — m e a n i n g u s u a l l y pure c u l t u r e — w o r k on organisms that produce toxins o r i n h i b i t o r s and a l s o on organisms that are a f f e c t e d by such substances. Use of simple models which are p l a u s i b l e but which have low c r e d i b i l i t y because they have not had extensive experimental t e s t i n g and refinement suggests that a p a i r of populations which i n t e r a c t by amensalism o r antagonism only, or by a combination of amensalism o r antagonism w i t h competition f o r a s i n g l e resource, cannot c o e x i s t i n d e f i n i t e l y i n a common, homogeneous environment (28). An experimental system which involved competition and amensalism was devised by Adams et a l . (33). They found that the two populations, both of which were s t r a i n s of E s c h e r i c h i a c o l i , d i d not c o e x i s t i n a chemostat and that the i d e n t i t y of the popul a t i o n which was excluded depended on the d e n s i t i e s of the popul a t i o n s at the beginning of the experiment. Both of these r e s u l t s are p r e d i c t e d by simple models (28), and thus, the n o t i o n that populations which i n t e r a c t by amensalism or antagonism cannot c o e x i s t gains some p l a u s i b i l i t y .



210


Amensalism i s probably a means by which some organisms or groups of organisms can defend t h e i r h a b i t a t against invaders who would compete w i t h them f o r the resources of the h a b i t a t . I f an a s s o c i a t i o n of organisms occurs i n a h a b i t a t , then the c o n j e c t u r a l p r i n c i p l e s t a t e d above r e q u i r e s that these organisms s h a l l not i n t e r a c t by amensalism; r a t h e r , amensalism comes i n t o play when an invader appears. A r e l a t i v e l y simple example of t h i s s o r t of thing i s shown i n F i g u r e 2. In t h i s f i g u r e , A and Β are the organisms of the a s s o c i a t i o n . They compete f o r the resources, S, of t h e i r h a b i t a t , but Β i s commensally dependent on A through the by-product, P, of the growth of A; Ρ i s r e q u i r e d by Β but cannot by synthesized by that organism from a v a i l a b l e precursors. T h i s a s s o c i a t i o n leads to s t a b l e coexistence steady s t a t e s , i n s p i t e of the competition; see the d i s c u s s i o n of commensalism given below. In a d d i t i o n , the commensal population produces a substance, T, which i s not i n h i b i t o r y to i t s e l f or to i t s host, but which i s i n h i b i t o r y to many p o t e n t i a l invaders of the h a b i t a t . When such an invader, I, appears, amensalism comes i n t o p l a y , and i f the amensalism i s strong enough, the invader w i l l be destroyed. I t would be very i n t e r e s t i n g to f i n d an experimental r e a l i z a t i o n of the scheme shown i n F i g u r e 2, and to see what i t s dynamics were. Commensalism. One of the d i f f i c u l t i e s with the scheme of c l a s s i f i c a t i o n used here i s that i t does not recognize d i f f e r e n c e s i n mechanisms of i n t e r a c t i o n s . T h i s may a l s o be one of i t s s t r e n g t h s , though I am not so sure about t h a t . The d i f f i c u l t y i s w e l l i l l u s t r a t e d by the i n t e r a c t i o n of commensalism; a l l of the f o l l o w i n g s i t u a t i o n s are commensalism, and a l l i n v o l v e q u i t e d i f f e r e n t mechanisms. ( i ) Population Η r e l e a s e s a by-product of growth, P, which i s required by another p o p u l a t i o n , C, f o r i t s growth; ( i i ) p o p u l a t i o n Η produces a set of exoenzymes, E, which a t t a c k i n s o l u b l e m a t e r i a l s , S , to produce s o l u b l e s u b s t r a t e s , S, which are then used by another p o p u l a t i o n , C; ( i i i ) p o p u l a t i o n Η consumes a substance, I , which i n h i b i t s the growth of another p o p u l a t i o n , C; and ( i v ) p o p u l a t i o n Η produces an exoenzyme, E, which destroys a substance, I, that i s t o x i c to another p o p u l a t i o n , H. In a l l of these s i t u a t i o n s , and i n others that one can imagine, the host population (H) performs a f u n c t i o n which changes the chemical environment i n a way that favors the growth of the commensal population (C), but the a c t i v i t i e s of the commensal are such that the favor i s not r e c i p r o c a t e d . Mechanisms ( i ) - ( i v ) above are d i f f e r e n t forms of commensalism, and we may t h i n k of them as elementary or simple forms of t h i s i n t e r a c t i o n . C l e a r l y , these forms may occur i n combination with one another, and thus, even a s i t u a t i o n of pure commensalism might be complex i n the sense that s e v e r a l d i f f e r e n t mechanisms are involved i n i t . The same t h i n g can be s a i d about most of the other i n t e r a c t i o n s named i n F i g u r e 1. The nature of the commensal i n t e r a c t i o n s j u s t described i s such that many of those that we might f i n d i n nature or construct 1



FREDRiCKSON

Interactions

of Microbial

Populations

A Β

Î

I

/

Figure 2. An association of two populations that interact by commensalism and competition, and that are protected from invasion by the production of a toxin.



212


i n the l a b o r a t o r y would not be pure but would be complicated by competition of host and commensal f o r a s u b s t r a t e . Meers (34) pointed t h i s out f o r mechanism ( i ) above and i t i s c l e a r that i t i s l i k e l y to be true of the other mechanisms as w e l l . The occurrence of commensalism of mechanism ( i ) can prevent competitive e x c l u s i o n from happening, and that the a s s o c i a t i o n of host and commensal i s s t a b l e even though they compete has been demonstrated c o n v i n c i n g l y both by experiment and by mathematical models; see Megee et a l . (35), G o t t s c h a l et a l . (26), Miura et_ a l . (29,36). I would think that the other kinds of commensalism l i s t e d above would a l s o permit competing host and commensal populations to coexist. R e i l l y (37) pointed out another s e t of complications that o f t e n a f f e c t commensal systems; t h i s was suggested by some e x p e r i ments performed by Chao and R e i l l y (38). The complications that R e i l l y mentioned a r i s e from the production of metabolic by-products by the commensal population that have e f f e c t s , e i t h e r s t i m u l a t o r y or i n h i b i t o r y , on the host p o p u l a t i o n . The production of such substances changes the i n t e r a c t i o n of pure commensalism i n t o an i n t e r a c t i o n of pure mutualism or protocooperation, or i n t o a comb i n a t i o n of commensalism and amensalism. R e i l l y presented computer s o l u t i o n s of the d i f f e r e n t i a l equations f o r v a r i o u s model systems of t h i s type, and more r e c e n t l y Sheintuch (39) made a d e t a i l e d a n a l y s i s of commensal systems complicated by the product i o n of substances having i n h i b i t o r y e f f e c t s . In s p i t e of the l i k e l i h o o d that the foregoing complications w i l l occur, there are probably a f a i r number of s i t u a t i o n s where commensalism i s pure or r e l a t i v e l y pure; that i s , not much comp l i c a t e d by competition or by the production of substances by the commensal which a f f e c t the host. As an example, I c i t e the s i t u a t i o n s t u d i e d by Lee et a l . (40). The organisms used, L a c t o b a c i l l u s plantarum and Propionibacterium shermanii, are a s s o c i a t e d together i n the manufacture of Swiss cheese. The p o t e n t i a l f o r competition of these organisms i s present, f o r both can use, say, glucose as the source of carbon and a v a i l a b l e energy. However, P. shermanii can s u b s t i t u t e l a c t i c acid f o r glucose, and i n f a c t , i t was shown (41) that t h i s organism takes up no glucose when s u f f i c i e n t amounts of l a c t i c a c i d are present. Hence, the l a c t i c acid produced by L. plantarum i s used by shermanii, and by i t s preference f o r l a c t i c a c i d over glucose, P. shermanii avoids competition with L. plantarum, although i t does so at the expense of becoming commensally dependent on the l a t t e r organism. One would expect that many s i t u a t i o n s where a p o p u l a t i o n having the c a p a c i t i e s to use s e v e r a l to many s u b s t i t u t a b l e resources and to e x h i b i t s u b s t r a t e p r e f e r e n c e — a g e n e r a l i s t p o p u l a t i o n — f o r m s an a s s o c i a t i o n w i t h a population l a c k i n g these features but having the a b i l i t y to grow r a t h e r r a p i d l y i n c e r t a i n r a t h e r s p e c i a l i z e d e n v i r o n m e n t s — a s p e c i a l i s t p o p u l a t i o n — o c c u r i n nature.


