Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Metabolic fitness landscapes predict the evolution of antibiotic resistance

Abstract

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.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

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 https://github.com/fe-pinheiro/RibosomeTargetingDrugsFitDR.

References

  1. Levy, S. B. & Marshall, B. Antibacterial resistance worldwide: causes, challenges and responses. Nat. Med. 10, S122–S129 (2004).

    CAS  PubMed  Article  Google Scholar 

  2. Lipsitch, M., Bergstrom, C. T. & Levin, B. R. The epidemiology of antibiotic resistance in hospitals: paradoxes and prescriptions. Proc. Natl Acad. Sci. USA 97, 1938–1943 (2000).

    CAS  PubMed  Article  Google Scholar 

  3. Gullberg, E. et al. Selection of resistant bacteria at very low antibiotic concentrations. PLoS Pathog. 7, e1002158 (2012).

    Article  CAS  Google Scholar 

  4. Łuksza, M. & Lässig, M. A predictive fitness model for influenza. Nature 507, 57–61 (2014).

    PubMed  Article  CAS  Google Scholar 

  5. Lässig, M., Mustonen, V. & Walczak, A. M. Predicting evolution. Nat. Ecol. Evol. 1, 0077 (2017).

  6. Sommer, M. O., Munck, C., Toft-Kehler, R. V. & Andersson, D. I. Prediction of antibiotic resistance: time for a new preclinical paradigm? Nat. Rev. Microbiol. 15, 689–696 (2017).

    CAS  PubMed  Article  Google Scholar 

  7. Weinreich, D. M., Delaney, N. F., DePristo, M. A. & Hartl, D. L. Darwinian evolution can follow only very few mutational paths to fitter proteins. Science 312, 111–114 (2006).

    CAS  PubMed  Article  Google Scholar 

  8. Palmer, A. C. et al. Delayed commitment to evolutionary fate in antibiotic resistance fitness landscapes. Nat. Commun. 6, 7386 (2015).

  9. Wistrand-Yuen, E. et al. Evolution of high-level resistance during low-level antibiotic exposure. Nat. Commun. 9, 1599 (2018).

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  10. Zwart, M. P. et al. Unraveling the causes of adaptive benefits of synonymous mutations in TEM-1 β-lactamase. Heredity 121, 406–421 (2018).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  11. Das, S. G., Direito, S. O., Waclaw, B., Allen, R. J. & Krug, J. Predictable properties of fitness landscapes induced by adaptational tradeoffs. eLife 9, 908574 (2020).

    Google Scholar 

  12. Tenaillon, O. et al. The molecular diversity of adaptive convergence. Science 335, 457–461 (2012).

    CAS  PubMed  Article  Google Scholar 

  13. Toprak, E. et al. Evolutionary paths to antibiotic resistance under dynamically sustained drug selection. Nat. Genet. 44, 101 (2012).

    CAS  Article  Google Scholar 

  14. Kryazhimskiy, S., Rice, D. P., Jerison, E. R. & Desai, M. M. Global epistasis makes adaptation predictable despite sequence-level stochasticity. Science 344, 1519–1522 (2014).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  15. Chevereau, G. et al. Quantifying the determinants of evolutionary dynamics leading to drug resistance. PLoS Biol. 13, e1002299 (2015).

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  16. Monod, J. The growth of bacterial cultures. Annu. Rev. Microbiol. 3, 371–394 (1949).

    CAS  Article  Google Scholar 

  17. Scott, M., Gunderson, C. W., Mateescu, E. M., Zhang, Z. & Hwa, T. Interdependence of cell growth and gene expression: origins and consequences. Science 330, 1099–1102 (2010).

    CAS  PubMed  Article  Google Scholar 

  18. Deris, J. B. et al. The innate growth bistability and fitness landscapes of antibiotic-resistant bacteria. Science 342, 1237435 (2013).

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  19. Greulich, P., Scott, M., Evans, M. R. & Allen, R. J. Growth‐dependent bacterial susceptibility to ribosome‐targeting antibiotics. Mol. Syst. Biol. 11, 796 (2015).

