Diversity in the dynamical behaviour of a compartmentalized programmable biochemical oscillator

Journal name:
Nature Chemistry
Volume:
6,
Pages:
295–302
Year published:
DOI:
doi:10.1038/nchem.1869
Received
Accepted
Published online
Corrected online

Abstract

In vitro compartmentalization of biochemical reaction networks is a crucial step towards engineering artificial cell-scale devices and systems. At this scale the dynamics of molecular systems becomes stochastic, which introduces several engineering challenges and opportunities. Here we study a programmable transcriptional oscillator system that is compartmentalized into microemulsion droplets with volumes between 33 fl and 16 pl. Simultaneous measurement of large populations of droplets reveals major variations in the amplitude, frequency and damping of the oscillations. Variability increases for smaller droplets and depends on the operating point of the oscillator. Rather than reflecting the stochastic kinetics of the chemical reaction network itself, the variability can be attributed to the statistical variation of reactant concentrations created during their partitioning into droplets. We anticipate that robustness to partitioning variability will be a critical challenge for engineering cell-scale systems, and that highly parallel time-series acquisition from microemulsion droplets will become a key tool for characterization of stochastic circuit function.

At a glance

Figures

  1. An in vitro transcriptional oscillator.
    Figure 1: An in vitro transcriptional oscillator.

    a, Schematic representation of the two-switch negative-feedback oscillator circuit. Arrowheads indicate activation of a downstream component, and the blunt end indicates inhibition. b, Molecular representation of involved reactions. DNA strands are represented by coloured lines. Complementary sub-sequences are coloured identically. RNA signals are represented by wavy lines. Black dashed lines connect transcription substrate and product, and dotted lines connect degradation substrates and remaining products. Switches SW12 (SW21) from a consist of genelets T12 (T21) that can be switched to a transcriptional active state by hybridization of an activator strand A2 (A1), which completes the promoter sequence for T7 RNAP (boxes with arrows indicate the direction of transcription). Inhibitor strands dI1 (rI2), which are complementary to activators, switch transcription off by toehold-mediated strand displacement. Excesses of activator A2 and inhibitor dI1 act as thresholds by sequestering free RNA signals up to a certain level, and thus cause a delay in the negative feedback loop that leads to oscillatory behaviour. Genelet T21 is labelled with a fluorophore (red circle) and A1 is labelled with a quencher (black circle), which results in high fluorescence for low transcription activity and vice versa. DNA sequences are given in the Supplementary Methods. c, The fluorescent time trace of switch T21 (black) and corresponding fit of the extended model (blue) of the oscillator circuit exhibit sustained oscillations. The eventual decay of oscillator amplitude and period is attributed to the build-up of incomplete RNA degradation products.

  2. Compartmentalized synthetic transcriptional oscillators.
    Figure 2: Compartmentalized synthetic transcriptional oscillators.

    a, Epifluorescence microscopy image of the transcriptional oscillator in microemulsion droplets (scale bar, 100 µm); see also the example microscopy in Supplementary Videos V1–V3. b, Fluorescent time traces for two droplets that contain the same reaction mix as the bulk oscillator in Fig. 1. Sustained oscillations in droplets were observed for more than 20 hours. The droplet image series shows microscope snapshots in fluorescent mode during the oscillation reactions. The corresponding phases in the time traces are indicated by dashed lines. Rel. amp., relative amplitude.

  3. Dynamical diversity in oscillatory behaviour caused by encapsulation of sustained and damped synthetic oscillator circuits.
    Figure 3: Dynamical diversity in oscillatory behaviour caused by encapsulation of sustained and damped synthetic oscillator circuits.

    Only droplets that identifiably oscillate are considered here. Traces were normalized to their maximum value for this figure. a, Top panel, 20 example traces (blue) for the sustained oscillator in droplets with r = 2–5 µm compared to the bulk oscillation trace (black). Bottom panel, population average of n traces (blue) and corresponding standard deviation (indicated by the purple shaded area around the average). b, As in a, but for oscillators encapsulated in droplets with r > 8 µm. c, Top, 20 example traces (blue) for the damped oscillator (r = 2–5 µm) compared to the bulk oscillation trace (black). Bottom, population average of n traces (blue) and corresponding standard deviation (purple shaded area). d, As in c, but for oscillators encapsulated in droplets with r > 8 µm.