9.

FREDRICKSON

Interactions of Microbial

Populations

Mutualism and Protocooperation. I f the a c t i v i t i e s of two populations are such that each produces and excretes i n t o the common environment a substance o r s e t of substances which serves as r e q u i r e d s u b s t r a t e or growth f a c t o r f o r the other, and i f such substances are not s u p p l i e d t o the environment from e x t e r n a l sources, then the i n t e r a c t i o n between the populations w i l l i n v o l v e mutualism. Other mechanisms g i v i n g r i s e to mutualism might be imagined a l s o , but the one d e s c r i b e d , which i s sometimes c a l l e d syntrophism and sometimes c r o s s - f e e d i n g , i s l i k e l y to be the form of mutualism most o f t e n encountered. Experimental examples of i t have been provided by Nurmikko ( 4 2 ) Wolfe and Pfennig (43), S l a t e r (44), and Lamb and Garver (45), as w e l l as by others. Three remarks about t h i s kind of mutualism seem p e r t i n e n t . F i r s t , the f a c t that two organisms w i l l grow together i n a batch of medium i n which they w i l l not grow s e p a r a t e l y i s o f t e n taken to be an i n d i c a t i o n that the organisms are e x h i b i t i n g syntrophism. In many cases where t h i s observation i s made the i n f e r e n c e i s no doubt c o r r e c t . But even i f i t i s v a l i d , i t does not f o l l o w that the syntrophism can be put to use i n , say, a chemostat type o f apparatus. I have shown elsewhere (2) that i n order f o r m u t u a l i s t i c steady s t a t e s to be p o s s i b l e i n a chemostat i t i s necessary that the production and consumption of the substances which produce the i n t e r a c t i o n must be such that more o f them i s produced than i s consumed. I f that i s the case, the system i s s u p e r c r i t i c a l , and mutualism can produce a steady s t a t e of coexistence i n a chemostat. But i f the system i s only c r i t i c a l or s u b c r i t i c a l , no such steady s t a t e i s p o s s i b l e . Hence, i f we wish to e x p l o i t a s i t u a t i o n of syntrophism i n a chemostat, we have t o be sure that the s i t u a t i o n at hand i s s u p e r c r i t i c a l or the attempt at e x p l o i t a t i o n w i l l f a i l . The second p o i n t i s that even f o r syntrophic p a i r s of organisms which are s u p e r c r i t i c a l , the steady s t a t e of washout from a chemostat i s always s t a b l e with respect to s m a l l p e r t u r b a t i o n s (46) . Therefore, the steady s t a t e o f coexistence of the populat i o n s cannot be s t a b l e with respect to a l l l a r g e p e r t u r b a t i o n s , so coexistence of the partners i s always menaced by l a r g e p e r t u r b a t i o n s of t h e i r system. The t h i r d p o i n t i s that there w i l l o f t e n (always?) be two coexistence steady s t a t e s f o r a p a i r of s y n t r o p h i c organisms i n a chemostat. In one of these, the only i n t e r a c t i o n between the populations i s mutualism but i n the other, some other i n t e r a c t i o n , such as competition f o r a n u t r i e n t s u p p l i e d from o u t s i d e the s y s tem, occurs a l s o . I t turns out that the steady s t a t e of pure mutualism i s unstable always (46), so that i f we wanted to study i t we would have t o t r y t o s t a b i l i z e i t by adding some c o n t r o l s to the chemostat. Protocooperation d i f f e r s from mutualism i n that i n mutualism n e i t h e r population can s u r v i v e without the other whereas i n protocooperation one o r both populations can s u r v i v e without the other. One could d e f i n e two sub-cases of protocooperation, depending upon whether the presence of the second population i s necessary f o r 9


213



214


s u r v i v a l of one population or n e i t h e r p o p u l a t i o n . The example provided by Wilkinson et_ a l (47) seems to be of the former kind of protocooperation. Here, a Pseudomonas species produces methanol from methane, and i s s t r o n g l y a u t o - i n h i b i t e d by the a l c o h o l ; a Hyphomicrobium species consumes the a l c o h o l and thus r e l e a s e s the Pseudomonas from a u t o - i n h i b i t i o n . The i n t e r a c t i o n may be somewhat more complex, f o r Wilkinson et a l . were unable to grow t h e i r Pseudomonas i n pure c u l t u r e , and two other populations, an Acinetobacter species and a Flavobacter s p e c i e s , were present a l s o i n t h e i r mixed c u l t u r e system and may have played some r o l e i n i t . I t appears that removal of i n h i b i t o r y substances plays a l a r g e r o l e i n many protocooperative i n t e r a c t i o n s that we can imagine, and when we attempt to construct mathematical models of these i n t e r a c t i o n s we are faced with the d i f f i c u l t y that we do not have models f o r the k i n e t i c s of i n h i b i t o r y a c t i o n i n which we can place a l o t of confidence. Advancement of the theory of protocooperation therefore would seem to depend on advancement of a u t e c o l o g i c a l knowledge of the k i n e t i c s of i n h i b i t o r a c t i o n . E c c r i n o l y s i s . C o n s t r u c t i o n of t h e o r i e s of t h i s i n t e r a c t i o n i s faced with d i f f i c u l t i e s s i m i l a r to those f a c i n g c o n s t r u c t i o n of t h e o r i e s of protocooperation, but the d i f f i c u l t i e s are even more severe. In order to construct such a theory, we would need knowledge of the k i n e t i c s of formation of exoenzymes by the one popul a t i o n and of the k i n e t i c s of a c t i o n of those enzymes on the other population of the p a i r . The k i n e t i c s of both processes are complex, i f we may judge from some recent attempts at modeling exoenzyme production and a c t i o n presented by Van Dedem and Moo Young (48), and thus, i t i s not s u r p r i s i n g that attempts to make models of systems e x h i b i t i n g e c c r i n o l y s i s seem not to have been made. The i n t e r a c t i o n i s probably of importance i n some n a t u r a l systems, f o r i t must be involved i n the c y c l i n g of minerals. Therefore, attempts to study i t q u a n t i t a t i v e l y should be made. We turn now to d i r e c t i n t e r a c t i o n s between p a i r s of m i c r o b i a l populations. Feeding. The f i r s t thing to be s a i d about t h i s subject at the present time i s that i n s u f f i c i e n t a t t e n t i o n has been paid to the d i f f e r e n c e s i n the modes of feeding e x h i b i t e d by phagotrophic microorganisms. Such d i f f e r e n c e s may be i l l u s t r a t e d by c o n s i d e r i n g the feeding of Didinium nasutum, D i c t y o s t e l i u m discoideum, and Tetryhymena p y r i f o r m i s , a l l organisms which have been used i n l a b o r a t o r y s t u d i e s of what i s u s u a l l y c a l l e d m i c r o b i a l prédation. Didinum nasutum i s a c i l i a t e d protozoan that was used by Gause (49) i n h i s seminal s t u d i e s of m i c r o b i a l i n t e r a c t i o n s , and many subsequent s t u d i e s using t h i s organism have been made; f o r a resume of l i t e r a t u r e , see Berger (50). Didinium feeds by a t t a c k i n g and i n g e s t i n g other protozoa, normally Paramecium, which i t encounters during i t s swimming a c t i v i t y . Attacks are on one Paramecium c e l l


