Synchronous long-term oscillations in a synthetic gene circuit

Abstract

Synthetically engineered genetic circuits can perform a wide variety of tasks but are generally less accurate than natural systems. Here we revisit the first synthetic genetic oscillator, the repressilator1, and modify it using principles from stochastic chemistry in single cells. Specifically, we sought to reduce error propagation and information losses, not by adding control loops, but by simply removing existing features. We show that this modification created highly regular and robust oscillations. Furthermore, some streamlined circuits kept 14 generation periods over a range of growth conditions and kept phase for hundreds of generations in single cells, allowing cells in flasks and colonies to oscillate synchronously without any coupling between them. Our results suggest that even the simplest synthetic genetic networks can achieve a precision that rivals natural systems, and emphasize the importance of noise analyses for circuit design in synthetic biology.

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Figure 1: Reducing reporter interference.
Figure 2: Identifying and eliminating inherent sources of error.
Figure 3: The modified repressilator shows great robustness to growth conditions.

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Acknowledgements

We thank M. Elowitz for the repressilator plasmids, D. Landgraf for strains and plasmids, P. Cluzel for the fluorescent proteins, S. G. Megason and his laboratory for their microscope, R. Chait and M. Baym for the macroscope and C. Saenz for technical help on the microfluidics device. Some work was performed at the Harvard Medical School Microfluidics Facility and the Center for Nanoscale Systems, a member of the National Nanotechnology Infrastructure Network supported by NSF award ECS-0335765. L.P.-T. acknowledges fellowship support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Fonds de recherche du Québec – Nature et technologies. This work was supported by National Institutes of Health (NIH) grants (GM081563 and GM095784) and NSF award 1517372.

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Authors

Contributions

L.P.-T. and J.P. conceived the study and did the theoretical analysis with G.V. Experiments and data analysis were done by L.P.T. with help from N.D.L. All authors wrote the paper.

Corresponding author

Correspondence to Johan Paulsson.

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The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks J. Stelling and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Figure 1 Oscillations in the original and integrated repressilator circuits.

a, b, Original (NDL332, GFP production rate) (a) and integrated (LPT25, YFP concentration) (b) repressilator oscillations are sustained for more than 100 generations. The two time traces were normalized to their respective means. Three peaks in a indicated by asterisks have been clipped owing to their high amplitude (5.9, 7.1 and 4.8) to allow better visualization of the oscillations. IPTG was added to the media for the time period indicated by the red bar (in a) to synchronize the cells in the device.

Extended Data Figure 2 Interference from the reporter plasmid.

a, b, Oscillations of the integrated repressilator with the PLtet-mCherry-ASV plasmid (LPT54) have a more constant peak amplitude compared to the original repressilator (a), indicated by the CV of the peak amplitude decreasing from 0.78 to 0.36 (b). The inset in b zooms in on the tails of the distributions. c, Additional plasmid loss event of integrated repressilator with PLtet-mCherry-ASV reporter. The reporter plasmid is lost around generation 34, as evidenced by the loss of red fluorescence. The oscillation period shifts quickly from approximately 2 to 5 generations after the plasmid loss event. d, Example time trace of the integrated repressilator, without the reporter plasmid (LPT25). The YFP production rate oscillates (yellow trace), whereas the segmentation marker (blue trace) stays relatively constant (close-up of the shaded region on top). Both traces were normalized to their respective means. e, ACF and PSD were calculated over the whole population (8,694 total generations) and demonstrate strong oscillatory behaviour, with an average period of 5.6 generations. The width of the window function used for calculating the power spectrum is indicated by a red line.

