Building biological memory by linking positive loops

Dong-Eun Changa, Shelly Leunga, Mariette R. Atkinsona, Aaron Reiflera, Daniel Forgerb, and Alexander J. Ninfaa,1

aDepartment of Biological Chemistry, University of Michigan Medical School; and bDepartment of Mathematics and Center for Computational Medicine and Biology, University of Michigan, Ann Arbor, MI 48109

Edited by Clyde A. Hutchison III, The J. Craig Venter Institute, San Diego, CA, and approved November 20, 2009 (received for review July 23, 2009) A common topology found in many bistable genetic systems is two transcriptional promoter to the concentration of activator protein interacting loops. Here we explore how this must display a kinetic order or sensitivity greater than one (8, 10– relatively simple topology can allow bistability over a large range 12). If these minimal requirements are met, bistability may be of cellular conditions. On the basis of theoretical arguments, we anticipated to occur under some environmental conditions. predict that nonlinear interactions between two positive feedback An important example of a bistable genetic system consisting of loops can produce an ultrasensitive response that increases the a single positive feedback loop was provided by the work of range of cellular conditions at which bistability is observed. This Novick and Weiner, who studied the so-called “preinduction ef- prediction was experimentally tested by constructing a synthetic fect” of the lacZYA operon in Escherichia coli (13). The lac op- genetic circuit in Escherichia coli containing two well-characterized eron preinduction effect is observed when the operon is induced positive feedback loops, linked in a coherent fashion. The concerted by nonphysiological xenobiotic inducers, known as gratuitous in- action of both positive feedback loops resulted in bistable behavior ducers, that are not metabolized by the cell but can bind to the over a broad range of inducer concentrations; when either of the LacI repressor protein and cause it to release the lac operator feedback loops was removed, the range of inducer concentrations DNA. The preinduction effect refers to the observation that a at which the system exhibited bistability was decreased by an order higher concentration of gratuitous inducer was required for the of magnitude. Furthermore, bistability of the system could be induction of naive (uninduced) cells than was required to main- tuned by altering growth conditions that regulate the contribution tain preinduced cells in the fully induced state. At certain con- of one of the feedback loops. Our theoretical and experimental centrations of inducer, known as the maintenance concentrations, work shows how linked positive feedback loops may produce the naive cells remained uninduced, and previously induced cells re- robust bistable responses required in cellular networks that regu- mained in the induced state, indefinitely (13). Even when cultures late development, the , and many other cellular responses. showed an intermediate level of induction, the lacZYA operon was either fully on or fully off in the individual cells (13, 14). Al- bistability | genetic network | synthetic biology | ultrasensitivity | though the original lacZYA operon preinduction effect experi- ments were performed using a chemostat and with TMG as the istable genetic systems display a discontinuity of expression inducer, we show in the supporting information that the effect can Bstates, where two distinct stable steady states are obtained be demonstrated using standard flask-grown cultures and with without the presence of stable intermediate steady states. The IPTG as the inducer (Fig. S1). Mathematical modeling has con- previous history of the system determines which stable steady firmed the mechanism of bistability in the lacZYA operon and state is occupied. One of the important problems in systems confirmed the role of both positive feedback and high sensitivity biology is to understand how genetic bistability is established and (14–17). This system remains the most well-characterized and regulated. This is because bistable genetic switches play an widely used example of cellular bistability. important role in a variety of cellular processes, such as cellular The lacZYA operon preinduction effect is due to the positive oscillators, progression through the eukaryotic cell cycle, and the feedback of the lacY product, galactoside permease, on its own development of differentiated cell and tissue types in organisms expression (13, 18). This permease allows the gratuitous inducer ranging from the temperate bacteriophage to the human (1–7). to enter into the cell. When cells lack the galactoside permease, Many previous studies have focused on whether a given circuit as in the naive state, a high concentration of gratuitous inducer is topology has the capacity to display bistability for some range of required for induction. However, upon induction of the operon, environmental conditions (e.g., refs. 8–10). Although the possi- the cells come to acquire many molecules of the galactoside bility of bistable behavior is important, it is also important that the permease that can bring about further internalization of the in- range of environmental conditions at which it occurs be large ducer (positive feedback). The presence of permease protein GENETICS enough to achieve practical control of biological processes. Here, molecules allows the induced cells to maintain a high intracellular we focus upon identification and manipulation of the parameters concentration of the inducer, even when the extracellular con- that control the range of environmental conditions at which bis- centration is low. As expected, the lac preinduction effect is tablity is obtained for systems known to be capable of bistability. eliminated upon mutation of the lacY gene (18). Furthermore, We use the methods of synthetic biology to create model ex- the preinduction effect is minimized under conditions where the perimental systems to address the functions of multiple positive function of the LacY protein is down-regulated (19). Inhibition of feedback loops in bistability. Theoretical studies have argued that the minimal requirements

