Programmable chemical controllers made
from DNA
Yuan-Jyue Chen
1
, Neil Dalchau
2
, Niranjan Srinivas
3
,AndrewPhillips
2
, Luca Car delli
2
,
David Soloveichik
4
*
and Georg Seelig
1,5
*
Biological organisms use complex molecular networks to navigate their environment and regulate their internal state. The
development of synthetic systems with similar capabilities could lead to applications such as smart therapeutics or
fabrication methods based on self-organization. To achieve this, molecular control circuits need to be engineered to
perform integrated sensing, computation and actuation. Here we report a DNA-based technology for implementing the
computational core of such controllers. We use the formalism of chemical reaction networks as a ’programming language’
and our DNA architecture can, in principle, implement any behaviour that can be mathematically expressed as such. Unlike
logic circuits, our formulation naturally allows complex signal processing of intrinsically analogue biological and chemical
inputs. Controller components can be derived from biologically synthesized (plasmid) DNA, which reduces errors
associated with chemically synthesized DNA. We implement several building-block reaction types and then combine them
into a network that realizes, at the molecular level, an algorithm used in distributed control systems for achieving
consensus between multiple agents.
M
olecular devices have captured the imagination of chemists
and engineers for at least 30 years
1
. Rationally designed
‘active’ molecules include nanoparticles for the targeted
delivery of drugs and imaging agents
2
, or molecular motors that
move along tracks and deliver cargo
3
. DNA nanotechnology
4,5
is
in a unique position among the many actively pursued strategies
for constructing molecular nanorobots, demonstrating progress
towards the rational design of all the required elements: sensors
and amplifiers
6–11
, circuits
12–25
, motors
26–30
and structures
4,31,32
.A
rationally designed molecular robot has even combined structural
elements with sensing and actuation, although it lacked complex
embedded control
33
. The DNA-only construction of digital logic
circuits and Boolean neural networks with over a hundred rationally
designed parts forms possibly the most dramatic demonstration of a
systematic engineering approach to building molecular circuits
16,17
.
However, these approaches to constructing molecular information-
processing systems do not realize the full spectrum of analogue and
temporal dynamics naturally present in chemistry, which can be
harnessed to control active molecular devices.
We experimentally demonstrate a design strategy for building
DNA-only chemical controllers capable of being programmed to
execute analogue temporal dynamics. The technology is designed
around a signalling protocol based on short single-stranded DNA
sequences. Molecular sensors (for example, aptamer switches) can
release or expose such short sequences, and actuators (for
example, antisense drugs or ribozymes) can be triggered by them.
MicroRNAs can also be used as inputs to DNA circuits
18,34
. The
control system we design sits in between, receiving inputs in the
form of DNA sequences, and producing outputs in the form of
other sequences (Fig. 1a). The treatment of controller, sensor and
actuator as independent modules has proved indispensible in
other fields of engineering.
Our DNA components are, in principle, capable of realizing the
entire diversity of dynamic behaviours of chemical kinetics as math-
ematically captured by a chemical reaction network (CRN)
12,19
.
Although CRNs started out as a tool to understand experimental
observations of elementary chemical reactions, they form a
general framework for modelling systems with many interacting
components, such as gene regulatory networks, animal populations
and sensor networks. CRNs can embody a wide range of digital and
analogue behaviours, including temporal pattern generation, multi-
stability and memory, Boolean logic, signal processing, control
systems or distributed algorithms
13,35–40
. Moreover, viewed as a pro-
gramming language, CRNs provide a natural and intuitive formal-
ism for delineating and reasoning about molecular interactions,
without making underlying physical details explicit.
We use the familiar language of chemistry to write programs for
our DNA architectur e (Fig. 1a). The ‘instruction’ A þ B C þ D
means that the signals A and B are transformed into signals C and
D, where A, B, C and D are DNA strands we design. The reaction is
not elementary; rather, it is systematically ‘compiled’ into a sequence
of DNA strand displacement reactions. Our use of this chemical
programming language is not gratuitous—a central contribution
of this Article is to provide experimental evidence that our DNA
architecture produces the expected stoichiometry and mass action
kinetics of chemical reactions, so that our algorithms can behave
similarly to what one might naively expect.
