Modelling multidrug resistance driven by efflux pump expression in Gram-negative bacteria

Efflux pumps are an essential mechanism for bacteria that can account for antibiotic resistance. If an efflux pump can expel an antibiotic so that its concentration within the cell is below a killing threshold the bacteria can become resistant to the antibiotic. Efflux pumps may be specific or they may pump various different substances and com- pounds. The latter is one main reason that many efflux pumps are linked with multi drug resistance (MDR). In particular overexpression of the AcrAB−TolC efflux pump system is commonly linked with MDR in both Escherichia coli (E. coli) and Salmonella. We look at the complex gene regulation network (GRN) central to controlling the efflux pump genes acrAB and acrEF in Salmonella and their resulting effect on intracellular antibiotic concentration. By using mathematical modelling, we first represent the gene regulatory network solely, we present a model in the form of a system of ordinary differential equations (ODEs). Using time dependent asymptotic analysis, we can examine in detail the behaviour of the efflux system on various different timescales before analysing asymptotically approximated steady states. In our second model, we produce a spatial model governing the diffusion and efflux of antibiotic in Salmonella, via the efflux pumps AcrAB, AcrEF, MdsAB and MdtAB. Using parameter fitting techniques on experimental data, we are able to establish the behaviour of multiple Salmonella strains, which enables us to produce efflux profiles for each individual efflux pump system. In our final model, by using insights from our asymptotic analysis we produce a multiscale model, combining our ODE and PDE models. This model implements a feedback mechanism between the intracellular antibiotic concentration and components of the GRN, enabling us to model the behaviour of the bacteria in response to antibiotic. By performing parameter sensitivity analysis, we are then able to look into various different methods to inhibit efflux pumps, preventing expulsion of antibiotic to counter MDR.