for genetic bistability are twofold. First, there must be some type Author contributions: D.-E.C., D.F., and A.J.N. designed research; D.-E.C., S.L., A.R., and of positive feedback controlling gene expression. Examples of D.F. performed research; M.R.A. contributed new reagents/analytic tools; D.-E.C., S.L., positive feedback are when an activator protein drives its own D.F., and A.J.N. analyzed data; and D.-E.C., D.F., and A.J.N. wrote the paper. expression or when an even number of linked negative regulatory The authors declare no conflict of interest. steps are present, such as when a repressor blocks the expression This article is a PNAS Direct Submission. of a repressor of its own expression. Second, the kinetic order or Freely available online through the PNAS open access option. sensitivity of the system to the positive feedback element must be 1To whom correspondence should be addressed. E-mail: [email protected]. – high (8, 10 12). For example, in the simple case where a tran- This article contains supporting information online at www.pnas.org/cgi/content/full/ scriptional activator drives its own expression, the response of the 0908314107/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.0908314107 PNAS | January 5, 2010 | vol. 107 | no. 1 | 175–180 Downloaded by guest on October 3, 2021 the LacY permease activity occurs when the PTS component and Results glc signal-transduction protein EIIA is present in its un- A Graphic Analysis of the Problem. To understand the factors phosphorylated state and binds to LacY (20). This occurs when controlling the range of bistability of the activator module of the the cell is grown in the presence of PTS sugars, such as glucose, Atkinson et al. oscillator, we use rate-balance plots following the and, to lesser extents, when the cell is grown in the presence of work of Ferrell and Xiong (10, 11). In this method, the rates of other substrates that exert catabolite repression (21). Thus, the activator production and decay are plotted as a function of ac- lac preinduction effect was not discernible in glucose-grown cells tivator concentration. Because activator has no direct effect on (Fig. S1). Even in succinate-grown cells, the lac preinduction its own decay, we expect activator decay to be a simple linear effect was a fairly weak bistability; in an experiment using IPTG function of activator concentration (Fig. 1). Conversely, bio- as the inducer, the range of inducer concentrations at which chemical studies of the activation of transcription by the NRI ∼ P fl bistability was observed was narrow [about 4-fold in ask-grown activator indicated a high kinetic order and an S-shaped re- fl fi cells (Fig. S1)]. Indeed, in ask-grown cells, it was dif cult to sponse (25) (Fig. 1). Steady states are possible only where the demonstrate a maintenance concentration of IPTG (Fig. S1). curves for production rate of activator and decay rate of activator In nature, simple bistable systems with a single positive feed- intersect (Fig. 1). A key feature of the genetic toggle switch used back loop are rarely encountered; instead, natural systems are in our studies is that activator and repressor compete for the complex and contain multiple feedback loops that could be promoter that drives transcription of the activator structural direct or indirect and using a variety of biochemical mechanisms, gene (Fig. 1A). In this genetic system, activator has no direct in combination with additional regulatory mechanisms. Fourteen effect on the LacI repressor, which is present at a low con- examples of such systems have been noted by Brandman et al. stitutive level. The inducer IPTG serves to decrease the con- (22). For example, in the genetic system that controls pro- centration of functional repressor. Thus, changes in the IPTG gression through the cell cycle, the mitotic trigger protein Cdc2 concentration may be thought of as shifting the curve for pro- participates in three positive feedback loops (Cdc2 → Cdc25 → duction of activator to the right or the left, as depicted in Fig. 1. Cdc2; Cdc2-| Wee-1-| Cdc2; Cdc2-| Myt1-| Cdc2) (22). Similarly, The range of IPTG concentrations at which the system displays for traversal of the start of the cell cycle in budding yeast, the bistability is thus limited to the extent to which the production Cdc28 protein participates in two positive feedback loops curve may be shifted to the right or the left while still maintaining (Cdc28-| SicI-| Cdc28; Cdc28 → Cln → Cdc28). Other systems showing multiple positive feedback loops include those respon- at least two points of intersection with the decay curve (Fig. 1). sible for p53 regulation, Xenopus oocyte maturation, mammalian In the system considered above, activator production rate dis- calcium signal transduction, eukaryotic chemotaxis, B cell fate played a high sensitivity, whereas activator decay rate was linear, specification, EGF receptor signaling, blood clotting, and pla- in accordance with the experimental system we use. However, it telet aggregation (noted in ref. 22). The Bcl2 apoptotic switch should be noted that having a nonlinear degradation rate could provides an additional example, where two independent positive also help achieve bistability. This result was presented by Ferrell feedback loops participate in producing bistability (23). and Xiong, who considered a signal transduction system (26). Foundational work on the behavior of biological systems Simple inspection of Fig. 1 reveals two of the key parameters affecting the range of inducer concentrations at which the system containing multiple feedback loops was presented by Thomas fi and D’Ari (24). This work showed how the presence of multiple will display bistability. The rst of these is the steepness (sensi- feedback loops could lead to an unexpectedly large number of tivity, kinetic order) of the activator production curve; the steady states. steeper this response curve is, the greater it may be shifted to the Two additional hypotheses for the presence of multiple pos- left or the right while still maintaining two intersections with the itive feedback loops are that different timescales of the loops decay curve. A second key parameter affecting the range of in- provide for resistance to noise under certain circumstances (22) ducer concentrations at which bistability is observed is the ab- or make bistability robust to certain parameter variations (23). solute magnitude of the activator's effect on itself. That is, the Ferrell has noted that coherent linkage of a positive feedback absolute height of the S-shaped activator production curve limits loop and a double-negative feedback loop in a system of op- the distance it may be displaced to the left or the right while still posing enzymes could result in bistability over a wide range of maintaining at least two intersections with the decay curve. In conditions (10). In natural systems with complex circuit archi- this work, we focus on controlling the steepness of the pro- tectures, testing the roles of the multiple positive feedback loops duction curve. In support of the simple graphic method used in is nontrivial and much of the work in this area to date has been Fig. 1, a more formal analysis of our specific system leading to purely theoretical. the same conclusions is presented in the SI Text. We developed an experimental multiloop system by combining the “activator module” of the synthetic genetic oscillator of How Can the Steepness of the Activator Production Curve Be Increased? Atkinson et al. (12) with the galactoside permease feedback loop The sensitivity of a promoter to its activator is dependent upon of the lacZYA operon. The activator module of the Atkinson et al. numerous factors, such as the oligomeric state of the activator oscillator, when placed into cells that express LacI repressor protein, the number of molecules that are required for tran- constitutively, forms a genetic toggle switch in which an activator scriptional activation, and the details of the interactions of protein, the phosphorylated form of the glnG product (NRI or activator and polymerase with each other and with other mac- NtrC), activates the transcription of the glnG structural gene, and romolecules that interact with them and therefore compete for LacI represses transcription of the glnG gene. Because activator them. In most cases, these parameters are difficult to adjust in a and repressor compete for control of transcription of the glnG systematic way and thus a general solution to the problem of gene, the system displays hysteresis, with the level of IPTG re- increasing the apparent kinetic order of an activator’s effect on quired for induction dependent on the prior history of induction itself must employ a different approach. It has long been known (12). The hysteresis of this system was more prominent than that that ultrasensitive responses to a stimulus may be obtained in displayed by the galactoside permease system, in that bistability signal transduction systems consisting of linked cycles of rever- was observed over an ≈10-fold range of IPTG concentrations sible covalent modification, when the stimulus regulates multiple (12). We show that the multiloop system obtained by linking the distinct activities in the signaling system (27) (reviewed in ref. activator module and galactoside permease feedback loops dis- 28). Such ultrasensitivity is referred to as “multistep ultra- played extensive bistability, indicating that bistability could be sensitivity” (27). Recently, Rossi and colleagues used a model built up by linkage of distinct feedback loops. experimental system to show that the apparent kinetic order of a

