Skip to main content
SpringerLink
Log in

A community model of ciliateTetrahymena and bacteriaE. coli: Part II. Interactions in a batch system

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Premised on relatively simple assumptions, mathematical models like those of Monod, Pirt or Droop inadequately explain the complex transient behavior of microbial populations. In particular, these models fail to explain many aspects of the dynamics of aTetrahymena pyriformis-Escherichia coli community. In this study an alternative approach, an individual-based model, is employed to investigate the growth and interactions ofTetrahymena pyriformis andE. coli in a batch culture. Due to improved representation of physiological processes, the model provides a better agreement with experimental data of bacterial density and ciliate biomass than previous modeling studies. It predicts a much larger coexistence domain than rudimentary models, dependence of biomass dynamics on initial conditions (bacteria to ciliate biomasses ratio) and appropriate timing of minimal bacteria density. Moreover, it is found that accumulation ofE. coli sized particles andE. coli toxic metabolites has a stabilizing effect on the system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Alexander, M. 1981. Why microbial predators and parasites do not eliminate their prey and hosts.Ann. Rev. Microbiol. 35, 113–133.

    Article  Google Scholar 

  • Bailey, J. E. and D. F. Ollis. 1986.Biochemical Engineering Fundamentals, 2nd ed. New York: McGraw-Hill.

    Google Scholar 

  • Bader, F. G., H. M. Tsuchija and A. G. Fredrickson. 1976. Grazing of ciliates on blue-green algae: effect of ciliate encystment and related phenomena.Biotech Bioeng. 18, 311–331.

    Article  Google Scholar 

  • Bonomi A. and A. G. Fredrickson. 1976. Protozoan feeding and bacterial cell growth.Biotech. Bioeng. 18, 239–252.

    Article  Google Scholar 

  • Bungay, H.R., III and M. L. Bungay. 1968. Microbial interaction in continuous cultures.Adv. Appl. Microbiol. 10, 269–290.

    Article  Google Scholar 

  • Canale, R. P., T. D. Lustig, P. M. Kehrberger and J. E. Salo. 1973. Experimental and mathematical modeling studies of protozoan predation on bacteria.Biotech. Bioeng. 12, 353–378.

    Article  Google Scholar 

  • Cunningham, A. and R. M. Nisbet. 1983. Transients and oscillations in continuous culture. InMathematical Methods in Microbiology, J. Bazin (Ed). New York: Academic Press.

    Google Scholar 

  • Curds, C. R. 1982. The ecology and role of protozoa in aerobic sewage treatment processes.Ann. Rev. Microbiol. 36, 27–46.

    Article  Google Scholar 

  • Danso, S. K. and M. Alexander. 1975. Regulation of predation by prey density: the protozoan-Rhizobium relationship.Appl. Microbiol. 29, 515–521.

    Google Scholar 

  • Dive, D. 1975. Influence de la concentration bacterienne, sur la croissance deColpidium campylum.J. Protozool. 22, 545–550.

    Google Scholar 

  • Drake, J. F., J. L. Jost, A. G. Fredrickson and H. M. Tsuchiya. 1968. The food chain. InBiogenerative Systems J. F. Sandauers (Ed), Vol. 165, pp.87–95. Washington DC: NASA.

    Google Scholar 

  • Fenchel, T. 1980. Suspension feeding in ciliated protozoa: feeding rates and their ecological significance.Microb. Ecol. 6, 13–25.

    Article  Google Scholar 

  • Fredrickson, A. G. 1991. Segregated, structured, distributed, models and their role in microbial ecology: A case study based on work done on the filter-feeding ciliateTetrahymena pyriformis.Microb. Ecol. 22, 139–159.

    Google Scholar 

  • Graham, J. M. and R. P. Canale. 1982. Experimental and modelling studies of a four-trophic level predator-prey system.Microb. Ecol. 8, 217–232.

    Article  Google Scholar 

  • Habte, M. and M. Alexander. 1978. Protozoan density and the coexistence of prorozoan predators and bacterial prey.Ecology 59, 140–146.

    Article  Google Scholar 

  • Hatzis, C., F Srienc and A. G. Fredrickson. 1994. Feeding heterogeneity in ciliate populations: effects of culture age and nutritional state.Biotech. Bioeng. 43, 371–380.

    Article  Google Scholar 

  • Holling, C. S. 1959. The components of predation as revealed by a study of small mammal predation of the European pine sawfly.Can. Ent. 91, 293–320.

    Article  Google Scholar 

  • Jaworska, J. S. 1993. Ecology and toxicology ofTetrahymena pyriformis—E. coli microbial community—a modeling study. Ph.D. dissertation, University of Tennessee, Knoxville.

    Google Scholar 

  • Jost, J. L., J. F. Drake, A. G. Fredrickson and H. M. Tsuchiya. 1973. Interactions ofTetrahymena pyriformis, Escherichia coli, Azotobacter vinelandii, and glucose in a minimal medium.J. Bacteriol. 113, 834–840.

    Google Scholar 

  • Lavin, D. P., C. Hatzis, F. Srienc and A. G. Fredrickson. 1990. Size effects on the uptake of particles by populations ofTetrahymena pyriformis cells.J. Protozool. 37, 157–163.

    Google Scholar 

  • Leboy, P. S., S. G. Cline and R. L. Conner. 1964. Phosphate, purines and pyrimidines as excretory products ofTetrahymena.J. Protozool. 11, 217–222.

    Google Scholar 

  • Maihile, N. J. and B. H. Satir. 1986. Protein secretion inTetrahymena, characterization of the major proteinaceous secretory proteins.J. Biol. Chem. 261, 7566–7570.

