ltexMethods references

# Synthesis and materialization of a reaction-diffusion French flag pattern

Anton Zadorin1,2, Yannick Rondelez3,4, Guillaume Gines3, Vadim Dilhas1,2,
Adrian Zambrano1,2, Jean-Christophe Galas1,2,∗, André Estevez-Torres1,2,∗

1Université Pierre et Marie Curie, Laboratoire Jean Perrin, 4 place Jussieu,
75005 Paris, France.
2CNRS, UMR 8237, 75005, Paris, France. 3LIMMS/CNRS-IIS, University of Tokyo,
Komaba 4-6-2 Meguro-ku, Tokyo, Japan. 4Ecole supérieure de physique et chimie
industrielle,
Laboratoire Gulliver, 10 rue Vauquelin, 75005, Paris, France. ∗To whom
correspondence should be
addressed; E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
During embryo development, patterns of protein concentration appear in
response to morphogen gradients. The archetypal pattern is the French flag
composed of three chemically-distinct zones separated by sharp borders.
Chemical concentration serves the underlying cells both as an indicator of
location and as a fate selector. This strategy could be advantageously
transposed to engineer materials capable of morphogenesis, however synthetic
analogues of the French flag, let alone their materialization, have remained
elusive. Here we introduce an experimental model of gradient-induced pattern
formation and its coupling to a material. We engineered artificial analogues
of transcriptional networks based on short DNA single strands that interpret a
morphogen gradient. Firstly, bistable networks created immobile, sharp and
long-lasting concentration fronts. Secondly, the combination of two bistable
circuits generated a French flag pattern whose phenotype was reprogrammed by
network mutation. Finally, the patterns controlled the macroscopic
organization of a complex material, namely DNA-decorated particles. This
experimental framework could be used to test morphogenetic models and design
programmable materials capable of morphogenesis.

Biological matter has the astonishing capability of self-constructing into
predefined shapes: living embryos develop from a simple form into a complex
one through a reproducible process called morphogenesis. The embryo is first
structured chemically through pattern formation, a process during which out-
of-equilibrium molecular programs generate highly ordered concentration
patterns of $\mu$m to mm size[1]. In this context, synthesizing concentration
patterns using artificial molecular programs[2, 3, 4, 5, 6] has two important
goals. First, in a reductionist perspective, it allows testing theoretical
models in simplified, yet relevant, experimental conditions[7]. Second, from a
synthetic standpoint[8], it enables the conception of a new kind of materials
capable of autonomous morphogenesis.

Two archetypal mechanisms account for pattern formation in living systems: the
symmetry-breaking Turing mechanism [9, 10, 11] and the processing of
positional information [12, 13, 14]. In the latter, a pre-existing morphogen
gradient is interpreted by a molecular program in a reaction-diffusion (RD)
process producing several chemically-distinct regions with sharp borders.
Lewis Wolpert named this the French Flag problem to illustrate the issue,
fundamental because it arises in the development of virtually all complex
organisms, of creating three distinct regions of space from an amorphous mass
and a shallow concentration gradient (Figure 1A). Well-known examples are
provided by the gap gene system in _Drosophila_[13], where the three regions
become the head, the thorax and the abdomen, and by sonic hedgehog in the
patterning of the vertebrate neural tube[15]. Turing patterns were first
demonstrated experimentally in a purely chemical system in 1990[16, 17]
whereas synthetic systems capable of interpreting a morphogen pre-pattern have
remained elusive.

Here we take inspiration from the early development of a living embryo to
create a primitive material that self-organizes following two principles
acting sequentially: i) pattern formation creates chemically well-defined
regions of space and ii) the chemical pattern influences the final structure
of an initially homogeneous material. In a learning-by-doing approach to this
question [2, 3, 4, 18, 5, 6] we set out with the goal of synthesizing a French
flag pattern outside of a living organism.

