Proc Natl Acad Sci U S A 109(47): E3212-E3220

Bottom-up construction of in vitro switchable memories

Oligonucleotides.

DNA oligonucleotides were purchased from either Integrated DNA Technologies or biomers.net, with HPLC purification. All templates have three phosphorothioate backbone modifications at their 5′ end to protect them from degradation by the exonuclease. Templates αtoiβ and βtoiα are modified at their 3′ end with FAM and TAMRA NHS ester modification, respectively. All the other templates are phosphorylated at their 3′ end to prevent any polymerization. Template sequences and concentrations are provided in SI Appendix, section II.3.

Reaction Assembly.

Reactions were assembled in a buffer containing 10 mM KCl, 10 mM (NH₄)₂SO₄, 50 mM NaCl, 2 mM MgSO₄, 45 mM Tris⋅HCl, 5 mM MgCl₂, 6 mM DTT, 2 μM Netropsin (Sigma–Aldrich), 100 μg/mL BSA (New England Biolabs), 0.1% Synperonic F108 (Sigma–Aldrich), and dNTPs (200 μM each). Exonuclease ttRecJ was a kind gift from R. Masui (Osaka University, Japan) and used at a concentration of 50 nM throughout this study. Unless otherwise specified, Bst DNA polymerase, large fragment (New England Biolabs) was used at a concentration of 25.6 U/mL. For the Nt.BstNBI nicking endonuclease (New England Biolabs), we noticed a large fluctuation in the activity from batch to batch, and consequently used the enzyme at a concentration ranging from 32 to 400 U/mL. Experimental adjustment of Nt.BstNBI concentration was done by comparing the activity of a new batch with the activity of the previous batch, using the assay presented in SI Appendix, Fig. S3.

Reactions were run at 42 °C (except if specified otherwise) in a Bio-Rad iQ5 or CFX96 real-time thermocycler in a 20-μL volume. Experiments for which the bistable circuit was flipped from one state to the other required administration of an external input (γ or δ) that was diluted in TE buffer and injected in a volume of 0.6 μL while the run was paused for a minimal period.

Fluorescence Curve Acquisition and Normalization.

Fluorescence cross-talk between FAM and TAMRA was removed by the Bio-Rad built-in thermocycler software. For the experiments requiring an injection of external input, instantaneous signal artifacts at the time of injection (e.g., due to a slight displacement of the tube or the production of bubbles during mixing) were corrected to keep the curve continuity. “Charge levels” were normalized from fluorescence data: to the high plateau (ON state of the autocatalytic module; if unavailable, a reference tube with the same reacting mix set in the ON state was used) and low plateau (OFF state of the autocatalytic module; if unavailable, the reaction was run until depletion of dNTPs, thus revealing the OFF state of the autocatalytic module).

Simulations.

The simple model of the bistable reaction circuit was analytically analyzed using Mathematica (Wolfram) (SI Appendix, section III.1). Detailed models of the bistable circuit, switchable memory, and push-push memory were made with a set of measured and predicted (DINAMelt) parameters, refined by fitting on the experimental curves of the switching memory, using Mathematica (SI Appendix, section III.4). The set of refined parameters was used for all other model predictions.

Supplementary Material

Supporting Information:

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Author Summary

Keeping memory of past decisions is a fundamental operation of cellular information processing (1). Networks of reactions within cells may be bistable, and therefore exist in two mutually exclusive steady states. These bistable networks provide cells with long-term information storage. Such memory systems need not only to be robust but switchable; that is, able to update their state on detection of environmental stimuli. We show here that it is possible to reproduce these functions in vitro and to obtain addressable memories using simplified DNA biochemistry (2, 3). Our approach provides an unmatched opportunity to study the relationships between the structure of a biochemical reaction network and its dynamic function (4).

