Building biological memory by linking positive feedback 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 positive feedback 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 cell cycle, 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 | hysteresis 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