PMC3871705_01
Diagram of simulated genetic circuits.. A, inducible GFP. A stable GFP is under the control of the arabinose-inducible  promoter; B, acid stress response. An acidic metabolic product, P, positively regulates the expression of an acid stress gene; C, nitrite reductase induction by low oxygen. Oxygen represses transcription of nirS; D, quorum sensing circuit. A homoserine lactone synthase, lasI, produces a quorum sensing signal molecule or autoinducier, AI. AI positively regulates the production of its own biosynthetic enzyme. This simple feedback loop gives the essential autoinduction property. AI also positively regulates the expression of a second gene, rsaL, which is itself a negative regulator of many of the quorum sensing controlled genes. Like the nirS circuit, rsaL is expressed under conditions of low oxygen and repressed under conditions of high oxygen.
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Denitrification is energetically less favorable than respiration of oxygen, so denitrification genes are typically repressed in the presence of oxygen (Figure 1B). The intervals of applicability for Eqns. (9) and (10) and location of boundaries reflected in the boundary conditions correspond to the following interpretation of the experimental results shown in Figure 1 of. The function  describes an exponential repression of nirS gene expression by oxygen (see Figure S1). Lactate is an acidic waste product that will be assumed to induce the expression of the gene (Figure 1C). The form of  was assumed to allow for full expression of the gene above a certain product concentration (500 mg/L in this case) with only weak expression at very low product concentrations (Figure S1). Thus this circuit, diagrammed in Figure 1D, involves two substrates and two genes which are interlinked through two positive and two negative interactions. This functional form for , which is graphed in Figure S1, provides the positive feedback of increasing expression of lasI with increasing autoinducer concentration.