Growth of mixed cultures on mixtures of substitutable substrates: the operating diagram for a structured model
Introduction
The growth of mixed cultures on mixtures of substrates is a phenomenon of considerable practical and theoretical interest. A fundamental understanding of this problem has repercussions for
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Food processing: Cheese is manufactured by mixtures of Streptococci and Lactobacilli, and yogurt is the product of Lactobacillus bulgaricus and Streptococcus thermophilus. The production of sauerkraut, beer, wine, and vinegar also depends on mixed-culture systems (Harrison and Wren, 1976).
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Production of ethanol from renewable resources: The feedstock for production of fuel-grade ethanol from plants consists of two streams derived from the cellulosic and the hemicellulosic fractions of lignocellulose. The cellulosic stream consists of hexoses; the hemicellulosic stream contains a mixture of pentoses and hexoses. In the current process, each of these streams is fermented separately by distinct recombinant strains. To make this process economically viable, it would be desirable to carry out both fermentations in a single reactor (Ingram et al., 1999).
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Bioremediation: Xenobiotic contaminants degrade faster if they are attacked by microbial consortia, rather than pure species.
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the supply of nutrients is not constant;
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the nutrients are not homogeneously distributed;
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multiple growth-limiting substrates are present in the environment.
Despite the importance of the problem, review articles show that the experimental data are sparse (Fredrickson, 1977; Gottschal 1986, Gottschal 1993). This reflects the difficulty of measuring the population densities of multiple species. In the past, this was done by exploiting morphological differences between the species, or by selective plating techniques in which inhibitors are added to block the growth of all but one of the species. These methods are tedious and prone to error. Recent developments in flow cytometry and 16S RNA-based probes permit quick and accurate measurements of multiple population densities (Porter and Pickup, 2000). These technological advances are likely to foster rapid growth of the experimental literature on mixed cultures (for recent applications, see Muller et al., 2000; Rogers et al., 2000). The goal of this paper is to submit conclusions derived from a structured model that can be subjected to the test of these experiments. We shall be concerned, in particular, with the following questions
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What are the flow rates and feed concentrations of the two substitutable substrates at which both species coexist?
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How is their coexistence affected if one of the species excretes a product that influences the growth of the other species?
The paper is organized as follows. In Section 2, we extend our earlier model of mixed-substrate growth to mixed cultures. In Section 3, we compute the operating diagram delineating the region of the parameter space in which coexistence is feasible (Pavlou and Fredrickson, 1989). This is done for two types of inter-specific interactions—pure competition and commensalism. Finally, the conclusions are summarized in Section 4. The key results are as follows:
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If the interaction between the two species is purely competitive, then:
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At any given flow rate, coexistence is possible only if the ratio of the two feed concentrations lies within a certain interval. Excessive supply of either one of the two substrates results in extinction of one of the species.
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The operating diagram delineating the flow rate and feed concentrations at which the two species coexist has a particularly simple geometry.
- (a)
- 2.
If, however, one of the species excretes a product that can support the growth of the other species, the coexistence region is significantly enhanced.
Section snippets
Model
The kinetic scheme of our model is shown in Fig. 1. As a notational convention for the rest of the paper, the index i will denote the species number, and the index j will denote the substrate number. Thus, Ci denotes the ith species, Sj denotes the jth substrate, Eij denotes the “lumped” system of inducible enzymes catalysing the uptake and peripheral catabolism of Sj by Ci, Xij denotes the inducer for Eij, and Ci− denotes all intracellular constituents in the ith species, except Eij and Xij.
Simulations
The simulations were done using Mathematica (Wolfram, 1999) and CONTENT (Kuznetsov, 1998). The parameter values used in the simulations are shown in Table 1. Appendix C shows the rationale for order-of-magnitude estimates of the parameters. The parameter values were then adjusted to ensure that C1 and C2 have opposite substrate preferences. Specifically, the parameter values for C1 were chosen so that S1 is the preferred substrate for C1; that is, s1 approaches at a rate slower than the
Conclusions
We extended our earlier structured model for growth of a single species on two substitutable substrates to accommodate the growth of two species on two substitutable substrates. Our goal was to determine
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The dilution rates and feed concentrations at which both species coexist.
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The influence of excretion on this region of coexistence.
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If the interaction between the two species is purely competitive, the coexistence region is completely determined by the
Acknowledgements
During the course of this research, Gregory Reeves was partially supported by the University Scholars Program at the University of Florida.
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