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Metabolic fitness landscapes predict the evolution of antibiotic resistance


Bacteria evolve resistance to antibiotics by a multitude of mechanisms. A central, yet unsolved question is how resistance evolution affects cell growth at different drug levels. Here, we develop a fitness model that predicts growth rates of common resistance mutants from their effects on cell metabolism. The model maps metabolic effects of resistance mutations in drug-free environments and under drug challenge; the resulting fitness trade-off defines a Pareto surface of resistance evolution. We predict evolutionary trajectories of growth rates and resistance levels, which characterize Pareto resistance mutations emerging at different drug dosages. We also predict the prevalent resistance mechanism depending on drug and nutrient levels: low-dosage drug defence is mounted by regulation, evolution of distinct metabolic sectors sets in at successive threshold dosages. Evolutionary resistance mechanisms include membrane permeability changes and drug target mutations. These predictions are confirmed by empirical growth inhibition curves and genomic data of Escherichia coli populations. Our results show that resistance evolution, by coupling major metabolic pathways, is strongly intertwined with systems biology and ecology of microbial populations.

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Fig. 1: Drug metabolism and resistance evolution.
Fig. 2: Genomics and mechanisms of resistance evolution.
Fig. 3: Resistance evolution by membrane mutations.
Fig. 4: Predicting mutant growth and resistance.
Fig. 5: Predicting mechanisms of drug resistance.

Data availability

Fastq files with whole-genome sequences of resistant mutants have been uploaded at NCBIs SRA database with the bioproject accession number PRJNA668682.

Code availability

Custom code written in MatLab 2016b to fit dosage–response curves is available from


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We acknowledge discussions with M. Scott, T. Bollenbach, S. Kryazhimskiy, A. de Visser, D. Marmiroli and I. Gordo. This work has been partially funded by Deutsche Forschungsgemeinschaft grant no. CRC 1310 to M.L. and Swedish Research Council grant no. 2017-01527 to D.I.A.

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All authors were involved in the investigation, original draft writing, review and editing of the final manuscript.

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Correspondence to Dan I. Andersson or Michael Lässig.

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Extended data

Extended Data Fig. 1 Membrane-associated resistance mutations: genes, pathways and functions.

See ref. 58 for a description of genes, encoded proteins and their physiological role.

Extended Data Fig. 2 Drug-dependent growth inhibition curves.

(a) Rich medium (LB, liquid culture). Data points (black) show growth rates for three replicates of the wild type and of membrane mutants at different drug levels d (measured in units of the half-inhibitory concentration of the wild type, \(d_{50}^{{\mathrm{wt}}} = 8.7{\mathrm{mg}}/{\mathrm{l}}\)). Coloured points show the average growth across replicates and bars indicate rms. experimental uncertainties, colours mark the drug level of the Luria–Delbrück assay used to elicit each mutant, \(d_{{\mathrm{LD}}}/d_{50}^{{\mathrm{wt}}} = 0.9\), 1.8, 3.6 (violet, pink, red). The wild type is shown for comparison (grey curves). Empirical growth inhibition curves, \(\lambda (d)/\lambda _0^{{\mathrm{wt}}} = G(d;W,d^ \ast ,\lambda ^ \ast )\) (lines) involve three independent fit parameters for each mutant: the drug-free growth rate, \(W = \lambda _0/\lambda _0^{{\mathrm{wt}}}\) and the drug response parameters19 d*, λ*; see equation (17). These fits also produce estimates of the membrane transport rates, γin and γout and of the characteristic drug levels dc and d50. For each mutant, the critical point (dc, G(dc)) (square) gives the empirical growth rate at the predicted critical drug concentration; this point is used in Fig. 4a. Inferred growth and resistance parameters for all membrane mutants are listed in the table in Extended Data Fig. 3, raw data are reported in Supplementary Table 1. (b) Minimal glycerol liquid medium. Data points show growth rates of the wild type and of Cpx stress response mutants elicited at \(d_{{\mathrm{LD}}}/d_{50}^{{\mathrm{ref}}} = 0.9\). All drug levels are measured in units of \(d_{50}^{{\mathrm{ref}}} = 8.7{\mathrm{mg}}/{\mathrm{l}}\). The fit procedure is detailed in Methods.

Extended Data Fig. 3 Growth and resistance data of membrane mutants.

(1) Mutant number. (2) Drug level of Luria–Delbrück assay, \(d_{{\mathrm{LD}}}/d_{50}^{{\mathrm{wt}}}\). (3,4,5) Posterior average parameters of the membrane evolution model: resistance cost, \(W = \lambda _0/\lambda _0^{{\mathrm{wt}}}\); drug response parameters, d*/\(d_ \ast ^{{\mathrm{wt}}}\), \(\lambda _ \ast /\lambda _ \ast ^{{\mathrm{wt}}}\). (6,7) Membrane transport rates: uptake rate \(\varepsilon = \gamma _{{\mathrm{in}}}/\gamma _{{\mathrm{in}}}^{{\mathrm{wt}}}\); release rate, \(\gamma _{{\mathrm{out}}}/\gamma _{{\mathrm{out}}}^{{\mathrm{wt}}}\). (8) Resistance, \(R = d_{50}/d_{50}^{{\mathrm{wt}}}\). (9) Critical drug level, \(d_{\mathrm{c}}/d_{50}^{{\mathrm{wt}}}\). All concentrations and rates are reported in units of the wild-type parameters \(d_{50}^{{\mathrm{wt}}} = 8.66{\mathrm{mg}}/{\mathrm{l}},d_ \ast ^{{\mathrm{wt}}} = 3.13{\mathrm{mg}}/{\mathrm{l}}\), \(\lambda _0^{{\mathrm{wt}}} = 2/{\mathrm{h}},\lambda _ \ast ^{{\mathrm{wt}}} = 0.37/{\mathrm{h}}\). Measured growth rates and inferred growth inhibition curves are shown in Extended Data Fig. 2. Inference procedures are detailed in section 3 of Methods.

