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High-resolution mapping of bifurcations in nonlinear biochemical circuits

Nature Chemistry volume 8, pages 760–767 (2016)Cite this article

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Abstract

Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator–prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.

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Figure 1: Workflow for mapping the bifurcation diagram of nonlinear biochemical systems.
Figure 2: Biochemical details of the nonlinear circuits.
Figure 3: Experimental bifurcations in a bistable circuit.
Figure 4: Bifurcation diagram of a synthetic molecular predator–prey oscillator.

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Acknowledgements

This work was financially supported by the PHC Sakura program (project number 34171WG), implemented by the French Ministry of Foreign Affairs, the French Ministry Of Higher Education and Research and Japan Society for the Promotion of Science (JSPS), a Grant-in-Aid to Y.R. from the JSPS for Scientific Research on Innovative Areas ‘Synthetic Biology for Comprehension of Biomolecular Networks’ (project number 23119001), a l'Agence Nationale de la Recherche (ANR) Retour Postdoc grant (ANR-13-PDOC-0001) and a JSPS postdoctoral fellowship to A.J.G., and a PhD fellowship from Region Alsace to J.F.B. We thank H. Fujita and M. C. Tarhan for the loan of a microfluidic pump, A. Zadorin for discussions about the theory of bifurcations, K. Hasatani for preliminary work, E. Winfree for detailed comments on the manuscript and A. Estevez-Torres and Y. Tauran for expressing and purifying the exonuclease.

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Author notes

  1. A. J. Genot and A. Baccouche: These authors contributed equally to this work

Authors and Affiliations

  1. LAAS, CNRS, UPR 8001, 7 av. Col. Roche, Toulouse, 31400, France

    A. J. Genot

  2. LIMMS, CNRS-Institute of Industrial Science, UMI 2820, University of Tokyo, Tokyo, 153-8505, Japan

    A. J. Genot, A. Baccouche, R. Sieskind, T. Fujii & Y. Rondelez

  3. LCBPT, CNRS, UMR 8601, Université Paris Descartes, 45 rue des Saints Pères, Paris, 75006, France

    A. Baccouche

  4. Electrical Engineering and Applied Physics department (EEA), Ecole Normale Superieure of Cachan, 61 avenue du Président Wilson, Cachan, 94230, France

    R. Sieskind

  5. Laboratoire Gulliver, CNRS, UMR 7083, ESPCI, 10 rue Vauquelin, Paris, 75005, France

    R. Sieskind & Y. Rondelez

  6. Ochanomizu University, Tokyo, 112-8610, Japan

    N. Aubert-Kato

  7. Earth- Life Science Institute (ELSI), Tokyo Institute of Technology, Tokyo, 152-8550, Japan

    N. Aubert-Kato

  8. Sorbonne Universités, UPMC Université Paris 06, CNRS, ISIR, Paris, F-75005, France

    N. Bredeche

  9. LCAMB, UMR 7199, CNRS/Université de Strasbourg, Illkirch, F-67400, France

    J. F. Bartolo

  10. Université Paris Sorbonne Cité, INSERM UMR-S1147, CNRS SNC 5014, Centre Universitaire des Saints-Pères, 45 rue des Saints-Pères, Paris Cedex 06, 75270, France

    J. F. Bartolo & V. Taly

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  1. A. J. Genot
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Contributions

A.J.G. designed the study, performed experiments, analysed the data and wrote the manuscript. A.B. performed experiments, improved the droplet chambers and contributed to experimental design and writing of the manuscript. R.S. developed the microfluidic platform. N.A.K. and N.B. designed, performed and analysed the fitting process. J.F.B. and V.T. synthesized the surfactant. V.T. and T.F. provided support with the droplet-based microfluidic platform. Y.R. conceived, designed and supervised the study, analysed data and wrote the manuscript. All the authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Y. Rondelez.

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The authors declare no competing financial interests.

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Genot, A., Baccouche, A., Sieskind, R. et al. High-resolution mapping of bifurcations in nonlinear biochemical circuits. Nature Chem 8, 760–767 (2016). https://doi.org/10.1038/nchem.2544

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