Mathematical Modelling Highlights the Potential for Genetic Manipulation as an Adjuvant to Counter Efflux-Mediated MDR in Salmonella

Bacteria have developed resistance to antibiotics by various mechanisms, notable amongst these is the use of permeation barriers and the expulsion of antibiotics via efflux pumps. The resistance-nodulation-division (RND) family of efflux pumps is found in Gram-negative bacteria and a major contributor to multidrug resistance (MDR). In particular, Salmonella encodes five RND efflux pump systems: AcrAB, AcrAD, AcrEF, MdsAB and MdtAB which have different substrate ranges including many antibiotics. We produce a spatial partial differential equation (PDE) model governing the diffusion and efflux of antibiotic in Salmonella, via these RND efflux pumps. Using parameter fitting techniques on experimental data, we are able to establish the behaviour of multiple wild-type and efflux mutant Salmonella strains, which enables us to produce efflux profiles for each individual efflux pump system. By combining the model with a gene regulatory network (GRN) model of efflux regulation, we simulate how the bacteria respond to their environment. Finally, performing a parameter sensitivity analysis, we look into various different targets to inhibit the efflux pumps. The model provides an in silico framework with which to test these potential adjuvants to counter MDR.