Extended Data Figure 3 Summary of results explaining the difference in period between the original and integrated repressilator.

a, The PLtet sponge (LPT44) makes the oscillation slightly shorter and more regular compared to the empty plasmid (LPT45), but cannot explain the change in period. b, Increasing the expression of ‘competing’ substrates tagged with the asv tag makes the oscillations faster. The period gradually decreases from 5.5 generations for the empty plasmid (LPT45) to 4.2 with PLtet-peptide-ASV (LPT46), to 2.6 with PLtet-mCherry-ASV (LPT54), and to 2.3 with Pconst-darkGFP-ASV (LPT53). c, Removing the degradation tag on the reporter of the original repressilator (LPT60) produces oscillations very similar to the integrated repressilator with the sponge (LPT44). d, Summary of the period of the different construct presented in this figure, compared to the original (NDL332) and integrated repressilator (LPT25). Introduction of ASV-tagged molecules is sufficient to explain the change in period, whereas introduction of LAA-tagged molecules slows down the oscillations (LPT55). Overexpressing a functional ClpP–mGFPmut3 fusion protein makes the period slightly faster (5.4 generations, LPT159), but does not rescue the effect of the ASV-tagged proteins (2.8 generations, LPT165). e, Expressing ASV-tagged molecules in the absence of the repressilator lowers the mean abundances of ssrA-tagged molecules around fourfold, suggesting that the presence of ASV-tagged molecules causes faster degradation rates. f, In the ΔclpXP background, the oscillations are not affected by the presence of ASV-tagged molecules or additional reporter. gi, Triple reporter with PLtet sponge (LPT127), triple reporter with PLtet-mCherry-ASV (LPT118) and single reporter with PLtet-mCherry-ASV (LPT64) have very similar autocorrelation functions and ring patterns. There were slight variations in the imaging conditions owing to manual focusing and non-uniformity of the LED illumination.

Extended Data Figure 4 Modelling results.

a, The repressilator can display harmonic or relaxation oscillations. The gradual transition between the regimes is shown by varying the parameter K in the minimal model (λ = 2,000 and n = 4, Supplementary Information 4.1). b, The experimental data suggest that the repressilator oscillates in the relaxation regime. Simulated time trace (blue, K = 13, λ = 103, and n = 3) is overlaid with the time trace of experimental data (from Fig. 2c, LPT64, yellow). c, Close-up of a simulated time trace (minimal model, K = 0.2, λ = 103, and n = 2, Supplementary Information 4.1) in the relaxation regime showing the three different repressors (blue, red and yellow). The oscillations can be separated into two distinct phases: an accumulation phase during which the protein (blue) is completely derepressed (red below threshold) and starts at very low numbers, and a decay phase that starts when the repressor is completely repressed (red above threshold) and ends when it goes below the repression threshold of the next component (yellow starts to accumulate). d, Relaxation oscillators have different parameter requirements for oscillations. Simulated time traces (solid lines) show oscillations without biochemical cooperativity or phase shift owing to the presence of mRNA (minimal model, K = 0.01, λ = 103, and n = 1, Supplementary Information 4.1). The deterministic differential equations with the same parameters show damped oscillations (dashed lines with flipped colours). e, Even for perfect threshold mechanism, substantial noise comes from the decay phase if the threshold (S) is too low (or too high) with respect to the peak value (N). If S << N, then the CV in one decay step goes down very slowly (1/log(N/(S + 1))). However, if it is reasonably close to its optimal value (for example, 0.05 < S/N < 0.3), it goes down much faster (). The CV is shown for different combination of S and N, as well as the asymptotic traces. f, Simulated time trace of the model of Supplementary Information 4.3.1 shows oscillations of similar shape, peak amplitude numbers, period and phase drift as the experimental data by using reasonable parameters (λ = 60, K = (5, 10, 10) for the three repressors, n = 1.5 for all repressors, , ).

Extended Data Figure 5 Period histograms and kymographs of selected strains.

Peak-to-peak distance of the oscillations was calculated as described in Methods, and the average period and the CV are reported in the figure panels. a, Original repressilator (NDL332). b, Integrated repressilator (LPT25). c, Integrated repressilator in ΔclpXP (LPT61). d, Integrated repressilator in ΔclpXP with PLtet-mCherry-ASV (LPT64). e, Integrated repressilator with PLtet sponge (LPT44). f, Integrated repressilator with PLtet-mCherry-ASV (LPT54). g, Kymographs (xyt montage) of the raw data are presented for three strains. The image of a single growth channel is presented every 1, 2 and 7 frames (5 min per frame) for the top, middle and bottom panel, respectively. The oscillations in concentration are difficult to see in the fast oscillator (although clear when looking at production rate), but can be clearly seen in the slow oscillators. The growth channels are open towards the bottom of the images, where media is flowing (as represented in the schematic of Fig. 1a).