We test the major reaction classes—non-catalytic, catalytic and
autocatalytic reactions. We then combine multiple such building
blocks into a network implementing a distributed control algorithm
for achieving consensus between multiple agents. Although the con-
nection between distributed computing and chemistry has been
noted many times in the literature (for example, Petri nets
41
), the
sophistication of the molecular engineering required has deterred
1
University of Washington Department of Electrical Engineering, 185 Stevens Way, Paul Allen Center – Room AE100R, Campus Box 352500, Seattle,
Washington 98195-2500, USA,
2
Microsoft Research, 21 Station Road, Cambridge CB1 2FB, UK,
3
Computation and Neural Systems, California Institute of
Technology, 1200 E California Boulevard, Mail Code 136-93, Pasadena, California 91125, USA,
4
Center for Systems and Synthetic Biology, University of
California, 1700 4th Street, Byers Hall 401, Box 2540, San Francisco, California 94158, USA,
5
Department of Computer Science and Engineering,
University of Washington, Box 352350, Seattle, Washington 98195-2350, USA.
*
e-mail: david.soloveichik@ucsf.edu; gseelig@uw.edu
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experimental implementations. Our experiments corroborate that
we can realize complex behaviours previously out of reach of
synthetic molecular systems.
Among the many proposed architectures for strand displacement
computation
2,10–13,15–19
, ours is unique in that it relies exclusively on
linear, double-stranded DNA complexes (processed by ‘nicking’ one
of the strands)
10
. Because this structure is compatible with natural
DNA, we are able to produce our computational elements in a
highly pure form by bacterial cloning. Thus, we bypass the practical
limitations in the length and purity of synthetic strands.
Signal transduction mechanism
We identify signals (A, B, C, .. .) with single-stranded DNA mol-
ecules (signal strands, Fig. 1b). Nicked double-stranded DNA
(ndsDNA) gate complexes mediate interactions between these
signal strands with the help of additional auxiliary single-stranded
Output signals
(to actuator)
Input signals
(from sensor)
tc* c* c*
tc c
Reporter strategy
Fork
C
−3 Fork
C
−2 Fork
C
−1 Fork
C
i* tc* c* tr* r* tq*
i tc c tr r
r tq
tr r
c tr
i tc
ta* a* tb* b* tr* r* tq*
a tb b tr r tq
ta a a tb
Ta r g e t
behaviour
DNA
architecture
Programming
language
Computational subsystem
Nucleic acid nanocontroller
a
b
c
DNA reaction mechanism for A+B C
k
tb b tr r r tq To Fork
C
b tr
To Reporter
C
From Join
AB
Join
AB
Join
AB
−1 Join
AB
−2 Join
AB
−3
i
C
c
c
C
C
C
A B
Reporter
C
tc*
k
X + Y 2B
B + X 2X
B + Y 2Y
k
k
Figure 1 | DNA realization of a formal CRN. a, A standardized signalling protocol based on short single strands of DNA enables the components of the
nanocontroller to communicate with each other. The formalism of CRNs serves as a progr amming languag e that specifies the desired behaviour for the
computational subsystem. The target beha viour is experimentally realized by the DNA architecture. b, Reaction mechanism. DNA strands are drawn as lines
with arro ws at the 3
′
end. F unctional domains are labelled with low er case letters; * indicates Watson–Crick complement. Speci es A, B and C of the formal
reaction are represented by DNA signal strands A (kta al, green), B (ktb bl,orange)andC (ktc cl, red), respectively. Implementa tion of the bimolecular
reaction A þ B C requires two multistranded gate complexes Join
AB
and Fork
C
, as well as the auxiliary strands ktr rl, kctrl and kitcl. The reaction proceeds
through a se quence of six strand displa cement reactions, where each step provides a toehold for initiation of the next. c, Reporting stra tegy for reaction
kinetics used in this Article. The reporter consists of two strands, one labelled with fluorophor e (red dot) and the other with a quencher (black dot).
Fluorescence is que nched when fluorophore and quencher are co-localized. Displacement of the quencher-labelled strand by sig nal C leads to an increase in
fluorescence proportional to the amount of C detected.
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NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2013.189
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© 2013 Macmillan Publishers Limited. All rights reserved
species. All signal strands have the same sequence domain
structure (see for example, signal strands A (kta al, green),
B(ktb bl, orange) and C (ktc cl, red) in Fig. 1b) with a short
toehold domain (labels ta, tb, ...) that initiates binding to a gate,
followed by a long domain (a, b, ...) that determines signal identity.
