Synthesis and materialization of a reaction–diffusion French flag pattern

Journal name:
Nature Chemistry
Year published:
Published online


During embryo development, patterns of protein concentration appear in response to morphogen gradients. These patterns provide spatial and chemical information that directs the fate of the underlying cells. Here, we emulate this process within non-living matter and demonstrate the autonomous structuration of a synthetic material. First, we use DNA-based reaction networks to synthesize a French flag, an archetypal pattern composed of three chemically distinct zones with sharp borders whose synthetic analogue has remained elusive. A bistable network within a shallow concentration gradient creates an immobile, sharp and long-lasting concentration front through a reaction–diffusion mechanism. The combination of two bistable circuits generates a French flag pattern whose ‘phenotype’ can be reprogrammed by network mutation. Second, these concentration patterns control the macroscopic organization of DNA-decorated particles, inducing a French flag pattern of colloidal aggregation. This experimental framework could be used to test reaction–diffusion models and fabricate soft materials following an autonomous developmental programme.

At a glance


  1. In a shallow gradient of morphogen, a bistable DNA network produces a Polish flag; a sharp and immobile concentration profile.
    Figure 1: In a shallow gradient of morphogen, a bistable DNA network produces a Polish flag; a sharp and immobile concentration profile.

    a, Scheme of Wolpert's French flag problem, where a gradient of morphogen yields three chemically distinct zones: blue, white and red. b, Molecular mechanism of a DNA-based bistable network where A1 self-activation is supported by template TA1 (1), and A1 is repressed by R1 (2) and continuously degraded (3). Harpooned thick arrows are ssDNA where colours indicate sequence domains and light hue indicates complementarity. Straight black arrows denote chemical reactions. W1 is a waste strand that cannot activate TA1. Pol., polymerase; nick., nicking enzyme; exo., exonuclease. c, Sketch of the experimental setup. d, Kymograph of the fluorescence shift due to A1 inside a capillary containing the network in b with homogeneous initial condition A1(x,t = 0) = 1 nM and pre-patterned with the gradient R1(x,t = 0) as in e. The red dashed line indicates the stationary position of the profile. e, Profiles of R1 (yellow) and the fluorescence shift due to A1 (blue) along the channel at initiation and after 1,200 min.

  2. A DNA-based network with two self-activating nodes that repress each other generates two immobile fronts that repel each other.
    Figure 2: A DNA-based network with two self-activating nodes that repress each other generates two immobile fronts that repel each other.

    a, Reaction network used here where H and K self-activate on their templates (TH and TK) and repress each other. bg, Experiments (bd) and simulations (eg) showing the kymograph of the fluorescence shift (b,e) for species H (red) and K (blue) inside a capillary containing the network in a and pre-patterned with a gradient of TH (yellow) and the fluorescence shift profiles at t = 600 min (c,f). d,g, Front position, velocity and width as a function of time extracted from the kymograph (colours as in c,f).

  3. The combination of two orthogonal bistable networks produces a French flag pattern of DNA concentration that can be simply reprogrammed.
    Figure 3: The combination of two orthogonal bistable networks produces a French flag pattern of DNA concentration that can be simply reprogrammed.

    a,b, From top to bottom: network topology, initial morphogen gradient, kymograph and fluorescence shift profiles at steady state for two bistables coupled through either a double-repressor strand, R2–R3 (a), or a template-repressor strand, TA2–R3 (b), each used as morphogen in the gradient. Dashed rectangles are zooms of the kymographs where the two French flag patterns were stationary.

  4. Materialization of Polish and French flag patterns with conditional bead aggregation.
    Figure 4: Materialization of Polish and French flag patterns with conditional bead aggregation.

    a, Sketch of the mechanism of bead aggregation where a pair i of 1-μm beads decorated with two different DNA constructs (black and hatched disks) are aggregated in the presence of linker strand Li. b, Scheme of the reaction network motif used to couple a bistable network based on species Aj with the linear production of Li supported by template TLi. ce, Polish flag pattern of bead aggregation obtained after 40 h in a channel containing the beads i = 1 and a network j = 1 with an initial gradient of R1. c, Bright-field image at the centre of the channel. d, Number of particles per unit area (blue diamonds, left axis) and initial concentration of R1 (yellow line, right axis) along the longitudinal axis of the channel. The dashed lines correspond to the position where c was recorded. e, Zoomed brightfield images associated to the positions indicated by coloured squares in d. f, French flag pattern of bead aggregation obtained after 40 h in a channel containing the beads i = (1,2) and two networks j = (1,3) with initial gradients of R1 and R3.


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Author information


  1. Laboratoire Jean Perrin, Université Pierre et Marie Curie, 4 place Jussieu, 75005 Paris, France

    • Anton S. Zadorin,
    • Vadim Dilhas,
    • Adrian Zambrano,
    • Jean-Christophe Galas &
    • André Estevez-Torres
  2. CNRS, UMR 8237, 75005 Paris, France

    • Anton S. Zadorin,
    • Vadim Dilhas,
    • Adrian Zambrano,
    • Jean-Christophe Galas &
    • André Estevez-Torres
  3. LIMMS/CNRS-IIS, University of Tokyo, Komaba 4-6-2 Meguro-ku, Tokyo, Japan

    • Yannick Rondelez &
    • Guillaume Gines
  4. Ecole supérieure de physique et chimie industrielles, Laboratoire Gulliver, 10 rue Vauquelin, 75005, Paris, France

    • Yannick Rondelez
  5. Ludwig-Maximilians-Universität München, Fakultät für Physik, Amalienstraße 54, 80799 Munich, Germany

    • Georg Urtel


A.S.Z., J.-C.G. and A.E.-T. performed most experiments and analysed the data. Y.R. and G.G. designed the network in Fig. 1 and J.-C.G. and A.E.-T. designed the networks in Figs 3 and  4. A.Z. and V.D. set up the bead experiments. G.U. performed critical control experiments. All the authors discussed the results. J.-C.G., A.S.Z., Y.R. and A.E.-T. designed research and J.-C.G. and A.E.-T. wrote the manuscript.

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The authors declare no competing financial interests.

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