Extended Data Figure 6 Oscillations of the repressilator without degradation tags.

a, Schematic of integrated repressilator without degradation tags, with or without the PLtet titration sponge. b, Without the titration sponge (LPT120), the oscillations are erratic in amplitude, with a correlation coefficient of 0.1 after one period. c, Addition of the sponge (LPT124) makes the oscillations much more regular, with a correlation coefficient of 0.25 after one period. d, Time trace and autocorrelation of integrated repressilator without degradation tags in ΔclpXP (LPT128). Introduction of the mutation did not change the oscillations substantially (compared to c). e, The colonies of integrated repressilator without degradation tags with PLtet sponge (LPT124) exhibit spatiotemporal ring patterns in the YFP images. f, Close-up view of the colonies show that the spatiotemporal patterns were similar if the titration sponge contained only the promoter (LPT124) or expressed an ASV-tagged peptide (LPT125), suggesting that these strains have similar oscillations.

Extended Data Figure 7 Macroscopic spatial patterns of the repressilator.

a, Time course growth of a single colony grown from a ΔclpXP mutant cell containing the integrated repressilator and titration sponge (LPT64, PLtet-mCherry-ASV). Oscillations in YFP levels produce macroscopic, ringed structures in the YFP channel (bottom), whereas such patterns are absent in the constitutive segmentation marker (CFP, middle) and gross colony morphology (bright-field, top). The bottom and left white spots in the bright-field images are reflections from the white LEDs. b, On the left, unsynchronized cells were plated and different phases of the oscillators are represented by different ring patterns (dark or bright centre of different sizes). Synchronization of the cells with IPTG makes the patterns similar, with a dark centre of the same size. c, The ring patterns do not synchronize when adjacent colonies merge into each other. d, Only the presence of the PLtet sponge is required for macroscopic oscillations, while titration of the other repressors do not greatly affect the oscillations. From left to right: LPT153, LPT154, LPT157, LPT143, LPT155, LPT156 and LPT152. Several strains were also evaluated in the microfluidic device.

Extended Data Figure 8 Characterization of the microfluidic device and of the oscillations.

a, The average division time of the integrated repressilator (LPT25) is constant over time. The inset shows the distribution of growth rates of two independent experiments (45,828 and 9,135 points are shown in the blue and red distributions, respectively), with a slight difference in the mean (1%). b, The period of the oscillations is constant in space (position in field of view, distance to inlets and outlets and different media channels) and time. Each point represents a bin of 400 (a) or 100 (b) points, with the error bars indicating s.e.m. c, The induction/repression switch of cI (reported by YFP) occurs when the transcriptional reporter for TetR (CFP) is below the detection limit. Typical time trace of multireporter repressilator without repressor degradation and with PLtet-peptide-ASV plasmid (ΔclpXP, LPT117). The production rate of YFP is shown alongside the CFP concentration. The inset shows that the switch from induction to repression occurs below the detection limit of 50 fluorescent units (FU). d, The distribution of peak amplitude of the repressilator without degradation but with titration sponge shows substantial heterogeneity (LPT64, CV of 35%). e, The peak amplitude has a small influence on the next period, owing to exponential dilution. The red line shows a fit to y = 1.99 × log(x) + 13.18, and explains 25% of the variance in the periods. Black circles are bins of 15 points of black dots (LPT64) and blue dots (LPT156). f, Estimating partitioning root mean squared (r.m.s.) errors at cell division during the dilution phase showed that it scaled binomially, and allowed us to roughly estimate a fluorescence units to protein scaling factor. Black circles are bins of 50 blue dots (LPT64). The red line shows the fit (after conversion) to , in which ni is the number of proteins in the daughters right after division, and N = n1 + n2 the number in the mother cell. g, Typical time trace of triple-reporter repressilator without degradation with a titration sponge (LPT127) in estimated protein numbers (concentration × average cell size).