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) DNA-based bistable network
with A1 self-activation supported by template T${}_{A_{1}}$, repressed by R1
and continuously degraded, together with its molecular mechanism. Harpooned
thick arrows are ssDNA where colors indicate sequence domains and light hue
indicates complementarity. Straight black arrows denote chemical reactions.
pol, nick and exo stand for polymerase, nicking enzyme and exonuclease,
respectively. W1 is a waste strand that cannot activate T${}_{A_{1}}$. (C)
Sketch of the experimental setup. (D) Kymograph of the fluorescence shift due
to $A_{1}$ inside a capillary containing the network in (B) with initial
condition $A_{1}(x,0)=1$ nM and pre-patterned with the gradient $R_{1}(x,0)$
as in (E). The red dashed line indicates the stationary position of the
profile. (E) Profiles of $R_{1}$ (yellow) and the fluorescence shift due to
$A_{1}$ (blue) along the channel at initial time and after 1200 min.

Our design for building a French flag pattern consists of two immobile
concentration fronts. The conversion of a shallow morphogen gradient into a
concentration boundary that is both sharp and immobile requires a reaction
network that interprets the gradient in a non-linear fashion. Diverse evidence
[19, 20, 21] suggest that bistability is an essential property of such
networks but the role of diffusion during gradient interpretation in living
embryos remains controversial[22, 21, 23]. The strong historical influence of
the _reaction-only_ French flag model, which was initially opposed to the
_reaction-diffusion_ Turing mechanism[9, 24], resulted in diffusion being
neglected when considering gradient-induced patterning[19]. Modern experiments
in _Drosophila_ conclude that diffusion is not needed to fit expression
data[25] but it is necessary to explain the robustness of patterning to
fluctuations[14]. In the following, we show experimentally in an artificial
system that combining bistability and diffusion yields a robust patterning
mechanism, providing evidence for recent hypotheses suggesting that a Turing-
Wolpert mechanism could be at play _in vivo_[23, 24].

DNA oligonucleotides are particularly well suited to construct pattern-forming
molecular programs[18, 4, 26, 27]. On the one hand, the reactivity of the
hybridization reaction obeys simple rules and a wide array of methods coming
from biotechnology renders their synthesis, analysis and modification
straightforward. On the other hand, they can be easily interfaced with
materials such as DNA nanostructures[28], aptamers[29], nanoparticles [30] and
hydrogels [31]. We thus engineered a series of bistable networks using the PEN
DNA toolbox, a molecular programming language designed to construct networks
analogous to transcriptional ones but using only simple biochemical
reactions[32] . This technology has recently been applied to construct out-of-
equilibirum networks displaying oscillations[32, 33], bistability[34] and
traveling concentration waves[4, 27, 35]. Figure 1B depicts the simplest
bistable network used here, with a first-order positive feedback loop and a
non-linear repressor (Extended Data Figures 1-2). The nodes of the network, A1
and R1, are respectively 11 and 15-mer single-stranded DNAs (ssDNAs),
analogous to transcription factors. Self-activation is set by T${}_{A_{1}}$, a
22-mer ssDNA template that plays the role of a gene. Repression is encoded by
promoting the degradation of A1 with a threshold given by $R_{1}$[36]
—italized species names indicate concentration throughout the text. Three
enzymes —a polymerase, an exonuclease and a nicking enzyme— provide the
metabolic functions homologous to the transcription-translation machinery and
dissipate free energy from a reservoir of deoxynucleotides (dNTPs). As it
happens in transcription networks, A1 is continuously produced and degraded
but the total template —gene— concentration is fixed. In contrast to networks
in vivo, molecular interactions are well-known and the mechanism and kinetic
rates can be precisely determined[32].

Our first goal was to create an immobile concentration front in the presence
of a morphogen gradient, which we have called a Polish flag. We performed
patterning experiments within 5 cm-long sealed glass microchannels of $4\times
0.2$ mm2 cross-section (Figure 1C). An exponential gradient of morphogen R1
with a characteristic length $l=2$ cm was generated along the longitudinal
axis of the channel by partially mixing two solutions with different $R_{1}$
by Taylor dispersion (Figure 1E and Extended Data Figure 3). In this geometry
the gradient was stable within 10% over 10 h (Extended Data Figure 3).
Initially the channel contained homogeneous concentrations of the three
enzymes, dNTPs, $T_{A_{1}}=25$ nM, $A_{1}=1$ nM, and a gradient of $R_{1}$ in
the range $0-200$ nM. The evolution of $A_{1}$ was measured by adding a
fluorescent DNA intercalator and recording time-lapse fluorescence images in
an inverted microscope. Figure 1D displays the spatio-temporal dynamics of the
patterning process. A short, purely reactional, initial phase generated a
sharp profile of $A_{1}$ at a location corresponding to low morphogen
concentration (Extended Data Figure 4a). This profile later moved to the right
through a reaction-diffusion (RD) mechanism, progressively decelerating until
it stopped at the center of the channel at a position where $R_{1}^{RD}=30\pm
5$ nM. The characteristic width of the front was 2 mm, 10-fold sharper than
the morphogen gradient, and remained immobile up to 15 h (Extended Data Figure
4b). When, instead of the repressor, the autocatalyst template was used as the
morphogen, the complementary Polish flag pattern was obtained (Figure S3-S4).
Stationary patterns were observed also when the morphogen gradient was
immobilized on a surface (Figure S7).

