Time dependent asymptotic analysis of the gene regulatory network of the AcrAB-TolC efflux pump system in gram-negative bacteria

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  • University of Nottingham


Efflux pumps are a mechanism of intrinsic and evolved resistance in bacteria. If an efflux pump can expel an antibiotic so that its concentration within the cell is below a killing threshold the bacteria are resistant to the antibiotic. Efflux pumps may be specific or they may pump various different substances. This is why many efflux pumps confer multi drug resistance (MDR). In particular over expression of the AcrAB-TolC efflux pump system confers MDR in both Salmonella and Escherichia coli. We consider the complex gene regulation network that controls expression of genes central to controlling the efflux associated genes acrAB and acrEF in Salmonella. We present the first mathematical model of this gene regulatory network in the form of a system of ordinary differential equations. Using a time dependent asymptotic analysis, we examine in detail the behaviour of the efflux system on various different timescales. Asymptotic approximations of the steady states provide an analytical comparison of targets for efflux inhibition.

Bibliographic note

Funding Information: SJ gratefully acknowledges support from the Biotechnology and Biological Sciences Research Council (Grant Code: BB/M021386/1). GHY is supported by an Engineering and Physical Sciences Doctoral Training Partnership award (EP/N509590/1). GHY was funded through a joint University of Birmingham and University of Nottingham scholarship. LJVP gratefully acknowledges support from the Medical Research Council (Grant Code: MR/P022596/1). All time-dependent numerical solutions were computed using ode23 and ode45 solvers in MATLAB R2018b (The MathWorks, Inc.). Publisher Copyright: © 2021, The Author(s).


Original languageEnglish
Article number31
JournalJournal of Mathematical Biology
Issue number4
Early online date10 Mar 2021
Publication statusPublished - 10 Mar 2021


  • AcrAB-TolC, Asymptotic analysis, Escherichia coli, Mathematical modelling, Salmonella