Extended Data Figure 9 Robustness and synchronization of the oscillations.

a, The phase of the oscillations is independent of the phase of the cell cycle. The average phase of the oscillation phase is shown as a function of the position in the cell cycle. Each point represents a bin of 3,000 data points, which have been averaged in x and y after being sorted on their x values. The error bars represent s.e.m. and are of similar size to the symbols. Similar results were obtained for different strains, but are shown here for the integrated repressilator (LPT25). b, Synchronization of different cells in the microfluidic device was done by introducing 1 mM IPTG. The original repressilator (NDL332) shows a modest level of synchrony in the oscillations of the GFP production rate. c, The integrated repressilator shows a more robust synchronization in the YFP production rates, but takes more time to recover from the perturbation.

Extended Data Figure 10 Schematic of the major changes to the repressilator and resulting effects on the oscillations.

The original repressilator displays sustained oscillation with a period of 2.4 generations, albeit with a variable amplitude. Integrating the reporter on the pSC101 plasmid decreases the peak amplitude CV from 78% to 36%. Removing the presence of the ASV-tagged molecules then increases the period to 5.7 generations, owing to the interference with degradation of the repressors in the former case. Removing degradation entirely increases the period to 10 generations, but considerable amplitude fluctuations and phase drift subsist. Reintroducing a sponge of binding site for the TetR repressors raises the repression threshold and enables the repressilator to exhibit precise oscillations (as well as macroscopic oscillations), by decreasing the period CV from 28% to 14% and increasing the period to 14 generations. Typical time traces are shown from top to bottom of NDL332, LPT54, LPT25, LPT61 and LPT127.

Supplementary information

Supplementary Information

This file contains information about the strains, protocols for the microfluidic master fabrication, supplementary results and discussion, details on the theory and an appendix on fundamental constraints on the accuracy of the repressilator. (PDF 667 kb)

Oscillations of bacterial cultures grown in flasks

Cells containing the multi-reporter repressilator without repressor degradation and with PLtet-peptide-ASV plasmid (δclpXP, LPT117) were grown in liquid culture in 25mL flasks. After the culture was initially synchronized with IPTG, it was kept in exponential phase via dilution. Macroscopic oscillations were imaged with a digital camera equipped with appropriate LED and filters (Methods). 14 frames were acquired in total at 50 min intervals to form a time lapse, and the flask oscillates between green (YFP) and blue (CFP) for 2 cycles. (MOV 444 kb)

Image time series showing the oscillations of the original repressilator (NDL332)

The video is played at 10 frames/s and the images acquired every 5 min. From 58 to 60s, 1mM IPTG was introduced to synchronize the phase of the cells. (MOV 3553 kb)

Image time series showing the oscillations of the integrated repressilator, with PLtet-mCherry-ASV (LPT54)

The oscillations are reported by a YFP (green) while a constitutive CFP is expressed as segmentation marker (blue). The video is played at 10 frames/s and the images were acquired every 5 min. (MOV 695 kb)

Image time series showing the oscillations of the integrated repressilator (LPT25)

The video is played at 10 frames/s and the images were acquired every 5 min. From 58 to 60s, 1mM IPTG was introduced to synchronize the phase of the cells. (MOV 842 kb)

Image time series showing the oscillations of the repressilator without degradation and without titration sponge (LPT61)

The video is played at 10 frames/s and the images were acquired every 5 min. The oscillations are reported by a YFP (green) while a constitutive CFP is expressed as segmentation marker (blue). (MOV 1166 kb)

Image time series showing the oscillations of the triple reporter repressilator, without degradation and with titration sponge (LPT117)

The video is played at 10 frames/s and the images were acquired every 8 min. The cells alternate between red (RFP), green (YFP) and blue (CFP) (MOV 1665 kb)

Oscillations of repressilator without degradation and with titration sponge (LPT64), in poor growth conditions (early stationary media, OD600 ~2)

The video is played at 10 frames/s and the images acquired were every 8 min. The oscillations are reported by a YFP (green) while a constitutive CFP is expressed as segmentation marker (blue). Even though the cells have a very different physiology and are subject to stressful conditions (frequent cell deaths, filamentation, etc.), they are still oscillating with a period of ~14 generations. (MOV 588 kb)

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Potvin-Trottier, L., Lord, N., Vinnicombe, G. et al. Synchronous long-term oscillations in a synthetic gene circuit. Nature 538, 514–517 (2016). https://doi.org/10.1038/nature19841

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