Figure 2: A DNA-based network that mimics part of the gap gene regulatory
network generates two fronts that repel each other. (A) Topology of the gap
gene network, from [25], the portion reproduced here is highlighted. (B)
Analogue DNA-based network for the principal interactions between Bicoid, bcd,
Hunchback, hb and Knirps, kni. Their DNA couterparts are respectively noted
TH, H and K. Experiments (C, D, E) and simulations (F, G, H) showing the
kymograph of the fluorescence shift (C, F) for species H (red) and K (blue)
inside a capillary containing the network in (B) and pre-patterned with a
gradient of TH (yellow) and fluorescence shift profiles at $t=600$ min (D) and
$t=100$ a.u. (G). (E, H) Front position, velocity and width as a function of
time extracted from the kymograph (colors as in D and G).

The gap gene network, which interprets the Bicoid morphogen gradient during
the development of the _Drosophila_ blastoderm (Figure 2A), is definitely more
complex than the bistable network used so far. For instance, Bicoid activates
Hunchback, which grows autocatalytically and strongly represses Knirps, which
also grows autocatalytically and represses Hunchback[25]. We designed a
network that mimics these interactions [34] (Figures 2B and Extended Data
Figure 5) and recorded the patterning dynamics in a gradient of the Bicoid
analogue, TH (Figure 2C-E, Movie S1). At short times, a purely reactional
phase created two independent and sharp fronts of the analogues of Hunchback,
H, and Knirps, K. Subsequently, during an RD phase, the fronts traveled in
opposite directions until they collided in the middle of the channel. At this
time, the two profiles partially overlapped and a slow phase made the two
fronts go backwards until reaching a steady-state where the overlap
disappeared. 1-dimensional simulations with a 4-variable model (see SI
Methods) displayed a similar behavior and suggested that this last phase was
due to a slow synthesis of the repressors (Figure 2F-H). This patterning
process was highly reproducible (Figure S5-S6).

Figure 3: The combination of two orthogonal bistable networks produces a
French flag pattern that can be simply reprogrammed. 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, $\mathrm{R}_{2}-\mathrm{R}_{3}$ (A), or a template-repressor
strand, $\mathrm{T}_{A_{2}}-\mathrm{R}_{3}$ (B), each used as morphogen
gradient. Dashed rectangles are zooms of the kymographs where the two French
flag patterns were stationary.

To implement a French flag pattern with three chemically-distinct zones
(Figure 3, Extended Data Figures 6-7 and Movie S2) we combined two orthogonal
bistables, A2 and A3, (Figure S8) into a single network using two different
approaches. We used a bifunctional morphogen bearing either both repressors,
$\mathrm{R}_{2}-\mathrm{R}_{3}$, or one autocatalyst template and a repressor,
$\mathrm{T}_{A_{2}}-\mathrm{R}_{3}$. In a gradient of
$\mathrm{R}_{2}-\mathrm{R}_{3}$, a channel containing a uniform concentration
of $\mathrm{T}_{A_{2}}$ and $\mathrm{T}_{A_{3}}$ generated a French flag
pattern that divided space into three regions,
$\textrm{A}_{2}+\textrm{A}_{3}$, $\textrm{A}_{2}$ and $\emptyset$, for 100 min
(Figure 3A). By contrast, with a gradient of
$\mathrm{T}_{A_{2}}-\mathrm{R}_{3}$ and a uniform concentration of
$\mathrm{R}_{2}$ and $\mathrm{T}_{A_{3}}$ a different pattern separated the
space into $\textrm{A}_{3}$, $\textrm{A}_{2}+\textrm{A}_{3}$ and
$\textrm{A}_{2}$.

