In order to establish cells and organisms with predictable properties, synthetic biology makes use of controllable, synthetic genetic devices. These devices are used to replace or to interfere with natural pathways. Alternatively, they may be interlinked with endogenous pathways to create artificial networks of higher complexity. While these approaches have been already successful in prokaryotes and lower eukaryotes, the implementation of such synthetic cassettes in mammalian systems and even animals is still a major obstacle. This is mainly due to the lack of methods that reliably and efficiently transduce synthetic modules without compromising their regulation properties.
To pave the way for implementation of synthetic regulation modules in mammalian systems we utilized lentiviral transduction of synthetic modules. A synthetic positive feedback loop, based on the Tetracycline regulation system was implemented in a lentiviral vector system and stably integrated in mammalian cells. This gene regulation circuit yields a bimodal expression response. Based on experimental data a mathematical model based on stochasticity was developed which matched and described the experimental findings. Modelling predicted a hysteretic expression responsewhich was verified experimentally. Thereby supporting the idea that the system is driven by stochasticity.
The results presented here highlight that the combination of three independent tools/methodologies facilitate the reliable installation of synthetic gene circuits with predictable expression characteristics in mammalian cells and organisms.
Citation: May T, Eccleston L, Herrmann S, Hauser H, Goncalves J, Wirth D (2008) Bimodal and Hysteretic Expression in Mammalian Cells from a Synthetic Gene Circuit. PLoS ONE 3(6): e2372. doi:10.1371/journal.pone.0002372
Editor: Andrea Califano, Columbia University, United States of America
Received: February 5, 2008; Accepted: April 7, 2008; Published: June 4, 2008
Copyright: © 2008 May et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: Lee Eccleston would like to thank The MathWorks for their funding through The Math-Works Scholarship. Jorge Goncalves would like to thank the Nuffield Foundation and EPSRC for their support and funding. The work of Tobias May, Hansjörg Hauser and Dagmar Wirth was supported by the Bundesministerium für Bildung und Forschung (BMBF FKZ 0313940), the DFG (WI2648) and the Helmholtz Association (SBCancer). Further support was obtained from EU (Clinigene and FlpFlex (513769)).
Competing interests: The authors have declared that no competing interests exist.
To date, most of the synthetic gene networks have been created for bacteria or for lower eukaryotes –. They were successfully employed to investigate different regulatory networks within these biological systems. A wealth of information could be provided by these studies. To facilitate systems biology based approaches for the elucidation of complex regulatory networks involved in immunology, developmental biology or infection, the development of appropriate synthetic modules as well as their establishment in mammalian cells and animals is indispensable. A thorough understanding and mathematical description of these modules in complex organisms would further pave the way to exploit such circuits within systems biology and also for applications in gene or cell therapy .
Pioneering studies demonstrated that the creation of synthetic gene circuits is feasible also in mammalian systems. The designed devices encompassed a toggle switch , a hysteretic switch  and a time-delay circuit . A major limitation is that the manipulation of mammalian cells is tedious and time-consuming. Especially stable integration of synthetic gene circuits remains a challenge and is up to now only achieved in immortalized cell lines which usually do not or only partially reflect relevant properties of the cells they have been derived of. This can be partially attributed to the genetic changes which are required to provide unlimited cell growth. To implement synthetic cassettes in primary cells novel tools have to be developed.
Viruses have evolved strategies to efficiently transduce their genetic information to mammalian cells. In particular, adenoviruses, adeno-associated viruses and retroviruses were exploited for their potential to genetically modify mammalian cells , For this purpose, non-replicating viral vectors have been developed that can be transduced with the help of packaging cells [e.g. 13], . While non-replicating extrachromosomal vectors (e.g. derived from adenoviruses) remain in an extrachromosomal state they lead to a transient expression in proliferating cells. Retroviral and especially lentiviral vectors are the optimal tools to provide stable integration of expression cassettes into the host's genome and thus guarantee the maintenance of the cassettes in replicating cells. Pseudotyping of lentiviral vectors allow to to transduce a broad range of different cell types from different species. Importantly, they are also capable of infecting slowly or non-proliferating cells and thus are preferential tools for many primary cells including stem cells.