9.

FREDRICKSON

Interactions

of Microbial

Populations

215


at a time, and chemotaxis seems to play a r o l e i n these (51,52) . Feeding i s s e l e c t i v e both i n regard to d i f f e r e n c e s i n the f r e quency of attacks on p r e f e r r e d and non-preferred food as w e l l as i n regard t o d i f f e r e n c e s i n the percentages of u n s u c c e s s f u l attacks on d i f f e r e n t organisms (50,52). I t seems q u i t e appropriate to apply the term prédation to t h i s kind o f feeding behavior. I t should be noted that Didinium i s not what Slobodkin (53) has c a l l e d a "prudent predator," f o r i t commonly makes the p o t e n t i a l l y l e t h a l mistake o f consuming a l l of i t s prey when i t i s i n o c u l a t e d i n t o a batch of them (49,54,55). D i c t y o s t e l i u m discoideum i s an a c e l l u l a r slime mold that has been used much by b i o l o g i s t s studying such processes as chemotaxis, c e l l aggregation, and morphogenesis. Feeding forms of t h i s organism are amoebae, and i n n a t u r a l s i t u a t i o n s , these g l i d e over s o l i d surfaces and engulf b a c t e r i a l c e l l s , t h e i r food, when they encounter them. Tsuchiya e t a l . (56) grew t h i s organism on b a c t e r i a i n l i q u i d c u l t u r e i n chemostats, and they observed the o s c i l l a t i o n s of population d e n s i t i e s that t h e o r e t i c i a n s had been p r e d i c t i n g f o r so long. Dr. Bazin has been working with t h i s organism i n recent y e a r s , and I hope he w i l l t e l l us more about i t . Tetrahymena p y r i f o r m i s i s a c i l i a t e d protozoan whose feeding has been s t u d i e d by many workers; a recent l i t e r a t u r e survey i s given by Swift et a l . (57). A c e l l of T\ p y r i f o r m i s has a b u c c a l c a v i t y which has a l a r g e undulating membrane on one s i d e and three s m a l l e r , moving membranes on the other. The beating of these membranes d i r e c t s water i n t o the b u c c a l c a c i t y , and p a r t i c l e s , e s p e c i a l l y b a c t e r i a , suspended i n t h i s water are c o l l e c t e d by the organism i f they are of appropriate s i z e , n e i t h e r too l a r g e nor too s m a l l . I t would seem that t h i s k i n d of f o o d - c o l l e c t i n g apparatus should have no a b i l i t y t o s e l e c t p a r t i c l e s except on the b a s i s of p r o p e r t i e s that are hydromechanically s i g n i f i c a n t , such as s i z e , shape, and d e n s i t y . I t i s not appropriate to apply the name prédation to t h i s kind o f feeding, and the term suspension-feeding advocated by J^rgensen (58) w i l l be used i n s t e a d . The remainder of my remarks on feeding w i l l be about suspens i o n - f e e d i n g . This i s not because I consider t h i s to be the most important kind of m i c r o b i a l feeding but r a t h e r because i t i s the kind with which I have f i r s t hand experience. An i n t e r e s t i n g f a c t which emerges from many l a b o r a t o r y s t u d i e s of suspension-feeding of Tetrahymena and s i m i l a r bacterivorous protozoans i s that these organisms have not been observed t o consume a l l of the b a c t e r i a i n t h e i r h a b i t a t . Hence, they are examples of S l o b o d k i n s "prudent predators," although I w i l l change h i s term to prudent feeders. The f e a t u r e s of a suspension-feeder's behavior which make i t "prudent" are not the same f o r a l l such organisms. F o r example, Bader ejt a l . (59) studied feeding on the blue-green a l g a Anacystis nidulans by the c i l i a t e d protozoan Colpoda s t e i n i i . [The i d e n t i 1




