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

George Youlden; Vito Ricci; Xuan Wang Kan; Laura Piddock; Sara Jabbari; John R. King

doi:10.1007/s00285-021-01576-4

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

George Youlden, Vito Ricci, Xuan Wang Kan, Laura Piddock, Sara Jabbari, John R. King

Research output: Contribution to journal › Article › peer-review

136 Downloads (Pure)

Abstract

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.

Original language	English
Article number	31
Journal	Journal of Mathematical Biology
Volume	82
Issue number	4
Early online date	10 Mar 2021
DOIs	https://doi.org/10.1007/s00285-021-01576-4
Publication status	Published - 10 Mar 2021

Bibliographical 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).

Keywords

AcrAB-TolC
Asymptotic analysis
Escherichia coli
Mathematical modelling
Salmonella

ASJC Scopus subject areas

Modelling and Simulation
Agricultural and Biological Sciences (miscellaneous)
Applied Mathematics

Access to Document

10.1007/s00285-021-01576-4Licence: Creative Commons: Attribution (CC BY)

YouldenGH2021TimeFinal published version, 5.09 MBLicence: Creative Commons: Attribution (CC BY)

Understanding how bacteria respond to efflux inhibition
Piddock, L.
Medical Research Council, Match Equipment - MRC
1/09/17 → 28/02/21
Project: Research
Maths-AIM: A Mathematical and experimental approach for the rational assessment of bacterial Adhesion Inhibitor Materials in vivo
Jabbari, S. & Krachler, A.
Biotechnology & Biological Sciences Research Council
14/09/15 → 30/11/18
Project: Research Councils

Cite this

@article{b62ec3f37a2b4a9297772e485dc4cd22,

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

abstract = "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.",

keywords = "AcrAB-TolC, Asymptotic analysis, Escherichia coli, Mathematical modelling, Salmonella",

author = "George Youlden and Vito Ricci and {Wang Kan}, Xuan and Laura Piddock and Sara Jabbari and King, {John R.}",

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: {\textcopyright} 2021, The Author(s).",

year = "2021",

month = mar,

day = "10",

doi = "10.1007/s00285-021-01576-4",

language = "English",

volume = "82",

journal = "Journal of Mathematical Biology",

issn = "0303-6812",

publisher = "Springer Nature",

number = "4",

}

TY - JOUR

T1 - Time dependent asymptotic analysis of the gene regulatory network of the AcrAB-TolC efflux pump system in gram-negative bacteria

AU - Youlden, George

AU - Ricci, Vito

AU - Wang Kan, Xuan

AU - Piddock, Laura

AU - Jabbari, Sara

AU - King, John R.

N1 - 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).

PY - 2021/3/10

Y1 - 2021/3/10

N2 - 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.

AB - 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.

KW - AcrAB-TolC

KW - Asymptotic analysis

KW - Escherichia coli

KW - Mathematical modelling

KW - Salmonella

UR - http://www.scopus.com/inward/record.url?scp=85102335138&partnerID=8YFLogxK

U2 - 10.1007/s00285-021-01576-4

DO - 10.1007/s00285-021-01576-4

M3 - Article

C2 - 33694073

SN - 0303-6812

VL - 82

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

IS - 4

M1 - 31

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Projects

Understanding how bacteria respond to efflux inhibition

Maths-AIM: A Mathematical and experimental approach for the rational assessment of bacterial Adhesion Inhibitor Materials in vivo

Cite this