The Lac Operon
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The lac operon – 1/3 – – 2/3 – – 3/3 – letters to nature 19. Arnheim, N., Treco, D., Taylor, B. & Eicher, E. M. Distribution of ribosomal gene length variants for global analysis. The lac operon comprises three genes required among mouse chromosomes. Proc. Natl Acad. Sci. USA 79, 4677–4680 (1982). 20. Birky, C. W. Heterozygosity, heteromorphy, and phylogenetic trees in asexual eukaryotes. Genetics for the uptake and metabolism of lactose and related sugars (Fig. 1): 144, 427–437 (1996). lacZ, lacY and lacA. lacZ codes for b-galactosidase, an enzyme 21. Hosny, M., Gianinazzi-Pearson, V. & Dulieu, H. Nuclear DNA content of 11 fungal species in responsible for the conversion of lactose into allolactose and Glomales. Genome 41, 422–428 (1998). subsequent metabolic intermediates. lacY codes for the lactose 22. Otto, S. P. & Whitton, J. Polyploid incidence and evolution. Annu. Rev. Genet. 34, 401–437 (2000). 23. Mogie, M. & Ford, H. Sexual and asexual Taraxacum species. Biol. J. Linn. Soc. 35, 155–168 (1988). permease (LacY), which facilitates the uptake of lactose and similar 24. Kondrashov, A. S. The asexual ploidy cycle and the origin of sex. Nature 370, 213–216 (1994). molecules, including thio-methylgalactoside (TMG), a non- 25. Swofford, D. L. PAUP: phylogenetic analysis using parsimony (and other methods). Ver. 4 (Sinauer, metabolizable lactose analogue. lacA codes for an acetyltransferase, Sunderland, MA, 1998). which is involved in sugar metabolism. The operon has two transcriptional regulators: a repressor (LacI) and an activator (the Supplementary Information accompanies the paper on www.nature.com/nature. cyclic AMP receptor protein, CRP). Inducers, among them allolac- Acknowledgements We thank W. Pawlowski for help with the spore nuclei count; P. Bethke for tose and TMG, bind to and inhibit repression by LacI, whereas advice on nuclei microdissection; D. Baker, T. Galagher, B. King, T. Lee and T. Szaro for technical cAMP binds to and triggers activation by CRP.The concentration of assistance; J. A. Fortin for G. intraradices; D. Douds for the DC1 isolate of Ri T-DNA-transformed cAMP drops in response to the uptake of various carbon sources, carrot roots developed by G. Be´card; and D. J. Read, T. Bruns, A. Burt and the members of the 18 Taylor laboratory for comments on the manuscript. This work was supported by the Torrey Mesa including glucose and lactose ; glucose uptake also interferes with 18 Research Institute-Syngenta Biotechnology and the National Research Initiative Competitive LacY activity, leading to exclusion of the inducer . Together these Grants Program (NRICGP) of the US Department of Agriculture. effects mediate catabolite repression—theabilityofglucoseto inhibit lac expression. Crucially, cAMP levels are not affected by Competing interests statement The authors declare that they have no competing financial interests. TMG uptake. Therefore, the extracellular concentrations of TMG and glucose can be used to independently regulate the activities of LacI Correspondence and requests for materials should be addressed to T.E.P. and CRP, the two cis-regulatory inputs of the lac operon19. However, ([email protected]). The sequences are deposited in GenBank under accession the response of the operon must be considered within the broader numbers AY330523–AY330580 (G. etunicatum PLS), AY330582–AY330597 (G. etunicatum ITS1–5.8S–ITS2 rDNA) and AY394030–AY394033 (G. intraradices ITS1 rDNA). context of the network. The uptake of TMG induces the synthesis of LacY, which in turn promotes further TMG uptake; the resulting positive feedback loop creates the potential for bistability20,21. To probe the network’s bistable response, we incorporated a single copy of the green fluorescent protein gene (gfp) under the .............................................................. control of the lac promoter into the chromosome of E. coli MG1655 (Fig. 1). We placed this reporter in the chromosome rather than on a Multistability in the lactose multicopy plasmid to minimize the titration of LacI molecules by utilization network of extraneous LacI-binding sites. The cells also contained a plasmid encoding a red fluorescent reporter (HcRed) under the control Escherichia coli of the galactitol (gat) promoter. This promoter includes a CRP- binding site, as well as a binding site for the galactitol repressor, Ertugrul M. Ozbudak1*, Mukund Thattai1*, Han N. Lim1, Boris I. Shraiman2 & Alexander van Oudenaarden1 1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 2Department of Physics and the BioMAPS Institute, Rutgers University, Piscataway, New Jersey 08854, USA * These authors contributed equally to this work ............................................................................................................................................................................. 