216

f i c a t i o n of t h i s protozoan was challenged by Frenchel (60) on the grounds that "the r e a l Colpoda s t e i n i i i s about 10 times smaller than that recorded i n the reference (to a new handbook of suspens i o n - f e e d i n g by J ^ r g e n s e n ) I have not yet seen J^rgensen's work. A c t u a l l y , Bader ej: a l . made no statement about the s i z e of t h e i r c i l i a t e , but they used the same c u l t u r e used by Drake and Tuschiya (61) , and the c e l l volume data reported by these workers i s w i t h i n , comfortably so, the range of c e l l s i z e s commonly s t a t e d f o r Colpoda s t e i n i i , as by Kudo (62), f o r example]. When c e r t a i n conditions a r i s e i n c u l t u r e s of Colpoda s t e i n i i , i t s m o t i l e , feeding c e l l s undergo morphological change and become non-motile, nonfeeding c y s t s . Conditions which cause encystment are by no means f u l l y understood, but they seem to i n c l u d e a low density of food, a high d e n s i t y of feeding c e l l s , or, at intermediate d e n s i t i e s of the two populations, some combination of the d e n s i t i e s . Many suspension-feeders are known to form c y s t s , and i t seems l i k e l y that a l l having t h i s capacity w i l l be found to be "prudent" feeders. P r o t o z o o l o g i s t s have not been able to confirm a few reports that Tetrahymena p y r i f o r m i s encysts ( C o r l i s s (63)) and so t h i s organism must be regarded to be non-encysting. Nevertheless, i t appears to be "prudent" because when i t i s i n o c u l a t e d i n t o a batch of v i a b l e but non-growing b a c t e r i a i t does not consume a l l of them but instead only reduces the d e n s i t y of v i a b l e b a c t e r i a to the order of 10 - 10 mlT . This observation was made by Habte and Alexander (64) and confirmed by Watson et a l . (65). Experiments reported i n these papers prove that f a i l u r e to consume a l l of the b a c t e r i a i s not due to death of the protozoa, to a u t o i n h i b i t i o n of the protozoa, to exhaustion of some e s s e n t i a l m a t e r i a l which the protozoa get from the l i q u i d medium r a t h e r than from feeding on the b a c t e r i a , or to l o s s of the protozoan's a b i l i t y to feed on the bact e r i a . One could t r y to e x p l a i n the r e s u l t s mentioned by saying that the b a c t e r i a present i n i t i a l l y have a d i s t r i b u t i o n of s t a t e s and that b a c t e r i a f a l l i n g i n t o some domain or domains of t h i s d i s t r i b u t i o n cannot be consumed by the protozoa. For example, Fenchel (60,66) has shown that the a b i l i t y of a suspension-feeder to c o l l e c t l a t e x beads i s confined to beads of a c e r t a i n s i z e range, and s i n c e the same r e s u l t a p p l i e s without much doubt to c o l l e c t i o n of b a c t e r i a , the argument may be made that the b a c t e r i a which comp r i s e the residuum l e f t a f t e r v i a b l e b a c t e r i a l d e n s i t y i n a batch ceases to f a l l are those that are too s m a l l , or too l a r g e , or too small and too l a r g e , to be c o l l e c t e d by the protozoans. One cannot t e s t t h i s hypothesis d i r e c t l y by measuring the changes produced i n the s i z e d i s t r i b u t i o n of v i a b l e b a c t e r i a by the feeding because the d e n s i t y of v i a b l e b a c t e r i a present toward the middle and end of the experiment i s always much l e s s than the density of d e t r i t a l part i c l e s having s i z e s comparable to the b a c t e r i a and which are always produced by feeding. The foregoing hypothesis, w h i l e p l a u s i b l e , i s c o n t r a d i c t e d by some a d d i t i o n a l experiments done by Habte and Alexander (64) . They found that T. p y r i f o r m i s f a i l e d to s t a r t c o l l e c t i n g b a c t e r i a when 5

7

1



9.

FREDRiCKSON

Interactions

of Microbial

Populations

217

i n o c u l a t e d a t high d e n s i t y i n t o a c u l t u r e of non-growing b a c t e r i a , even though i n o c u l a t i o n of T_. p y r i f o r m i s at low d e n s i t y i n t o a c u l t u r e of non-growing b a c t e r i a d i d r e s u l t i n c o l l e c t i o n (the i n i t i a l b a c t e r i a l d e n s i t i e s were the same i n both experiments). I do not think that the observed f a i l u r e to s t a r t feeding i n the high d e n s i t y case i s an a r t i f a c t to be a t t r i b u t e d to the procedures used to prepare the protozoan inoculum, although that does need to be checked out. An a l t e r n a t e working hypothesis which i s suggested by the foregoing d i s c u s s i o n i s that T. p y r i f o r m i s c e l l s possess sensing and c o n t r o l mechanisms which lead to c e s s a t i o n of t h e i r feeding a c t i v i t y under c e r t a i n c o n d i t i o n s of environmental s t a t e . A c o r o l l a r y of t h i s hypothesis i s that T. p y r i f o r m i s c e l l s which do not eat b a c t e r i a l c e l l s under one set of c o n d i t i o n s can eat these c e l l s — t h e same o n e s — u n d e r a d i f f e r e n t set of c o n d i t i o n s . T e s t i n g of these d i f f e r e n t hypotheses i s something that we are t r y i n g to do at the present time. A d d i t i o n a l adaptations which make m i c r o b i a l feeders "prudent" or which allow m i c r o b i a l "predators" to c o e x i s t with t h e i r "prey" are discussed i n a recent review by Alexander (67). C e s s a t i o n of feeding, whether i t be caused by encystment o r by some process that i s not accompanied by a morphological t r a n s formation of the feeders, implies that there i s some threshold d e n s i t y of food. The threshold d e n s i t y i s such that feeding w i l l stop (or f a i l to s t a r t ) i f the density f a l l s (or i s ) below the threshold d e n s i t y . One would expect that the threshold density of food would depend on the i d e n t i t i e s of the feeding and fed-upon populations as w e l l as on such things as the composition of the medium. However, there i s some evidence that i n a d d i t i o n to these f a c t o r s the threshold d e n s i t y of food changes with the density of the feeders themselves. F o r example, i n the experiment of Habte and Alexander c i t e d above (64) , Tetrahymena c e l l s i n o c u l a t e d at high d e n s i t y f a i l e d to s t a r t feeding whereas Tetrahymena c e l l s i n o c u l a t e d at a low density d i d s t a r t , and t h i s i s evidence that the threshold density of b a c t e r i a i s r a i s e d by increase of the protozoan d e n s i t y . Bader £t a l . (59) reached s i m i l a r conclusions about thresholds f o r encystment of Colpoda s t e i n i i , and a d d i t i o n a l evidence from the l i t e r a t u r e could be c i t e d . Results such as these suggest that tht threshold r e l a t i o n between the two d e n s i t i e s might be as shown i n F i g u r e 3. Herein, feeding w i l l occur i f the combination of d e n s i t i e s l i e s above and to the l e f t of the curve but feeding w i l l not occur i f the combin a t i o n l i e s below and to the r i g h t of the curve. The curve shown i s drawn with a h o r i z o n t a l asymptote because, i f the d e n s i t y of the feeding p o p u l a t i o n i s s u f f i c i e n t l y low, there can be no e f f e c t s o f crowding i n t h i s population. Under such cond i t i o n s , the threshold d e n s i t y of the fed-upon p o p u l a t i o n — i f there i s such a threshold d e n s i t y — m u s t be independent of the density of the feeding population. The curve i s drawn with a v e r t i c a l asymptote, a l s o . This i s because one expects t h a t , under very



218


° c > ο W CO

I!

Feeding

ο,ο. ο tr α

Figure 3. Conjectural relation between densities of feeding and fed-on popula tion where cessation of feeding by a "prudent" feeder occurs.

No Feeding

Logarithm of the Density of the Feeding Population



9.

