A noisy linear map underlies oscillations in cell size and gene expression in bacteria (original) (raw)

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The wrong equation was mistakenly inserted in the online version of the Methods, this has now been corrected.

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Acknowledgements

We thank S. Jun for providing the original mother machine and P. Cluzel for providing their data set on E. coli and B. subtilis growth. We also thank the Light Microscopy Core Facility at Duke University for their help in conducting microscopy experiments. This work was partially supported by a National Science Foundation Career Award (L.Y.), the National Institutes of Health (NIH) (L.Y., R01GM098642, R01GM110494), a DuPont Young Professorship (L.Y.), a David and Lucile Packard Fellowship (L.Y.), a DARPA Biochronicity Grant (DARPA-BAA-11-66, N.E.B.), a NIH Director's New Innovator Award (DP2 OD008654-01, N.E.B.), and a Burroughs Wellcome Fund CASI Award (BWF 1005769.01, N.E.B.).

Author information

Author notes

  1. Yu Tanouchi, Anand Pai and Heungwon Park: These authors contributed equally to this work.

Authors and Affiliations

  1. Department of Biomedical Engineering, Duke University, Durham, 27708, North Carolina, USA
    Yu Tanouchi, Anand Pai, Shuqiang Huang & Lingchong You
  2. Department of Physics, Duke University, Durham, 27708, North Carolina, USA
    Heungwon Park & Nicolas E. Buchler
  3. Department of Biology, Duke University, Durham, 27708, North Carolina, USA
    Heungwon Park & Nicolas E. Buchler
  4. Computational Biology and Bioinformatics, Duke University, Durham, 27708, North Carolina, USA
    Rumen Stamatov
  5. Center for Genomic and Computational Biology, Duke University, Durham, 27708, North Carolina, USA
    Nicolas E. Buchler & Lingchong You

Authors

  1. Yu Tanouchi
  2. Anand Pai
  3. Heungwon Park
  4. Shuqiang Huang
  5. Rumen Stamatov
  6. Nicolas E. Buchler
  7. Lingchong You

Contributions

Y.T. conceived the research, designed and performed both modelling and experimental analyses, interpreted the results, and wrote the manuscript. A.P. conceived the research, designed and performed experimental analyses, interpreted the results, and wrote the manuscript. H.P. designed and performed experimental analyses and interpreted the results. S.H. fabricated the microfluidic device and performed experiments. R.S. developed the software for image analysis. N.E.B. assisted in data interpretation and manuscript revisions. L.Y. conceived the research, assisted in research design and data interpretation, and wrote the manuscript. All authors approved the manuscript.

Corresponding author

Correspondence toLingchong You.

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Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Analysis of cell growth parameters.

a–c, Division ratio (a), growth rate (b) and doubling time (c) are plotted against initial cell length (n = 11,168). Black and red lines show binned average and trend line, respectively. In a and b, the trend lines are the linear regression line, whereas equation (4) was used in c. The error bars indicate standard deviation of each bin.

Extended Data Figure 2 A noisy linear map in E. coli cell size control across different growth temperatures and strains.

The same analysis as in Fig. 1e (_L_I versus _L_F) was performed for MC4100 grown at 27 °C (a, n = 3,772), MC4100 grown at 25 °C (b, n = 4,539), MG1655 grown at 37 °C (c, n = 10,964), and B/r strain grown at 37 °C (d, n = 5,541). The data sets for MG1655 and B/r strain were from a previous study3. Black and red lines show binned average and linear regression line, respectively. In a–d, a = 1.02, 1.08, 1.03 and 1.14, respectively. The error bars indicate standard deviation of each bin.

Extended Data Figure 3 Frequency analysis of noisy linear map.

a, Time-frequency analysis of the noisy linear map model for _L_I. The top panel shows a spectrogram of 700-generation simulation constructed using 70-generation segments with 50% overlap. The bottom panel shows the temporal dynamics of L_I. The same parameters as in Fig. 2a were used. b, The power spectrum of noisy linear map (X(f)). Equation (3) is plotted for different a (0 ≤ a ≤ 1.8 with 0.2 interval). X(f) = 1/(2_πf)2 for a = 2 is the straight line in this log–log plot. Note that the maximum value of f is 0.5 as the time resolution is 1 generation. c, Dependence of oscillation frequencies on a simulated using the rescaled linear map (equation (2)). The noisy linear map model was simulated (Fig. 3a–c) and the distributions of oscillation frequencies are shown for four different values of a (from top to bottom, n = 24, 76, 117 and 79, respectively).

Extended Data Figure 4 Comparison of _L_I oscillation characteristics between all lineages (blue) and lineages without aberrant cell cycles (red).

a–g, Probability of oscillation (a), average oscillation frequency (b), and distributions of oscillation frequencies (c–g) are shown. In a and b, filled symbols represent experimental data (data shown in red are the same as Fig. 3a, b): circles are MC4100 grown at three different temperatures; squares and triangles are MG1655 and B/r strain, respectively. The unfilled circles were generated from simulations using the rescaled linear map (equation (2), the same plot as Fig. 3a, b). In a, the data shown in blue include 160 (37 °C), 54 (27 °C) and 65 (25 °C) lineages for MC4100, 158 lineages for MG1655, and 80 lineages for B/r strain. The data shown in red include 143 (37 °C), 48 (27 °C), and 57 (25 °C) lineages for MC4100, 97 lineages for MG1655, and 60 lineages for B/r strain. In b–g, only lineages that were considered oscillatory were used. For the data set in blue, n = 58 (37 °C), 21 (27 °C), and 39 (25 °C) for MC4100, 46 for MG1655, and 26 for B/r strain. For the data set in red, n = 51 (37 °C), 18 (27 °C) and 36 (25 °C) for MC4100, 34 for MG1655, and 23 for B/r strain.

Extended Data Figure 5 A noisy linear map in total per-cell YFP.

Total YFP before division is plotted against total YFP at birth (n = 11,168), revealing a linear map with a = 1.05. Black and red lines show binned average and the linear regression line, respectively. The error bars indicate standard deviation of each bin.

Extended Data Figure 6 Oscillation in [Y] observed in MC4100 at 27 °C.

a, Oscillation scores of YFP concentration are shown in an ascending order. The dashed line indicates a threshold for oscillation. b, For four different oscillation frequencies, ACFs with the highest oscillation scores are shown. c, The distribution of oscillation frequencies (n = 47).

Extended Data Figure 10 A noisy linear map in cell size control in the data sets from ref. 12 and our experimental data of S. pombe

The same analysis as in Fig. 1e (_L_I versus _L_F) was performed. These data sets were obtained using a microfluidic device different from the mother machine. a–c, E. coli growth under three different media as indicated (n = 8,795, 4,637 and 684, respectively). d, e, Growth of B. subtilis (n = 1,592) (d) and of S. pombe (n = 85) (e). Black and red lines show binned average and the linear regression line, respectively. In a–e, a = 1.20, 0.864, 0.684, 1.41 and 0.645, respectively. Cell length (µm) (a–d) and cell area (µm2) (e) are shown. The error bars indicate standard deviation of each bin.

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Tanouchi, Y., Pai, A., Park, H. et al. A noisy linear map underlies oscillations in cell size and gene expression in bacteria.Nature 523, 357–360 (2015). https://doi.org/10.1038/nature14562

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