We describe a DNA-based toolbox for building in vitro reaction circuits. It is based on enzymatic polymerization and depolymerization of short DNA strands that mediate the communication between the elements of the circuit. The toolbox is composed of three modules: activation, autocatalysis, and inhibition (Fig. P1A). One can arbitrarily wire these modules in circuits encoding time-responsive behaviors. We use the DNA toolbox to rationally construct reaction circuits implementing memory functions of increasing complexity. We start with a foundational bistable system composed of two autocatalytic modules that mutually repress each other through two inhibition modules (Fig. P1B). This architecture is similar to that of in vivo bistable circuits. A simple mathematical model allows us to extract the important design parameters. These are then translated into the DNA sequences of the four modules. Experimentally, we incubate these DNA modules in presence of a DNA polymerase, a nicking enzyme, and an exonuclease. The resulting biochemical system indeed possesses two exclusive steady states. The state that the system ultimately displays depends only on the initial stimulus. The relative attractiveness of the two states can be adjusted by tuning the concentrations of the DNA modules. We also show that the two steady states are very resilient to perturbations in the sense that the system in one state will not switch to the other state unless a very strong perturbation is applied. On the flip side, this means that a dedicated strategy is necessary to use them as addressable memory elements.

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Object name is pnas.1212069S109fig01.jpg

Fig. P1.

Modular assembly of in vitro memory circuits. (A) The three modules of the DNA toolbox. (B) Bistable circuit: α activates the production of inhibitor iβ, which inhibits the production of β. Similarly, β activates the production of inhibitor iα, which inhibits the production of α. (C) Switchable memory circuit: two activation modules are wired to the bistable core. They take two different external inputs, γ and δ. (D) Experimental (thick line) and fitted model (thin line) time plot of the normalized concentration (1 for the steady state and 0 for the lowest) of α and β. The switchable memory circuit starts on state A, switches to B on injection of δ, and then switches back to A on injection of γ. (E) Push-push memory circuit: two additional inhibition modules feed the state of the bistable element back to the input, providing state-dependent switching upon injection of the same exogenous input.

We therefore connect the bistable core to two activation modules that read two separate exogenous inputs (γ and δ) (Fig. P1C) and amplify them into long-lasting stimulations. Experimentally, we obtain a system that can both flip reversibly between states (Fig. P1D) and robustly maintain the memorized state. The behavior of this circuit is remarkably well described by a detailed model that takes into account the full set of reactions (Fig. P1D).

Our third target is a push-push memory circuit, that is, a bistable memory that can be switched back and forth by the same stimulus. This supposes that upon reading of its unique external input, the circuit integrates the current state of the memory and accordingly produces a long-lasting stimulus directed to the opposite state. Because our design process is modular, we are able to reuse the previous bistable element and to plug in four additional DNA modules to perform the switching function. It works as follows: Two activation modules receive and convert the same external input, but they are controlled by two inhibition modules that are linked to the state of the bistable system (Fig. P1E). The full experimental circuit contains eight modules, and it is indeed able to flip in both directions upon reading of a unique external input.

From three fully modular biochemical reactions, activation, autocatalysis, and inhibition, we show that it is possible to build dynamic circuits with predefined functions; here, memories. In this framework, simple circuit motifs can be reused for the assembly of more integrated functions. In the future, it should be possible to build even more complex dynamic in vitro circuits by iterating this modular approach. This design strategy is also very close to the one observed in cellular reaction networks, where elementary biochemical processes (e.g., regulation of gene expression) are repeatedly used in the assembly of large systems driving complicated functions (5). By building in vitro information-processing systems at the chemical scale, we are therefore also exploring the underlying design rules of the reaction circuits controlling cells.

Laboratory for Integrated Micro-Mechatronic Systems, Centre National de la Recherche Scientifique/Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

^{To whom correspondence should be addressed. E-mail:}pj.ca.oykot-u.sii@zelednor.

Edited by David A. Tirrell, California Institute of Technology, Pasadena, CA, and approved October 2, 2012 (received for review July 14, 2012)

Author contributions: A.P. and Y.R. designed research; A.P. performed research; T.F. contributed new reagents/analytic tools; A.P. and Y.R. analyzed data; and A.P. and Y.R. wrote the paper.