FREDRiCKSON

Interactions

of Microbial

Populations

219

crowded c o n d i t i o n s , the best t h i n g f o r a feeding population to do would be to stop e a t i n g and so prevent f u r t h e r increase of crowd i n g . Under such c o n d i t i o n s , there i s no threshold d e n s i t y of the fed-upon population, of course. F i g u r e 3 must be regarded almost e n t i r e l y as s p e c u l a t i o n , s i n c e , so f a r as I know, a complete f i g u r e l i k e i t has never been e s t a b l i s h e d f o r any p a i r of microorganisms. S a l t (68) gave data f o r the predator-prey system Woodruffia metabolica-Paramecium a u r e l i a , but these are of l i m i t e d extent and do not show the asymptotes of F i g u r e 3. Bader ejt a l . ( 5 9 ) gave a f i g u r e f o r con d i t i o n s of population d e n s i t i e s which lead to encystment of the suspension-feeder Colpoda s t e i n i i when i t feeds on Anacystis nidulans. T h e i r data do suggest that asymptotes e x i s t , but the data are i n s u f f i c i e n t to prove that they do, and i n a d d i t i o n , are badly s c a t t e r e d . Threshold and i n t r a s p e c i f i c crowding phenomena are of fundamental b i o l o g i c a l and e c o l o g i c a l s i g n i f i c a n c e , and so work to c l a r i f y the p i c t u r e that we have of them now should be pursued with v i g o r . I f there i s indeed a threshold density of b a c t e r i a below which protozoans l i k e Tetrahymena do not feed, then i t follows that growth and feeding of such organisms cannot be described by Monod's model of growth (69). A model that suggests i t s e l f f o r s i t u a t i o n s l i k e this i s b
b_

where φ ^ ) i s the feeding r a t e per protozoan c e l l when the bac t e r i a l d e n s i t y i s b, b i s the threshold density of b a c t e r i a , and φ and L are model parameters, the former being the maximum, or s a t u r a t i o n v a l u e , of φ ^ ) . Models l i k e t h i s are inconvenient from the mathematical and computational point of view, however. The m u l t i p l e s a t u r a t i o n model of J o s t et a l . (17) i s t

π1

*

( b )

"

(L,

Λ(L

2

+ b)

( 2 )

and i t avoids the mathematical and computational d i f f i c u l t i e s inherent i n use of an e x p l i c i t threshold model, l i k e Equation (1). Equation (2) does not have a threshold value of b, of course, but i t does p r e d i c t that (3)



220


which i s c h a r a c t e r i s t i c of a t r u e threshold model but not of Monod's model. I t has been shown that the m u l t i p l e s a t u r a t i o n model does a much b e t t e r job of c o r r e l a t i n g data f o r feeding of Tetrahymena on b a c t e r i a than does Monod's model (17 ,70 ,71 ,72) . As pointed out above, Tetrahymena p y r i f o r m i s c o n s i s t e n t l y f a i l s to c l e a r batches of water of b a c t e r i a , and the explanation f o r t h i s may be that some of the b a c t e r i a are too small or too l a r g e to be captured by the protozoans. I f t h i s i s the case, then there i s no t h r e s h o l d d e n s i t y of the b a c t e r i a , of course, so there would be l i t t l e j u s t i f i c a t i o n f o r using models l i k e Equations (1) or ( 2 ) . In t h i s circumstance, what one needs to do i s to d i v i d e the b a c t e r i a i n t o sub-populations, one which i s eaten by the p r o t o zoans and one or more which i s (are) not eaten by them. Monod's model might be assumed f o r feeding of the protozoans on the subpopulation of b a c t e r i a that they can eat, and models f o r t r a n s f e r of b a c t e r i a from one sub-population to another would be needed, also. A c t u a l l y use of models l i k e those that we have been d i s c u s s i n g can probably never y i e l d b e t t e r than order-of-magnitude p r e d i c t i o n s of p o p u l a t i o n d e n s i t i e s i n dynamic, t r a n s i e n t s i t u a t i o n s . Recent s t u d i e s of the responses of Tetrahymena p y r i f o r m i s to sudden changes i n the b a c t e r i a l d e n s i t y of i t s surroundings r e v e a l phenomena (57 ,65) which seem to r e q u i r e p a r t i a l d i f f e r e n t i a l equations r a t h e r than o r d i n a r y d i f f e r e n t i a l equations f o r t h e i r accurate description. F i n a l l y , i t should be mentioned that feeding by protozoans would be expected to exert strong r e g u l a t o r y e f f e c t s on the bact e r i a l populations on which they feed, e s p e c i a l l y i f these l a t t e r populations compete with one another f o r n u t r i e n t s . J o s t et a l . (17), f o r example, found that f e e d i n g of Tetrahymena p y r i f o r m i s on E s c h e r i c h i a c o l i and Azotobacter v i n e l a n d i i i n a chemostat seemed to lead to coexistence of the three populations i n a p e r p e t u a l l y t r a n s i e n t s t a t e ; i n the absence of the protozoans, however, Azotob a c t e r was excluded by E. c o l i . C l e a r l y , an important f a c t o r to be considered i n s i t u a t i o n s l i k e the foregoing i s the p o s s i b i l i t y that the protozoans may e x h i b i t preference f o r one b a c t e r i a l species over the other. As mentioned p r e v i o u s l y , i t seems l i k e l y that food preference by suspension-feeding microorganisms must be based e n t i r e l y , or almost e n t i r e l y , on d i f f e r e n c e s i n hydromechanically s i g n i f i c a n t propert i e s l i k e s i z e , shape, and d e n s i t y , of the food organisms. Experiments i n which protozoans are presented which choice of food, the food organisms d i f f e r i n g i n the p r o p e r t i e s noted, need to be done. We are c u r r e n t l y p r e s e n t i n g Tetrahymena p y r i f o r m i s with E. c o l i and A. v i n e l a n d i i , these being b a c t e r i a whose s i z e s are q u i t e d i f f e r e n t . But experiments i n which a suspension-feeder i s presented with b a c t e r i a having the same s i z e and shape, but d i f f e r i n g i n some p r o p e r t i e s that are not hydromechanically s i g n i f i c a n t , need to be done, too. One expects no preference i n such cases, and the one experiment of the kind that I know of showed no preference


9.