  4. Oscillations induced by compartmentalization.
    Figure 4: Oscillations induced by compartmentalization.

    a, Population of droplets containing a reaction mixture that displays only strongly damped behaviour in bulk. The white solid box indicates the position of a droplet with r ≈ 5 µm that displays sustained oscillations, and the dashed box indicates the position of a droplet that shows damped oscillations, with r ≈ 8 µm (scale bar, 50 µm). b, Fluorescence time trace recorded from the oscillating droplet from a (light blue), the strongly damped droplet (orange) and the strongly damped bulk signal (black). The bulk trace is classified as ‘not identifiably oscillating’ by our filtering algorithms. The y axis represents the relative oscillation amplitude of the traces, which were scaled and shifted for clarity.

  5. Variation of oscillation periods and amplitudes with droplet radius for the sustained, damped and strongly damped oscillator tunings.
    Figure 5: Variation of oscillation periods and amplitudes with droplet radius for the sustained, damped and strongly damped oscillator tunings.

    ac, Dependence of mean oscillation period on droplet radius. Bars indicate the standard deviation, whereas the shaded areas represent the range in which 60% of the population resides. Black dots on the right-hand side of a and b indicate the behaviour (period) of the bulk reactions. df, Corresponding amplitudes as functions of radius. The analysis is based on a total number of 1,193, 978 and 644 identifiably oscillating droplets for the sustained, damped and strongly damped tunings, respectively. The smallest data bins in c and f (orange) only contain a few droplets slightly below r = 2 µm. a.u., arbitrary units.

  6. Numerical modelling of the compartmentalized oscillator.
    Figure 6: Numerical modelling of the compartmentalized oscillator.

    a, Concentrations of oscillator species T21 for r = 2 µm droplet radii simulated stochastically using Gillespie's algorithm (without ‘partitioning noise’) (top), and deterministically with varying initial conditions chosen according to Poisson statistics (middle) and gamma statistics (with β = 10) (bottom), all based on the sustained oscillation tuning. b, Distribution of periods as a function of droplet radius for stochastic simulations without partitioning noise. c, Distribution of oscillation periods as a function of radius for Poisson and gamma (β = 10, dark green; β = 100, light green) partitioning noise, as well as additional loss of enzyme activity during droplet production, simulated for the sustained tuning (left), the damped tuning (middle) and the strongly damped tuning (right). The bulk oscillation period is marked as a dot on the right axis for the sustained and damped tunings; for the strongly damped tuning, the bulk reaction did not identifiably oscillate. For RNase H a global loss of ∼10% was assumed, whereas RNAP activity varied from 63% of the bulk value at r = 10 µm to 42% at r = 2 µm (see Supplementary Section Modelling). Error bars in b and c denote standard deviations. Shaded areas are between the 20% and 80% quantiles. d, Phase diagrams calculated from the oscillator model that display period, amplitude and damping coefficient of the oscillations as a function of RNAP and RNase H concentrations. Also indicated are the (bulk) initial conditions for the sustained (s), damped (d) and strongly damped (sd) cases. Small black or white ellipses indicate the standard deviation expected from Poisson statistics, and large white ellipses show the standard deviation for the gamma distribution (β = 10) for droplets with r = 2 µm radius. Dashed arrows indicate the effect of enzyme loss.

Change history

Corrected online 22 April 2014
The authors wish to add the following to the Acknowledgements section of this Article ‘E.F. and F.C.S. gratefully acknowledge funding from the Bavaria California Technology Center (BaCaTeC).’ The online versions of the Article have been amended accordingly.