Figure 4: Materialization of a Polish flag pattern with conditional particle
aggregation. (A) Sketch of the mechanism of particle aggregation where 1
$\mu$m particles decorated with two different DNA constructs (black and gray
disks) are aggregated in the presence of linker strand L. (B) Scheme of the
reaction network used here, where a bistable is coupled to the linear
production of L with template T${}_{\textrm{L}}$. All data were recorded after
40 h from a channel containing the particles, the network in panel (B) and an
initial gradient of $R_{1}$. (C) Brightfield image at the center of the
channel. (D) Average size of particle aggregates (blue disks, left axis) and
initial concentration of $R_{1}$ (yellow line, right axis) along the
longitudinal axis of the channel. The colored squares indicate the positions
at which the brighfield images in (E) were recorded. The dashed lines
correspond to the position where (C) was recorded.

In the embryo, pattern formation induces tissue differentiation by providing
localized chemical cues to pluripotent cells [1]. Artificial materials
inspired by this mechanism would bear astonishing properties, such as the
capability to adapt their shape or function to different environmental
conditions. As a proof of concept we coupled a Polish flag-generating network
to the conditional aggregation of 1 $\mu$m diameter beads[30] (Figure 4).
Streptavidin-labeled particles were decorated with two types of biotin-labeled
DNAs that had two different 11-mer ssDNA dangling ends. In the working buffer,
the beads aggregated only in the presence of a linker strand L complementary
to both ssDNA portions (Extended Data Figure 8). A capillary containing i) a
homogeneous dispersion of both types of beads, ii) a bistable network coupled
to the linear production of L and iii) a gradient of $\textrm{R}_{1}$,
produced a Polish flag of bead aggregation (Figure 4C-E). The aggregation
pattern was stable for up to a month (Extended Data Figure 9). Interestingly,
the width of the aggregation front was 500 $\mu$m, 4-fold sharper than the
front of fluorescence due to species $\textrm{A}_{1}$ in Figure 1. This
primitive morphogenetic material thus uses two different sharpening
mechanisms. The first one results from coupling the bifurcation of a bistable
dynamic system to diffusion while the second is probably due to the
cooperativity of bead-bead aggregation. This multi-level sharpening recalls
hierarchical patterning mechanisms in vivo and could be advantageously used
for microfabrication.

Our results demonstrate that DNA-based molecular programming is well suited to
engineer concentration patterns reminiscent of those observed during early
morphogenesis. They indicate that the combination of a bistable reaction
network with diffusion is a simple engineering solution to generate immobile
concentration fronts that are both sharp and long lasting. Our experimental
model may help understanding the role of regulative and diffusive processes
during development and suggests that relatively simple networks may have
enabled patterning at an early stage of evolution. Importantly, the simplicity
of the method allowed us to record the patterning dynamics in real time,
showing that a purely reactional initial phase is followed by a reaction-
diffusion one. Finally, by coupling programmable patterns with matter we have
engineered a morphogenetic material. This approach could be interfaced with
other DNA-compatible materials and devices [28, 29, 31] or peptide-based
materials[37] to create morphogenetic matter.

## Acknowledgments

We thank Erwin Frey for insightful discussions, Alexis Vlandas for help with
gradient generation and Ben Caller and Damien Woods for comments on the text.
Supported by European commission FET-STREP under award Ribonets, by ANR jeunes
chercheurs program under award Dynano, and by C’nano Ile-de-France (DNA2PROT
grant).

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## Methods

DNA strands were purchased from Biomers (Ulm, Germany). The Bst DNA polymerase
and the two nicking enzymes (Nb.BsmI and Nt.BstNBI) were purchased from New
England Biolabs. The _Thermus thermophilus_ RecJ exonuclease was expressed in
_E. coli_ and purified by chromatography according to a published
protocolWakamatsu2010. Experiments were performed at 45 °C for the Polish and
French flag generating networks and at 42 °C for the gap gene-like network.
Details on the the sample preparation, the DNA sequences, the experimental
conditions, the data analysis and the simulations are provided in the
Supplementary Information.