FREDRiCKSON

Interactions

of

Microbial

221

Populations


(73), but more data of the same kind are needed before one can conclude that food preference by suspension-feeders i s based s o l e l y on d i f f e r e n c e s of hydromechanically s i g n i f i c a n t p r o p e r t i e s of food organisms. P a r a s i t i s m . In t h i s d i r e c t i n t e r a c t i o n a p a r a s i t e c e l l or p a r t i c l e attaches i t s e l f to a host c e l l and makes a p a r t i a l or t o t a l p e n e t r a t i o n i n t o i t , where i t then uses the host's biomass or metabolic a c t i v i t i e s to grow and reproduce i t s e l f . Examples are provided by the p a r a s i t i s m of v i r u s e s on b a c t e r i a and other microorganisms, by the p a r a s i t i s m of the very small bacterium B d e l l o v i b r i o on other b a c t e r i a , and by the p a r a s i t i s m of b a c t e r i a on protozoa (30,74_,75) . P a r a s i t i s m i s c h a r a c t e r i z e d by a v a r i a b l e but always high degree of host s p e c i f i c i t y . That i s , a given p a r a s i t e i s able to i n f e c t only a l i m i t e d number of h o s t s , and i n some cases, the number may be small indeed. A number of mathematical models f o r h o s t - p a r a s i t e r e l a t i o n s have been published. For references to l i t e r a t u r e appearing before 1977, see F r e d r i c k s o n (2). A more recent model has been given by L e v i n ^ t a l . (76). P a r a s i t i s m can serve to r e g u l a t e competition between d i f f e r e n t host populations. An example i s provided by the work of L e v i n et a l . (76). They found that p a r a s i t i s m by the v i r u l e n t b a c t e r i o phage T2 on two s t r a i n s of E s c h e r i c h i a c o l i s t a b i l i z e d the compe t i t i o n of the s t r a i n s f o r sugar, and allowed the competitors to c o e x i s t i n a chemostat. One of the s t r a i n s was s u s c e p t i b l e to i n f e c t i o n by T2 but the other was not. A most i n t e r e s t i n g aspect of the v i r u s - b a c t e r i a h o s t - p a r a s i t e i n t e r a c t i o n i s the tendency f o r genetic changes of the populations to keep a l t e r i n g the dynamics of the i n t e r a c t i o n . T h i s i s w e l l i l l u s t r a t e d by some a d d i t i o n a l work of Chao et a l . (77). A host bacterium B (a s t r a i n of E. c o l i ) and a bacteriophage T were introduced i n t o a chemostat; B was s u s c e p t i b l e to i n f e c t i o n by T . Mutation of B produced a new s t r a i n of b a c t e r i a , B^, which was not s u s c e p t i b l e to i n f e c t i o n by T . However, mutation of the phage produced a new v i r u s , T^, which was capable of i n f e c t i n g both B and B^. A second mutuation of the b a c t e r i a produced a t h i r d s t r a i n , Β£, which was immune to i n f e c t i o n by T and T-^. In these experiments, the v a r i o u s s t r a i n s of b a c t e r i a competed with one another f o r sugar, but the presence of the p a r a s i t e s prevented competitive e x c l u s i o n s from o c c u r r i n g . When a s t r a i n of b a c t e r i a that was not s u s c e p t i b l e to i n f e c t i o n by any of the p a r a s i t e s was present, sugar c o n c e n t r a t i o n was low and b a c t e r i a l and phage den s i t i e s were high. However, when a l l s t r a i n s of b a c t e r i a present were s u s c e p t i b l e to i n f e c t i o n by the phages, sugar c o n c e n t r a t i o n was high and b a c t e r i a l and phage d e n s i t i e s were low. These obser v a t i o n s of Chao et a l . (77) suggest that the h o s t - p a r a s i t e r e l a t i o n i s a kind of genetic race between the two groups of organisms. Undoubtedly, analagous s i t u a t i o n s occur with other i n t e r m i c r o b i a l i n t e r a c t i o n s , and e f f o r t s to detect and analyze such s i t u a t i o n s would very l i k e l y prove to be most f r u i t f u l . Q

Q

Q

0

Q

Q

Q

q


222



Symbiosis. T h i s i s a d i r e c t i n t e r a c t i o n between two microb i a l populations which i s c h a r a c t e r i z e d not only by the mutual (even i f i m p e r f e c t l y understood) b e n e f i t s which i t confers upon the partners i n the a s s o c i a t i o n but a l s o , l i k e p a r a s i t i s m , by i t s high degree of s p e c i f i c i t y . That i s , the two partners are more or l e s s uniquely adapted to l i v e together, and i t i s impossible or very d i f f i c u l t to r e p l a c e one of the partners i n the a s s o c i a t i o n by another organism of s i m i l a r k i n d . Undoubtedly, syntrophism i s involved i n many m i c r o b i a l symbioses, and perhaps models l i k e those f o r t h i s m u t u a l i s t i c i n t e r a c t i o n would be a p p l i c a b l e to symbiosis. Q u a n t i t a t i v e models f o r symbiosis seem to be none x i s t e n t at the present time, however. Crowding. T h i s i n t e r a c t i o n i s important when population d e n s i t i e s become so l a r g e that the a v a i l a b i l i t y of space becomes a l i m i t i n g f a c t o r i n the growth of the populations. The i n t e r s p e c i f i c i n t e r a c t i o n of crowding i s probably not of much importance i n s i t u a t i o n s where the i n t e r a c t i n g populations are suspended i n a l i q u i d medium, because d e n s i t i e s t h e r e i n are not l i k e l y to become so high that a v a i l a b i l i t y of space becomes a r a t e - l i m i t i n g f a c t o r f o r both populations. I n t r a s p e c i f i c crowding can become important i n l i q u i d c u l t u r e s , i t appears; the existence of the v e r t i c a l asymptote i n the graph of F i g u r e 3 i s an example of an e f f e c t due to i n t r a s p e c i f i c crowding. I n t e r s p e c i f i c crowding may be of great importance when we are d e a l i n g with systems i n which much s u r f a c e area, upon which the organisms attach themselves, i s present. A good d e a l of e f f o r t has been expended i n recent years to understand the mechanisms involved i n attachment of organisms to s u r f a c e s . The mechanisms are complex, even when only a s i n g l e population i s i n v o l v e d , f o r the d e n s i t y of attached c e l l s i s found to depend on the i d e n t i t y and p h y s i o l o g i c a l s t a t e of the organism, the i d e n t i t y of the m a t e r i a l of which the surface i s made as w e l l as the p r i o r t r e a t ment of the s u r f a c e , the composition of the l i q u i d medium adjacent to the s o l i d s u r f a c e , the d e n s i t y of the organisms i n the l i q u i d medium, and the time of contact between the suspension of organisms and the s u r f a c e (78). F a m i l i a r concepts that apply to adsorption of molecules on s u r f a c e s , l i k e that of the a c t i v e s i t e , seem not to apply, and t h i s means that the Langmuir-Hinshelwood model of adsorption, or one of i t s g e n e r a l i z a t i o n s , i s not l i k e l y to apply, either. Instead, i t seems that we need to construct dynamic s t o c h a s t i c models which w i l l make the p r o b a b i l i t y of attachment of one c e l l to a given area of s u r f a c e i n a short i n t e r v a l of time dependent upon the number of c e l l s already attached to that s u r face as w e l l as to the d e n s i t y of c e l l s present i n the bulk l i q u i d , e t c . Since I am not aware that models l i k e t h i s have been worked out even f o r s i n g l e populations, I cannot say anything meaningful about models f o r competition of two populations f o r


9.

FREDRiCKSON

Interactions

of Microbial

Populations

223

space on a s o l i d substratum. We are t r y i n g to study t h i s i n t e r a c t i o n i n our l a b o r a t o r y a t the present time, but i t i s not an easy t h i n g to do. I t was pointed out above that "crowding" as I have used the term r e f e r s t o an i n t e r s p e c i f i c i n t e r a c t i o n but that b i o l o g i s t s o f t e n use the term f o r an i n t r a s p e c i f i c i n t e r a c t i o n . The context w i l l make i t c l e a r i n most cases which kind of i n t e r a c t i o n i s being r e f e r r e d to, so there should be no d i f f i c u l t y i n using the same word f o r two d i f f e r e n t kinds of s i t u a t i o n s .