  20. Qi, Q., Preston, G. M. & MacLean, R. C. Linking system-wide impacts of RNA polymerase mutations to the fitness cost of rifampin resistance in Pseudomonas aeruginosa. mBio 5, e01562–01514 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  21. Rodrigues, J. V. et al. Biophysical principles predict fitness landscapes of drug resistance. Proc. Natl Acad. Sci. USA 113, E1470–E1478 (2016).

    CAS  PubMed  Article  Google Scholar 

  22. Tamer, Y. T. et al. High-order epistasis in catalytic power of dihydrofolate reductase gives rise to a rugged fitness landscape in the presence of trimethoprim selection. Mol. Biol. Evol. 36, 1533–1550 (2019).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  23. Basan, M. et al. Overflow metabolism in Escherichia coli results from efficient proteome allocation. Nature 528, 99–104 (2015).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  24. Yang, J. H. et al. A white-box machine learning approach for revealing antibiotic mechanisms of action. Cell 177, 1649–1661 (2019).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  25. Zampieri, M. et al. Metabolic constraints on the evolution of antibiotic resistance. Mol. Syst. Biol. 13, 917 (2017).

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  26. Dunphy, L. J., Yen, P. & Papin, J. A. Integrated experimental and computational analyses reveal differential metabolic functionality in antibiotic-resistant Pseudomonas aeruginosa. Cell Syst. 8, 3–14 (2019).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  27. Yang, Y. et al. Changes in the carbon metabolism of Escherichia coli during the evolution of doxycycline resistance. Front. Microbiol. 10, 2506 (2019).

    PubMed  PubMed Central  Article  Google Scholar 

  28. Krause, K. M., Serio, A. W., Kane, T. R. & Connolly, L. E. Aminoglycosides: an overview. Cold Spring Harb. Perspect. Med. 6, a027029 (2016).

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  29. Scott, M., Klumpp, S., Mateescu, E. M. & Hwa, T. Emergence of robust growth laws from optimal regulation of ribosome synthesis. Mol. Syst. Biol. 10, 747 (2014).

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  30. Paulsen, I. T. & Skurray, R. A. The POT family of transport proteins. Trends Biochem. Sci. 19, 404 (1994).

    CAS  PubMed  Article  Google Scholar 

  31. Yagupsky, P. & Nolte, F. Quantitative aspects of septicemia. Clin. Microbiol. Rev. 3, 269–279 (1990).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  32. Coulthard, M. G. Defining urinary tract infection by bacterial colony counts: a case for 100,000 colonies/ml as the best threshold. Pediatr. Nephrol. 34, 1639–1649 (2019).

    PubMed  Article  Google Scholar 

  33. Paulander, W., Maisnier-Patin, S. & Andersson, D. I. The fitness cost of streptomycin resistance depends on rpsL mutation, carbon source and RpoS (σS). Genetics 183, 539–546 (2009).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  34. Ruiz, N. & Silhavy, T. J. Sensing external stress: watchdogs of the Escherichia coli cell envelope. Curr. Opin. Microbiol. 8, 122–126 (2005).

    CAS  PubMed  Article  Google Scholar 

  35. Kurabayashi, K., Hirakawa, Y., Tanimoto, K., Tomita, H. & Hirakawa, H. Role of the CpxAR two-component signal transduction system in control of fosfomycin resistance and carbon substrate uptake. J. Bacteriol. 196, 248–256 (2014).

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  36. Galdiero, S. et al. Microbe–host interactions: structure and role of Gram-negative bacterial porins. Curr. Protein Pept. Sci. 13, 843–854 (2012).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  37. Shigemura, K. et al. Association of overexpression of efflux pump genes with antibiotic resistance in Pseudomonas aeruginosa strains clinically isolated from urinary tract infection patients. J. Antibiot. 68, 568–572 (2015).

    CAS  Article  Google Scholar 

  38. Boolchandani, M., D’Souza, A. W. & Dantas, G. Sequencing-based methods and resources to study antimicrobial resistance. Nat. Rev. Genet. 20, 356–370 (2019).

  39. Shoval, O. et al. Evolutionary trade-offs, Pareto optimality, and the geometry of phenotype space. Science 336, 1157–1160 (2012).

    CAS  PubMed  Article  Google Scholar 

  40. Li, Y., Petrov, D. A. & Sherlock, G. Single nucleotide mapping of trait space reveals Pareto fronts that constrain adaptation. Nat. Ecol. Evol. 3, 1539–1551 (2019).

