Predicting stability of mixed microbial cultures from single species experiments. II: Physiological model. (English) Zbl 1073.92010
Summary: We study the equilibria of a physiological model describing the continuous culture in which two microbial populations compete for two substitutable resources. This work is an extension of the stability analysis of the phenomenological model of mixed microbial growth in part I of the authors’ paper [ibid. 192, 85–109 (2004; Zbl 1074.92043)] and of M. M. Ballyk and G. S. K. Wolkowicz [ibid. 118, 127–180 (1993; Zbl 0815.92016)]. Here, we investigate the influence of the peripheral enzymes that catabolize the substrate uptake on the stability of the mixed culture.
We show that, under steady state conditions, an increase in the concentration of one substrate inhibits the uptake of the other substrate(s). We present the criteria for existence, uniqueness, and stability of various types of equilibria. We formulate these criteria in terms of growth isoclines and consumption curves for each of the competing species. Since both types of curves can be obtained from a single species experiment, our approach provides a direct connection between theory and experiment and allows one to infer the dynamics of mixed cultures from the dynamics of single species cultures. By expressing the stability criteria in terms of intracellular properties, the model establishes a link between ecology and molecular biology.
We show that, under steady state conditions, an increase in the concentration of one substrate inhibits the uptake of the other substrate(s). We present the criteria for existence, uniqueness, and stability of various types of equilibria. We formulate these criteria in terms of growth isoclines and consumption curves for each of the competing species. Since both types of curves can be obtained from a single species experiment, our approach provides a direct connection between theory and experiment and allows one to infer the dynamics of mixed cultures from the dynamics of single species cultures. By expressing the stability criteria in terms of intracellular properties, the model establishes a link between ecology and molecular biology.
MSC:
| 92C40 | Biochemistry, molecular biology |
| 92D40 | Ecology |
| 92C37 | Cell biology |
| 37N25 | Dynamical systems in biology |
Keywords:
Microbial growth; Physiological model; Mixed cultures; Substitutable substrates; Peripheral enzyme; Stable coexistence; Growth isocline; Consumption curveReferences:
| [1] | Gilpin, M. E.; Justice, K. E., Nature, London, 236, 273 (1972) |
| [2] | Leon, J. A.; Tumpson, D. B., Competition between two species for two complementary or substitutable substrates, J. Theor. Biol., 50, 185 (1975) |
| [3] | Tilman, D., Resources: a graphical-mechanistic approach to competition and predation, Am. Nat., 116, 3, 362 (1980) |
| [4] | Butler, G. J.; Wolkowicz, G. S.K., Exploitative competition in a chemostat for two complementary, and possibly inhibitory, resources, Math. Biosci., 83, 1 (1985) · Zbl 0609.92035 |
| [5] | Ballyk, M. M.; Wolkowicz, G. S.K., Exploitative competition in the chemostat for two perfectly substitutable resources, Math. Biosci., 118, 127 (1993) · Zbl 0815.92016 |
| [6] | S.S. Pilyugin, G.T. Reeves, A. Narang, Predicting stability of mixed microbial cultures from single species experiments: 1. Phenomenological model, Math. Biosci, x-link:doi:10.1016/j.mbs.2004.10.003; S.S. Pilyugin, G.T. Reeves, A. Narang, Predicting stability of mixed microbial cultures from single species experiments: 1. Phenomenological model, Math. Biosci, x-link:doi:10.1016/j.mbs.2004.10.003 · Zbl 1074.92043 |
| [7] | J.R. Beckwith, D. Zipser, The Lactose Operon, Cold Spring Harbor Laboratory, 1970; J.R. Beckwith, D. Zipser, The Lactose Operon, Cold Spring Harbor Laboratory, 1970 |
| [8] | Narang, A.; Konopka, A.; Ramkrishna, D., The dynamics of microbial growth on mixtures of substrates in batch reactors, J. Theor. Biol., 184, 301 (1997) |
| [9] | Narang, A.; Konopka, A. E.; Ramkrishna, D., New patterns of mixed-substrate utilization during batch growth of Escherichia coli K12, Biotech. Bioeng., 55, 747 (1997) |
| [10] | Narang, A., The dynamical analogy between microbial growth on mixtures of substitutable substrates and population growth of competing species, Biotech. Bioeng., 59, 116 (1998) |
| [11] | Narang, A., The steady states of microbial growth on mixtures of substitutable substrates in a chemostat, J. Theor. Biol., 190, 241 (1998) |
| [12] | Egli, T., The ecological and physiological significance of the growth of heterotrophic microorganisms with mixtures of substrates, Adv. Microbiol. Ecol., 14, 305 (1995) |
| [13] | Reeves, G. T.; Narang, A.; Pilyugin, S. S., Growth of mixed cultures on mixtures of substitutable substrates: the operating diagram for a structured model, J. Theor. Biol., 226, 143 (2004) · Zbl 1439.92117 |
| [14] | Frederickson, A. G., Formulation of structured growth models, Biotech. Bioeng., 18, 1481 (1976) |
| [15] | Egli, T.; Käppeli, O.; Fiechter, A., Mixed substrate growth of methylotrophic yeasts in chemostat culture: influence of dilution rate on the utilization of a mixture of methanol and glucose, Arch. Microbiol., 131, 8 (1982) |
| [16] | Egli, T.; Bosshard, C.; Hamer, G., Simultaneous utilization of methanol-glucose mixtures by Hansenula polymorpha in chemostat: Influence of dilution rate and mixture composition on utilization pattern, Biotechn. Bioeng., 28, 1735 (1986) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
