Why most transporter mutations that cause antibiotic resistance are to efflux pumps rather than to import transporters

Genotypic microbial resistance to antibiotics with intracellular targets commonly arises from mutations that increase the activities of transporters (pumps) that cause the efflux of intracellular antibiotics. A priori it is not obvious why this is so much more common than are mutations that simply inhibit the activity of uptake transporters for the antibiotics. We analyse quantitatively a mathematical model consisting of one generic equilibrative transporter and one generic concentrative uptake transporter (representing any number of each), together with one generic efflux transporter. The initial conditions are designed to give an internal concentration of the antibiotic that is three times the minimum inhibitory concentration (MIC). The effect of varying the activity of each transporter type 100-fold is dramatically asymmetric, in that lowering the activities of individual uptake transporters has comparatively little effect on internal concentrations of the antibiotic. By contrast, increasing the activity of the efflux transporter lowers the internal antibiotic concentration to levels far below the MIC. Essentially, these phenomena occur because inhibiting individual influx transporters allows others to ‘take up the slack’, whereas increasing the activity of the generic efflux transporter cannot easily be compensated. The findings imply strongly that inhibiting efflux transporters is a much better approach for fighting antimicrobial resistance than is stimulating import transporters. This has obvious implications for the development of strategies to combat the development of microbial resistance to antibiotics and possibly also cancer therapeutics in human.


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Genotypic microbial resistance to antibiotics with intracellular targets commonly arises from 51 mutations that increase the activities of transporters (pumps) that cause the efflux of intracellular 52 antibiotics. A priori it is not obvious why this is so much more common than are mutations that 53 simply inhibit the activity of uptake transporters for the antibiotics. We analyse quantitatively a 54 mathematical model consisting of one generic equilibrative transporter and one generic 55 concentrative uptake transporter (representing any number of each), together with one generic 56 efflux transporter. The initial conditions are designed to give an internal concentration of the 57 antibiotic that is three times the minimum inhibitory concentration (MIC). The effect of varying the 58 activity of each transporter type 100-fold is dramatically asymmetric, in that lowering the activities 59 of individual uptake transporters has comparatively little effect on internal concentrations of the 60 antibiotic. By contrast, increasing the activity of the efflux transporter lowers the internal antibiotic 61 concentration to levels far below the MIC. Essentially, these phenomena occur because inhibiting 62 individual influx transporters allows others to 'take up the slack', whereas increasing the activity of 63 the generic efflux transporter cannot easily be compensated. The findings imply strongly that 64 Introduction 72 In order to understand genotypic antimicrobial resistance and how to combat it, a starting point 73 should be an understanding of the main kinds of mutation that can cause it. For present purposes, 74 we assume that the molecular targets of the antibiotic are intracellular (and indeed when the 75 microbes themselves are inside host cells, their access presents its own problems 1 ). Broadly, 76 these mutations are of then of three kinds 2-4 : (i) mutations in or overproduction of one or more 77 targets of the antibiotic (e.g. DNA gyrase and topoisomerase IV for ciprofloxacin 5 ), (ii) mutations 78 that lead to inactivation of the antibiotic (e.g. of chloramphenicol 6 and aminoglycosides 7 ), or (iii) 79 mutations that affect the ability of the antibiotic to be transported to a compartment containing its 80 sites of action in the target microbe. 81

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To enter the target microbe, antibiotics (as do other drugs, e.g. 8-14 ) require transporters. (In Gram-83 negatives, outer-membrane proteins may also play a role [15][16][17] .) The precise identities of these 84 uptake transporters are in general not well understood, because mutations tend to lead only to 85 partial resistance. However, they have been identified for antibiotics such as aminoglycosides 18 , 86 chloramphenicol 19 , cycloserine 20 and fosfomycin 21, 22 . In addition, bacteria have also evolved a 87 variety of efflux pumps that serve to remove such antibiotics (see later, and also many other 88 substances 23, 24 ) from the cells. Thus, mutations that affect transporter activity can in principle 89 involve uptake transporters, efflux transporters, or upstream regulators of their activity. Our focus is 90 on this collective class, viz. transporters. In particular, consistent with the difficulty of identifying 91 transporters for their uptake, we note that the very great bulk of transporter-mediated resistance is 92 mediated via (multi-drug) efflux rather than influx transporters (e.g. 25-45 ). The focus of this article is 93 to enquire as to the reasons why this might be so. 94

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To this end, we create a very simple and generic model (Fig 1), consisting of two types of influx 96 and one type of efflux transporter. For the influx transporters, one is a generic equilibrative 97 transporter and one is concentrative for uptake, i.e. it has the capability of raising the concentration 98 of the drug of interest to a higher level inside than outside. Such transporters necessarily require a 99 source of free energy; in prokaryotes this is mainly ATP 46, 47 . The effluxer is also taken to be ATP-driven. We assume that a drug (antibiotic) has been added at 3x the minimum inhibitory 101 concentration (MIC), which for our purposes is taken to be 1 concentration unit in the case of the 102 wild type, but that the drug does not itself alter the expression levels of the transporters (cf. 48 ). 103 suggests the general reason why a partial inhibition of uptake activity might have comparatively 111 little effect. Of course if we start with the drug at a level above its MIC it is clear that increasing the 112 effluxer activity can serve to bring to a level below the MIC (and that lowering any starting efflux 113 activity would increase antibiotic sensitivity). We now wish to assess these intuitions by putting 114 some concrete numbers on these fluxes. In systems biology 49-53 , this is commonly done by casting 115 the enzymatic rate equations into the form of ordinary differential equations, and this is what we do 116 here. 117

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As previously 54 , all simulations were performed using COPASI, here version 4.27, with the LSODA 120 integrator 55-57 (http://copasi.org/), which reads and writes SBML-compliant models 58-60 . It contains 121 a full suite of enzyme rate equations, and admits automated parameter sweeps. Model files 122 including the precise parameters are included as supplementary data. 123

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The simulations were carried out with a differential equation-based model with three compartments 125 Kinetic parameters for the efflux pump (C) come from Nagano and Nikaido for AcrB (part 143 of acrAB/tolC) with nitrocefin 66 ; they cite a K m of 5 µM, k cat of 10 s -1 and a V max of 2.35×10 -11 144 mol/s/10 9 cells, which implies a total of 2.35×10 -12 mol of transporter. Considering that our 145 simulation contains 10 6 cells, the adjusted amount of transporter is then 2.35×10 -15 mol (considering the surface area estimated above, this corresponds to a surface density of 6.8×10 -15 147 mol/cm 2 ) with a V max of 2.35×10 -14 mol/s, assuming the same k cat as for nitrocefin. For K m 148 we chose a higher value (500 µM). and only a marginal effect when the activity of the concentrator is raised (Fig 3, top right).