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 natural1–6 and synthetic7–9 systems has been attributed to positive feedback loops in their regulatory networks10. How- ever, 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- Figure 1 The lactose utilization network. Red lines represent regulatory interactions, with type system can be converted to an ultrasensitive graded pointed ends for activation and blunt ends for inhibition; black arrows represent protein response14,15. The phase diagram thus serves as a sensitive creation through transcription and translation, and dotted arrows represent uptake across probe of molecular interactions and as a powerful tool for the cell membrane. In our experiments we vary two external inputs, the extracellular rational network design. concentrations of glucose and TMG, and measure the resulting levels of two fluorescent The bistability of the lactose utilization network has been under reporter proteins: GFP, expressed at the lac promoter, and HcRed, expressed at the gat investigation since 1957 (refs 16, 17). The basic components of this promoter. LacY catalyses the uptake of TMG, which induces further expression of LacY, network have been well characterized13, making it an ideal candidate resulting in a positive feedback loop. 737 NATURE | VOL 427 | 19 FEBRUARY 2004 | www.nature.com/nature © 2004 Nature Publishing Group letters to nature GatR. However, GatR is absent in E. coli MG1655 (ref. 22). There- The green fluorescence levels at each glucose and TMG concen- fore, transcription at the gat promoter, measured by red fluores- tration can be written as a function of three parameters: a, b and r. cence, is a direct measure of CRP-cAMP levels. In our experiments, The maximal activity, a, is the lac expression level that would be we measure the response of single cells, initially in a given state of lac obtained if every repressor molecule were inactive. The repression expression, to exposure to various combinations of glucose and factor, r, gives the ratio of maximal to basal activities, the latter TMG levels (Fig. 2a). It is crucial to use cells with well-defined initial being the expression level that would be obtained if every repressor states, either uninduced or fully induced, because the response of a molecule were active. The transport rate, b, gives the TMG uptake bistable system is expected to depend on its history. rate per LacY molecule. We find that a is directly proportional to the We find, in the absence of glucose, that the lac operon is red fluorescence level (Fig. 3b), demonstrating that the lac and gat uninduced at low TMG concentrations (,3 mM) and fully induced promoters respond identically to CRP-cAMP. By contrast, a is at high TMG concentrations (.30 mM) regardless of the cell’s essentially independent of TMG levels, suggesting that LacI and history. Between these switching thresholds, however, system CRP bind independently to the lac operator site. We find the response is hysteretic (history dependent): TMG levels must exceed repression factor r to be 170 ^ 30 regardless of the glucose and 30 mM to turn on initially uninduced cells but must drop below TMG levels (Fig. 3c). This confirms a strong prediction of our 3 mM to turn off initially induced cells (Fig. 2b). As we approach the model—that r should be a function of the LacI concentration alone. boundaries of this bistable region, stochastic mechanisms cause Assuming an effective LacI concentration in the nanomolar range13, growing numbers of cells to switch from their initial states, resulting this value of r implies a dissociation constant between LacI and its in a bimodal distribution of green fluorescence levels, with induced major DNA-binding site of about 10210 to 10211 M, which is cells having over one hundred times the fluorescence levels