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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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.
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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