NATURE | VOL 403 | 20 JANUARY 2000 | www.nature.com 339 letters to nature ................................................................. Construction of a genetic toggle switch in Escherichia coli Timothy S. Gardner*��, Charles R. Cantor* & James J. Collins*�� * Department of Biomedical Engineering, �� Center for BioDynamics and ��� Center for Advanced Biotechnology, Boston University, 44 Cummington Street, Boston, Massachusetts 02215, USA .............................................................................................................................................. It has been proposed1 that gene-regulatory circuits with virtually any desired property can be constructed from networks of simple regulatory elements. These properties, which include multistabil- ity and oscillations, have been found in specialized gene circuits such as the bacteriophage l switch2 and the Cyanobacteria circadian oscillator3. However, these behaviours have not been demonstrated in networks of non-specialized regulatory compo- nents. Here we present the construction of a genetic toggle switch���a synthetic, bistable gene-regulatory network���in Escherichia coli and provide a simple theory that predicts the conditions necessary for bistability. The toggle is constructed from any two repressible promoters arranged in a mutually inhibitory network. It is flipped between stable states using transient chemical or thermal induction and exhibits a nearly ideal switching threshold. As a practical device, the toggle switch forms a synthetic, addressable cellular memory unit and has implications for biotechnology, biocomputing and gene therapy. The design and construction of synthetic gene-regulatory net- works would be greatly facilitated by a theory with predictive capability. Previous work using a reconstituted enzyme system4 showed that nonlinear mathematics can predict qualitative beha- viours of biochemical reaction networks, including multistability and hysteresis. However, a practical theory of gene-regulatory networks has lagged behind that of enzyme regulatory networks. A variety of physical and mathematical approaches, including logical (discrete)5���10, piecewise linear11, nonlinear12���14, statistical��� mechanical15,16 and stochastic17���19 formulations of the underlying biochemical dynamics, have been used in the past. Owing to the difficulty of testing their predictions, these theories have not, in general, been verified experimentally. Here we have integrated theory and experiment by constructing and testing a synthetic, bistable gene circuit based on the predictions of a simple mathe- matical model. The toggle switch is composed of two repressors and two constitutive promoters (Fig. 1). Each promoter is inhibited by the repressor that is transcribed by the opposing promoter. We selected this design for the toggle switch because it requires the fewest genes and cis-regulatory elements to achieve robust bistable behaviour. By robust, we mean that the toggle exhibits bistability over a wide range of parameter values and that the two states are tolerant of the fluctuations inherent in gene expression (the toggle switch will not flip randomly between states). Although bistability is theoretically possible with a single, autocatalytic promoter, it would be less robust and more difficult to tune experimentally. In addition, the chosen toggle design does not require any specialized promoters, such as the PR/PRM promoter of bacteriophage l. Bistability is possible with any set of promoters and repressors as long as they fulfil the minimum set of conditions described in Box 1 and Fig. 2. The bistability of the toggle arises from the mutually inhibitory arrangement of the repressor genes. In the absence of inducers, two stable states are possible: one in which promoter 1 transcribes repressor 2, and one in which promoter 2 transcribes repressor 1. Switching is accomplished by transiently introducing an inducer of the currently active repressor. The inducer permits the opposing repressor to be maximally transcribed until it stably represses the originally active promoter. All toggle switches are implemented on E. coli plasmids confer- ring ampicillin resistance and containing the pBR322 ColE1 repli- cation origin. The toggle switch genes are arranged as a type IV plasmid, as shown in Fig. 3. Although all genes and promoters are Box 1 The toggle model The behaviour of the toggle switch and the conditions for bistability can be understood using the following dimensionless model for the network: du dt �� a1 1 �� vb 2 u ��1a�� dv dt �� a2 1 �� ug 2 v ��1b�� where u is the concentration of repressor 1, v is the concentration of repressor 2, a1 is the effective rate of synthesis of repressor 1, a2 is the effective rate of synthesis of repressor 2, b is the cooperativity of repression of