Extended Data Fig. 4 Membrane-based evolution of drug resistance.

(a) Measured streptomycin uptake rate for representative membrane mutants relative to the wild type. Label numbers identify specific mutants listed in Extended Data Fig. 2. Dots show measurements for two replicates. (b–d) Model-based inference. We compare (b) uptake rate, \(\varepsilon = \gamma _{{\mathrm{in}}}/\gamma _{{\mathrm{in}}}^{{\mathrm{wt}}}\), (c) drug-free growth rate, \(W = \lambda _0/\lambda _0^{{\mathrm{wt}}}\) and (d) resistance, \(R = d_{50}/d_{50}^{{\mathrm{wt}}}\), of membrane mutants obtained from our full inference procedure with the corresponding values from a constrained model with fixed parameter \(\lambda _ \ast = 2\left( {\gamma _{{\mathrm{out}}}\kappa _t^0K} \right)^{1/2} = \lambda _ \ast ^{{\mathrm{wt}}}\). Bars show rms. measurement errors. Drug-free growth and resistance show insignificant changes, the uptake rate changes significantly in only three mutants. Hence, variation of the parameter γout does not affect the inference of the membrane model (equation (3)), of the evolutionary trade-off W(R) (Fig. 3) and of the empirical data reported in Fig. 4.

Extended Data Fig. 5 Comparison of evolutionary resistance mechanisms.

Evolutionary trade-off curves, W(R) and maximum-growth trajectories, Gc(d), are shown for the following models: (a) Minimal membrane permeability evolution (reduction of uptake rates, \(\gamma _{{\mathrm{in}}}/\gamma _{{\mathrm{in}}}^{{\mathrm{wt}}}\) = \(\kappa _n/\kappa _n^{{\mathrm{wt}}}\), at constant release rate, \(\gamma _{{\mathrm{out}}}/\gamma _{{\mathrm{out}}}^{{\mathrm{wt}}} = 1\), as in main text) and an extended model (reduction of uptake and release rates, \(\gamma _{{\mathrm{in}}}/\gamma _{{\mathrm{in}}}^{{\mathrm{wt}}}\) = \(\kappa _n/\kappa _n^{{\mathrm{wt}}}\) = \(\gamma _{{\mathrm{out}}}/\gamma _{{\mathrm{out}}}^{{\mathrm{wt}}}\)) are compared in the growth regime of irreversible drug metabolism19 (\(r^{{\mathrm{wt}}} \gg 1\)). In this regime, release rates have a negligible influence on growth and resistance, supporting use of the minimal model. Model parameters: \(q^{{\mathrm{wt}}} = 5.9,r^{{\mathrm{wt}}} = 5.4\) as in main text. (b,c) Evolution of drug efflux pumps (increase of drug release rate by overexpression of efflux genes, \(\gamma _{{\mathrm{out}}}/\gamma _{{\mathrm{out}}}^{{\mathrm{wt}}} = \varphi _{{\mathrm{efl}}}/\varphi _{{\mathrm{efl}}}^{{\mathrm{wt}}}\)) and minimal membrane evolution are compared in regimes of irreversible (\(r^{{\mathrm{wt}}} \gg 1\)) and reversible growth (\(r^{{\mathrm{wt}}} \lesssim 1\)). Efflux pumps are predicted to be relatively inefficient specifically under irreversible growth. Model parameters: efflux cost parameter, cefl = 5×10−3, 1 × 10−2, 1.5×10−2 (top to bottom), qref = 5.9, rref = 5.4 (irreversible regime, as in main text), qwt = 5.9, rwt = 0.9 (reversible regime). The reversible regime can be attained by applying a drug with reduced ribosome binding affinity (that is, with increased equilibrium constant K) for a given wild-type (that is, at constant \(\lambda _0^{{\mathrm{wt}}}\)). This results in increased drug response parameters \(\lambda _ \ast ^{{\mathrm{wt}}}\) and \(d_ \ast ^{{\mathrm{wt}}}\) compared to the reference drug; see equation (17).

Extended Data Fig. 6 Resistance mutation spectra in evolution and selection assays.

(a) Spectrum of resistance mutation rates, U(R), inferred from Luria–Delbrück assays (cyan: membrane mutations; orange: rpsL mutations). Dashed horizontal lines indicate threshold population sizes; resistance effects above a given line are likely to be represented in a population of given size N. (b) Resulting spectrum of mutant growth rates in rich LB at different drug levels, U(G;d), aggregated from the mutation rate spectrum U(R), the fitness model for membrane mutations and the measured growth rates of target mutations. Arrows mark the maximum growth rate attainable by short-term evolution at a given population size. The low-growth component corresponds to unobservable low-resistance mutants. (c,d) Resulting normalized distributions of resistance effects and growth rates of mutant colonies in Luria–Delbrück assays, PLD(R;d) and PLD(G;d), at different drug levels. Filled squares indicate growth rate segments with probability > 0.04, dots mark observed mutants (as in Fig. 5a).

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Pinheiro, F., Warsi, O., Andersson, D.I. et al. Metabolic fitness landscapes predict the evolution of antibiotic resistance. Nat Ecol Evol 5, 677–687 (2021).

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