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Coexistence in the chemostat as a result of metabolic by-products

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Abstract

Classical chemostat models assume that competition is purely exploitative and mediated via a common, limiting and single resource. However, in laboratory experiments with pathogens related to the genetic disease Cystic Fibrosis, species specific properties of production, inhibition and consumption of a metabolic by-product, acetate, were found. These assumptions were implemented into a mathematical chemostat model which consists of four nonlinear ordinary differential equations describing two species competing for one limiting nutrient in an open system. We derive classical chemostat results and find that our basic model supports the competitive exclusion principle, the bistability of the system as well as stable coexistence. The analytical results are illustrated by numerical simulations performed with experimentally measured parameter values. As a variant of our basic model, mimicking testing of antibiotics for therapeutic treatments in mixed cultures instead of pure ones, we consider the introduction of a lethal inhibitor, which cannot be eliminated by one of the species and is selective for the stronger competitor. We discuss our theoretical results in relation to our experimental model system and find that simulations coincide with the qualitative behavior of the experimental result in the case where the metabolic by-product serves as a second carbon source for one of the species, but not the producer.

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Authors and Affiliations

  1. Department of Mathematics and Physics, Albert-Ludwigs-University, Hermann-Herder-Str. 3, 79104, Freiburg, Germany

    Julia Heßeler

  2. Department of Bioprocess Engineering, Otto-von-Guericke-University, Universitätsplatz 2, 39106, Magdeburg, Germany

    Julia K. Schmidt & Udo Reichl

  3. Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106, Magdeburg, Germany

    Udo Reichl & Dietrich Flockerzi

Authors
  1. Julia Heßeler
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  2. Julia K. Schmidt
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  3. Udo Reichl
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  4. Dietrich Flockerzi
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Correspondence to Julia Heßeler.

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Julia Heßeler and Julia K. Schmidt contributed equally to this work

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Heßeler, J., Schmidt, J.K., Reichl, U. et al. Coexistence in the chemostat as a result of metabolic by-products. J. Math. Biol. 53, 556–584 (2006). https://doi.org/10.1007/s00285-006-0012-3

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  • DOI: https://doi.org/10.1007/s00285-006-0012-3

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