Gene expression patterns in eukaryotes can be classified into two distinct types: graded and bimodal . In the graded pattern, cells respond uniformly to increasing levels of the stimulant. In contrast, in the bimodal pattern, the level of the stimulant affects only the probability that a gene will be expressed in a given cell; this expression is always “maximal”. Bistable expression of metabolic genes such as those for galactose utilization in yeast  and lactose utilization in E.coli  have been shown to result from positive feedback. One prominent example for bistability in eukaryotes is the cell-cycle oscillator, a biochemical system that has been shown to promote irreversible transitions between distinct mitotic and interphase states –. But also in the immune system the T helper activation is governed by an bimodal expression of the transcription factor NFATc2 which integrates graded T cell receptor activation into a bimodal IL2 expression , .
The bimodal expression mode may lead to multimodal variation in the phenotype of an isogenic cellular culture and in organisms (i.e. differentiation). In genetic networks this confers a memory to past events or environmental changes. Thus, stochasticity is an important feature of many biological processes in mammalian cells. Several means have been described to achieve a bimodal expression pattern. Amongst them are positive feedback loops and mutual repression . As an example, the latter can be accomplished using two interlinked negative feedback loops which create a toggle switch , . This toggle switch setup was employed in another study as a memory subsystem. This was implemented and used for recording the outputs of a larger DNA-damage sensor network . Bimodal expression was further achieved by employing two opposing transcriptional regulators . Becskei et al. (2001)  finally proved that in yeast even a less complex network based on the tet-system can result in a bimodal expression pattern upon gradual increase of the inducer tetracycline.
The aim of this study was to provide and evaluate a strategy to efficiently implement a bimodal synthetic gene circuit in mammalian cells. For this purpose, three different methodologies were exploited. A synthetic positive feedback system resulting in binary expression response was transduced via lentiviral transduction. This combination ensures that the synthetic gene circuit can be installed a broad range of mammalian cells including primary cells. After stable integration into the host cell the synthetic gene circuit displayed a bimodal expression pattern and the resulting experimental data were used to construct a mathematical model. The model followed closely the observed in vivo data and predicted a strong hysteretic response of the positive feedback loop. The in silico data were experimentally verified demonstrating the value of this concerted approach.
Bimodal expression from a lentiviral transduced positive feedback loop
Efficient transduction and long-term stable expression of transgenes is achieved with the help of lentiviral transfer vectors both for basic research and gene therapeutic approaches . Several generations of lentiviral vectors have been developed and allowed to successively reduce viral sequences . These modifications led to higher safety. Importantly, through the deletion of the viral cis-acting regulatory elements (viral promoter, enhancer) the expression pattern is determined by the nature of the transduced expression cassette.
We chose a 3rd generation lentiviral vector devoid of any viral promoter elements for transduction of the synthetic expression module. This excluded any interference in between the viral vector backbone and the synthetic gene regulation circuit. A transcriptionally regulated gene circuit based on the Tetracycline(tet)-system was implemented in the lentiviral vector. This synthetic module was designed to generate a positive feedback response. Initiation of the positive feedback loop is achieved by a low basal level of the transactivator rtTA (Fig. 1A). This configuration meets the requirements for a synthetic gene circuit as its regulation is simple and homogenously achievable without any adverse/side effects mediated by the inducer. Secondly, it facilitates rapid induction and repression kinetics as well as multiple cycles of induction and repression. To precisely follow the induction/repression properties of this gene circuit a destabilized enhanced green fluorescent protein (eGFP) mutant  is coregulated, thereby reflecting the transcription of the transactivator. eGFP can be monitored in viable cells and facilitates the monitoring of expression on single cell level e.g. by flow cytometry.
(a) Vector map of pJSARGFP transducing the positive feedback loop. (b) NIH3T3 cells were stably transduced through lentiviral infection with pJSARGFP. A representative clone was cultivated for four days with the indicated Dox concentrations (in µg/ml) and analyzed for GFP expression using flow cytometry. The numbers in brackets represent the percentage of cells which fall in the respective marker regions. The bimodal response is clearly visible from this data.
Each node corresponds to a reaction governed by a transition propensity, with lines and arrows representing reactants and products, respectively. A dotted line signifies that the ‘reactant’ is not consumed.
The simulations based on the Gillespie algorithm were run as described in the text. Increasing concentrations of Dox (0, 0.5, 1, 1.5 and 2.5 µg/mL) were applied as indicated. The resulting transactivator molecule counts were monitored. The population histograms show the probability of a respective transactivator level. The system parameters were kon = 20, koff = 20, sA = 50, sR = 5, sP = 0.2, δM = 0.1, δP = 0.05, k+ = 20 and k− = 10.
