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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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.
The authors declare that they have no competing financial interests.
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