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Synchronous Long-Term Oscillations in a Synthetic Gene Circuit

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Synchronous Long-Term Oscillations in a Synthetic Gene Circuit View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Apollo Noise-proofing the repressilator: synchronous long-term oscillations in a synthetic gene circuit Laurent Potvin-Trottier†‡ Nathan D. Lord† Glenn Vinnicombe§ Johan Paulsson† Synthetically engineered genetic circuits can perform a error propagation from the reporter system, from core cellular 55 wide range of tasks but generally with lower accuracy than processes, and from within the circuit itself. 5 natural systems. Here we revisited the first synthetic ge- netic oscillator, the repressilator1, and modified it based The repressilator consists of three genes – tetR from the Tn10 transposon, cI from bacteriophage λ and lacI from the lac- on principles from stochastic chemistry in single cells. 20 Specifically, we sought to reduce error propagation and in- tose operon – and each repressor has a C-terminal ssrA tag formation losses, not by adding control loops, but by sim- that targets it for degradation (Fig. 1A). The whole circuit was 60 encoded on a low-copy pSC101 plasmid in an Escherichia coli 10 ply removing existing features. This created highly reg- ular and robust oscillations. Some streamlined circuits strain lacking lacI, and a second high-copy ColE1 reporter plas- mid encoded GFP under the control of TetR with a modified kept 14 generation periods over a range of growth con- 1,21 ditions and kept phase for hundreds of generations in sin- degradation tag . We first reevaluated this circuit using a gle cells, allowing cells in flasks and colonies to oscillate microfluidic device in which cells are trapped in short chan- 65 nels and newborn cells are washed away by fresh medium22,23 15 synchronously without any coupling between them. Our results show that even the simplest synthetic genetic net- (Fig. 1A). Tracking reporter levels under the microscope for works can achieve a precision that rivals natural systems, hundreds of consecutive generations across hundreds of single- and emphasize the importance of noise analyses for cir- cell traces (Methods) revealed clear oscillatory dynamics in all cuit design in synthetic biology. cells (Figs. 1B and S1A), particularly in the rate of production 70 (Fig. S1A). This shows that the simple design was sound and 20 Many biological systems show remarkably precise and ro- that some of the erratic behavior originally reported was due bust dynamics. For example, the circadian clock in cyanobacte- to the limited imaging platforms available at the time. ria uses a combination of transcriptional and post-translational We next evaluated how much of the noise reflected error 2,3 control mechanisms to keep phase for weeks without en- propagation from the reporter system. Mathematical predic- 75 trainment, while displaying robustness to changes in temper- tions have suggested that high-copy ColE1 cloning vectors 3–5 25 ature and growth rate . Synthetic circuits built from well- fluctuate substantially and slowly, due to poorly controlled self- characterized parts can also exhibit a wide range of dynam- replication, and therefore effectively transmit fluctuations to en- ical features – including arithmetic computations6,7, oscilla- coded proteins24. Moving the YFP reporter onto the low-copy 1,8–13 14 15 tions , logic gates and edge detection – but often with repressilator plasmid indeed reduced the relative standard de- 80 lower accuracy. For example, the repressilator1, a now iconic viation in amplitude greatly, from 78% to 36% (Fig. 1D, S2F and 30 device that helped jump-start the field of synthetic biology 15 S3B). Degradation tagged reporter proteins have also been pre- years ago, showed clear signs of oscillations using a simple dicted to potentially have ‘retroactivity’ effects on oscillations25 design where three genes inhibit each other’s production in a due to competition for shared proteases. Protease competi- single loop (A B C A). However, only about 40% of cells were tion has in fact been cleverly exploited for improved control in 85 ⊣ ⊣ ⊣ found to support oscillations, and those oscillations were quite synthetic circuits13, but stochastic theory24,26 suggests that sat- 35 irregular. Subsequent synthetic oscillators evaluated different urated degradation enzymes also can create effects related to control topologies or repression mechanisms8–13, but most were dynamic instability of microtubules, with large random fluctu- again quite irregular in both phase and amplitude despite being ations in single cells. Comparing a range of constructs indeed mathematically designed to display sustained oscillations in a showed that the synthetic degradation tag caused fluctuations 90 broad range