176 | www.pnas.org/cgi/doi/10.1073/pnas.0908314107 Chang et al. Downloaded by guest on October 3, 2021 Fig. 1. Design and function of the genetic toggle switch. (A) Basic circuit design for the genetic toggle switch. The LacI repressor was produced from the natural wild-type lacI gene. The activator module containing the glnG structural gene was located in the rbs region of the E. coli chromosome. The activator and repressor competed for control of the expression of the activator module promoter; when neither activator nor repressor proteins were present, a weak promoter (not depicted) allowed for transcription of the activator gene (12). The reporter consisted of a fusion of the activator-dependent glnK promoter with the lacZ gene, located in the trp region of the chromosome. For the system as shown with a single positive feedback loop, the lacY gene was next to lacZ, but contained a null mutation. (B) Graphic representation of the factors affecting the range of IPTG concentrations at which bistability is obtained. All of the plots depict rate of activator production or destruction vs. the concentration of activator. The destruction of activator is not regulated by activator and thus is likely to have a slope of 1, as depicted. Conversely, the production of activator is known to display high kinetic order and is depicted as the S-shaped curve. The role of IPTG is to shift this S-shaped curve to the right or the left, as depicted. Steady states occur when the two curves intersect, as indicated by small circles. The dotted circle in the Center plot depicts an unstable steady state. Factors controlling the shape of the S-shaped activator production curve, such as the steepness of this curve or its absolute height, control the range of bistability of the system.

