Research ArticleMICROBIOLOGY

Negative feedback increases information transmission, enabling bacteria to discriminate sublethal antibiotic concentrations

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Science Advances  28 Nov 2018:
Vol. 4, no. 11, eaat5771
DOI: 10.1126/sciadv.aat5771
  • Fig. 1 Structure of TetR/TetA circuit and experimental setup.

    (A) Scheme of analog (graded) and digital (on/off) responses against a signal. (B) Scheme of TetR/TetA circuit. (C) Experimental design (right) showing TetRmkate2 fusion cloned under the transcriptional control of a regulatable pBAD promoter (INPUT) and GFP cloned under pA promoter (OUTPUT). Microphotographs show Escherichia coli cells carrying both reporters (left). Cells were grown on agarose pads, as described in Materials and Methods. Exposure times were 50 ms (phase) and 500 ms (mkate2 and GFP). (D to F) Each panel shows input (TetRmkate2) versus output (GFP) fluorescence levels (fluorescence arbitrary units) for 9000 individual cells, corresponding to different genomic constructions: input and output cloned in the same plasmid (D), on two separate plasmids (E), and into the chromosome (F). Lighter solid lines indicate population averages, and darker solid lines correspond to median values.

  • Fig. 2 Extracting MI values from scatterplot data.

    Measuring entropy and MI from scatterplot data. (A) To measure MI, scatterplot data showing input and output values (upper left panel) must be transformed into a two-dimensional probability density plot (upper right panel). To do so, we used Grenander’s method of sieves, as discussed in Supplementary Results. The middle and bottom panels of the figure show the application of two sieves of different bin sizes. The middle panel shows a sieve with a low number of bins, while the bottom panel shows a sieve with a high number of bins. On the right of the figure, the probability density maps result from applying different sieves on the same scatterplot map. (B) Scatterplot of 9000, log-distributed, random input/output pairs used to test the performance of discretization methods. Because this dataset was randomly generated, discretization should result into 0 bits of MI. (C) MI values extracted from scatterplots from (B) using the discretization methods indicated in the figure. Blue, direct HML estimation; green, direct HML estimation under jackknife correction; red, HCML estimation (maximum likelihood with Miller’s correction). As shown in the figure, Miller’s correction was required to prevent information inflation due to increasing bin number. (D) Datasets of different sizes generated to test the effect of undersampling on MI estimation. From the experimental dataset shown in Fig. 1D, we randomly drew 2000, 1000, 500, and 250 cells, generating the four datasets shown in the figure. (E) Effect of sampling size on MI estimation with and without jackknife correction. On the left panel, lines indicate the MI estimation for different bin sizes (x axis), retrieved when applying HCML estimation with (green lines) and without (blue lines) jackknife correction. On the right panel, MI estimations for datasets shown in (D) with (green bars) and without (blue bars) jackknife correction. As detailed in Supplementary Results, jackknife correction provided only a marginal improvement of less than 1% of the MI.

  • Fig. 3 Determining the MI between TetRmkate2 and pA.

    (A to C) MI values (top) and density maps (bottom) for the different genomic constructions. Input/output scatterplots were transformed into density plots by applying a mesh of variable bin sizes, as described in the main text. Upper chart shows MI values (y axis) as a function of the number of bins (x axis). Asymptotic MI values were taken as the lower bound of the MI. Density maps correspond to bin sizes yielding maximum MI. (D to F) Probability density maps for equiprobable inputs. Upper charts shows TetRmkate input distributions. Lower charts show joint probability density maps P(TetRmkate, pA::GFP). Probability densities follow the color bars on the right.

  • Fig. 4 Measuring information transmission by the inducer, Tc.

    (A to D) Data for one-plasmid experimental system without NFL. (E to L) Data for one-plasmid system under TetR NFL. From these, (E) to (H) show data from pR::TetRmkate2 expression, while (I) to (L) correspond to pA::GFP values. (A, E, and I) Scatterplots showing fluorescence intensity (y axis, arbitrary fluorescence units) in response to increasing Tc concentrations (x axis, in μg/ml). Solid lines correspond to average values. (B, F, and J) Density maps obtained using optimal bin sizes, as described in the main text. (C, G, and K) Histogram of input (top) and output levels (bottom). Upper chart shows uniform distribution of input Tc concentrations. Lower chart shows the output fluorescence distribution produced from pR or pA promoters. (D, H, and L) Probability density maps for the joint input/output probability distributions. Probability densities are indicated according to the color bar.

  • Fig. 5 Discrimination of sublethal antibiotic concentrations.

    (A) Output pA::GFP noise levels, expressed as variance divided by squared average achieved by the one-plasmid system. Values shown in the figure correspond to the circuit without feedback under arabinose or Tc induction (orange and gray lines, respectively) and to the circuit with NFL under Tc induction (green line) (inset: MI values observed in each experimental condition; x axis corresponds to the number of bins for the output). (B) Tc transfer function for pA::GFP (green line) and pR::TetRmkate2 (red line) (y axis, promoter induction levels, expressed as % of the maximum; x axis, Tc concentration, in μg/ml). (C) Discriminative regions in pR/pA expression levels. White lines indicate boundaries between expression levels that unambiguously correspond to different Tc concentrations. (D) Model of pR/pA responses versus Tc concentration. Bars indicate percentage of cells located in each of the pR/pA regions, as Tc concentration increases (right). (E) Correlation between Tc effect and pR/pA activation levels. Upper chart shows increases in the doubling time (y axis, in minutes), plotted against Tc concentration (x axis, in μg/ml). Middle and lower charts show the percentage of cells showing values within pR and pA expression levels, respectively. (F) Channel capacity optimization. Top: Experimental MI values (green line) compared to the theoretical channel capacity (red line) calculated by rate-distortion methods. Bottom: Experimental output distribution (green bars) compared to optimal output distribution calculated by rate-distortion methods (red line).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/11/eaat5771/DC1

    Supplementary Results

    Supplementary Calculations

    Fig. S1. Genetic constructions used in this work and signal calibration.

    Fig. S2 Validation of TetRmkate2 translational fusion.

    Fig. S3. Induction of TetRmkate2 from pBAD.

    Fig. S4. TetRmkate2 induction histograms are gamma distributed.

    Fig. S5. Average responses and noise levels in arabinose-inducible constructions.

    Fig. S6. Output distributions and MI for equiprobable, arabinose-induced inputs.

    Fig. S7. Influence of feedback cooperativity on MI.

    Table S1. Bacterial strains and bacteriophages used in this work.

    Table S2. Oligonucleotides used in this work.

    Table S3. Bacterial plasmids used in this work.

    Table S4. List of reagents used in this work.

    Table S5. Image data depository.

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Results
    • Supplementary Calculations
    • Fig. S1. Genetic constructions used in this work and signal calibration.
    • Fig. S2 Validation of TetRmkate2 translational fusion.
    • Fig. S3. Induction of TetRmkate2 from pBAD.
    • Fig. S4. TetRmkate2 induction histograms are gamma distributed.
    • Fig. S5. Average responses and noise levels in arabinose-inducible constructions.
    • Fig. S6. Output distributions and MI for equiprobable, arabinose-induced inputs.
    • Fig. S7. Influence of feedback cooperativity on MI.
    • Table S1. Bacterial strains and bacteriophages used in this work.
    • Table S2. Oligonucleotides used in this work.
    • Table S3. Bacterial plasmids used in this work.
    • Table S4. List of reagents used in this work.
    • Table S5. Image data depository.

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