Coexistence in the chemostat as a result of metabolic byproducts
 Julia Heßeler,
 Julia K. Schmidt,
 Udo Reichl,
 Dietrich Flockerzi
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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 byproduct, 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 byproduct serves as a second carbon source for one of the species, but not the producer.
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 Title
 Coexistence in the chemostat as a result of metabolic byproducts
 Journal

Journal of Mathematical Biology
Volume 53, Issue 4 , pp 556584
 Cover Date
 20061001
 DOI
 10.1007/s0028500600123
 Print ISSN
 03036812
 Online ISSN
 14321416
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Competition
 Chemostat
 Coexistence
 Metabolite
 Interspecific Competition
 Inhibitor
 Quantitative TRFLP
 Industry Sectors
 Authors

 Julia Heßeler ^{(1)}
 Julia K. Schmidt ^{(2)}
 Udo Reichl ^{(2)} ^{(3)}
 Dietrich Flockerzi ^{(3)}
 Author Affiliations

 1. Department of Mathematics and Physics, AlbertLudwigsUniversity, HermannHerderStr. 3, 79104, Freiburg, Germany
 2. Department of Bioprocess Engineering, OttovonGuerickeUniversity, Universitätsplatz 2, 39106, Magdeburg, Germany
 3. Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106, Magdeburg, Germany