Summary and d i s c u s s i o n The foregoing d i s c u s s i o n shows that improved understanding of i n t e r a c t i o n s between m i c r o b i a l populations w i l l r e q u i r e research i n a number of r e l a t e d areas. A p a r t i a l l i s t i s as follows. Much work remains to be done on the autecology of m i c r o b i a l populations; that i s , on the responses of i n d i v i d u a l populations to changes i n t h e i r environment and on the changes produced i n the a b i o t i c environment by the a c t i v i t i e s of such p o p u l a t i o n s . Of p a r t i c u l a r importance i n s o f a r as osmotrophic microorganisms a r e concerned i s research aimed at p r o v i d i n g good models f o r the e f f e c t s of m u l t i p l e n u t r i e n t l i m i t a t i o n on growth r a t e s , f o r the k i n e t i c s of s u b c e l l u l a r processes i n general, f o r the k i n e t i c s of formation of e x t r a c e l l u l a r chemicals and enzymes, f o r the k i n e t i c s of a c t i o n of i n h i b i t o r s , t o x i n s , and l y t i c enzymes, e t c . More work i s needed on the autecology of phagotrophic microorganisms, a l s o . The mechanisms that make such organisms "prudent" feeders need t o be e s t a b l i s h e d and compared and the question of the extent to which they s e l e c t t h e i r food needs to be examined f u r t h e r . Almost a l l attempts t o c o n s t r u c t mathematical models of popul a t i o n i n t e r a c t i o n s assume that the populations present are e n t i t i e s of f i x e d genetic c o n s t i t u t i o n . I f they allow f o r the occurrence of mutuation, i t i s almost always i n the sense of assuming that a mutant of given p r o p e r t i e s has formed, and then t r y i n g to see how the system of mutant, w i l d organism, and any other organisms present, w i l l evolve i n time. Models which are b u i l t on some of the e x c i t i n g new information that m i c r o b i a l g e n e t i c i s t s have provided need t o be developed and a p p l i e d to systems of i n t e r a c t i n g populations. High p r i o r i t y should be given to producing models which take i n t o account mechanisms of mutation and genetic recombination. Several b i n a r y i n t e r a c t i o n s have been neglected by people who take a q u a n t i t a t i v e , mathematical approach t o such processes. Amensalism, antagonism, and e c c r i n o l y s i s are i n d i r e c t i n t e r a c t i o n s which f a l l i n t o t h i s category, and there i s room and motivation for much work on them. In a d d i t i o n , there are many elementary mechanisms of commensalism, mutualism, and protocooperation that have been neglected. Among the d i r e c t i n t e r a c t i o n s , nothing q u a n t i t a t i v e i s known about crowding and symbiosis, and the former i n t e r a c t i o n , at l e a s t , should be made the object o f study q u i t e soon.



224


New experimental techniques and apparatus f o r studying popul a t i o n i n t e r a c t i o n s need to be developed. A l t e r n a t e and improved methods of o b t a i n i n g census data on systems c o n t a i n i n g two or more populations are c r i t i c a l needs, and improved, automated means of making chemical analyses of a b i o t i c media would be most h e l p f u l , too. New mathematical techniques f o r d e a l i n g with the systems of n o n l i n e a r d i f f e r e n t i a l equations that r e s u l t from models of popul a t i o n i n t e r a c t i o n s need to be found. D i s c u s s i o n s with mathemat i c i a n s make i t c l e a r that techniques which would seem to be u s e f u l have not been much developed, so r a p i d progress i s not to be expected i n t h i s d i f f i c u l t l i n e of endeavor. However, some progress has been made. For example, Stephanopoulos (79,80) has shown how the theory of the Poincaré index can be a p p l i e d to the equations of b i n a r y p o p u l a t i o n i n t e r a c t i o n s . The problem with t h i s technique i s that i t works only when the problem can be reduced to two o r d i n a r y d i f f e r e n t i a l equations. Many s i t u a t i o n s of b i n a r y i n t e r a c t i o n f a l l i n t o t h i s category (79), but many do not and of course ternary, quaternary, e t c . i n t e r a c t i o n s do not, either. Another l i n e of research, e n t i r e l y d i f f e r e n t from what has j u s t been mentioned, concerns the a p p l i c a t i o n s of mixed c u l t u r e s and of knowledge about i n t e r a c t i o n s i n mixed c u l t u r e s . I t seems to me that i t would now be worthwhile to t r y to think of i n d u s t r i a l operations where mixed c u l t u r e s could be used to advantage. Development of g e n e t i c engineering techniques f o r making microorganisms capable of doing s p e c i f i c , assigned tasks would seem to have increased the l i k e l i h o o d that s u c c e s s f u l mixed c u l t u r e processes can be developed, and work on developing them might now prove to be rewarding. There i s a l s o the a d d i t i o n a l f i e l d of a p p l i c a t i o n of models and t h e o r i e s of p o p u l a t i o n i n t e r a c t i o n s to problems of understanding the dynamics of n a t u r a l ecosystems. M i t i g a t i o n of p o l l u t i o n of lakes and streams, cleanup of o i l and chemical s p i l l s , prevention of acid mine drainage, and so on, are a l l r e a l and l a r g e problems, and i t i s reasonable to expect that a p p l i c a t i o n of the models and t h e o r i e s noted can be of help i n s o l v i n g such problems. Acknowledgement The support of the N a t i o n a l Science Foundation, through grants ENG77-21632 and CPE-8020783, i s acknowledged with thanks.


9. FREDRiCKSON

Interactions of Microbial Populations

225

Literature Cited 1. 2. 3. 4. 5.


6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

Odum, P. "Fundamentals of Ecology", 3rd. ed., Saunders: Philadelphia, 1971, pp. 211-213. Fredrickson, A. G. Annu. Rev. Microbiol. 1977, 31, 63. Kaiser, D.; Manoil, C . ; Dworkin, M. Annu. Rev. Microbiol. 1979, 33, 595. Fredrickson, A. G.; Stephanopoulos, G. N. Science 1981, 213, 972. Stephanopoulos, G. N.; Fredrickson, A. G. Biotechnol. Bioeng. 1979, 21, 1491. Stewart, F. M.; Levin, B. R. Am. Nat. 1973, 107, 171. Grenney, W. J.; Bella, D. Α.; Curl, H. C., Jr. Am. Nat. 1973, 107, 405. Chisholm, S. W.; Nobbs, P. A. "Modeling Biochemical Processes in Aquatic Ecosystems", Canale, R. P. Ed., Ann Arbor Science: Ann Arbor, Michigan, 1976, pp. 337-355. Stephanopoulos, G. N.; Fredrickson, A. G.; Aris, R. AIChE J. 1979, 25, 863. Hsu, S. B. J. Math. Biol. 1980, 9, 115. Smith, H. L. SIAM J. Appl. Math. 1981, 40, 498. Hsu, S. B.; Hubbell, S.; Waltman, P. SIAM J. Appl. Math. 1977, 32, 366. Hsu, S. B. SIAM J. Appl. Math. 1978, 34, 760. Koch, A. L. J. Theor. Biol. 1974, 44, 387. Hsu, S. B.; Hubbell, S. P.; Waltman, P. SIAM J. Appl. Math. 1978, 35, 617. Hus, S. B.; Hubbell, S. P.; Waltman, P. Ecol. Monogr. 1978, 48, 337. Jost, J . L.; Drake, J . F . ; Fredrickson, A. G.; Tsuchiya, H. M. J . Bacteriol. 1973, 113, 834. León, J . Α.; Tumpson, D. B. J. Theor. Biol. 1975, 50, 185. Peterson, R. Am. Nat. 1975, 109, 35. Taylor, P. Α.; Williams, P. J . LeB. Can. J. Microbiol. 1975 21, 90. Yoon, H.; Blanch, H. W. J. Appl. Chem. Biotechnol. 1977, 27, 260. Yoon, H.; Klingzing, G.; Blanch, H. W. Biotechnol. Bioeng. 1977, 19, 1193. Stephanopoulos. G. N.; Schuelke, L. M.; Stephanopoulos, G. Theor. Pop. Biol. 1979, 16, 126. Smouse, P. E. Theor. Pop. Biol. 1980, 17, 16. Hsu, S. B.; Cheng, K-S.; Hubbell, S. P. SIAM J. Appl. Math. 1981, 41, 422. Gottschal, J. C.; de Vries, S.; Kuenen, J . G. Arch. Micro biol. 1979, 121, 241. Laanbroek, H. J.; Smit, A. J.; Nulend, G. M.; Veldkamp, H. Arch. Microbiol. 1979, 120, 61. DeFreitas, M.; Fredrickson, A. G. J . Gen. Microbiol. 1978, 106, 307.