    Google Scholar 

  • Mallory, L. M., C. S. Yuk, L. N. Liang and M. Alexander. 1983. Alternative prey: a mechanism for elimination of bacterial species by protozoa.Appl. Environ, Microbiol. 46, 1073–1079.

    Google Scholar 

  • May, R. M. 1973.Stability and Complexity in Model Ecosystems Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Muller, M. 1972. Secretion of acid hydrolases and its intracellular source.J. Cell Biol. 52, 478–487.

    Article  Google Scholar 

  • Neidhardt, F. C. (Ed.) 1987.Escherichia coli and Salmonella typhimurium; Cellular and Molecular Biology. Washington, DC: Am. Soc. Microbiol.

    Google Scholar 

  • Nilsson, J. R. 1987. On food vacuoles inTetrahymena pyriformis GL.J. Protozool. 24, 502–507.

    Google Scholar 

  • Nisbet, R. M., A. Cunningham and S. C. Gurney. 1983. Endogenous metabolism and the stability of microbial prey-predator systems.Biotech. Bioeng. 25, 301–306.

    Article  Google Scholar 

  • Pavlou, S. 1985. Dynamics of a chemostat in which one microbial population feeds on another.Biotech. Bioeng. 27, 1525–1532.

    Article  Google Scholar 

  • Pavlou, S. and A. G. Fredrickson. 1983. Effects of the inability of suspension-feeding protozoa to collect all cell sizes of a bacterial population.Biotech. Bioeng. 25, 1747–1772.

    Article  Google Scholar 

  • Prescott, D. M. 1958. The growth rate ofTetrahymena geleii HS under optimal conditions.Physiol. Zool. 31, 111–117.

    Google Scholar 

  • Sambanis, A. and A. G. Fredrickson, 1987. Persistence of bacteria in the presence of viable, nonencysting, bactivorous ciliates.Microb. Ecol. 16, 197–211.

    Article  Google Scholar 

  • Sambanis, A. and A. G. Fredrickson. 1989. Effect of addition of wall growth to a model of ciliate bacterial interactions.Biotech. Bioeng. 34, 875–881.

    Article  Google Scholar 

  • Sambanis, A., S. Pavlou and A. G. Fredrickson. 1986. Analysis of the dynamics of ciliate bacterial interactions in a CSTR.Chem. Eng. Sci. 41, 1455–1469.

    Article  Google Scholar 

  • Sambanis, A., S. Pavlou and A. G. Fredrickson. 1987. Coexistence of bacteria and feeding ciliates growth of bacteria on autochthonous substrates as a stabilizing factor for coexistence.Biotech. Bioeng. 29, 714–728.

    Article  Google Scholar 

  • Satir, B., C. Schooley and P. Satir. 1983. Membrane fusion in a model system: Mucocyst secretion inTetrahymena, J. Cell Biol. 56, 153–176.

    Article  Google Scholar 

  • Sudo, R., K. Kobayashi and S. Aiba. 1975. Some experiments and analysis of a predator-prey model: Interaction betweenColpidium campylum andAlcaligenes faecalis in continuous and mixed culture.Biotech. Bioeng. 17, 167–184.

    Article  Google Scholar 

  • Suhr-Jessen, P. 1987. Constitutive and induced excretion of polypeptides inTetrahymena thermophila.J. Protozool. 34, 54–57.

    Google Scholar 

  • Swift, S. T., I. Y. Najita, K. Ohtaguchi and A. G. Fredrickson. 1982. Some physiological aspects of the autoecology of the suspension feeding protozoanTetrahymena pyriformis.Microb. Ecol. 8, 201–215.

    Article  Google Scholar 

  • Tsangraropoulou, E. and S. Pavlou. 1990. Effects of spatial heterogeneity on the dynamics of a microbial feeding interaction.Biotech. Bioeng. 35, 1024–1033.

    Article  Google Scholar 

  • Watson, P. J., K. Ohtaguchi and A. G. Fredrickson. 1981. Kinetics of growth of the ciliateTetrahymena pyriformis onEscherichia coli.J. Gen. Microbiol. 122, 323–333.

    Google Scholar 

  • Williams, F. M. 1980. On understanding predator-prey interactions. InContemporary Microbial Ecology, D. C. Ellwood, J. N. Hedger, J. M. Latham, J. M. Lynch and J. H. Slater (Eds), pp. 349–370. London: Academic Press.

    Google Scholar 

Download references

Author information

Author notes

  1. Joanna S. Jaworska

    Present address: Environmental Sciences Division, Oak Ridge National Laboratory, 37831-6038, Oak Ridge, TN

Authors and Affiliations

  1. Graduate Program in Environmental Toxicology, University of Tennessee, Knoxville, Tennessee, USA

    Joanna S. Jaworska

  2. Department of Mathematics and Graduate Program in Ecology, University of Tennessee, Knoxville, Tennessee, USA

    Thomas G. Hallam

  3. College of Veterinary Medicine, University of Tennessee, Knoxville, Tennessee, USA

    T. Wayne Schultz

Authors
  1. Joanna S. Jaworska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas G. Hallam
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. Wayne Schultz
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jaworska, J.S., Hallam, T.G. & Wayne Schultz, T. A community model of ciliateTetrahymena and bacteriaE. coli: Part II. Interactions in a batch system. Bltn Mathcal Biology 58, 265–283 (1996). https://doi.org/10.1007/BF02458309

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02458309

Keywords

Search

Navigation