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Multistability in the lactose utilization network of Escherichia coli

Author

Listed:
  • Ertugrul M. Ozbudak

    (Massachusetts Institute of Technology)

  • Mukund Thattai

    (Massachusetts Institute of Technology)

  • Han N. Lim

    (Massachusetts Institute of Technology)

  • Boris I. Shraiman

    (Rutgers University)

  • Alexander van Oudenaarden

    (Massachusetts Institute of Technology)

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.

Suggested Citation

  • Ertugrul M. Ozbudak & Mukund Thattai & Han N. Lim & Boris I. Shraiman & Alexander van Oudenaarden, 2004. "Multistability in the lactose utilization network of Escherichia coli," Nature, Nature, vol. 427(6976), pages 737-740, February.
    • Handle: RePEc:nat:nature:v:427:y:2004:i:6976:d:10.1038_nature02298
    DOI: 10.1038/nature02298
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    Cited by:

    1. Marco Montalva-Medel & Thomas Ledger & Gonzalo A. Ruz & Eric Goles, 2021. "Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements," Mathematics, MDPI, vol. 9(6), pages 1-19, March.
    2. Xiu-Deng Zheng & Xiao-Qian Yang & Yi Tao, 2011. "Bistability, Probability Transition Rate and First-Passage Time in an Autoactivating Positive-Feedback Loop," PLOS ONE, Public Library of Science, vol. 6(3), pages 1-10, March.
    3. Tobias May & Lee Eccleston & Sabrina Herrmann & Hansjörg Hauser & Jorge Goncalves & Dagmar Wirth, 2008. "Bimodal and Hysteretic Expression in Mammalian Cells from a Synthetic Gene Circuit," PLOS ONE, Public Library of Science, vol. 3(6), pages 1-7, June.
    4. Xu, Yong & Zhu, Ya-nan & Shen, Jianwei & Su, Jianbin, 2014. "Switch dynamics for stochastic model of genetic toggle switch," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 461-466.
    5. Chen, Aimin & Tian, Tianhai & Chen, Yiren & Zhou, Tianshou, 2022. "Stochastic analysis of a complex gene-expression model," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    6. Ermelinda Porpiglia & Daniel Hidalgo & Miroslav Koulnis & Abraham R Tzafriri & Merav Socolovsky, 2012. "Stat5 Signaling Specifies Basal versus Stress Erythropoietic Responses through Distinct Binary and Graded Dynamic Modalities," PLOS Biology, Public Library of Science, vol. 10(8), pages 1-19, August.
    7. Avraham E Mayo & Yaakov Setty & Seagull Shavit & Alon Zaslaver & Uri Alon, 2006. "Plasticity of the cis-Regulatory Input Function of a Gene," PLOS Biology, Public Library of Science, vol. 4(4), pages 1-1, March.
    8. Zhou, Peipei & Cai, Shuiming & Liu, Zengrong & Chen, Luonan & Wang, Ruiqi, 2013. "Coupling switches and oscillators as a means to shape cellular signals in biomolecular systems," Chaos, Solitons & Fractals, Elsevier, vol. 50(C), pages 115-126.
    9. Carl Song & Hilary Phenix & Vida Abedi & Matthew Scott & Brian P Ingalls & Mads Kærn & Theodore J Perkins, 2010. "Estimating the Stochastic Bifurcation Structure of Cellular Networks," PLOS Computational Biology, Public Library of Science, vol. 6(3), pages 1-11, March.
    10. Navneet Rai & Rajat Anand & Krishna Ramkumar & Varun Sreenivasan & Sugat Dabholkar & K V Venkatesh & Mukund Thattai, 2012. "Prediction by Promoter Logic in Bacterial Quorum Sensing," PLOS Computational Biology, Public Library of Science, vol. 8(1), pages 1-14, January.
    11. Lai, Qiang & Norouzi, Benyamin & Liu, Feng, 2018. "Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 230-245.
    12. Tomas Tokar & Jozef Ulicny, 2013. "The Mathematical Model of the Bcl-2 Family Mediated MOMP Regulation Can Perform a Non-Trivial Pattern Recognition," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-8, December.
    13. Paul Miller & Anatol M Zhabotinsky & John E Lisman & Xiao-Jing Wang, 2005. "The Stability of a Stochastic CaMKII Switch: Dependence on the Number of Enzyme Molecules and Protein Turnover," PLOS Biology, Public Library of Science, vol. 3(4), pages 1-1, March.
    14. Matthieu Wyart & David Botstein & Ned S Wingreen, 2010. "Evaluating Gene Expression Dynamics Using Pairwise RNA FISH Data," PLOS Computational Biology, Public Library of Science, vol. 6(11), pages 1-14, November.
    15. Song, Yi & Xu, Wei & Wei, Wei & Niu, Lizhi, 2023. "Dynamical transition of phenotypic states in breast cancer system with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 627(C).
    16. Hao Ge & Pingping Wu & Hong Qian & Xiaoliang Sunney Xie, 2018. "Relatively slow stochastic gene-state switching in the presence of positive feedback significantly broadens the region of bimodality through stabilizing the uninduced phenotypic state," PLOS Computational Biology, Public Library of Science, vol. 14(3), pages 1-24, March.
    17. Najme Khorasani & Mehdi Sadeghi & Abbas Nowzari-Dalini, 2020. "A computational model of stem cell molecular mechanism to maintain tissue homeostasis," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-25, July.
    18. Jan Hasenauer & Christine Hasenauer & Tim Hucho & Fabian J Theis, 2014. "ODE Constrained Mixture Modelling: A Method for Unraveling Subpopulation Structures and Dynamics," PLOS Computational Biology, Public Library of Science, vol. 10(7), pages 1-17, July.
    19. Marc Weber & Javier Buceta, 2013. "Stochastic Stabilization of Phenotypic States: The Genetic Bistable Switch as a Case Study," PLOS ONE, Public Library of Science, vol. 8(9), pages 1-8, September.
    20. Li, Chunbiao & Sprott, Julien Clinton & Kapitaniak, Tomasz & Lu, Tianai, 2018. "Infinite lattice of hyperchaotic strange attractors," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 76-82.
    21. Cheng Lv & Xiaoguang Li & Fangting Li & Tiejun Li, 2014. "Constructing the Energy Landscape for Genetic Switching System Driven by Intrinsic Noise," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-10, February.
    22. Kazunari Mouri & Jose C Nacher & Tatsuya Akutsu, 2009. "A Mathematical Model for the Detection Mechanism of DNA Double-Strand Breaks Depending on Autophosphorylation of ATM," PLOS ONE, Public Library of Science, vol. 4(4), pages 1-14, April.
    23. Benjamin B Kaufmann & Qiong Yang & Jerome T Mettetal & Alexander van Oudenaarden, 2007. "Heritable Stochastic Switching Revealed by Single-Cell Genealogy," PLOS Biology, Public Library of Science, vol. 5(9), pages 1-8, September.
    24. Georg Fritz & Judith A Megerle & Sonja A Westermayer & Delia Brick & Ralf Heermann & Kirsten Jung & Joachim O Rädler & Ulrich Gerland, 2014. "Single Cell Kinetics of Phenotypic Switching in the Arabinose Utilization System of E. coli," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-12, February.
    25. Shintaro Nagata & Macoto Kikuchi, 2020. "Emergence of cooperative bistability and robustness of gene regulatory networks," PLOS Computational Biology, Public Library of Science, vol. 16(6), pages 1-24, June.

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