promoter 2 and g is the cooperativity of repression of promoter 1. The above model is derived from a biochemical rate equation formulation of gene expression24���27. The final form of the toggle equations preserves the two most fundamental aspects of the network: cooperative repression of constitutively transcribed promoters (the first term in each equation), and degradation/dilution of the repressors (the second term in each equation). The parameters a1 and a2 are lumped parameters that describe the net effect of RNA polymerase binding, open-complex formation, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide elongation. The cooperativity described by b and g can arise from the multimerization of the repressor proteins and the cooperative binding of repressor multimers to multiple operator sites in the promoter. An additional modification to equation (1) is needed to describe induction of the repressors (Fig. 5). The geometric structure of equation (1), illustrated in Fig. 2a and b, reveals the origin of the bistability: the nullclines (du=dt �� 0 and dv=dt �� 0 in Fig. 2) intersect at three points, producing one unstable and two stable steady states. From Fig. 2a and b, three key features of the system become apparent. First, the nullclines intersect three times because of their sigmoidal shape, which arises for b, g . 1. Thus, the bistability of the system depends on the cooperative repression of transcription. Second, the rates of synthesis of the two repressors must be balanced. If the rates are not balanced, the nullclines will intersect only once, producing a single stable steady state. This situation arises in plasmid pIKE105. Third, the structure of the toggle network creates two basins of attraction. Thus, a toggle with an initial condition anywhere above the separatrix will ultimately settle to state 1, whereas a toggle starting below the separatrix will settle to state 2. The conditions for a bistable toggle network are illustrated in Fig. 2c and d. As the rates of repressor synthesis are increased, the size of the bistable region increases. Furthermore, the slopes of the bifurcation lines, for large a1 and a2, are determined by b and g. Thus, to obtain bistability, at least one of the inhibitors must repress expression with cooperativity greater than one. Moreover, higher order cooperativity will increase the robustness of the system, allowing weaker promoters to achieve bistability and producing a broader bistable region. Reporter Repressor 1 Repressor 2 Promoter 1 Promoter 2 Inducer 2 Inducer 1 Figure 1 Toggle switch design. Repressor 1 inhibits transcription from Promoter 1 and is induced by Inducer 1. Repressor 2 inhibits transcription from Promoter 2 and is induced by Inducer 2.

contained on a single plasmid, they could, in principle, be divided into two separate plasmids without altering the functionality of the toggle. Two classes of toggle switch plasmids were constructed���the pTAK class and the pIKE class. Both classes use the Lac repressor (lacI) in conjunction with the Ptrc-2 promoter for one promoter��� repressor pair. For the second promoter���repressor pair (P1, R1 in Fig. 3), pTAK plasmids use the PLs1con promoter in conjunction with a temperature-sensitive l repressor (cIts), whereas pIKE plasmids use the PLtetO-1 promoter in conjunction with the Tet repressor (tetR). pTAK plasmids are switched between states by a pulse of isopropyl-b-D-thiogalactopyranoside (IPTG) or a thermal pulse. pIKE plasmids are switched between states by a pulse of IPTG or a pulse of anhydrotetracycline (aTc). The promoters used in the toggle are PLtetO-1 (ref. 20) (TetR repressed), Ptrc-2 (LacI repressed) and PLs1con (CI repressed). The ranked order of the transcriptional efficiencies of the promoters is PLs1con . Ptrc-2 . PLtetO-1. In all variants of the toggle switch, the sequence of the three promoters is unchanged. The rates of synthesis of the repressors (a1 and a2 in the model) or the reporter genes are modified by exchanging the downstream ribosome bind- ing sites (RBS). The promoter and RBS sequences and their relative strengths are described in the Supplementary Information. In all toggle plasmids, the gfpmut3 gene21 is arranged as the second cistron downstream of the Ptrc-2 promoter. Thus, tran- scription from Ptrc-2, and hence, repression of P1, results in the expression of green fluorescent protein (GFP)mut3. For clarity, this state is termed the ���high��� state. The opposing state, in which P1 is transcribed and Ptrc-2 is repressed, is termed the ���low��� state. Unless otherwise indicated, gfpmut3 is the reporter used in all plasmids. To investigate the conditions required for bistability, six variants of the toggle switch (four pTAK plasmids and two pIKE plasmids) were constructed by inserting RBS sequences of differing strengths into the RBS1 