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Stability of two competing populations in chemostat where one of the population changes its average mass of division in response to changes of its population

Smith, F; Velayudhan, A; Voulgarelis, D; (2019) Stability of two competing populations in chemostat where one of the population changes its average mass of division in response to changes of its population. PLoS ONE , 14 (3) , Article e0213518. 10.1371/journal.pone.0213518. Green open access

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Abstract

This paper considers a novel dynamical behaviour of two microbial populations, competing in a chemostat over a single substrate, that is only possible through the use of population balance equations (PBEs). PBEs are partial integrodifferential equations that represent a distribution of cells according to some internal state, mass in our case. Using these equations, realistic parameter values and the assumption that one population can deploy an emergency mechanism, where it can change the mean mass of division and hence divide faster, we arrive at two different steady states, one oscillatory and one non-oscillatory both of which seem to be stable. A steady state of either form is normally either unstable or only attainable through external control (cycling the dilution rate). In our case no external control is used. Finally, in the oscillatory case we attempt to explain how oscillations appear in the biomass without any explicit dependence on the division rate (the function that oscillates) through the approximation of fractional moments as a combination of integer moments. That allows an implicit dependence of the biomass on the number of cells which in turn is directly dependent on the division rate function.

Type: Article
Title: Stability of two competing populations in chemostat where one of the population changes its average mass of division in response to changes of its population
Open access status: An open access version is available from UCL Discovery
DOI: 10.1371/journal.pone.0213518
Publisher version: https://doi.org/10.1371/journal.pone.0213518
Language: English
Additional information: © 2019 Voulgarelis et al. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/).
Keywords: Cell cycle and cell division, Oxygen, Simulation and modeling, Cell growth, Population dynamics, Mathematical models, Signal processing, Signaling molecules
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Biochemical Engineering
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10070283
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