Thermodynamic Inhibition in Chemostat Models

With an Application to Bioreduction of Uranium

Abstract

We formulate a mathematical model of bacterial populations in a chemostat setting that also accounts for thermodynamic growth inhibition as a consequence of chemical reactions. Using only elementary mathematical and chemical arguments, we carry this out for two systems: a simple toy model with a single species, a single substrate, and a single reaction product, and a more involved model that describes bioreduction of uranium[VI] into uranium[IV]. We find that in contrast to most traditional chemostat models, as a consequence of thermodynamic inhibition the equilibria concentrations of nutrient substrates might depend on their inflow concentration and not only on reaction parameters and the reactor’s dilution rate. Simulation results of the uranium degradation model indicate that thermodynamic growth inhibition quantitatively alters the solution of the model. This suggests that neglecting thermodynamic inhibition effects in systems where they play a role might lead to wrong model predictions and under- or over-estimate the efficacy of the process under investigation.

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Notes

  1. 1.

    Note: In Reactions 1-4, U[VI] is equivalent to \(\hbox {U}^{6+}\) and U[IV] is equivalent to \(\hbox {U}^{4+}\).

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Acknowledgements

The authors thank Professor William Smith (University of Guelph) for his help with the thermodynamic formulation and Heather M Gaebler (Wilfrid Laurier University) for her help with general chemistry background. HJG was supported by an Ontario Graduate Scholarship and by a Highdale Farms—Arthur and Rosmarie Spoerri Scholarship in Natural Sciences. HJE was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grants RGPIN-2019-05003 and RTI-2016-00080.

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Correspondence to Harry J. Gaebler.

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Gaebler, H.J., Eberl, H.J. Thermodynamic Inhibition in Chemostat Models. Bull Math Biol 82, 76 (2020). https://doi.org/10.1007/s11538-020-00758-3

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Keywords

  • Chemostat model
  • Gibbs free energy
  • Thermodynamic inhibition
  • Uranium bioreduction

Mathematics Subject Classification

  • 92D25
  • 80A30
  • 34C60