References

  1. Kim, J., White, K. S. & Winfree, E. Construction of an in vitro bistable circuit from synthetic transcriptional switches. Mol. Sys. Biol. 2, 68 (2006).
  2. Forster, A. C. & Church, G. M. Synthetic biology projects in vitro. Genome Res. 17, 16 (2007).
  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. 7, 466 (2011).
  4. Zhou, H-X., Rivas, G. & Minton, A. P. Macromolecular crowding and confinement: biochemical, biophysical, and potential physiological consequences. Ann. Rev. Biophys. 37, 375397 (2008).
  5. De, T. & Maitra, A. Solution behaviour of aerosol OT in non-polar solvents. Adv. Colloid Interface Sci. 59, 95193 (1995).
  6. Gillespie, D. T. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 23402361 (1977).
  7. Noireaux, V. & Libchaber, A. A vesicle bioreactor as a step toward an artificial cell assembly. Proc. Natl Acad. Sci. USA 101, 1766917674 (2004).
  8. Shin, J. & Noireaux, V. An E. coli cell-free expression toolbox: application to synthetic gene circuits and artificial cells. ACS Synthetic Biol. 1, 2941 (2012).
  9. Matsuura, T. et al. Effects of compartment size on the kinetics of intracompartmental multimeric protein synthesis. ACS Synthetic Biol. 1, 431437 (2012).
  10. Theberge, A. B. et al. Microdroplets in microfluidics: an evolving platform for discoveries in chemistry and biology. Angew. Chem. Int. Ed. 49, 58465868 (2010).
  11. Rotman, B. Measurement of activity of single molecules of beta-D-galactosidase. Proc. Natl Acad. Sci. USA 47, 19811991 (1961).
  12. Nakano, M. et al. Single-molecule PCR using water-in-oil emulsion. J. Biotechnol. 102, 117124 (2003).
  13. Miller, O. J. et al. Directed evolution by in vitro compartmentalization. Nature Methods 3, 561570 (2006).
  14. Lu, W-C. & Ellington, A. D. In vitro selection of proteins via emulsion compartments. Methods 60, 7580 (2013).
  15. Epstein, I. et al. Chemical oscillators in structured media. Acc. Chem. Res. 45, 21602168 (2011).
  16. Nagypal, I. & Epstein, I. R. Fluctuations and stirring rate effects in the chlorite thiosulfate reaction. J. Phys. Chem. 90, 62856292 (1986).
  17. Vanag, V. & Epstein, I. Pattern formation in a tunable medium: the Belousov–Zhabotinsky reaction in an aerosol OT microemulsion. Phys. Rev. Lett. 87, 228301 (2001).
  18. Elowitz, M. B. & Leibler, S. A synthetic oscillatory network of transcriptional regulators. Nature 403, 335338 (2000).
  19. Fung, E. et al. A synthetic gene-metabolic oscillator. Nature 435, 118122 (2005).
  20. Stricker, J. et al. A fast, robust and tunable synthetic gene oscillator. Nature 456, 516539 (2008).
  21. Tigges, M., Marquez-Lago, T. T., Stelling, J. & Fussenegger, M. A tunable synthetic mammalian oscillator. Nature 457, 309312 (2009).
  22. Danino, T., Mondragón-Palomino, O., Tsimring, L. & Hasty, J. A synchronized quorum of genetic clocks. Nature 463, 326330 (2010).
  23. Ackermann, J., Wlotzka, B. & McCaskill, J. In vitro DNA-based predator–prey system with oscillatory kinetics. Bull. Math. Biol. 60, 329354 (1998).
  24. Kim, J. & Winfree, E. Synthetic in vitro transcriptional oscillators. Mol. Syst. Biol. 7, 465 (2011).
  25. Franco, E. et al. Timing molecular motion and production with a synthetic transcriptional clock. Proc. Natl Acad. Sci. USA 108, E784E793 (2011).
  26. Winfree, A. T. The Geometry of Biological Time (Springer, 1980).
  27. Gonze, D., Halloy, J. & Goldbeter, A. Robustness of circadian rhythms with respect to molecular noise. Proc. Natl Acad. Sci. USA 99, 673678 (2002).
  28. Vilar, J. M. G., Kueh, H. Y., Barkai, N. & Leibler, S. Mechanisms of noise-resistance in genetic oscillators. Proc. Natl Acad. Sci. USA 99, 59885992 (2002).