transcriptional response to a stimulus was increased when the little direct effect on transcription of the lacZYA structural genes in stimulus affected both the activation and the repression of a the recombinant context, whereas expression should be tightly promoter, relative to the situations where a single function was controlled by activator. We chose the glnK promoter and this spe- regulated (29). We regard this result as a special class of multi- cific operon fusion for our experiments because prior work has step ultrasensitivity and reasoned that we could similarly increase shown that this operon fusion has negligible basal expression in the the apparent kinetic order of activator’s response to itself by absence of the activator protein (30). A version of the glnKp-lacZYA having activator influence not only the activation of its structural operon fusion containing an internal deletion within the lacY gene gene, but also the repression of its own gene. Furthermore, un- was generated by recombineering (31). To provide the maximum like the system of Rossi et al. (29), which requires specifically stability for our synthetic genetic system, the genetic toggle switch engineered proteins, we sought to have activator function to (activator module of the Atkinson et al. clock) was incorporated decrease repression of the system indirectly. This was accom- into the E. coli chromosome in the rbs region, as described pre- plished by having activator drive the expression of the galacto- viously (12). The activator of this system requires phosphorylation side permease that brings about the internalization of the for activity, and we provided this function by including within the inducer that inactivates the repressor. In the brief formal analysis cell an altered kinase protein that brings about the phosphor- of our specific system presented in SI Text, we observed that by ylation of activator regardless of nitrogen status. To provide a extending the activity of activator to inhibition of repression, the control system lacking the galactoside permease positive feedback already high kinetic order of the response to activator could be loop, we simply used the version of the system with the lacY null GENETICS significantly increased. mutation. To provide a control system lacking the positive feed- back loop of the activator module, but containing the positive Combining Well-Characterized Feedback Loops to Create a Composite feedback loop based upon galactoside permease, additional ge- System with Coherent Loops. The experimental system with two netic manipulations were required (Fig. 2B). For this purpose, we positive feedback loops, and two control systems each with a single created a system in which the lacZYA promoter region (from the positive feedback loop, is depicted in Fig. 2. We used a previously upstream lacO3 site through the translational initiation codon of described chromosomally integrated fusion of the E. coli glnK the lacZ gene) was fused to the activator structural gene. This was promoter to the structural genes of the lacZYA operon (30). Ex- placed into the rbs region of the chromosome, analogous to the pression from the glnK promoter is dependent upon the activator positioning of the genetic toggle switch, and combined in cells with of the genetic toggle switch, NRI ∼ P. The glnK promoter-lacZYA the glnKp-lacZYA fusion, creating a system where repressor con- fusion was constructed such that the novel joint corresponded to trol of the lac promoter regulated activator expression, with acti- the translational start codon of the lacZ gene. Thus, in the re- vator then driving expression of lacZYA. combinant operon, the major lac operon operator element (lacO1) was not present and neither was the minor lacO3 operator. The Synergy of Positive Feedback Loops. To measure the range of minor lacO2 operator was present, as this element is found within inducer concentrations at which bistability was obtained, cultures the lacZ structural gene. Nevertheless, in the absence of the major were incubated for 12–14 h in the absence of inducer on in the lac operator (lacO1), it is anticipated that LacI repressor will have presence of saturating inducer. The cells were then washed

