Letter | Published:

A noisy linear map underlies oscillations in cell size and gene expression in bacteria

Nature volume 523, pages 357360 (16 July 2015) | Download Citation

This article has been updated


During bacterial growth, a cell approximately doubles in size before division, after which it splits into two daughter cells. This process is subjected to the inherent perturbations of cellular noise1,2 and thus requires regulation for cell-size homeostasis. The mechanisms underlying the control and dynamics of cell size remain poorly understood owing to the difficulty in sizing individual bacteria over long periods of time in a high-throughput manner. Here we measure and analyse long-term, single-cell growth and division across different Escherichia coli strains and growth conditions3. We show that a subset of cells in a population exhibit transient oscillations in cell size with periods that stretch across several (more than ten) generations. Our analysis reveals that a simple law governing cell-size control—a noisy linear map—explains the origins of these cell-size oscillations across all strains. This noisy linear map implements a negative feedback on cell-size control: a cell with a larger initial size tends to divide earlier, whereas one with a smaller initial size tends to divide later. Combining simulations of cell growth and division with experimental data, we demonstrate that this noisy linear map generates transient oscillations, not just in cell size, but also in constitutive gene expression. Our work provides new insights into the dynamics of bacterial cell-size regulation with implications for the physiological processes involved.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Change history

  • 05 June 2015

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


  1. 1.

    & Nature, nurture, or chance: stochastic gene expression and its consequences. Cell 135, 216–226 (2008).

  2. 2.

    & Random partitioning of molecules at cell division. Proc. Natl Acad. Sci. USA 108, 15004–15009 (2011).

  3. 3.

    et al. Robust growth of Escherichia coli. Curr. Biol. 20, 1099–1103 (2010).

  4. 4.

    , & Concerted control of Escherichia coli cell division. Proc. Natl Acad. Sci. USA 111, 3431–3435 (2014).

  5. 5.

    et al. Cell-size control and homeostasis in bacteria. Curr. Biol. 25, 385–391 (2015).

  6. 6.

    et al. A constant size extension drives bacterial cell size homeostasis. Cell 159, 1433–1446 (2014).

  7. 7.

    Introduction to Time Series Modeling 31–48 (Chapman and Hall/CRC, 2010).

  8. 8.

    & Coupling the initiation of chromosome replication to cell size in Escherichia coli. Curr. Opin. Microbiol. 6, 146–150 (2003).

  9. 9.

    , & Chromosome replication and segregation in bacteria. Annu. Rev. Genet. 46, 121–143 (2012).

  10. 10.

    , & FtsZ in bacterial cytokinesis: cytoskeleton and force generator all in one. Microbiol. Mol. Biol. Rev. 74, 504–528 (2010).

  11. 11.

    Advances in understanding E. coli cell fission. Curr. Opin. Microbiol. 13, 730–737 (2010).

  12. 12.

    , & The single-cell chemostat: an agarose-based, microfluidic device for high-throughput, single-cell studies of bacteria and bacterial communities. Lab Chip 12, 1487–1494 (2012).

  13. 13.

    & Long-term single cell analysis of S. pombe on a microfluidic microchemostat array. PLoS ONE 9, e93466 (2014).

  14. 14.

    Cell size regulation in bacteria. Phys. Rev. Lett. 112, 208102 (2014).

  15. 15.

    , & Functional roles of pulsing in genetic circuits. Science 342, 1193–1200 (2013).

  16. 16.

    , , , & Tunability and noise dependence in differentiation dynamics. Science 315, 1716–1719 (2007).

  17. 17.

    et al. Dynamic persistence of antibiotic-stressed mycobacteria. Science 339, 91–95 (2013).

  18. 18.

    , , , & Interdependence of cell growth and gene expression: origins and consequences. Science 330, 1099–1102 (2010).

  19. 19.

    et al. Coordination of bacterial proteome with metabolism by cyclic AMP signalling. Nature 500, 301–306 (2013).

  20. 20.

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

  21. 21.

    et al. Stochasticity of metabolism and growth at the single-cell level. Nature 514, 376–379 (2014).

  22. 22.

    , & Emergent bistability by a growth-modulating positive feedback circuit. Nature Chem. Biol. 5, 842–848 (2009).

  23. 23.

    , , , & Oscillations by minimal bacterial suicide circuits reveal hidden facets of host-circuit physiology. PLoS ONE 5, e11909 (2010).

  24. 24.

    et al. Queueing up for enzymatic processing: correlated signaling through coupled degradation. Mol. Syst. Biol. 7, 561 (2011).

  25. 25.

    & A synthetic oscillatory network of transcriptional regulators. Nature 403, 335–338 (2000).

  26. 26.

    et al. A fast, robust and tunable synthetic gene oscillator. Nature 456, 516–519 (2008).

  27. 27.

    , , , & Entrainment of a population of synthetic genetic oscillators. Science 333, 1315–1319 (2011).

  28. 28.

    , , & An equivalence principle for the incorporation of favorable mutations in asexual populations. Science 311, 1615–1617 (2006).

  29. 29.

    , , , & Image analysis algorithms for cell contour recognition in budding yeast. Opt. Express 16, 12943–12957 (2008).

  30. 30.

    et al. Using buoyant mass to measure the growth of single cells. Nature Methods 7, 387–390 (2010).

Download references


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

    • Yu Tanouchi
    • , Anand Pai
    •  & Heungwon Park

    These authors contributed equally to this work.


  1. Department of Biomedical Engineering, Duke University, Durham, North Carolina 27708, USA

    • Yu Tanouchi
    • , Anand Pai
    • , Shuqiang Huang
    •  & Lingchong You
  2. Department of Physics, Duke University, Durham, North Carolina 27708, USA

    • Heungwon Park
    •  & Nicolas E. Buchler
  3. Department of Biology, Duke University, Durham, North Carolina 27708, USA

    • Heungwon Park
    •  & Nicolas E. Buchler
  4. Computational Biology and Bioinformatics, Duke University, Durham, North Carolina 27708, USA

    • Rumen Stamatov
  5. Center for Genomic and Computational Biology, Duke University, Durham, North Carolina 27708, USA

    • Nicolas E. Buchler
    •  & Lingchong You


  1. Search for Yu Tanouchi in:

  2. Search for Anand Pai in:

  3. Search for Heungwon Park in:

  4. Search for Shuqiang Huang in:

  5. Search for Rumen Stamatov in:

  6. Search for Nicolas E. Buchler in:

  7. Search for Lingchong You in:


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.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Lingchong You.

Extended data

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    This file contains a Supplementary Discussion and Supplementary References.

About this article

Publication history






Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.