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.

  • Letter
  • Published:

Multistability in the lactose utilization network of Escherichia coli

Abstract

Multistability, the capacity to achieve multiple internal states in response to a single set of external inputs, is the defining characteristic of a switch. Biological switches are essential for the determination of cell fate in multicellular organisms1, the regulation of cell-cycle oscillations during mitosis2,3 and the maintenance of epigenetic traits in microbes4. The multistability of several natural1,2,3,4,5,6 and synthetic7,8,9 systems has been attributed to positive feedback loops in their regulatory networks10. However, feedback alone does not guarantee multistability. The phase diagram of a multistable system, a concise description of internal states as key parameters are varied, reveals the conditions required to produce a functional switch11,12. Here we present the phase diagram of the bistable lactose utilization network of Escherichia coli13. We use this phase diagram, coupled with a mathematical model of the network, to quantitatively investigate processes such as sugar uptake and transcriptional regulation in vivo. We then show how the hysteretic response of the wild-type system can be converted to an ultrasensitive graded response14,15. The phase diagram thus serves as a sensitive probe of molecular interactions and as a powerful tool for rational network design.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: The lactose utilization network.
Figure 2: Hysteresis and bistability in single cells.
Figure 3: Single-cell in vivo measurement of network parameters.
Figure 4: Hysteretic and graded responses.

Similar content being viewed by others

References

  1. Ferrell, J. E. Jr & Machleder, E. M. The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes. Science 280, 895–898 (1998)

    Article  ADS  CAS  Google Scholar 

  2. Pomerening, J. R., Sontag, E. D. & Ferrell, J. E. Jr Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2. Nature Cell Biol. 5, 346–351 (2003)

    Article  CAS  Google Scholar 

  3. Sha, W. et al. Hysteresis drives cell-cycle transitions in Xenopus laevis egg extracts. Proc. Natl Acad. Sci. USA 100, 975–980 (2003)

    Article  ADS  CAS  Google Scholar 

  4. Hernday, A., Braaten, B. A. & Low, D. The mechanism by which DNA adenine methylase and PapI activate the pap epigenetic switch. Mol. Cell 12, 947–957 (2003)

    Article  CAS  Google Scholar 

  5. Blauwkamp, T. A. & Ninfa, A. J. Physiological role of the GlnK signal transduction protein of Escherichia coli: survival of nitrogen starvation. Mol. Microbiol. 46, 203–214 (2002)

    Article  CAS  Google Scholar 

  6. Siegele, D. A. & Hu, J. C. Gene expression from plasmids containing the araBAD promoter at subsaturating inducer concentrations represents mixed populations. Proc. Natl Acad. Sci. USA 94, 8168–8172 (1997)

    Article  ADS  CAS  Google Scholar 

  7. Gardner, T. S., Cantor, C. R. & Collins, J. J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000)

    Article  ADS  CAS  Google Scholar 

  8. Isaacs, F. J., Hasty, J., Cantor, C. R. & Collins, J. J. Prediction and measurement of an augoregulatory genetic module. Proc. Natl Acad. Sci. USA 100, 7714–7719 (2003)

    Article  ADS  CAS  Google Scholar 

  9. Becskei, A., Seraphin, B. & Serrano, L. Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion. EMBO J. 20, 2528–2535 (2001)

    Article  CAS  Google Scholar 

  10. Ferrell, J. E. Jr Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability. Curr. Opin. Cell Biol. 14, 140–148 (2002)

    Article  CAS  Google Scholar 

  11. Ma, S.-K. Modern Theory of Critical Phenomena (Perseus Books, Reading, Massachusetts, 1976)

    Google Scholar 

  12. Strogatz, S. H. Nonlinear Dynamics and Chaos (Perseus Books, Reading, Massachusetts, 1994)

    Google Scholar 

  13. Müller-Hill, B. The Lac Operon: A Short History of a Genetic Paradigm (Walter de Gruyter, Berlin, 1996)

    Book  Google Scholar 

  14. Louis, M. & Becskei, A. Binary and graded responses in gene networks. Science STKE [online], 30 July 2002 (doi:10.1126/stke.2002.143.pe33)

  15. Biggar, S. R. & Crabtree, G. R. Cell signaling can direct either binary or graded transcriptional responses. EMBO J. 20, 3167–3176 (2001)