site. All four pTAK plasmids exhibited bistability, whereas only one pIKE plasmid (pIKE107) exhibited bistability. The demonstration of bistability is illustrated in Fig. 4. In this experi- ment, the toggle and control plasmids were grown in E. coli strain JM2.300 for 23.5 h. At 6, 11 and 18 h, samples were washed and diluted into fresh medium with or without inducers, as appropriate. Cells were initially grown for 6 hours with 2 mM IPTG, inducing GFPmut3 expression in all toggles and the IPTG-inducible pTAK102 control plasmid. Cells were grown for an additional 5 h with no IPTG. The five bistable toggle plasmids, which had been switched to the high state, continued to express GFPmut3 in the absence of inducer, whereas the pTAK102 control plasmid and the monostable pIKE105 toggle plasmid returned to the low state. Cells were then grown at 42 8C (pTAK plasmids only) or grown in the presence of 500 ng ml-1 aTc (pIKE plasmids only). After 7 h of growth, GFPmut3 expression in all toggles was shut off, whereas GFPmut3 expression in the thermally-inducible pTAK106 control and the aTc-inducible pIKE108 control was activated. Cells were returned to standard temperature (see Methods) with no inducers. After an additional 5.5 h, the five bistable toggle plasmids remained in the low state, whereas the pTAK106 and pIKE108 controls returned, as expected, to their non-induced condition. Figure 4c shows the long-term stability of the two states of the pTAK117 toggle plasmid. In this experiment, a single culture of pTAK117 cells (initially in the low state) was divided into two cultures. The first group was grown in medium with no inducers, while the second group was grown in medium with 2 mM IPTG. After 6 h, cells were washed and diluted into fresh medium with no inducer. Both groups of cells were grown for an additional 22 h, being sampled and diluted into fresh medium every 6���8.5 h. The two groups of pTAK117 cells remained in their initial high or low states for the entire 22 h. Although all of the toggle plasmids contain the same configura- tion of elements, one plasmid, pIKE105, does not exhibit bistability. This result is probably due to the reduced efficiency of the Tet repressor relative to the l repressor. To maintain bistability, the reduced efficiency requires a corresponding decrease in the strength of the PLtetO-1 promoter relative to the PLs1con promoter (see Box 1). The PLtetO-1 promoter in the pIKE105 plasmid is not sufficiently reduced in strength to achieve bistability. However, the strength reduction provided by the PLtetO-1 promoter in the pIKE107 plasmid is sufficient. A qualitative prediction of the toggle model is that a genetic toggle will have nearly ideal switching thresholds. Induction by IPTG, aTc or heat alters the dynamic balance between the compet- ing promoters such that the toggle is pushed into a region of monostability. The transition from bistability to monostability occurs in a sharp, discontinuous fashion owing to the existence of a bifurcation. This bifurcation occurs when one of the stable steady states is annihilated by the unstable steady state. The ideal threshold, or bifurcation, in the pTAK117 toggle switch is illustrated both theoretically and experimentally in Fig. 5. In this experiment, pTAK117 (initially in the low state) and pTAK102 (as a control) were grown in 13 different concentrations of IPTG for 17 h letters to nature 340 NATURE | VOL 403 | 20 JANUARY 2000 | www.nature.com u State 1 (high state) State 2 (low state) Separatrix Unstable steady-state dv/dt =0 v du/dt =0 State 2 (low state) u b a dv/dt =0 du/dt =0 Bistable Mono- stable state 2 Monostable state1 log(��2) log(��2) 1 �� ��=��=1.1 ��=��=2 ��=��=3 d c log( �� 1 ) �� Figure 2 Geometric structure of the toggle equations. a, A bistable toggle network with balanced promoter strengths. b, A monostable toggle network with imbalanced promoter strengths. c, The bistable region. The lines mark the transition (bifurcation) between bistability and monostability. The slopes of the bifurcation lines are determined by the exponents b and g for large a1 and a2. d, Reducing the cooperativity of repression (b and g) reduces the size of the bistable region. Bifurcation lines are illustrated for three different values of b and g. The bistable region lies inside of each pair of curves. GFPmut3 R1 rbs E rbs B RBS1 P1 Ptrc-2 T1T2 T1T2 lacI Type IV Figure 3 The toggle switch plasmid. Promoters are marked by solid rectangles with arrowheads. Genes are denoted with solid rectangles. Ribosome binding sites and terminators (T1T2) are denoted by outlined boxes. Different P1 promoters, RBS1 ribosome binding sites, and/or R1 repressors, are used for the various toggle switches. Plasmid types I���III, used in the construction and testing of the toggle components, are described in the Supplementary Information.