of parameters. to propagate from the reporter proteins to the repressors via 40 The challenge when designing synthetic circuits to operate the proteolysis system. Surprisingly, however, the ’compet- reliably in single cells is that biochemical noise can do more ing’ reporter proteins accelerated the degradation of ssrA-tagged than just create different rate constants in different cells. On substrates (SI §3.1.1). Removing this interference created very one hand, simple intrinsic noise can in principle enhance con- regular oscillations, with periods increasing from 2.4 to 5.7 95 16 ∼ ∼ trol and even create high-quality oscillations in systems that generations (Fig. 1D-E, S1B, S2B and S3C). Characterizing the 45 could not display limit cycles for any rate constants in the ab- phase drift – the statistical tendency of oscillations in individual sence of noise17,18. On the other hand, any component present cells to go out of phase with each other – showed that on aver- in low numbers can in principle randomize behavior of the age this circuit oscillates for 5.5 periods before accumulating ∼ whole system, and a single stochastic signaling step can intro- half a period of drift (SI §2.5.5). 100 19 duce fundamental constraints that cannot be overcome by any In cell-free extracts, i.e., without the low-copy noise of single 50 control system. This suggests that simplicity could even help cells, the repressilator has been shown to display the sinusoidal achieve accurate oscillations as long as stochastic effects are ac- curves expected for harmonic oscillators27. However, analyz- counted for in the design, and that minimal control topologies ingthehighlyasymmetricshapeofthetimetracesinsinglecells ff 28 may be not only be elegant and interesting but also very e ec- shows that it effectively operates as a relaxation oscillator , i.e., 105 tive. We therefore revisited the original repressilator to reduce with a characteristic build-up phase sharply followed by an al- most pure dilution and degradation phase until concentrations Dept. of Systems Biology,Harvard Medical School, 200 Longwood † reach very low levels (Fig. 1D and Box 1). The mathematical Ave, Boston, MA 02115, USA ‡ Biophysics Program, Harvard Univer- sity, Cambridge, MA § Dept. of Engineering, University of Cambridge, conditions for sustained harmonic oscillations – cooperative 1 Cambridge CB2 1PZ, UK repression and similar mRNA and protein half-lives – are then 110 1 f = 0.10 div -1 Repressilator Reporter Time (minutes) max A B A 0.12 P 0 250 500 1 LlacO1 3 8 ∆clpXP 0.08 PLtetO1 cI-LAA tetR-LAA PSD tetR GFP-ASV 6 0.6 0.04 2 P 00 1 2 3 4 LtetO1 cI lacI 4 0.2 Freq. (f max ) PR 1 2 lacI-LAA ColE1 Ori -0.2 pSC101 Ori Concentration Concentration 0 0 Concentration ACF 0 5 10 15 20 0 10 20 30 40 50 60 0 10 20 30 Time (generations) Time (generations) Time (generations) 1 ) 0.12 2 C B YtoC RtoY Without With 0.08 f =0.42 div -1 8 * 0.5 max sponge sponge 0.04 CtoR TetR 15 Rate PSD 6 Media !ow 0 0 0 2 4 6 0 1 2 3 4 Time (generations) Frequency (f ) 4 CI LacI 10 Concentration ACF max DE 0.2 -1 2 5 fmax = 0.17 div 2 Concentration [YFP] 0.1 PSD 0 Avg (gen.) or Var (gen. 0 1 1 0 10 20 30 40 AvgVar Avg Var Time (generations) 0 0 mCherry-ASV 0.5 0 1 2 3 4 C 8 P ∆clpXP, 6 fmax = 2 LtetO1 Frequency (f max ) 0.2 Loss with 0.073 div -1 0.1 0 PSD 1 event 6 sponge 1 0 0 [mCherry] 0 20 40 ColE1 Ori Concentration ACF 0 1 2 3 4 0 -0.5 4 Freq. (f ) 0 10 20 30 40 50 0 5 10 15 20 0.5 max Time (generations) Time (generations) ) 200 2 2 F 0.6 Concentration 0 150 0.4 0 -0.5 100 0 10 20 30 40 50 60 Concentration ACF 0 10 20 30 40 Counts Time (generations) Time (generations) 50 0.2 0 0 0 1 2 3 4 5 Variance (period 0 1 2 3 4 5 Figure 2: Identifying and eliminating inherent sources of error. A) Interpeak distance (period) Number of periods Typical time trace in ∆clpXP cells (LPT61) where repressors are not degraded. ACF and PSD calculated over 5,356 cell divisions. The Figure 1: Reducing reporter interference. A) Schematics of the origi- average period was 10 generations, and the correlation coefficient nal repressilator plasmids as described in text and microfluidic device was 0.1. Dashed vertical lines are separated by an average period where E. coli cells are diffusively fed in growth channels and daugh- to illustrate periodicity in A-C. B) (Left) Time trace of multi-reporter ters eventually are washed away. B) Typical time trace of a single repressilator (∆clpXP, LPT113). TetR represses the production of YFP cell for original repressilator (NDL332). The GFP concentration (green (yellow trace), LacI inhibits the production of CFP (blue trace) and CI trace) oscillates noisily while a constantly expressed RFP (red trace) represses the production of RFP (red trace). Peak indicated by asterisk stays constant. Both traces were normalized to their means.
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