  29. Kar, S., Baumann, W. T., Paul, M. R. & Tyson, J. J. Exploring the roles of noise in the eukaryotic cell cycle. Proc. Natl Acad. Sci. USA 106, 64716476 (2009).
  30. Hong, C. I., Conrad, E. D. & Tyson, J. J. A proposal for robust temperature compensation of circadian rhythms. Proc. Natl Acad. Sci. USA. 104, 11951200 (2007).
  31. Fujii, T. & Rondelez, Y. Predator–prey molecular ecosystems. ACS Nano 7, 2734 (2013).
  32. Hasatani, K. et al. High-throughput and long-term observation of compartmentalized biochemical oscillators. Chem. Comm. 49, 80908092 (2013).
  33. Kaern, M., Elston, T. C., Blake, W. J. & Collins, J. J. Stochasticity in gene expression: from theories to phenotypes. Nature Rev. Genet. 6, 451464 (2005).
  34. Raj, A. & van Oudenaarden, A. Nature, nurture, or chance: stochastic gene expression and its consequences. Cell 135, 216226 (2008).
  35. Huh, D. & Paulsson, J. Non-genetic heterogeneity from stochastic partitioning at cell division. Nature Genet. 43, 95100 (2011).
  36. Huh, D. & Paulsson, J. Random partitioning of molecules at cell division. Proc. Natl Acad. Sci. USA 108, 1500415009 (2011).
  37. Rizzo, J., Gifford, L. K., Zhang, X., Gewirtz, A. M. & Lu, P. Chimeric RNA–DNA molecular beacon assay for ribonuclease H activity. 16, 277283 (2002).
  38. Holtze, C. et al. Biocompatible surfactants for water-in-fluorocarbon emulsions. Lab on a Chip 8, 16321639 (2008).
  39. Liu, Y., Jung, S-Y. & Collier, C. P. Shear-driven redistribution of surfactant affects enzyme activity in well-mixed femtoliter droplets. Anal. Chem. 81, 49224928 (2009).
  40. Maslak, M. & Martin, C. T. Effects of solution conditions on the steady-state kinetics of initiation of transcription by T7 RNA polymerase. Biochemistry 33, 69186924 (1994).
  41. Friedman, N., Cai, L. & Xie, X. S. Linking stochastic dynamics to population distribution: an analytical framework of gene expression. Phys. Rev. Lett. 97 (2006).
  42. Modesti, M. in Single Molecule Analysis (eds Peterman, E. J. G. & Wuite, G. J. L.) 101120 (Methods in Molecular Biology 783, Humana Press, 2011).
  43. Gutenkunst, R. N. et al. Universally sloppy parameter sensitivities in systems biology models. PLoS Comput. Biol. 3, e189 (2007).
  44. Subsoontorn, P., Kim, J. & Winfree, E. Ensemble Bayesian analysis of bistability in a synthetic transcriptional switch. ACS Synthetic Biol. 1, 299316 (2012).
  45. Schütze, T. et al. A streamlined protocol for emulsion polymerase chain reaction and subsequent purification. Anal. Biochem. 410, 155157 (2011).

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Author information

Affiliations

  1. Systems Biophysics and Bionanotechnology, Physik Department and WSI/ZNN, Technische Universität München, 85748 Garching, Germany

    • Maximilian Weitz,
    • Korbinian Kapsner &
    • Friedrich C. Simmel
  2. Bioengineering, California Institute of Technology, Pasadena, California 91125, USA

    • Jongmin Kim &
    • Erik Winfree
  3. Computation and Neural Systems, California Institute of Technology, Pasadena, California 91125, USA

    • Erik Winfree
  4. Computer Science, California Institute of Technology, Pasadena, California 91125, USA

    • Erik Winfree
  5. Mechanical Engineering, University of California at Riverside, Riverside, California 92521, USA

    • Elisa Franco

Contributions

E.W., E.F. and F.C.S. designed the research; M.W., J.K. and E.F. performed the research; M.W., J.K., K.K. and E.F. analysed the data; E.W., E.F. and F.C.S wrote the paper.

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The authors declare no competing financial interests.

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