    Article  CAS  Google Scholar 

  16. Novick, A. & Weiner, M. Enzyme induction as an all-or-none phenomenon. Proc. Natl Acad. Sci. USA. 43, 553–566 (1957)

    Article  ADS  CAS  Google Scholar 

  17. Cohn, M. & Horibata, K. Inhibition by glucose of the induced synthesis of the β-galactoside-enzyme system of Escherichia coli: Analysis of maintenance. J. Bacteriol. 78, 601–612 (1959)

    CAS  PubMed  PubMed Central  Google Scholar 

  18. Stulke, J. & Hillen, W. Carbon catabolite repression in bacteria. Curr. Opin. Microbiol. 2, 195–201 (1999)

    Article  CAS  Google Scholar 

  19. Setty, Y., Mayo, A. E., Surette, M. G. & Alon, U. Detailed map of a cis-regulatory input function. Proc. Natl Acad. Sci. USA 100, 7702–7707 (2003)

    Article  ADS  CAS  Google Scholar 

  20. Griffith, J. S. Mathematics of cellular control processes II: Positive feedback to one gene. J. Theor. Biol. 20, 209–216 (1968)

    Article  CAS  Google Scholar 

  21. Tyson, J. J. & Othmer, H. G. The dynamics of feedback control circuits in biochemical pathways. Prog. Theor. Biol. 5, 1–62 (1978)

    CAS  MATH  Google Scholar 

  22. Nobelmann, B. & Lengeler, J. W. Molecular analysis of the gat genes from Escherichia coli and of their roles in galactitiol transport and metabolism. J. Bacteriol. 178, 6790–6795 (1996)

    Article  CAS  Google Scholar 

  23. Oehler, S., Eismann, E. R., Kramer, H. & Müller-Hill, B. The three operators of the lac operon cooperate in repression. EMBO J. 9, 973–979 (1990)

    Article  CAS  Google Scholar 

  24. Chung, J. D. & Stephanopoulos, G. On physiological multiplicity and population heterogeneity of biological systems. Chem. Eng. Sci. 51, 1509–1521 (1996)

    Article  CAS  Google Scholar 

  25. Kepler, T. B. & Elston, T. C. Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. Biophys. J. 81, 3116–3136 (2001)

    Article  ADS  CAS  Google Scholar 

  26. Thattai, M. & Shraiman, B. I. Metabolic switching in the sugar phosphotransferase system of Escherichia coli. Biophys. J. 85, 744–754 (2003)

    Article  ADS  CAS  Google Scholar 

  27. Atkinson, M. R., Savageau, M. A., Myers, J. T. & Ninfa, A. J. Development of genetic toggle circuitry exhibiting toggle switch or oscillatory behavior in Escherichia coli. Cell 113, 597–607 (2003)

    Article  CAS  Google Scholar 

  28. Smolen, P., Baxter, D. A. & Byrne, J. H. Frequency selectivity, multistability, and oscillations emerge from models of genetic regulatory systems. Am. J. Physiol. 43, C531 (1998)

    Article  Google Scholar 

  29. Boyd, D., Weiss, D. S., Chen, J. C. & Beckwith, J. Towards single-copy gene expression systems making gene cloning physiologically relevant: lambda InCh, a simple Escherichia coli plasmid-chromosome shuttle system. J. Bacteriol. 182, 842–847 (2000)

    Article  CAS  Google Scholar 

  30. Lutz, R. & Bujard, H. Independent and tight regulation of transcriptional units in Escherichia coli via the LacR/O, the TetR/O and AraC/I1-I2 regulatory elements. Nucleic Acids Res. 25, 1203–1210 (1997)

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank G. Jacobson and H. Kornberg, J. Paulsson, M. Savageau and A. Sengupta for discussions and suggestions; H. Bujard and R. Lutz for supplying the pZ vector system; and D. Boyd for help with the λ-InCh technique. We thank D. Raut for his assistance with the initial lactose measurements and the construction of plasmids and strains. We also thank A. Becskei and J. Pedraza for critically reviewing the manuscript. This work was supported by NIH and DARPA grants, and an NSF-CAREER grant.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alexander van Oudenaarden.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Supplementary information

Supplementary Information

Mathematical background and other supplementary information. (PDF 309 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ozbudak, E., Thattai, M., Lim, H. et al. Multistability in the lactose utilization network of Escherichia coli. Nature 427, 737–740 (2004). https://doi.org/10.1038/nature02298

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature02298

This article is cited by

Comments

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.

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