Predicting stability of mixed microbial cultures from single species experiments: 1. Phenomenological model.

The growth of mixed microbial cultures on mixtures of substrates is a fundamental problem of both theoretical and practical interest. On the one hand, the literature is abundant with experimental studies of mixed-substrate phenomena [T. Egli, The ecological and physiological significance of the growth of heterotrophic microorganisms with mixtures of substrates, Adv. Microbiol. Ecol. 14 (1995) 305-386]. On the other hand, a number of mathematical models of mixed-substrate growth have been analyzed in the last three decades. These models typically assume specific kinetic expressions for substrate uptake and biomass growth rates and their predictions are formulated in terms of parameters of the model. In this work, we formulate and analyze a general mathematical model of mixed microbial growth on mixtures of substitutable substrates. Using this model, we study the effect of mutual inhibition of substrate uptake rates on the stability of the equilibria of the model. Specifically, we address the following question: How much of the dynamics exhibited by two competing species can be inferred from single species data? We provide geometric criteria for stability of various types of equilibria corresponding to non-competitive exclusion, competitive exclusion, and coexistence of two competing species in terms of growth isoclines and consumption curves. A growth isocline is a curve in the plane of substrate concentrations corresponding to the zero net growth of a given species. In [G.T. Reeves, A. Narang, S.S. Pilyugin, Growth of mixed cultures on mixtures of substitutable substrates: The operating diagram for a structured model, J. Theor. Biol. 226 (2004) 143-157], we introduced consumption curves as sets of all possible combinations of substrate concentrations corresponding to balanced growth of a single microbial species. Both types of curves can be obtained in single species experiments.

[1]  G Stephanopoulos,et al.  Microbial competition. , 1981, Science.

[2]  Sze-Bi Hsu,et al.  Limiting Behavior for Competing Species , 1978 .

[3]  G. Wolkowicz,et al.  Exploitative competition in the chemostat for two perfectly substitutable resources. , 1993, Mathematical biosciences.

[4]  S. Hubbell,et al.  Single-nutrient microbial competition: qualitative agreement between experimental and theoretically forecast outcomes. , 1980, Science.

[5]  T. Egli,et al.  Growth Kinetics of Suspended Microbial Cells: From Single-Substrate-Controlled Growth to Mixed-Substrate Kinetics , 1998, Microbiology and Molecular Biology Reviews.

[6]  J. Monod,et al.  Recherches sur la croissance des cultures bactériennes , 1942 .

[7]  A. Narang,et al.  New patterns of mixed-substrate utilization during batch growth of Escherichia coli K12. , 1997, Biotechnology and bioengineering.

[8]  Gail S. K. Wolkowicz,et al.  Global dynamics of a mathematical model of competition in the chemostat: general response functions and differential death rates , 1992 .

[9]  Paul Waltman,et al.  The Theory of the Chemostat , 1995 .

[10]  E. Powell.  Criteria for the growth of contaminants and mutants in continuous culture. , 1958, Journal of General Microbiology.

[11]  Horst R. Thieme,et al.  Asymptotically Autonomous Differential Equations in the Plane , 1993 .

[12]  G. Butler,et al.  Exploitative competition in a chemostat for two complementary, and possibly inhibitory, resources , 1987 .

[13]  Arthur E. Humphrey,et al.  Dynamics of a chemostat in which two organisms compete for a common substrate , 1977 .

[14]  T. Egli,et al.  Simultaneous utilization of methanol–glucose mixtures by Hansenula polymorpha in chemostat: Influence of dilution rate and mixture composition on utilization pattern , 1986, Biotechnology and bioengineering.

[15]  Gail S. K. Wolkowicz,et al.  An examination of the thresholds of enrichment: a resource-based growth model , 1995 .

[16]  David Tilman,et al.  Resources: A Graphical-Mechanistic Approach to Competition and Predation , 1980, The American Naturalist.

[17]  D. Tilman.  Resource competition and community structure. , 1983, Monographs in population biology.

[18]  T. Egli,et al.  Cultivation of Escherichia coli with mixtures of 3-phenylpropionic acid and glucose: steady-state growth kinetics , 1997, Applied and environmental microbiology.

[19]  W. Babel,et al.  Simultaneous utilization of heterotrophic substrates by Hansenula polymorpha MH30 results in enhanced growth rates , 2004, Applied Microbiology and Biotechnology.

[20]  J. A. León,et al.  Competition between two species for two complementary or substitutable resources. , 1975, Journal of theoretical biology.

[21]  Gregory T. Reeves,et al.  Growth of mixed cultures on mixtures of substitutable substrates: the operating diagram for a structured model. , 2004, Journal of theoretical biology.

[22]  Sze-Bi Hsu,et al.  A Mathematical Theory for Single-Nutrient Competition in Continuous Cultures of Micro-Organisms , 1977 .

[23]  T. Egli,et al.  Mixed substrate growth of methylotrophic yeasts in chemostat culture: Influence of the dilution rate on the utilisation of a mixture of glucose and methanol , 1982, Archives of Microbiology.

[24]  A. J. Lotka.  Elements of Physical Biology. , 1925, Nature.