Based on the simulations in Figure 3 and corresponding simulations of the on→off transitions. The lower curve represents the percentage of cells in the ‘HIGH’ expression region as the concentration of Dox is gradually increased. The upper curve shows the percentage of cells in the ‘HIGH’ expression region after a transition from a saturating Dox level to that shown.
(a) Cells carrying the autoregulated cassette (Fig. 1A) were cultivated with 1 µg/mL of Dox for 4 days and then sorted. The eGFP positive cell population is designated with ‘high’, the eGFP negative cell population is designated with ‘low’. After sorting the cells were cultivated for additional 4 days with the indicated Dox concentrations. (b) The number of GFP positive cells is plotted against the applied Dox concentration. The blue line reflects the off→on experiment, the red line the corresponding on→off experiment.
We implemented the autoregulatory expression module in NIH3T3 cells using lentiviral gene transfer. Cell clones were established and expression was monitored on the single cell level by flow cytometry (Data from a representative clone is shown.). Increasing concentrations of the inducer were applied to investigate the pattern of expression response (Fig. 1B). Saturating inducer concentrations (2.5 µg/mL Doxycycline (Dox)) caused homogeneous activation and all cells showed eGFP expression. At non-saturating concentrations of the inducer (0.5–1.5 µg/mL) the population was split and yielded a binary population distribution. By varying the inducer concentration, the ratio of expressing to non-expressing cells could be adjusted. This is a specific property of the positive feedback loop since constant high level expression of the transactivator yielded a graded transcriptional response (data not shown and ). Further, constitutive co-expression of the transactivator in these cells turned the response to a graded mode [data not shown].
Mathematical modelling of the binary expression module
A mathematical description of the synthetic module was produced. Standard stochastic techniques were employed to try and recreate the binary response , . For this purpose, the particular regulatory network was modelled as a discrete, multi-valued, continuous time Markov process. This mathematical simulation was based on the reaction scheme proposed in Fig. 2. For the sake of simplicity, the eGFP loop that is simultaneously activated and that mirrors tTA expression was excluded. In this reaction scheme, the ‘allowable’ events are synthesis and degradation of mRNA (at two rates, ON and OFF, respectively), synthesis and degradation of proteins, the binding of Dox to the rtTA to form the activator complex, gene switching upon binding of the activator complex to the promoter and a term which reflects competition for Dox within the cellular population. The system was simulated using the Gillespie algorithm . Since exact values for the state transition propensities are not available, we used typical values from Kaern et al. (2005), which were then uniformly scaled to calibrate with the expected time scales.
The simulations were run using different initial concentrations of the inducer Dox (off→on simulation). Fig. 3 summarises the results obtained from 20,000 independent simulations per given Dox concentration. These results demonstrate two distinct steady state levels of the transactivator, a ‘HIGH’ and a ‘LOW’ fraction. With increasing concentration of Dox the probability for the ‘HIGH’ fraction increases. Thus, the simulation reflects the bimodal distribution across the population as observed in the in vivo setting.
Hysteretic response of the positive-feedback
Strong positive feedback loops are often associated with hysteresis . We tested if the mathematical algorithms as applied here would predict such behaviour; for this purpose, the simulations were run with inducer concentrations of 0, 0.5, 1.0, 1.5 and 2.5 µg/mL, but applying initial condition vectors that were taken from the end of the earlier simulations at saturating inducer levels (on→off simulation). The mathematical simulation showed that for the on→off situation a much lower concentration of the inducer was needed to switch off the system and decrease the probability of a given cell being in the ‘HIGH’ fraction. A summary of the on→off simulations is provided in Figure 4; for comparison, the corresponding graph for the off→on simulation is also indicated. Thus, the history of the system clearly defines the distribution within the population: for example, while a shift from 0 to 1 µg/mL of Dox gives rise to a clear binary pattern with 70% of cells in the ‘HIGH’ fraction, the downward shift from 2.5 µg/mL to 1 µg/mL results in more than 80% of the cells remaining ‘HIGH’. Importantly, for all applied concentrations of Dox, the final distribution favoured the ‘HIGH’ expression level for the on→off simulation.