Chang et al. PNAS | January 5, 2010 | vol. 107 | no. 1 | 177 Downloaded by guest on October 3, 2021 Fig. 2. Strong bistability was obtained by linking distinct positive feedback loops. (A) Genetic toggle switch with a single positive feedback loop. (Left) Schematic depiction of the genetic system in which the genetic toggle switch drives the expression of the lacZYA operon, but the lacY gene contains a null mutation. (Right) Result of bistability experiment, showing an ∼12-fold range of IPTG concentrations at which the system displayed bistability. Symbols: , naive (uninduced) culture; , preinduced culture. (B) Genetic system with a single positive feedback loop based on galactoside permease. (Left) Schematic depiction of the genetic system where the lacZ promoter was used to drive the expression of glnG and the phosphorylated form of glnG drives the expression of lacZYA. The lacY product, galactoside permease, provides positive feedback by facilitating the uptake of IPTG, which inactivates repressor. (Right) Result of bistability experiment, showing an ∼4-fold range of inducer concentrations at which the system displayed bistability. Symbols are as in A. (C) Genetic system with two positive feedback loops. (Left) Schematic depiction of the genetic system in which the genetic toggle switch drives the expression of the lacZYA operon, as in A except with a wild-type lacY gene. (Right) Result of bistability experiment showing that bistability was obtained over an ∼480-fold range of IPTG. For A–C, cells were grown in minimal medium with succinate as the carbon source and glutamine as the nitrogen source.

thoroughly and diluted 1 millionfold into fresh medium con- The bistability of the double-toggle switch could be controlled taining various concentrations of inducer. These cultures were by increasing catabolite repression. For a very modest degree of then grown to midlog phase and the level of the lacZ product, catabolite repression, we included casein hydrolysate in the suc- β-galactosidase was measured (32). cinate growth medium. Under these conditions, the range of The greatest contribution of the positive feedback loops is IPTG concentrations at which the system was bistable was ∼100- expected in our system when the cells are grown on medium in fold (Fig. 3A). Stronger catabolite repression was obtained by which catabolite repression is minimized and thus the galactoside using medium containing both glucose and casein hydrolysate; permease loop is operating without inhibition. For this purpose, under these conditions the range of IPTG concentrations at which we used succinate-based minimal medium. Under these con- the system was bistable was only ∼25-fold (Fig. 3B). Apparently, ditions, the system with a single positive feedback loop in which catabolite repression could be used to control the contribution of activator drives its own transcription displayed bistability over a the galactoside permease feedback loop. Even though the gal- 12-fold range of inducer concentrations (Fig. 2A), consistent with actoside permease feedback loop, when acting alone, did not earlier observations (12). The control system lacking the positive display significant bistability in the presence of glucose (Fig. S1), feedback of the activator on its own transcription, but containing a in the context of the double-toggle switch this loop still increased single positive feedback loop formed by galactoside permease, the range of bistability about ∼2-fold in medium containing both displayed bistability over an ∼4 -fold range of inducer concen- glucose and casein hydrolysate. This can be discerned by com- trations (Fig. 2B), similar to the bistability observed for the native parison with the control strain with a null mutation in lacY grown lacZYA system (Fig. S1). Remarkably, under these same con- under the same conditions (Fig. 3C). ditions, the system with two functional positive feedback loops (strain DE1010), which we refer to as the “double-toggle switch,” Discussion displayed bistability over an ∼480-fold range of inducer concen- We observed that distinct positive feedback loops employing trations (Fig. 2C). Thus, the two positive feedback loops displayed different biochemical mechanisms could be linked to provide powerful synergy in increasing the range of inducer concen- powerful genetic bistability and that the functions of such systems trations over which bistability was observed. were scalable by factors that affected one of the feedback loops.