### Particle suspension.

1 $\mu$m diameter, streptavidin-coated, paramagnetic beads (Dynabeads MyOne
C1, Invitrogen) were functionalized with two types of biotinylated DNA
constructs, as describedLeunissen2009, making two types of beads, B1 and B2.
Each construct consists of a 49 bp-long dsDNA backbone terminated with an 12
bases-long single stranded sticky end. The construct corresponding to B1
(resp. B2) was biotin-labeled on the 5’ end (resp. 3’ end) and the
corresponding sticky end was on the 3’ side (resp. 5’ side). Such a design
implies that the DNA-decorated beads will be stable in solution when mixed,
unless the linker strand complementary to the sticky ends of each bead type is
present.

### Measurement of DNA concentrations.

DNA concentrations were measured by fluorescence. We used three different
strategies. i) Recording the green fluorescence, proportional to the
concentration of double stranded DNA, from EvaGreen dye (Biotium). ii)
Recording the fluorescence from dyes attached to the 3’ or 5’ end of template
strands (see Table S2 for details). When the corresponding inputs or outputs
hybridize on these templates fluorescence is quenched. iii) The concentrations
of morphogen were measured by adding 1 $\mu$M of cascade blue-dextran
M${}_{w}=3000$ Da (Thermo Fisher Scientific) to the solution with high
concentration of morphogen used to generate the gradient, and recording its
fluorescence in real time. The cascade blue-dextran has a molecular weight
similar to the DNA templates and thus a similar diffusion coefficient, as
verified in a control experiment. In all kymographs and plots we represented
the absolute value of the fluorescence shift, which is proportional to the
concentration of fluorescent species for both cases.

### Generation of the morphogen gradient.

Spatiotemporal (1D) experiments were performed within 50 mm$\times$4
mm$\times$0.2 mm glass capillaries (Vitrocom USA). The capillary was loaded
using a micropipette and a custom-made PDMS connector. The capillary was
filled with 45 $\mu$L of the reaction solution without morphogen strand and
then a pipette was inserted being in the ’push’ position into the PDMS
connector. The other end of the capillary was dipped into the reaction
solution containing the morphogen DNA strand. 15 up-and-down pumps of 12.5
$\mu$L of solution were performed to create the gradient. Finally, the pipette
was left in the ’pulled’ position and the pipette together with the PDMS
connector were removed. Extended Data Figure 3a shows two methylene blue dye
gradients prepared this way.

### Microscopy.

Once the gradient was formed, the capillary was laid on a $5\times 7.5$ cm
glass slide. 5-minutes Araldite epoxy was used both to seal the capillary ends
and to glue them to the glass slide. No evaporation at all was observed for 48
h at 45°C. The fluorescence along the capillary was recorded on a Zeiss Axio
Observer Z1 fully automated epifluorescence microscope equipped with a CoolLED
pE-2 fiber-coupled illuminator, DAPI, GFP, YFP and RFP filter sets, a
Marzhauser XY motorized stage, a Tokai Hit thermo plate, and Andor iXon Ultra
897 EMCCD camera, a shutter and a $2.5\times$ objective. These instruments
were controlled with MicroManager 1.4. For optimal thermal conduction, mineral
oil was added between the glass slide and the thermoplate on the microscope,
and also between the glass slide and the capillary. For each capillary, 16
contiguous 3.17$\times$3.17 mm2 ($128\times 128$ pixel2) images were recorded
automatically every 1 to 10 minutes. Multi-color fluorescence microscopy was
used to record the concentration of different DNA species over time. Images of
the beads were acquired in bright field with a 10 or a $40\times$ objective.

### Image treatment.

The raw data were treated with ImageJ / Fiji (NIH) and Matlab (The Mathworks).
Prior to data analysis, the 16 images making one capillary were stitched
together without overlapping. Subsequently, the inhomogeneous illumination was
corrected by two different protocols. When the initial concentration was flat
(for all species except for the morphogen) a division by the first frame was
performed. When the initial concentration was not homogeneous, for example for
the morphogen, a polynome was fitted to the raw data of one of the
3.17$\times$3.17 mm2 of the first frame and each image was divided by it.

