title: High-resolution mapping of bifurcations in nonlinear biochemical circuits.
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.
authors.affiliation: LAAS, CNRS, UPR 8001, 7 av. Col. Roche, 31400 Toulouse, France.|LIMMS, CNRS-Institute of Industrial Science, UMI 2820, University of Tokyo, 153-8505 Tokyo, Japan.
authors.forename: A J
authors.initials: AJ
authors.lastname: Genot
authors.affiliation: LIMMS, CNRS-Institute of Industrial Science, UMI 2820, University of Tokyo, 153-8505 Tokyo, Japan.|LCBPT, CNRS, UMR 8601, Université Paris Descartes, 45 rue des Saints Pères, 75006 Paris, France.
authors.forename: A
authors.initials: A
authors.lastname: Baccouche
authors.affiliation: LIMMS, CNRS-Institute of Industrial Science, UMI 2820, University of Tokyo, 153-8505 Tokyo, Japan.|Electrical Engineering and Applied Physics department (EEA), Ecole Normale Superieure of Cachan, 61 avenue du Président Wilson, 94230 Cachan, France.|Laboratoire Gulliver, CNRS, UMR 7083, ESPCI, 10 rue Vauquelin, 75005 Paris, France.
authors.forename: R
authors.initials: R
authors.lastname: Sieskind
authors.affiliation: Ochanomizu University, 112-8610 Tokyo, Japan.|Earth- Life Science Institute (ELSI), Tokyo Institute of Technology, 152-8550 Tokyo, Japan.
authors.forename: N
authors.initials: N
authors.lastname: Aubert-Kato
authors.affiliation: Sorbonne Universités, UPMC Université Paris 06, CNRS, ISIR, F-75005 Paris, France.
authors.forename: N
authors.initials: N
authors.lastname: Bredeche
authors.affiliation: LCAMB, UMR 7199, CNRS/Université de Strasbourg, F-67400 Illkirch, France.|Université Paris Sorbonne Cité, INSERM UMR-S1147, CNRS SNC 5014, Centre Universitaire des Saints-Pères, 45 rue des Saints-Pères, 75270 Paris Cedex 06, France.
authors.forename: J F
authors.initials: JF
authors.lastname: Bartolo
authors.affiliation: Université Paris Sorbonne Cité, INSERM UMR-S1147, CNRS SNC 5014, Centre Universitaire des Saints-Pères, 45 rue des Saints-Pères, 75270 Paris Cedex 06, France.
authors.forename: V
authors.initials: V
authors.lastname: Taly
authors.affiliation: LIMMS, CNRS-Institute of Industrial Science, UMI 2820, University of Tokyo, 153-8505 Tokyo, Japan.
authors.forename: T
authors.initials: T
authors.lastname: Fujii
authors.affiliation: LIMMS, CNRS-Institute of Industrial Science, UMI 2820, University of Tokyo, 153-8505 Tokyo, Japan.|Laboratoire Gulliver, CNRS, UMR 7083, ESPCI, 10 rue Vauquelin, 75005 Paris, France.
authors.forename: Y
authors.initials: Y
authors.lastname: Rondelez
mesh_terms: D001669:Biochemical Phenomena; D001683:Biological Clocks / Q000502:physiology; D004247:DNA; D004261:DNA Replication; D053263:Gene Regulatory Networks / Q000502:physiology*; D008954:Models, Biological; D008958:Models, Molecular; D036103:Nanotechnology / Q000379:methods*; D017711:Nonlinear Dynamics; D058615:Synthetic Biology / Q000379:methods*
chemical_list: D004247:DNA