178 | www.pnas.org/cgi/doi/10.1073/pnas.0908314107 Chang et al. Downloaded by guest on October 3, 2021 Fig. 3. Bistability of the double-toggle switch was tunable by growth substrates causing catabolite repression. (A and B) The double-toggle switch strain depicted in Fig. 2C was examined in medium containing succinate and casein hydrolysate (A) and in medium containing glucose and casein hydrolysate (B). (C) The experiment is as in B, but the strain contained a null mutation in lacY and thus had only a single functioning positive feedback loop.

Thus, bistability could be built up piecewise, by the coherent We argue that all of the cases of bistable systems with multiple linkage of biochemically distinct feedback mechanisms. Fur- interacting genetic feedback loops noted above may be demon- thermore, because the different feedback loops interacted with strating a form of the same multistep ultrasensitivity that was each other in a nonlinear way (in our case, by causing an increase studied in signal transduction systems 25 years ago (27, 28). A in the sensitivity of the response to activator), fairly weak feed- significant and well-understood limitation to bistability in genetic back loops acted synergistically to produce extensive bistability. systems is obtaining a sufficiently high sensitivity for the critical These observation provide a generally applicable foundation for regulatory step, such as the activator’s effect upon its own ex- the rational engineering of synthetic genetic bistable systems. The pression in our system (8, 10–12). We expect that this type of prevalence of complex natural systems with numerous interacting genetic multistep ultrasensitivity may play an important role in feedback loops, which regulate critical responses such as pro- genetic regulation requiring a high kinetic order in those cases gression through the cell cycle, circadian clocks, or development, where multiple feedback loops are focused on controlling the may reflect this capacity to build strong genetic bistability by expression of a gene. collaboration of multiple weak elements. The sharp state tran- sitions involved in clocks, cell cycles, and irreversible morpho- Methods genic pathways are likely to require genetic bistability over a Genetic Elements. The activator module of the NC12 synthetic genetic clock broad range of conditions (e.g., refs. 7 and 22), which could not and the fusion of the glnK promoter to the lacZYA structural genes were evolve in a single step and had to be built up piecewise. described previously (12, 30). The fusion of the lacZ promoter to the glnG To develop novel synthetic genetic bistable systems, the path- structural gene was constructed in several steps, as described in SI Text,and way followed by nature could be mimicked by developing circuitry the primers used for construction of the lacY null mutation by recombin- eering are listed in SI Text. All molecular cloning, PCR, P1vir transduction, where different feedback loops act coherently. Our work shows and plasmid transformation used standard techniques (33, 34). The bacterial that there is no necessity for using highly engineered proteins; strains used and their relevant genotypes are listed in Table S1. factors that indirectly affect transcriptional activation or repres- sion are just as good as factors that directly interact with the Physiology Experiments. Growth medium for bistability experiments used W- DNA, as long as they are effective. Thus, for example, in our case salts (12), with added vitamin B1 (0.004% wt/vol), tryptophan (0.04% wt/vol), we would expect that a circuit where activator brought about the and glutamine (0.2% wt/vol), and contained succinate at 0.4% wt/vol, casein repression of repressor synthesis (along with the activation of its hydrolysate at 0.5% wt/vol, and glucose at 0.4% wt/vol, as indicated. IPTG own synthesis) would also bring about very dramatic bistability. was used at 0.4 mM for overnight induction of the cultures. β-Galactosidase Such a system would be closer to that used by Rossi (29) than is activity was measured using the method of Miller (32). the system used in this paper. The flexibility of using indirect ACKNOWLEDGMENTS. We thank Patrick O’Brien for reviewing an early ver- methods, such as regulation of the permease that internalizes the sion of this manuscript. This work was supported by Grant GM63642 (to A.J. fi GENETICS inducer, follows the pathway used by bacteria and simpli es the N.) from the National Institutes of Health–National Institute of General engineering of systems. Medical Sciences.

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