### Data treatment.

Considering the 50 mm $\times 4$ mm capillary as a 1D reactor, we first
averaged the corrected fluorescence images over the width of the capillary
(along the $y$ axis). The kymographs were obtained by stacking these profiles
over time. To obtain the front position and width, the profiles averaged along
$y$ were further averaged along the $x$ axis by performing a moving average
over 25 pixels and subsequently normalized between 0 and 1. A sigmoid function
$f(x)=\frac{1}{1+e^{b*(-x+x_{0})}}$ was fitted to these data. The front
position corresponds to $x_{0}$ while the width of the front is defined as
$1/b$. To determine the front velocity, the data of front position over time
were fitted by a polynomial function to reduce noise. The velocity was
calculated as the time derivative of this polynomial fit.

unsrt fflag

## Extended data

(a)  (b)

Extended Data Figure 1: Detailed mechanism (a) and 0-dimensional dynamics (b)
of the 1-species bistable circuit. (a) The inset reminds the topology of the
network. This circuit uses a single autocatalytic template T producing A
exponentially, coupled to a species-specific degradation mechanism driven by
the repressor R. Only species that are not protected on the 5’ end are
degraded by the exonuclease (the top strands). This molecular program admits 2
stable states, defined by the amplification and non-amplification of the A
strand. (b) Dynamics of the 1-species bistable for different initial
conditions and different thresholded degradation rates. Red fluorescence shift
coming from Cy35 dye _vs_ time. Each plot represents a different initial
condition of A1 as indicated in the title and each curve represents a
different thresholded degradation rate given by the concentration of species
R1 (see legend, in nM). When the final fluorescence shift was above the dashed
black horizontal line the bistable was considered to be in state 1 (high) and
otherwise in state 0 (low). $T=45^{\circ}$, $T_{A_{1}}=25$ nM. Extended Data
Figure 2: Phase space of the 1-species bistable network as a function of
repressor concentration, $R_{1}$, and initial condition $A_{1}(t=0)$.
Triangles and circles correspond to systems ending in the high and low
concentration state, respectively. The shaded region indicates the range of
$R_{1}$ where the system is bistable. Plotted from data in Extended Data
Figure 1.

(a)

(b)  (c)

(d)

Extended Data Figure 3: Characterization of the morphogen gradient. (a)
Gradients of methylene blue dye generated inside the glass capillaries by
pipetting back and forth a constant volume of dye. Each extremity of the
capillary is sealed with a droplet of glue that serves also to attach it to a
glass slide. Methylene blue is not present in the experiments and is used here
solely for visualization. (b) The characteristic length of the morphogen
gradient is 17 mm. Exponential fit (red line) to the fluorescence intensity
from the cascade-blue-dextran gradient in Figure 1 of the Main Text. (c) The
generation of the morphogen gradient is fairly reproducible. Fluorescence
profiles of cascade-blue-dextran gradients in four different channels prepared
at the same time. The gradients were slide-averaged over 25 pixels. The
sawtooth shape of the curves is due to illumination inhomogeneities that were
not corrected here. (d) The morphogen gradient in solution is stable over the
duration of the experiment. Concentration profile within the channel of a
22-mer fluorescently-labeled oligonucleotide at $t=30$ min (green) and $t=10$
h (red). $T=42$°C.

(a)  (b)

Extended Data Figure 4: Short time and long time behavior of the Polish flag
pattern. (a) Kymograph of Figure 1 at short times. At $t\approx 70$ min a
purely reaction mechanism creates a front at $x\approx 5$ mm. Later this front
moves slowly through a reaction-diffusion mechanism from left to right. (b)
Polish flag patterning lasts up to 30 h. Experiment similar to the one shown
in Figure 1D-E in the Main Text. Each panel represents the kymograph (left),
the fluorescence profiles along the channel at different times (center) with
EvaGreen fluorescence in black and morphogen fluorescence in yellow (this last
one only at initial time), and the position of the front (right). The
fluorescence of EvaGreen is proportional to the concentration of dsDNA in the
capillary. At $2000$ min a strongly fluorescent species, called a ’parasite’,
emerges and kills the immobile front, see Supplementary Materials for a
discussion. Network Ib with R${}_{2}=0-400$ nM, and initial constant
concentrations of $T_{A_{1}}=25$ nM and $A_{1}=0.5$ nM. $T=45^{\circ}$C.