The reaction A þ B C is implemented with two gates (called
Join
AB
and Fork
C
in Fig. 1b). The join gate consumes (and thus
‘joins’) the two signals A and B and the fork gate releases the
signal C, which is initially bound to the fork gate Fork
C
, and thus
inactive. (The name ‘fork gate’ derives from the fact that multiple
signal strands can be released, as shown in later examples.) The
complete triggering of a join and a fork gate—corresponding to a
single formal reaction A þ B C—is a cascade of strand displace-
ment reactions in which each reaction exposes a toehold for the sub-
sequent reaction (Fig. 1b, Supplementary Section S1). The
displacing strand is a signal strand, an auxiliary strand or a strand
previously released in the cascade (for example, ‘translator’ strand
krtql is released by the join gate and triggers the fork gate). We
use a fluorescent reporter strategy to detect specific strands and
follow the reactions (Fig. 1c).
Each reaction is reversible until the very last displacement step
involving the fork gate. The reversibility of the first step is essential
to ensure stoichiometric correctness: the first formal reactant A
should not be consumed in the absence of the second, B.
Reversibility allows A to be re-released if the cascade does
not complete.
The two-gate design and use of auxiliary strands ensures that all
signal strands have the same domain structure and independent
sequence, which guarantees composability
12
. Signal strands can
thus be shared between multiple reactions to create a coupled
system. Without these constraints, we can implement an individual
bimolecular reaction with many fewer species, but we would lose the
ability to compose reactions into arbitrary CRNs.
Plasmid encoding of DNA gates
The performance of strand displacement systems is currently
limited by undesirable side reactions: leaks (the spontaneous
‘firing’ of a reaction cascade in the absence of the intended molecu-
lar trigger) or substoichiometric completion levels (unintentional
sequestration of the signal leading to reduced product
yield). These problems can at least in part be traced to errors in
chemical DNA synthesis
42
. Biologically synthesized DNA is a useful
alternativ e to synthetic DNA, even in non-biological applications
where large quantities of highly pure DNA are required
43–45
.
Our gates consist entirely of nicked double-stranded DNA
12
,
which makes them uniquely compatible with plasmid DNA as a
starting material. Plasmid-derived gates have the additional advan-
tage that they can be replicated and stored as bacterial glycerol
stocks (before enzymatic processing). Gate production is detailed
in Fig. 2a. Correct processing was tested using gel electrophoresis
(Fig. 2b, Supplementary Section S7). Enzyme selection and
additional design criteria are detailed in Supplementary Sections
S2 and S3. The sequence constraints imposed by the use of
nicking enzymes do not limit the generality of our method.
Signals can be made orthogonal to one another by designing the
sequences surrounding the nicking sites to be different. All data
shown in this Article were collected with plasmid-derived
ndsDNA gates except where otherwise indicated. Externally added
signal and auxiliary strands, as well as the reporter gates used for
following reaction kinetics, were chemically synthesized.
Testing fundamental reaction types
The modular nature of our design makes it easy to create reactions
with multiple products of unconstrained sequence, allowing us to
engineer the three major reaction classes: non-catalytic, catalytic
and autocatalytic. These are the building blocks for composition
of complex CRNs.
Extensive tests of the most basic reaction A þ B C verified
correct stoichiometry (are the correct amounts of reactants used
up and products generated?; Fig. 3a) and kinetics (are the reactants
and products being generated according to the target rate law?; see
section ‘Verification of the bimolecular rate law’). In the catalytic
reaction A þ B C þ B, even a small amount of B effectively ‘con-
verts’ all of A to C, but B remains conserved (Fig. 3b). Catalytic reac-
tions are ubiquitous in biological chemical controllers (for example,
transcriptional networks, kinase networks) as well as man-made
artificial systems
6–11
. In Supplementary Fig. S10, we quantitatively
analyse the catalytic turnover, showing that a single catalyst can
trigger multiple reaction cycles.
In the autocatalytic reaction A þ B C þ 2B, even a small
amount of B effectively ‘converts’ all of A to itself (C acts as a
‘readout’), resulting in the typical sigmoidal kinetic curves
(Fig. 3c). Because of the exponential growth kinetics, autocatalytic
reactions are common in settings where rapid (self-)amplification
is observed, such as replication or apoptosis. These properties also
make autocatalysis a key ingredient for propagating information
in proposed chemical algorithms
46
(see also section ‘Consensus
network’). Because autocatalysis is extremely sensitive to leaks
9–11
,
Cloning
Insert
templates
Enzymatic processing
Nick top strands
Release
dsDNA gates
Extract
plasmid
Sequence
colonies
Amplification and quality control
AAC T
a tb
b tr
Top short strands (27)
Impurity strands
Bottom strand (87)
Incomplete digest
Gel verification
1
100
80
30
20
23
10% denaturing PAGE gel
Lane 1: 10 nt ssDNA ladder
Lane 2: Synthesized gate
Lane 3: Plasmid-derived gate
ta* a* tb* b* tr* r* tq*
r tq
Grow
sequence-
verified colony
Pvull-HFNb.BsrDI
DNA gate production
ba
Plasmid
Transform
Synthesized
template
Nicked dsDNA-gates
Gates
Figure 2 | DNA gate production. a, Highly pure ndsDNA gates can be produced from plasmid DNA. Multiple copies of a double-stranded ndsDNA gate
template are inserted into a pla smid and transformed into E. coli cells. Clones are picked and plasmid sequence is verified. A clonal population is grown up,
and plasmid DNA is extracted using standard molecular techniques. Finally, the restriction enzyme PvuII-HF is used to release the gate from the plas m id, an d
the nicking enzyme Nb.BsrDI is used to generate nicks in the top strand. b, Analysis by 10% denaturing polyacrylamide gel electrophoresis (PAGE) of the
enzymatically processed gate. The long bottom strand (87-mer) and short top strands (27-mer) are visible on the D-gel.
NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2013.189
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it provides a good measurement of reactant quality. The estimated
amount of autocatalyst B leaked (black trace, Fig. 3c,ii) is less
than 2% (Supplementary Table S3); however, this leak is
exponentially amplified.
To compare the performance of plasmid-derived gates to that of
synthesized gates, we re-implemented the catalytic and autocatalytic
reactions with synthesized gates using the same sequences. We
observed that catalytic turnover is at least twice as high for the
plasmid-derived gates. This observation is indicative of incomplete
triggering due to unknown side reactions sequestering the catalyst in
the synthesized system. Comparing autocatalytic reactions, we
found that plasmid-derived gates suffered from noticeably less of
the untriggered amplification characteristic of a lower leak rate
(Supplementary Fig. S10). These data are consistent with the obser-
vation that there are fewer truncated strands detected in a gel
analysis of the plasmid-derived gates than for the synthetic gates
(Fig. 2b, Supplementary Section S3.3).
We tested bimolecular reactions with one, two or three products,
but our approach can be generalized to different numbers of pro-
ducts and reactants. Unimolecular reactions can be implemented
with a single-input join gate, while higher-order reactions can be
implemented using join gates with multiple inputs.
Verification of the bimolecular rate law
The reaction specification A þ B C delineates not only the pro-
duction/consumption relationships between A, B and C, but also
the dynamics. Despite the overall complex reaction mechanism
(which, for A þ B C, involves five reversible and one irreversible
stand displacement reactions, Fig. 1b), an analytical argument
shows that the overall kinetics should be well approximated by the
0.0 0.5
B
f
= A
0
+ B
0
B
0
1.0
0.0 0.5
iii. Autocatalyst B at 10 h
iii. Catalyst B at 10 h
iii. Product C at 10 h
ii. Kinetics (varying A
0
)
ii. Kinetics (varying B
0
)
ii. Kinetics (varying B
0
)
i. DNA implementation
i. DNA implementation
i. DNA implementation
a A+B → C
b A+B → C + B
c A+B → C + 2B
B
0
1.0
0.0
0.0
1.0
0.5
C
f
0.0
2.0
1.0
1.5
0.5
0.0
(1, 0)
(A
0
, B
0
)
(1, 0.1)
(1, 0.2)
(1, 0.3)
(1, 0.5)
(1, 1.0)
(0.5, 0)
(A
0
, B
0
)
(0.5, 0.05)
(0.5, 0.075)
(0.5, 0.1)
(0.5, 0.2)
(0.5, 0.3)
(0.5, 1.0)
(0.00, 2)
0
0.00
0.25
0.50
0.75
1.00
C
0.00
0.25
0.50
0.75
1.00
C
0.00
0.25
0.50
C
5
Time (h)
10
05
Time (h)
10
02
Time (h)
4
(A
0
, B
0
)
(0.25, 2)
(0.50, 2)
(0.75, 2)
(1.00, 2)
1.0
0.5
B
f
B
f
0.5
A
0
1.0
B
f
= B
0
C
f
= A
0
A B
B CB
c
RQ
ROX
tc* c*
i tb
b tb
b tc
c tr
tr r
A B
B
C
c
RQ
ROX
tc* c*
i tc
c tb
b tr
tr r
A B
C
c
RQ
ROX
tc* c*
i tc
c tr
tr r
Figure 3 | Testing fundamental reaction types. Panels (i) show a simplified representa tion of the gates, auxiliary strands, and signal strands used for the
corresponding experiments. Ex perimental kinetics data are shown in panels (ii) as full coloured lines. Concentrations of the signa l strands ar e indicated in the
same colour, 1× ¼ 50 nM. All join and fork gates were at 1.5× , and auxiliary strands were at 2×. Best fits of th e strand dis placement -le v el model to the data
are shown as crossed lines. Panels (iii) show data confirming the correct reaction stoichiometry. a, Non-catalytic bimolecular reaction A þ B C. Signal B
was at 2× and different amounts of signal strand A wer e added. Panel (iii) shows that levels of (product) signal C at the measurement end point (10 h) are
very close to the amounts of limiting inputs as expected for a stoichiometrically corr ect bimolecular reaction. b, Bimolecular catalytic reaction A þ B C þ B.