Edited by David A. Tirrell, California Institute of Technology, Pasadena, CA, and approved October 2, 2012 (received for review July 14, 2012)

Cellular information processing relies on dynamic networks of biochemical reactions (1). For example, genes and their products regulate each other in intricate assemblies that embrace numbers of components and interactions. The function of these assemblies (i.e., the computation that they perform at the molecular level) is encoded both in the structure and in the physical characteristics of the web of chemical interactions that links their components. These in vivo networks are often difficult to identify in their entirety. Indeed, a complete description requires (i) a detailed analysis of the macroscopic dynamic behavior, (ii) a molecular understanding of the structure of the underlying biological network sustaining the function, and (iii) a chemical (thermodynamic and kinetic) knowledge of the reactions at hand. For technical reasons, this information can be very hard to obtain, even in the simplest biological cases (2 –5).

Rather than attempting a systematic analysis of natural reaction networks, synthetic biology harnesses cells as a receptacle (i.e., the hardware) to implement artificially designed networks (6, 7). These networks are typically engineered through the recycling of original biological parts, their modification, and their reassembly in nonnatural architectures, which endow cells with additional functions (8, 9). This strategy aims at understanding the cell regulatory processes through a bottom-up approach, which is expected to reveal the underlying design rules (10). In this way, small-scale circuits encoding elementary functions, such as cascades (11), counters (12), bistability (7, 13 –15), or oscillations (6, 14), have successfully been engineered.

The richness of the cell’s inner biochemistry provides a platform that theoretically allows the engineering of an infinite number of increasingly complex synthetic networks (16). It also poses formidable challenges to a rational designer. In practice, only small synthetic networks (compared with their natural models) have been reported (17). One reason is that synthetic biologists face a shortage of known interoperable units (17, 18). Also, harnessing the cell’s machinery is a complex task; nonlinear effects (10, 19, 20) and unintended interactions between the synthetic circuit and the host housekeeping functions (21) are frequent and difficult to pinpoint. Moreover, the lack of quantitative knowledge of in vivo processes strongly constrains the predictive power of the in silico models used in the design process (16, 18).

Engineering analogs of gene networks out of the cell, in purposely created and better controlled in vitro environments, provides an attractive alternative (22 –25). Going cell-free offers better control of the system parameters, minimizes unintended couplings, and allows easier quantitative analysis (26). Like in vivo gene networks, in vitro analogs are constructed from elementary units; however, this time, one is freed from the constraints of the cellular machinery. Various and possibly simpler chemistries can be used, toxicity and host interference disappear, and stochastic effects can be handled. Still, in analogy to synthetic biology, it is possible to build basic functions, such as oscillators (23, 27), bistable systems (22, 28), or logic gates (29, 30), through a rational bottom-up strategy. The expectation is that it will be possible to assemble these elementary modules in a wealth of large-scale circuits (31, 32), potentially with life-like behaviors (33).

This paper focuses on in vitro reaction circuits encoding memory functions. In the context of biological circuits, memory refers to the ability to integrate a transient molecular stimulus into a sustained molecular response (34). In most cases, this information is digitized into a small number of alternative states, which correspond to the multiple steady states of a dynamic chemical system. In the cell, various mechanisms exist to keep memory of an event. Slowly changing protein levels can result in memory-like behaviors transmitted over a few cell generations (35). Phage-like genetic recombination can be used reversibly to switch one bit of information on the DNA of engineered cells (36), creating passive data storage that can be passed down through generations. Epigenetic switches use bistability to carry a robust, heritable memory (37 –39). Other bistable switches naturally occur in gene networks and play important roles in fundamental cell functions (3, 4), cell cycle (2, 40), cell commitment (5, 41), and signal transduction pathways (42).

Such biological memories based on multistability also require interfacing with upstream and downstream molecular processes. In particular, this includes the ability, given the correct stimuli, to toggle reversibly and sensitively between the reciprocally exclusive stable states (4, 5). From a chemical point of view, the memory function therefore incorporates a form of antagonism. On the one hand, robust information storage imposes stability against molecular perturbations or noise; however, on the other hand, the function also requires a sensitive mechanism to integrate environmental information and, if appropriate, update its state. The synthetic bistable switches constructed so far in vivo have not yet solved this dilemma. The host cells are typically forced on one state by exposition to strong inducer drugs for the whole switching time (7, 13, 43). Alternatively, nonmolecular stimuli, such as temperature or light, are used. For example, Lou et al. (15) have recently reported a synthetic switchable “push-push” bistable circuit in which UV stimulation was used to switch the system back and forth between its two stable states. However, such systems that use nonmolecular inputs cannot be cascaded (i.e., integrated into larger circuits). Additionally, in this case, extreme phototoxicity has a negative impact on the host cells.

Because the alternative states of a bistable system are all equally stable over time, thermodynamics imposes that multistability is fundamentally an energy-consuming, out-of-equilibrium process (44). Switching to the new state requires the complete disappearance or degradation of the constituents of the previous state. This poses a severe constraint for the design of in vitro analogs of biological memory circuits. Nevertheless, a couple of batch bistable systems (22, 28) have been reported, thanks to the use of an enzymatic sink to maintain the dynamics of the system. However, no attempt was made to switch these bistable networks after they first reached one of their steady states.

Herein, we use enzyme-catalyzed, DNA-based reactions (23) to construct various in vitro memory circuits in a rational manner. We present a DNA toolbox composed of three modules encoding elementary reactions: activation, autocatalysis, and inhibition. These modules can be arbitrarily connected in circuits encoding desired behaviors (SI Appendix, section I). We use these modules sequentially to construct three dynamic reaction circuits implementing memory functions of increasing complexity.

We start with a foundational bistable switch circuit, which always reaches one of only two possible steady states, depending on the initial conditions. This bistable switch is very robust to perturbation, and making it switchable requires a specific strategy. We use the modularity of the reactions to upgrade the bistable circuit to a two-input in vitro switchable memory circuit. This system comprises six modules and is able to flip between two stable states on administration of a small amount of the correct exogenous input. Next, we construct and experimentally characterize a push-push memory circuit that accepts a single external input. Depending on its present state, the same input flips it in one direction or the other. This push-push memory circuit culminates at eight modules, showing the ability of the DNA toolbox to serve as a tool to construct scaled-up in vitro reaction circuits rationally. All the experimental observations are rationalized by a quantitative mathematical analysis.

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Acknowledgments

We thank Ryoji Masui for the gift of ttRecJ. This work was funded by the Centre National de la Recherche Scientifique and a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Culture, Sports, Science and Technology (Grant 23119006).

Acknowledgments

Footnotes

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

See Author Summary on page 19047 (volume 109, number 47).

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1212069109/-/DCSupplemental.

Footnotes

1. Casadesús J, D’Ari R. Memory in bacteria and phage. Bioessays. 2002;24(6):512–518. [PubMed] [Google Scholar]

2. Kim J, White KS, Winfree E. Construction of an in vitro bistable circuit from synthetic transcriptional switches. Mol Syst Biol. 2006;2:68.[PMC free article] [PubMed] [Google Scholar]

3. Montagne K, Plasson R, Sakai Y, Fujii T, Rondelez Y. Programming an in vitro DNA oscillator using a molecular networking strategy. Mol Syst Biol. 2011;7:466.[PMC free article] [PubMed] [Google Scholar]

4. Tyson JJ, Chen KC, Novák B. Sniffers, buzzers, toggles and blinkers: Dynamics of regulatory and signaling pathways in the cell. Curr Opin Cell Biol. 2003;15(2):221–231. [PubMed] [Google Scholar]

5. Hartwell LH, Hopfield JJ, Leibler S, Murray AW. From molecular to modular cell biology. Nature. 1999;402(6761, Suppl):C47–C52. [PubMed] [Google Scholar]

References

1. Hartwell LH, Hopfield JJ, Leibler S, Murray AWFrom molecular to modular cell biology. Nature. 1999;402(6761) Suppl:C47–C52.[PubMed][Google Scholar]
2. Yao G, Tan C, West M, Nevins JR, You LOrigin of bistability underlying mammalian cell cycle entry. Mol Syst Biol. 2011;7:485.[Google Scholar]
3. Monod J, Jacob FTeleonomic mechanisms in cellular metabolism, growth, and differentiation. Cold Spring Harb Sym. 1961;26:389–401.[PubMed][Google Scholar]
4. Ozbudak EM, Thattai M, Lim HN, Shraiman BI, Van Oudenaarden AMultistability in the lactose utilization network of Escherichia coli. Nature. 2004;427(6976):737–740.[PubMed][Google Scholar]
5. Arkin A, Ross J, McAdams HHStochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. Genetics. 1998;149(4):1633–1648.[Google Scholar]
6. Elowitz MB, Leibler SA synthetic oscillatory network of transcriptional regulators. Nature. 2000;403(6767):335–338.[PubMed][Google Scholar]
7. Gardner TS, Cantor CR, Collins JJConstruction of a genetic toggle switch in Escherichia coli. Nature. 2000;403(6767):339–342.[PubMed][Google Scholar]
8. Hasty J, McMillen D, Collins JJEngineered gene circuits. Nature. 2002;420(6912):224–230.[PubMed][Google Scholar]
9. Guido NJ, et al A bottom-up approach to gene regulation. Nature. 2006;439(7078):856–860.[PubMed][Google Scholar]
10. Nandagopal N, Elowitz MBSynthetic biology: Integrated gene circuits. Science. 2011;333(6047):1244–1248.[Google Scholar]
11. Hooshangi S, Thiberge S, Weiss RUltrasensitivity and noise propagation in a synthetic transcriptional cascade. Proc Natl Acad Sci USA. 2005;102(10):3581–3586.[Google Scholar]
12. Friedland AE, et al Synthetic gene networks that count. Science. 2009;324(5931):1199–1202.[Google Scholar]
13. Kramer BP, et al An engineered epigenetic transgene switch in mammalian cells. Nat Biotechnol. 2004;22(7):867–870.[PubMed][Google Scholar]
14. Atkinson MR, Savageau MA, Myers JT, Ninfa AJDevelopment of genetic circuitry exhibiting toggle switch or oscillatory behavior in Escherichia coli. Cell. 2003;113(5):597–607.[PubMed][Google Scholar]
15. Lou C, et al Synthesizing a novel genetic sequential logic circuit: a push-on push-off switch. Mol Syst Biol. 2010;6:350.[Google Scholar]
16. Lu TK, Khalil AS, Collins JJNext-generation synthetic gene networks. Nat Biotechnol. 2009;27(12):1139–1150.[Google Scholar]
17. Purnick PEM, Weiss RThe second wave of synthetic biology: From modules to systems. Nat Rev Mol Cell Biol. 2009;10(6):410–422.[PubMed][Google Scholar]
18. Ellis T, Wang X, Collins JJDiversity-based, model-guided construction of synthetic gene networks with predicted functions. Nat Biotechnol. 2009;27(5):465–471.[Google Scholar]
19. Rondelez YCompetition for catalytic resources alters biological network dynamics. Phys Rev Lett. 2012;108(1):018102.[PubMed][Google Scholar]
20. Mather W, Bennett MR, Hasty J, Tsimring LSDelay-induced degrade-and-fire oscillations in small genetic circuits. Phys Rev Lett. 2009;102(6):068105.[Google Scholar]
21. Tan C, Marguet P, You LEmergent bistability by a growth-modulating positive feedback circuit. Nat Chem Biol. 2009;5(11):842–848.[Google Scholar]
22. Kim J, White KS, Winfree EConstruction of an in vitro bistable circuit from synthetic transcriptional switches. Mol Syst Biol. 2006;2:68.[Google Scholar]
23. Montagne K, Plasson R, Sakai Y, Fujii T, Rondelez YProgramming an in vitro DNA oscillator using a molecular networking strategy. Mol Syst Biol. 2011;7:466.[Google Scholar]
24. Shin J, Noireaux V. An E. coli cell-free expression toolbox: Application to synthetic gene circuits and artificial cells. ACS Synth Biol. 2012;1(1):29–41.[PubMed]
25. Soloveichik D, Seelig G, Winfree EDNA as a universal substrate for chemical kinetics. Proc Natl Acad Sci USA. 2010;107(12):5393–5398.[Google Scholar]
26. Simpson MLCell-free synthetic biology: A bottom-up approach to discovery by design. Mol Syst Biol. 2006;2:69.[Google Scholar]
27. Kim J, Winfree ESynthetic in vitro transcriptional oscillators. Mol Syst Biol. 2011;7:465.[Google Scholar]
28. Subsoontorn P, Kim J, Winfree EEnsemble Bayesian analysis of bistability in a synthetic transcriptional switch. ACS Synth Biol. 2012;1(8):299–316.[PubMed][Google Scholar]
29. Takinoue M, Kiga D, Shohda K-I, Suyama AExperiments and simulation models of a basic computation element of an autonomous molecular computing system. Phys Rev E Stat Nonlin Soft Matter Phys. 2008;78(4 Pt 1):041921.[PubMed][Google Scholar]
30. Seelig G, Soloveichik D, Zhang DY, Winfree EEnzyme-free nucleic acid logic circuits. Science. 2006;314(5805):1585–1588.[PubMed][Google Scholar]
31. Qian L, Winfree EScaling up digital circuit computation with DNA strand displacement cascades. Science. 2011;332(6034):1196–1201.[PubMed][Google Scholar]
32. Simpson ZB, Tsai TL, Nguyen N, Chen X, Ellington ADModelling amorphous computations with transcription networks. J R Soc Interface. 2009;6(Suppl 4):S523–S533.[Google Scholar]
33. Lincoln TA, Joyce GFSelf-sustained replication of an RNA enzyme. Science. 2009;323(5918):1229–1232.[Google Scholar]
34. Xiong W, Ferrell JE., Jr A positive-feedback-based bistable ‘memory module’ that governs a cell fate decision. Nature. 2003;426(6965):460–465.[PubMed]
35. Sigal A, et al Variability and memory of protein levels in human cells. Nature. 2006;444(7119):643–646.[PubMed][Google Scholar]
36. Bonnet J, Subsoontorn P, Endy DRewritable digital data storage in live cells via engineered control of recombination directionality. Proc Natl Acad Sci USA. 2012;109(23):8884–8889.[Google Scholar]
37. Casadesús J, D’Ari RMemory in bacteria and phage. Bioessays. 2002;24(6):512–518.[PubMed][Google Scholar]
38. Veening J-W, Smits WK, Kuipers OPBistability, epigenetics, and bet-hedging in bacteria. Annu Rev Microbiol. 2008;62:193–210.[PubMed][Google Scholar]
39. Robert L, et al Pre-dispositions and epigenetic inheritance in the Escherichia coli lactose operon bistable switch. Mol Syst Biol. 2010;6:357.[Google Scholar]
40. Zhang T, Schmierer B, Novák BCell cycle commitment in budding yeast emerges from the cooperation of multiple bistable switches. Open Biol. 2011;1(3):110009.[Google Scholar]
41. Dworkin J, Losick RDevelopmental commitment in a bacterium. Cell. 2005;121(3):401–409.[PubMed][Google Scholar]
42. Bhalla US, Ram PT, Iyengar RMAP kinase phosphatase as a locus of flexibility in a mitogen-activated protein kinase signaling network. Science. 2002;297(5583):1018–1023.[PubMed][Google Scholar]
43. Polynikis A, et al Design and construction of a versatile synthetic network for bistable gene expression in mammalian systems. J Comput Biol. 2011;18(2):195–203.[PubMed][Google Scholar]
44. Vellela M, Qian HStochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: The Schlögl model revisited. J R Soc Interface. 2009;6(39):925–940.[Google Scholar]
45. Wakamatsu T, et al Structure of RecJ exonuclease defines its specificity for single-stranded DNA. J Biol Chem. 2010;285(13):9762–9769.[Google Scholar]
46. Wakamatsu T, et al Role of RecJ-like protein with 5′-3′ exonuclease activity in oligo(deoxy)nucleotide degradation. J Biol Chem. 2011;286(4):2807–2816.[Google Scholar]
47. Padirac A, Fujii T, Rondelez YQuencher-free multiplexed monitoring of DNA reaction circuits. Nucleic Acids Res. 2012;40(15):e118.[Google Scholar]
48. Franco E, et al Timing molecular motion and production with a synthetic transcriptional clock. Proc Natl Acad Sci USA. 2011;108(40):E784–E793.[Google Scholar]
49. Ramakrishnan N, Bhalla USMemory switches in chemical reaction space. PLOS Comput Biol. 2008;4(7):e1000122.[Google Scholar]
50. François P, Hakim VDesign of genetic networks with specified functions by evolution in silico. Proc Natl Acad Sci USA. 2004;101(2):580–585.[Google Scholar]
51. Widder S, Macía J, Solé RMonomeric bistability and the role of autoloops in gene regulation. PLoS ONE. 2009;4(4):e5399.[Google Scholar]
52. Epstein IR, Pojman JA. 2012. An introduction to nonlinear chemical dynamics: Oscillations, Waves, Patterns, and Chaos (Oxford University Press, London)
53. Tyson JJ, Chen KC, Novák BSniffers, buzzers, toggles and blinkers: Dynamics of regulatory and signaling pathways in the cell. Curr Opin Cell Biol. 2003;15(2):221–231.[PubMed][Google Scholar]
54. Boissonade J, De Kepper PTransitions from bistability to limit-cycle oscillations—Theoretical-analysis and experimental-evidence in an open chemical-system. J Phys Chem. 1980;84:501–506.[PubMed][Google Scholar]
55. Siegal-Gaskins D, Mejia-Guerra MK, Smith GD, Grotewold EEmergence of switch-like behavior in a large family of simple biochemical networks. PLOS Comput Biol. 2011;7(5):e1002039.[Google Scholar]
56. Cherry JL, Adler FRHow to make a biological switch. J Theor Biol. 2000;203(2):117–133.[PubMed][Google Scholar]
57. Ferrell JE., Jr Self-perpetuating states in signal transduction: Positive feedback, double-negative feedback and bistability. Curr Opin Cell Biol. 2002;14(2):140–148.[PubMed]
58. Brandman O, Meyer TFeedback loops shape cellular signals in space and time. Science. 2008;322(5900):390–395.[Google Scholar]
59. Zhang DY, Seelig GDynamic DNA nanotechnology using strand-displacement reactions. Nat Chem. 2011;3(2):103–113.[PubMed][Google Scholar]
60. Casadesús J, D’Ari RMemory in bacteria and phage. Bioessays. 2002;24(6):512–518.[PubMed][Google Scholar]
61. Kim J, White KS, Winfree EConstruction of an in vitro bistable circuit from synthetic transcriptional switches. Mol Syst Biol. 2006;2:68.[Google Scholar]
62. Montagne K, Plasson R, Sakai Y, Fujii T, Rondelez YProgramming an in vitro DNA oscillator using a molecular networking strategy. Mol Syst Biol. 2011;7:466.[Google Scholar]
63. Tyson JJ, Chen KC, Novák BSniffers, buzzers, toggles and blinkers: Dynamics of regulatory and signaling pathways in the cell. Curr Opin Cell Biol. 2003;15(2):221–231.[PubMed][Google Scholar]
64. Hartwell LH, Hopfield JJ, Leibler S, Murray AWFrom molecular to modular cell biology. Nature. 1999;402(6761, Suppl):C47–C52.[PubMed][Google Scholar]