(a)

(b)  (c)

Extended Data Figure 5: Detailed mechanism (a) and 0-dimensional dynamics (b,
c) of the 2-species bistable circuit. (a) The inset reminds the simplified
topology. This circuit uses 4 catalytic templates: TH and TK catalyze the
exponential amplification of H and K respectively. The templates
T${}_{H2I_{K}}$ and T${}_{K2I_{H}}$ initiate the synthesis of IK and IH, using
respectively H and K strands as input. IK and IH are able to bind the cognate
autocatalytic template with a higher affinity that their input, preventing
therefore the amplification of the H and K nodes. Only species that are not
protected on the 5’ end are degraded by the exonuclease (the top strands). By
mixing these 4 templates, a 2-species bistable circuit is obtained, leading to
2 stables states where either H or K are amplified, depending on the
experimental initial conditions. (b) The concentration of TH is a bifurcation
parameter for the network in panel a. Fluorescence shift due to species H
(top) and K (bottom) as a function of time in well-mixed conditions. Curves
with same colors refer to identical experiments, each with a different
concentration of template TH that controls the growth rate of H. When the
concentration of TH is 8 nM or less, K grows and H dies and the final state is
$(H,K)=(0,1)$. When the concentration of TH is 9 nM or more, K dies and H
grows and the final state is $(H,K)=(1,0)$. $T=42^{\circ}$, $T_{K}=20$ nM,
$T_{H2R_{K}}=20$ nM, $T_{K2R_{H}}=20$ nM, initial conditions $H=K=0.5$ nM. (c)
Phase portrait from data in panel b. The dashed line separates the $T_{H}$
values for which the final state is $K$ and those for which the final state is
$H$.  Extended Data Figure 6: Two orthogonal 1-species bistable networks
produce a two fronts pattern which position can be independently controlled.
Networks Ib and VI (Figure S2) were introduced in a capillary. Two morphogens
were used, R2 and R3 and gradients of similar shape but different maximal
concentrations were generated. The concentration of dsDNA was followed by
measuring EvaGreen fluorescence. As the two 1-species bistable networks are
orthogonal, changing the morphogen gradient of one of the two networks only
affects the position of the corresponding front, that moves to the right.
Initial morphogen gradients (left) and Eva Green fluorescence kymographs
showing simultaneously the emergence of the two immobile fronts (right) for
three different maximum values of repressor R2 (red dashed lines): 400 (A),
200 (B) and 100 nM (C). In (C) the level of R2 is too low to stop the front.
$T_{A_{2}}=T_{A_{3}}=25$ nM, $A_{2}=A_{3}=0.5$ nM, $R_{3}=0-400$ nM (blue
lines). $T=45$°C. Extended Data Figure 7: Two French flag patterns are
presented in Figure 3 of the Main Text. They come from the combination of two
orthogonal 1-species bistable networks, one containing species A2 and the
other species A3. To follow independently the concentration of A2 and A3 the
$\textrm{T}_{A_{3}}$ was labeled with a yellow DY530 dye in 5’.
$\textrm{T}_{A_{2}}$ was not labeled. It appeared that in presence of
EvaGreen, only the A2 system fluoresced in green, while only the A3 fluoresced
in yellow. Here we show separately the two fluorescence channels that were
recorded independently during each experiment and that correspond to each
bistable for the French flag patterns in Figure 3 of the Main Text. Kymographs
for each color channels for the three French Flag patterns. Top row: green
fluorescence, corresponding to species A2. Bottom row: yellow fluorescence,
corresponding to species A3. Extended Data Figure 8: Brightfield microscopy
images show non-aggregated and aggregated beads after 1000 min incubation
respectively in the absence (left) and in the presence of 1 $\mu$M L (right)
in the 1-species bistable buffer without enzymes at 45°C. Extended Data Figure
9: The morphogenetic aggregation of beads is irreversible and visible to the
naked eye. A) At $t=0$, the dispersion of beads in the capillaries appears as
a brown homogeneous background. B) After 22 h, in the presence of 1-species
bistable network that does not produce linker L, the beads sediment
homogeneously along the longitudinal axis of the capillary but away from the
walls and do not aggregate. C) In contrast, in the presence of the 1-species
bistable network that does produce linker L, the bead aggregation is clearly
seen on the left hand side of the capillary. The pattern of bead aggregation
is stable for at least one month. The photos were taken in brightfield with a
Nikon D600 camera equipped with a 35 mm lens.