We asked if this mathematical prediction is supported by experimental data and transferred the conditions used for simulation to isogenic cells with different cultivation histories. For this purpose, cells were cultivated for four days with non-saturating inducer concentrations (1 µg/ml). This treatment generates two populations (see Fig. 1B). Both cell populations were sorted and subsequently again cultivated with different inducer concentrations (0, 0,1, 0,5, 0,75, 1,0, 1,5, 2,0 and 2,5 µg/mL Dox). As expected, both populations behaved uniformly for 0 Dox and 2,5 µg/mL Dox: both ceased expression of eGFP upon cultivation without any Dox, and showed fully activated expression under saturating conditions (2.5 µg/mL). However, the cell pools displayed an inhomogeneous expression pattern at non-saturating levels of 0.1–2.0 µg/mL: while cells from the ‘low’ population provided a bimodal distribution, the ‘high’ population cells remained fully induced at inducer levels of 0.5 µg/mL and above (Fig. 5A). Only cells, cultivated with low concentrations of the inducer (0.1 µg/mL and below) also showed a bimodal expression pattern resulting in two populations. In (Fig. 5B) the obtained expression are plotted against the Dox concentration. Together, these data confirm the hysteretic behaviour of the cells as predicted from the mathematical model.
A goal of synthetic biology is to describe and understand naturally occurring networks by constructing synthetic analogues. Mathematical modelling of such synthetic modules allows to describe and evaluate the installed networks. Further, predictions can be made which are subsequently experimentally verified. However, the installation of synthetic gene circuits in cells of higher eukaryotes is still not sufficiently solved. In particular, primary cells or even animals are so far not available for systems biology approaches. This is attributed not only to the genetic and phenotypic complexity of these natural systems but also to the lack of reliable methods to implement synthetic cassettes. Here, we show that expression cassettes conferring bimodal expression can be efficiently transduced with the help of lentiviral vectors. The results presented here were obtained with an immortalized cell line (NiH3T3 cells). However, the real strength of lentiviral transduction is that not only cell lines but also primary cells of different origin and from different species can be transduced. Preliminary data demonstrate that transduction of the synthetic gene regulation circuit is feasible and efficient also in primary cells, Importantly, the expression characteristics of the positive feedback loop are comparable to those observed in the NiH3T3 cells (data not shown). Establishing a mathematical model based on stochasticity we further describe and predict expression patterns.
Stochasticity is frequently encountered in biological systems. In particular, they contribute to transcriptional and translational processes , –. Generally, it would be expected that stochasticity would compromise the precise control of gene expression levels eventually with detrimental consequences. Indeed, this has been described for several situations , , . However, stochasticity also provides a mechanism to generate certain diversification of individual cells within a population–and thus is advantageous under certain conditions, e.g. when the cell encounters stress conditions . Different natural networks in which stochastic expression leads to a phenotypic heterogeneity of isogenic cells have been described [reviewed in 33]. This includes the lysogeny decision in phage lambda; here, an initially homogenous population is split due to molecular fluctuation . Also, the HIV-1 Tat expression module gives rise to fluctuations that create distinct phenotypes from a single proviral integration .
In mammalian systems, stochasticity seems to play a particularly important role in development and differentiation processes such as hematopoiesis . Such decisions are also encountered in networks governing apoptosis  and the cell cycle . Also, stochasticity can be involved in diseases, in particular in those which arise from transcription factor haploinsufficiency; upon stochastic simulation evidence was given that haploinsufficient systems are more susceptible to disturbances in expression . Experimental evidence confirmed this result, demonstrating a decreased probability of gene activation in haploinsufficient cells . In summary, it seems that stochastic fluctuations, whilst problematic in a homeostatic context, may prove to be essential within the context of development and differentiation of cellular populations.
In previous studies it was demonstrated that a bimodal expression pattern was realized when a repressor and a transactivator compete for the same DNA binding site  by two interlinked negative feedback loops ,  or by positive feedback and mutual expression . Here, we show that a less complex network consisting of a transactivator and its responsive promoter is sufficient for provoking bimodal expression in a mammalian system. In this respect, the described positive feedback modules represent ideal building blocks to artificially provoke all-or-nothing-answers in mammalian cells.
