Multistability in the lactose utilization network of Escherichia coli


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.

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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.


  1. 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)

    ADS  CAS  Article  Google Scholar 

  2. 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)

    CAS  Article  Google Scholar 

  3. 3

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

    ADS  CAS  Article  Google Scholar 

  4. 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)

    CAS  Article  Google Scholar 

  5. 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)

    CAS  Article  Google Scholar 

  6. 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)

    ADS  CAS  Article  Google Scholar 

  7. 7

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

    ADS  CAS  Article  Google Scholar 

  8. 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)

    ADS  CAS  Article  Google Scholar 

  9. 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)

    CAS  Article  Google Scholar 

  10. 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)

    CAS  Article  Google Scholar 

  11. 11

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

    Google Scholar 

  12. 12

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

    Google Scholar 

  13. 13

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

    Google Scholar 

  14. 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. 15

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

    CAS  Article  Google Scholar 

  16. 16

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

    ADS  CAS  Article  Google Scholar 

  17. 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. 18

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

    CAS  Article  Google Scholar 

  19. 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)

    ADS  CAS  Article  Google Scholar 

  20. 20

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

    CAS  Article  Google Scholar 

  21. 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. 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)

    CAS  Article  Google Scholar 

  23. 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)

    CAS  Article  Google Scholar 

  24. 24

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

    CAS  Article  Google Scholar 

  25. 25

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

    ADS  CAS  Article  Google Scholar 

  26. 26

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

    ADS  CAS  Article  Google Scholar 

  27. 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)

    CAS  Article  Google Scholar 

  28. 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. 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)

    CAS  Article  Google Scholar 

  30. 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)

    CAS  Article  Google Scholar 

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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.

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Correspondence to Alexander van Oudenaarden.

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Ozbudak, E., Thattai, M., Lim, H. et al. Multistability in the lactose utilization network of Escherichia coli. Nature 427, 737–740 (2004).

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