226 29. 30. 31. 32. 33. 34. 35.


36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59.

BIOCHEMICAL ENGINEERING Miura, Y.; Tanaka, H.; Okazaki, M. Biotechnol. Bioeng. 1980, 22, 929. Alexander, M. "Microbial Ecology", Wiley: New York, 1971, pp. 290; 327-368. van Gemerden, H. Microbial Ecol. 1974, 1, 104. Wilder, C. T.; Cadman, T. W.; Hatch, R. R. Biotechnol. Bioeng. 1980, 22, 89. Adams, J.; Kinney, T.; Thompson, S.; Rubin, L . ; Hellin, R. B. Genetics 1979, 91, 627. Meers, J . L. CRC Critical Rev. Microbiol. 1973, 2, 139. Megee, R. D., III; Drake, J . F . ; Fredrickson, A. G.; Tsuchiya, H. M. Can. J. Microbiol. 1972, 18, 1733. Miura, Y.; Sugiura, K.; Yoh, M.; Tanaka, H.; Okazaki, M.; Komenmushi, S. J . Ferment. Technol. 1978, 56, 339. Reilly, P. J . Biotechnol. Bioeng. 1974, 16, 1373. Chao, C . - C ; Reilly, P. J. Biotechnol. Bioeng. 1972, 14, 75. Sheintuch, M. Biotechnol. Bioeng. 1980, 22, 2557. Lee, I. H.; Fredrickson, A. G.; Tsuchiya, H. M. Biotechnol. Bioeng. 1976, 18, 513. Lee, I. H.; Fredrickson, A. G.; Tsuchiya, H. M. Appl. Microbiol. 1974, 28, 831. Nurmikko, V. Experientia 1956, 12, 245. Wolfe, R. S.; Pfennig, N. Appl. Env. Microbiol. 1977, 33, 427. Slater, J . H. "The Oil Industry and Microbial Ecosystems", Chater, K. W. Α.; Somerville, H. S. Eds., Heyden and Son, London, pp. 137-154. Lamb, S. C.; Garver, J . C. Biotechnol. Bioeng. 1980, 22, 2119. Meyer, J . S.; Tsuchiya, Η. M.; Fredrickson, A. G. Biotechnol. Bioeng. 1975, 17, 1065. Wilkinson, T. G.; Topiwala, H. H.; Hamer, G. Biotechnol. Bioeng. 1974, 16, 41. Van Dedem, G.; Moo-Young, M. Biotechnol. Bioeng. 1973, 15, 419. Gause, G. F. "The Struggle For Existence", Williams & Wilkins, Baltimore, 1934, pp. 114-140. Berger, J . Trans. Am. Micros. Soc. 1979, 98, 487. Seravin, L. N.; Orlovskaja, Ε. E. Acta Protozool. 1977, 16, 309. Berger, J . J . Gen. Microbiol. 1980, 118, 397. Slobodkin, L. B. Am. Zool. 1968, 8, 43. Luckinbill, L. S. Ecology 1973, 54, 1320. Luckinbill, L. S. Ecology 1974, 55, 1142. Tsuchiya, H. M.; Drake, J . F . ; Jost, J . L.; Fredrickson, A. G. J. Bacteriol. 1972, 110, 1147. Swift, S. T.; Najita, I. Y.; Ohtaguchi, K.; Fredrickson, A. G. paper in preparation, 1982. Jørgensen, C. B. "Biology of Suspension Feeding", Pergamon: Oxford, 1966. Bader, F. G.; Tsuchiya, H. M.; Fredrickson, A. G. Biotechnol. Bioeng. 1976, 18, 311.


9. 60. 61. 62. Ill., 63. 64. 65.


66. 67. 68. 69. 70.

71. 72. 73. 74. 75. 76. 77. 78. 79. 80.

FREDRICKSON

Interactions of Microbial Populations

227

Fenchel, T. Microbial Ecol. 1980, 6, 13. Drake, J . F . ; Tsuchiya, H. M. Appl. Env. Microbiol. 1977, 34, 18. Kudo, R. "Protozoology", 5th. ed., Thomas: Springfield, 1966, p. 870. Corliss, J . O. J . Protozool. 1970, 17, 198. Habte, M.; Alexander, M. Ecology 1978, 59, 140. Watson, P. J.; Ohtaguchi, K.; Fredrickson, A. G. J. Gen. Microbiol. 1981, 122, 323. Fenchel, T. Microbial Ecol. 1980, 6, 1. Alexander, M. Annu. Rev. Microbiol. 1981, 35, 113. Salt, G. W. Ecol. Monogr. 1967, 37, 113. Monod, J . "Recherches sur la croissance des cultures bactériennes", Hermann: Paris, 1942. Bader, F. G.; Fredrickson, A. G.; Tsuchiya, H. M. "Modeling Biochemical Processes in Aquatic Ecosystems", Canale, R. P. Ed., Ann Arbor Science: Ann Arbor, Michigan, 1976, pp. 257279. Stephanopoulos, G. N.; Fredrickson, A. G. Bull. Math. Biol. 1981, 43, 165. Ratnam, D. Α.; Pavlou, S.; Fredrickson, A. G. paper in preparation, 1982. Coleman, G. S. J . Gen. Microbiol. 1964, 37, 209. Stainer, R. Y.; Adelberg, Ε. Α.; Ingraham, J . "The Microbial World", 4th ed., Prentice-Hall: Englewood Cliffs, New Jersey, 1976, pp. 766-773. Atlas, R. M.; Bartha, R. "Microbial Ecology", Addison-Wesley: Reading, Mass., 1981, pp. 273-276. Levin, B. R.; Stewart, F. M.; Chao, L. Am. Nat. 1977, 111, 3. Chao, L.; Levin, B. R.; Stewart, F. M. Ecology 1977, 58, 369. Ellwood, D. C.; Melling, J.; Rutter, P., Eds., "Adhesion of Microorganisms to Surfaces", Society for General Microbiology: London, 1979. Stephanopoulos, G. N. AIChE J . 1980, 26, 802. Stephanopoulos, G. N. Biotechnol. Bioeng. 1981, 23, 2243.

RECEIVED

June 1, 1982


Interactions of Microbial Populations in Mixed Culture Situations - ACS

Recommend Documents