The mathematical model predicts a hysteretic expression pattern from the synthetic positive feedback loop. This prediction was experimentally verified. Such a strong a strong hysteretic response is expected to occur only from strong positive feedback loops. The hysteretic response of feedback modules can be tuned by the strength of the positive feedback . To achieve such a response with the synthetic modules presented here, transactivator mutants eliciting activation at different inducer levels  might be of benefit. Furthermore, the hysteretic response can be modulated to different strengths through the connection of a positive feedback loop with a transcriptional repressor .
This latter approach pinpoints that for the establishment of complex multigene networks, several non-interacting switches (transactivators) or relais (promoters) are needed. Progress has been made in the creation of independent gene regulation for mammalian systems [for review see 48]. The combination of different systems within single cells or animals would allow to differentially control distinct circuits. As exemplified by this study the lentiviral transduction of a synthetic positive feedback circuit proves useful. Exploiting this tool for transduction of independently regulated synthetic modules will allow to reliably install more complex networks in mammalian cells including primary cells. Thereby, it provides an important step to synthetically modify these systems for systems biology approaches.
Materials and Methods
Murine fibroblast NIH3T3 cells (ATCC CRL-1658) and 293T cells (human embryonal kidney cells transduced with the simian virus 40 large T antigen) were maintained in Dulbecco's modified Eagle's medium (DMEM). Media were supplemented with 10% fetal calf serum, 2 mM L-glutamine and penicillin (10 U/ml), and streptomycin (100 µg/mL). Doxycycline (Dox) was dissolved in ethanol, filtered and stored at −20°C. The genetic insert, pJSARGFP (synonym: TREAutoR3) was described previously .
Lentiviral production was achieved through calcium phosphate transfection of four plasmids. For this purpose, 2×105 (293T) cells were plated per 9 cm2 one day prior to transfection. The lentiviral expression module was transfected into 2×105 293T cells, along with the helper plasmids pLP1 (gag-pol), pLP2 (Rev) and pLP/VSV-g (VSV g) (all obtained from Invitrogen). For transfection, 1,3 µg of lentiviral expression plasmid with 0,9 µg of pLP1, 0,3 µg of LP2, and 0,5 µg of pLP/VSVg were mixed with 15 µL 2.5 M CaCl2, and adjusted with H2O to give a final volume of 150 µL. The DNA solution was dropwise added to 150 µL HEBS (280 mM NaCl, 50 mM HEPES, 1.5 mM Na2HPO4, pH 7.1) under vigorous vortexing and incubated at room temperature for 10 min. After 12 h the transfection media was renewed and the virus containing supernatant was collected two and three days after transfection. The supernatant was filtered (pore size 0.45 µm) and frozen at −70°C. For infection 1*105 NIH3T3 were plated per 9 cm2 dish a day prior to infection. At the day of infection the viral supernatant was supplemented with Polybrene (8 µg/mL) and added to the cells for 8 h. The multiplicity of infection was set to 1 to obtain single copy integration of the synthetic gene circuit.
Reporter Gene Expression
To determine eGFP expression 1×105 cells were cultivated per 6 well plate with the indicated Dox concentrations for the indicated time spans. The cells were washed with PBS, trypsinized and centrifuged at 200 g for five minutes. Cells were stained with Propidium iodide (50 µg/mL) to exclude dead cells from the analysis. The cells were analysed for eGFP expression by flow cytometry using a FACSCalibur (Becton Dickinson).
Mathematical modelling of the binary expression module
A mathematical description of the synthetic module was developed. This mathematical simulation was based on the reaction scheme proposed in Fig. 2. The particular regulatory network was modelled as a discrete, multi-valued, continuous time Markov process which is amenable to standard stochastic techniques. The actual simulations were performed using the Gillespie algorithm as implemented in the SimBiology package, produced by The MathWorks. , . In essence, the Gillespie algorithm maintains a count of the number of molecules of each species currently in the cell. These counts are updated at random times based on a set of propensities which are defined and calculated using a given reaction scheme.
Conceived and designed the experiments: DW TM LE JG. Performed the experiments: TM LE SH. Analyzed the data: DW TM HH LE JG. Wrote the paper: DW TM HH LE JG.
- 1. Becskei A, Serrano L (2000) Engineering stability in gene networks by autoregulation. Nature 405: 590–593.
- 2. Blake WJ, Kaern M, Cantor CR, Collins JJ (2003) Noise in eukaryotic gene expression. Nature 422: 633–637.