  41. Stokes, J. M., Lopatkin, A. J., Lobritz, M. A. & Collins, J. J. Bacterial metabolism and antibiotic efficacy. Cell Metab. 30, 251–259 (2019).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  42. Ojkic, N. et al. A roadblock-and-kill mechanism of action model for the DNA-targeting antibiotic ciprofloxacin. Antimicrob. Agents Chemother. 64, e02487–19 (2020).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  43. Kavčič, B., Tkačik, G. & Bollenbach, T. Minimal biophysical model of combined antibiotic action. PLoS Comput. Biol. 17, e1008529 (2020).

  44. Miller, J. A Short Course in Bacterial Genetics: A Laboratory Manual and Handbook for Escherichia coli and Related Bacteria (Cold Spring Harbor Lab Press, 1992).

  45. Gillet-Markowska, A., Louvel, G. & Fischer, G. bz-rates: a web tool to estimate mutation rates from fluctuation analysis. G3 5, 2323–2327 (2015).

    PubMed  Article  Google Scholar 

  46. Deatherage, D. E. & Barrick, J. E. in Engineering and Analyzing Multicellular Systems. Methods in Molecular Biology (Methods and Protocols) Vol. 1151 (eds Sun L. & Shou W.) 165–188 (Humana Press, 2014).

  47. Hui, S. et al. Quantitative proteomic analysis reveals a simple strategy of global resource allocation in bacteria. Mol. Syst. Biol. 11, 784 (2015).

  48. Scott, M. & Hwa, T. Bacterial growth laws and their applications. Curr. Opin. Biotechnol. 22, 559–565 (2011).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  49. Jun, S., Si, F., Pugatch, R. & Scott, M. Fundamental principles in bacterial physiology—history, recent progress, and the future with focus on cell size control: a review. Rep. Prog. Phys. 81, 056601 (2018).

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  50. Greulich, P., Doležal, J., Scott, M., Evans, M. R. & Allen, R. J. Predicting the dynamics of bacterial growth inhibition by ribosome-targeting antibiotics. Phys. Biol. 14, 065005 (2017).

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  51. Perfeito, L., Ghozzi, S., Berg, J., Schnetz, K. & Lässig, M. Nonlinear fitness landscape of a molecular pathway. PLoS Genet. 7, e1002160 (2011).

  52. Tritton, T. R. Ribosome–tetracycline interactions. Biochemistry 16, 4133–4138 (1977).

    CAS  PubMed  Article  Google Scholar 

  53. Nierhaus, D. & Nierhaus, K. H. Identification of the chloramphenicol-binding protein in Escherichia coli ribosomes by partial reconstitution. Proc. Natl Acad. Sci. USA 70, 2224–2228 (1973).

    CAS  PubMed  Article  Google Scholar 

  54. Praski Alzrigat, L., Huseby, D. L., Brandis, G. & Hughes, D. Fitness cost constrains the spectrum of marR mutations in ciprofloxacin-resistant Escherichia coli. J. Antimicrob. Chemother. 72, 3016–3024 (2017).

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  55. Pacheco, J. O., Alvarez-Ortega, C., Rico, M. A. & Martínez, J. L. Metabolic compensation of fitness costs is a general outcome for antibiotic-resistant Pseudomonas aeruginosa mutants overexpressing efflux pumps. mBio 8, e00500–e00517 (2017).

    Google Scholar 

  56. Dai, X. et al. Reduction of translating ribosomes enables Escherichia coli to maintain elongation rates during slow growth. Nat. Microbiol. 2, 16231 (2016).

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  57. Dennis, J. E. & Woods, D. J. New Computing Environments: Microcomputers in Large-scale Computing Vol. 27 (Siam, 1987).

  58. Keseler, I. M. et al. The EcoCyc database: reflecting new knowledge about Escherichia coli K-12. Nucleic Acids Res. 45, D543–D550 (2017).

    CAS  PubMed  Article  Google Scholar 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

Authors

Contributions

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

Corresponding authors

Correspondence to Dan I. Andersson or Michael Lässig.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Ecology & Evolution thanks the anonymous reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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).

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1038/s41559-021-01397-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41559-021-01397-0

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing