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Observation of universal ageing dynamics in antibiotic persistence


Stress responses allow cells to adapt to changes in external conditions by activating specific pathways1. Here we investigate the dynamics of single cells that were subjected to acute stress that is too strong for a regulated response but not lethal. We show that when the growth of bacteria is arrested by acute transient exposure to strong inhibitors, the statistics of their regrowth dynamics can be predicted by a model for the cellular network that ignores most of the details of the underlying molecular interactions. We observed that the same stress, applied either abruptly or gradually, can lead to totally different recovery dynamics. By measuring the regrowth dynamics after stress exposure on thousands of cells, we show that the model can predict the outcome of antibiotic persistence measurements. Our results may account for the ubiquitous antibiotic persistence phenotype2, as well as for the difficulty in attempts to link it to specific genes3. More generally, our approach suggests that two different cellular states can be observed under stress: a regulated state, which prepares cells for fast recovery, and a disrupted cellular state due to acute stress, with slow and heterogeneous recovery dynamics. The disrupted state may be described by general properties of large random networks rather than by specific pathway activation. Better understanding of the disrupted state could shed new light on the survival and evolution of cells under stress.

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Fig. 1: The tail of the lag time distribution correlates with survival under antibiotic treatment.
Fig. 2: Distribution of the lag time following starvation for various durations Tw of exposure to SHX.
Fig. 3: The RCCN model reproduces the ageing dynamics observed in the experiment.
Fig. 4: No ageing under gradual starvation.

Data availability

Source data for Figs. 14 are provided with the paper. Source data are provided with this paper.

Code availability

All Matlab scripts for the simulation52 are available through GitHub at the link:


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We thank B. Seo and J. Paulsson for the microfluidic mother-machine templates; and N. Barkai, Y. Burak and A. Rotem for comments on the manuscript and for illuminating discussions. This work was supported by the European Research Council (consolidator grant no. 681819), the Israel Science Foundation (grant no. 597/20) and the Minerva Foundation.

Author information

Authors and Affiliations



Y.K., E.O., O.G. and N.Q.B. designed, performed experiments and analysed the data. I.R. and I.L.-R. performed experiments and analysed the data. O.A., S.R., S.M., Y.K. and N.Q.B. provided theory. N.Q.B., Y.K. and O.A. wrote the manuscript.

Corresponding authors

Correspondence to Oded Agam or Nathalie Q. Balaban.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Bruce Levin, Nozomu Yachie and the other, 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 figures and tables

Extended Data Fig. 1 Ageing under abrupt SHX exposure.

a, Viability vs SHX exposure duration. The bars and error bars represent the mean and std (n=3 biological replicates). Each time point was compared to t0 using two-sided Student’s paired t-test. NS: p>0.05. b, Median time of the lag time distribution versus Tw. Colours indicate 3 biological replicates. Note that after about 1000 min, increasing the starvation duration does not increase the median lag time. c, To test whether long lagging colonies maintain this phenotype when regrown, a long lagging colony was isolated from a plate inoculated with an SHX-arrested culture. The appearance time of the isolated colony is indicated by the black arrow. d, Lag time distributions of the culture originating from the colony isolated in c shows the same aging phenotype under abrupt SHX exposure as the original culture, indicating that the long lag is not due to mutation.

Extended Data Fig. 2

Analogy between physical ageing in a spin network and ageing of bacteria under acute stress.

Extended Data Fig. 3 Correspondence between starvation and magnetic field (H) in the Randomly Connected Cycles Network model.

a, Schematic view of the time course of the simulation and experiments. First, no starvation (H=0), then an abrupt starvation leads to a switch OFF of the spins (here H=0.8). After a duration Tw, the conditions are returned back to H=0. b, Simulation (coloured lines) and analytical results according to Eq. S7 for the average magnetization (equal to twice the fraction of OFF nodes-1). Inset: An example for the simulation of one magnetization trace (linear scale) defined by Eq. S6, after the magnetic field is switched off. The lag time for each realization (bacterium) is defined by the first crossing of the magnetization back to zero.

Extended Data Fig. 4 Ageing dynamics are robust to changes in the parameters of the model but depend on its architecture.

ac, Different random model connection architectures that do not display ageing. Asymmetric Sherrington-Kirkpatrick model (a). Erdös-Renyi connections with p=40% (b). Rich-get-Richer connections (c). di, Variations in RCCN model parameters. Power law exponent, α=1.1 (d); γ=2 (e); System size, N=211 (solid lines), N=212 (dotted lines) (f). Maximal cycle length, Lmax=800 (g). Magnetic field, H=0.3 (h). Connections sparseness, p=10% (i). Violet curves: Tw=20; Yellow curves: Tw=3000. Other simulation parameters as in Supplementary Table 2.

Extended Data Fig. 5 Powerlaw tail of lag time distribution after saturation of ageing.

a, Experimental data of lag times after SHX exposure (green) plotted as (1-CDF). Inset of a: same data as a plotted on semilog shows that it cannot be fitted with an exponential function (dashed black line). b, Simulated lag time distribution curve (solid black curve). Magenta curve: simulation with a different strength of magnetic field shows that the powerlaw behavior is an asymptotic behavior and here does not fit the t−2 dependence as well. The dashed red curves in a and b show the t−2 behavior. c, Simulation average over architecture sampling is equivalent to average over random connections. Black: average of different random cycles and connections. Red: fixed cycles architecture averaged over random connection strength (i.e. |Jij|). Blue: same as the red curves, but for a different architecture sampled.

Extended Data Fig. 6 Slow relaxation dynamics from stress exposure protects against subsequent ampicillin exposure.

Microfluidic experiment of bacteria MGYΔmotA exposed to sodium azide for a duration of Tw=1720 min before the observations. Upon removal of sodium azide, ampicillin was added. Bacteria with a short lag were killed, whereas bacteria remaining at the lag phase during ampicillin treatment survived. The fate of 172 cells was followed. Death was determined by lysis. The probability for cells that grew (i.e. detectable increase in cell size) during the antibiotic die is 5.7 times that for cells that did not grow during the antibiotic.

Extended Data Fig. 7 Ageing upon exposure to sodium azide in wild-type E.coli (MG1655/pZA21RmCherry).

a, Growth curve of cultures exposed to sodium azide during exponential growth (solid line) or unexposed (dashed line). The times at which the culture was sampled are marked in colours corresponding to the results shown in b. b, Experimental results for the distribution of lag times as measured after starvation under sodium azide. Distributions are plotted as 1-CDF (Cumulative Distribution Function). Note that the lag time distribution becomes independent of starvation duration for long enough starvation, as predicted by the RCCN model. Different colours represent different duration of exposure to sodium azide, as marked in a. c, Viability under sodium azide. Only after 2800 min viability decreased significantly. Error bars are the std (n=3 biological replicates). Each time point was compared to t0 using two-sided Student’s paired t-test. ‘NS’, not significant; ‘*’, p=0.014. d, Bacteria were exposed to sodium azide for durations: 1454, 1546, 1644, and 2254 min. Upon removal of sodium azide, ampicillin was added. The survival fraction under 9.5 h ampicillin exposure was determined and plotted vs. the tail fraction measured in b. Dotted line: linear regression, two-sided Pearson’s correlation: 0.98, p=0.024.

Extended Data Fig. 8 After gradual starvation in M9 the recovery is fast and not affected by SHX.

a, Lag time distribution following gradual starvation in minimal medium reaching stationary phase (CASP - Constant Activity Stationary Phase)50. Adding SHX (solid line) or without SHX (dotted line) does not change the lag time distribution. For both curves SHX was maintained for Tw=1300 min. b, Zoom on a gradually starved culture reaching stationary phase (CASP) exhibits exponential exit of lag (dashed black line). c, The distributions of lag times after gradual starvation is narrow compared to after abrupt starvation, as evident from the standard deviations (STD) and Fig. 4c & Extended Data Fig. 9. For the gradual starvation, the STD, the two-fold exponential decay time, and the liquid culture’s doubling time are comparable. Abrupt starvation (EXP t1 and t2) results in large STD, even after shorter SHX duration.

Source data

Extended Data Fig. 9 Lag time distributions of biological replicates for all stress conditions tested.

Different columns represent different biological replicates of the same experiment. Stresses from top to bottom: aging conditions: Abrupt SHX, sodium azide, CAM, LB KLY prolonged starvation. Broad and slow lag can be seen for the stresses leading to aging. Non-aging conditions: LB EPEC prolonged starvation, gradual starvation M9 (CASP), gradual SHX exposure, NaCl. Note that some of these replicates also appear in main figures and are added here for completeness. Viability: Abrupt SHX (Extended Data Fig. 1a), sodium azide (Extended Data Fig. 7c). Other plots: Viability decrease compared to t0 non-significant (p>0.05). Stress exposure durations (coloured lines) in data file.

Extended Data Fig. 10 Quantification of ageing under various stress conditions.

Pink: acute stress (SHX, sodium azide, Cam, prolonged LB starvation-lab strain). Green: mild stress (gradual SHX, gradual starvation in M9, NaCl, LB starvation EPEC strain). a, b, Schematic Illustration of the measure of ageing. The times at which lag time survival functions intersect an arbitrary fraction, f: L, are used to measure the change in the functions with Tw: dL (a). Then for each pair of successive functions, dL/dTw is obtained in each experiment (b). c, The ageing measure, max(dL/dTw) was calculated for all conditions. Data include n=3 biological replicates, except for LB KLY and NaCl, for which n=2. For different fractions (here f=10%), results are similar. Significance tests: Two-sided unpaired t-test was performed on the natural logarithm of the ageing measure, to compare different conditions. Comparisons between gradual SHX and some other conditions are marked by a horizontal line. ‘NS’: not significant. ‘**’: p=0.00077, 0.00013, 0.00133 for Abrupt-SHX, sodium azide, and CAM, respectively. The ageing conditions SHX/sodium azide/CAM are significantly different from the natural or gradual starvations: CASP, gradual SHX, and in rich medium. Similar results were obtained for different f.

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This file contains the Supplementary Methods and Supplementary Notes on the RCCN Model, Supplementary Tables 1–3 and Supplementary References.

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Kaplan, Y., Reich, S., Oster, E. et al. Observation of universal ageing dynamics in antibiotic persistence. Nature 600, 290–294 (2021).

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