- 3. Elowitz MB, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature 403: 335–338.
- 4. Gardner TS, Cantor CR, Collins JJ (2000) Construction of a genetic toggle switch in Escherichia coli. Nature 403: 339–342.
- 5. Guet CC, Elowitz MB, Hsing W, Leibler S (2002) Combinatorial synthesis of genetic networks. Science 296: 1466–1470.
- 6. Hasty J, McMillen D, Collins JJ (2002) Engineered gene circuits. Nature 420: 224–230.
- 7. Becskei A, Boselli MG, van Oudenaarden A (2004) Amplitude control of cell-cycle waves by nuclear import. Nat Cell Biol 6: 451–457.
- 8. Weber W, Fussenegger M (2006) Pharmacologic transgene control systems for gene therapy. J Gene Med 8: 535–556.
- 9. Kramer BP, Viretta AU, Daoud-El-Baba M, Aubel D, Weber W, et al. (2004) An engineered epigenetic transgene switch in mammalian cells. Nat Biotechnol 22: 867–870.
- 10. Kramer BP, Fussenegger M (2005) Hysteresis in a synthetic mammalian gene network. Proc Natl Acad Sci U S A 102: 9517–9522.
- 11. Weber W, Stelling J, Rimann M, Keller B, Daoud-El Baba M, et al. (2007) A synthetic time-delay circuit in mammalian cells and mice. Proc Natl Acad Sci U S A 104: 2643–2648.
- 12. Kay MA, Glorioso JC, Naldini L (2001) Viral vectors for gene therapy: the art of turning infectious agents into vehicles of therapeutics. Nat Med 7: 33–40.
- 13. Loew R, Selevsek N, Fehse B, von Laer D, Baum C, et al. (2004) Simplified generation of high-titer retrovirus producer cells for clinically relevant retroviral vectors by reversible inclusion of a lox-P-flanked marker gene. Mol Ther 9: 738–746.
- 14. Schucht R, Coroadinha AS, Zanta-Boussif MA, Verhoeyen E, et al. (2006) A new generation of retroviral producer cells: predictable and stable virus production by Flp-mediated site-specific integration of retroviral vectors. Mol Ther 14: 285–292.
- 15. Fiering S, Whitelaw E, Martin DI (2000) To be or not to be active: the stochastic nature of enhancer action. Bioessays 22: 381–387.
- 16. Acar M, Becskei A, van Oudenaarden A (2005) Enhancement of cellular memory by reducing stochastic transitions. Nature 435: 228–232.
- 17. Ozbudak EM, Thattai M, Lim HN, Shraiman BI, van Oudenaarden A (2004) Multistability in the lactose utilization network of Escherichia coli. Nature 427: 737–740.
- 18. Pomerening JR, Sontag ED, Ferrell JE Jr (2003) Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2. Nat Cell Biol 5: 346–351.
- 19. Pomerening JR, Kim SY, Ferrell JE Jr (2005) Systems-level dissection of the cell-cycle oscillator: bypassing positive feedback produces damped oscillations. Cell 122: 565–578.
- 20. Sha W, Moore J, Chen K, Lassaletta AD, Yi CS, et al. (2003) Hysteresis drives cell-cycle transitions in Xenopus laevis egg extracts. Proc Natl Acad Sci U S A 100: 975–980.
- 21. Serfling E, Chuvpilo S, Liu J, Hofer T, Palmetshofer A (2006) NFATc1 autoregulation: a crucial step for cell-fate determination. Trends Immunol 27: 461–469.
- 22. Podtschaske M, Benary U, Zwinger S, Hofer T, Radbruch A, et al. (2007) Digital NFATc2 Activation per Cell Transforms Graded T Cell Receptor Activation into an All-or-None IL-2 Expression. PLoS ONE 2: e935.
- 23. Ferrell JE Jr (2002) Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability. Curr Opin Cell Biol 14: 140–148.
- 24. Kobayashi H, Kaern M, Araki M, Chung K, Gardner TS, et al. (2004) Programmable cells: interfacing natural and engineered gene networks. Proc Natl Acad Sci U S A 101: 8414–8419.
- 25. Rossi FM, Kringstein AM, Spicher A, Guicherit OM, Blau HM (2000) Transcriptional control: rheostat converted to on/off switch. Mol Cell 6: 723–728.
- 26. Becskei A, Seraphin B, Serrano L (2001) Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion. EMBO J 20: 2528–2535.
- 27. Wiznerowicz M, Trono D (2005) Harnessing HIV for therapy, basic research and biotechnology. Trends Biotechnol 23: 42–47.
- 28. Delenda C (2004) Lentiviral vectors: optimization of packaging, transduction and gene expression. J Gene Med 6: Suppl 1S125–S138.
- 29. Li X, Zhao X, Fang Y, Jiang X, Duong T, et al. (1998) Generation of destabilized green fluorescent protein as a transcription reporter. J Biol Chem 273: 34970–34975.
- 30. Kringstein AM, Rossi FM, Hofmann A, Blau HM (1998) Graded transcriptional response to different concentrations of a single transactivator. Proc Natl Acad Sci U S A 95: 13670–13675.
- 31. McAdams HH, Arkin A (1997) Stochastic mechanisms in gene expression. Proc Natl Acad Sci U S A 94: 814–819.
- 32. Gillespie DT (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computational Physics 22: 403–434.
- 33. Kaern M, Elston TC, Blake WJ, Collins JJ (2005) Stochasticity in gene expression: from theories to phenotypes. Nat Rev Genet 6: 451–464.
- 34. Xiong W, Ferrell JE Jr (2003) A positive-feedback-based bistable ‘memory module’ that governs a cell fate decision. Nature 426: 460–465.
- 35. Ozbudak EM, Thattai M, Kurtser I, Grossman AD, van Oudenaarden A (2002) Regulation of noise in the expression of a single gene. Nat Genet 31: 69–73.
- 36. Elowitz MB, Levine AJ, Siggia ED, Swain PS (2002) Stochastic gene expression in a single cell. Science 297: 1183–1186.
- 37. Golding I, Paulsson J, Zawilski SM, Cox EC (2005) Real-time kinetics of gene activity in individual bacteria. Cell 123: 1025–1036.
- 38. Raser JM, O'Shea EK (2005) Noise in gene expression: origins, consequences, and control. Science 309: 2010–2013.
- 39. Fraser HB, Hirsh AE, Giaever G, Kumm J, Eisen MB (2004) Noise minimization in eukaryotic gene expression. PLoS Biol 2: e137.
- 40. Blake WJ, Balazsi G, Kohanski MA, Isaacs FJ, Murphy KF, Kuang Y, Cantor CR, Walt DR, Collins JJ (2006) Phenotypic consequences of promoter-mediated transcriptional noise. Mol Cell 24: 853–865.
- 41. Arkin A, Ross J, McAdams HH (1998) Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. Genetics 149: 1633–1648.
- 42. Weinberger LS, Burnett JC, Toettcher JE, Arkin AP, Schaffer DV (2005) Stochastic gene expression in a lentiviral positive-feedback loop: HIV-1 Tat fluctuations drive phenotypic diversity. Cell 122: 169–182.
- 43. Hoang T (2004) The origin of hematopoietic cell type diversity. Oncogene 23: 7188–7198.
- 44. Legewie S, Bluthgen N, Herzel H (2006) Mathematical modeling identifies inhibitors of apoptosis as mediators of positive feedback and bistability. PLoS Comput Biol 2: e120.
- 45. Hat B, Paszek P, Kimmel M, Piechor K, Lipniacki T (2007) How the number of alleles influences gene expression. Journal of Statistical Physics 128 (1–2): 511–533.
- 46. Magee JA, Abdulkadir SA, Milbrandt J (2003) Haploinsufficiency at the Nkx3.1 locus. A paradigm for stochastic, dosage-sensitive gene regulation during tumor initiation. Cancer Cell 3: 273–283.
- 47. Baron U, Schnappinger D, Helbl V, Gossen M, Hillen W, et al. (1999) Generation of conditional mutants in higher eukaryotes by switching between the expression of two genes. Proc Natl Acad Sci U S A 96: 1013–1018.
- 48. May T, Hauser H, Wirth D (2006) Current status of transcriptional regulation systems. Cytotechnology 50 (1–3): 109–119.
- 49. Markusic D, Oude-Elferink R, Das AT, Berkhout B, Seppen J (2005) Comparison of single regulated lentiviral vectors with rtTA expression driven by an autoregulatory loop or a constitutive promoter. Nucleic Acids Res 33: e63.