Signal A was at 0.5× and different amounts of the catalytic signal B wer e introduced into the system. Panel (iii) shows that the final amount of free catalyst
B
f
is equal to the initial amount B
0
. The amount of catalyst signal B at 10 h was measur ed by adding a fluor escent reporter for B. c, Autocatalytic reaction
A þ B C þ 2B. Signal A was at 1× and the amount of signal B was varied. Panel (iii) sho ws that the final amount of the autocatalyst signal B is equal to
the sum of the initial amo unts of A an d B as expected for autoca talysis. The amount of autocatalyst signal B was measur ed at 10 h by adding a fluor escent
reporter for B.
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mass-action rate law expected of the formal reaction (that is,
d[C]/dt ¼ 2d[A]/dt ¼ 2d[B]/dt ¼ k[A][B]). As the derivation
in Supplementary Section S5 shows, the regime of best correspon-
dence (‘CRN regime’) is one in which gates and auxiliary strands,
including ‘backward’ auxiliary strands katbl and kbtrl,are
sufficiently in excess over the signal strands (Fig. 4a).
We experimentally confirmed that the multistep strand
displacement level mechanism implements the expected rate law
for A þ B C, and that the rate constant can be tuned by adjusting
the concentrations of gates and auxiliary species. Figure 4b shows six
sets of experimental data for the reaction A þ B C in or near the
CRN regime. Each set was obtained with a different concentration of
the backward auxiliary strands katbl and kbtrl and contains kinetics
traces corresponding to at least two different combinations of the
signals A and B. We chose to vary the concentration of the backward
auxiliary strands because our analysis suggests that the formal rate
constant can be effectively tuned in this way (Supplementary
Sections S5). We then fit the data from each set to a bimolecular
rate law. The best fit rate constants varied over about two orders
of magnitude from 3.5 × 10
4
M
21
s
21
to 5.3 × 10
2
M
21
s
21
as the concentration of backward auxiliary strands increased from
0× to 13× (Supplementary Section S5). The data show that the
reactions are symmetrical with regard to the two signals, as required
by the bimolecular rate law, although signal strands A and B react
sequentially with the join gate (see, for example, traces with A, B
at 1×, 0.3× and 0.3×,1× respectively).
Mechanistic strand displacement-level model
Each individual strand displacement step can be well modelled as a
bimolecular reaction between a signal or auxiliary strand and a gate
complex with a matching open toehold
47
. We used the Visual
DSD
14,48
software to develop a quantitatively constrained model of
0.00
0.25
0.50
05
Time (h)
C
0.00
0.25
0.50
0.00
3
4
5
0.25
0.50
C
0.00
0.25
0.50
0.00
0.25
0.50
0.00
0.25
0.50
10
05
Time (h)
10
0
05×
Log
10
k (M
−1
s
−1
)
a tb , b tr
: 0×
k = 34,587 (M
−1
s
−1
)
a tb , b tr
: 1×
k = 8,054 (M
−1
s
−1
)
a tb , b tr
: 3×
k = 7,954 (M
−1
s
−1
)
a tb , b tr
: 6×
k = 1,572 (M
−1
s
−1
)
a tb , b tr
: 9×
k = 961 (M
−1
s
−1
)
a tb , b tr
: 13×
k = 531 (M
−1
s
−1
)
a tb , b tr
10× 15×
5
Time (h)
10
05
Time (h)
10
05
Time (h)
10
05
Time (h)
10
(A
0
, B
0
)
(0.25, 0.25)
(0.25, 0.25)
(0.25, 0.25)
(0.25, 0.25)
(0.25, 0.25)
(0.25, 0.25)
(0.5, 0.25)
(0.5, 0.25)
(0.25, 0.5)
(0.25, 0.5)
(0.5, 0.25)
(0.5, 0.25)
(0.25, 0.5)
(0.25, 0.5)
(0.5, 0.5)
(A
0
, B
0
)
(A
0
, B
0
)
(A
0
, B
0
)
(A
0
, B
0
)
(A
0
, B
0
)
(0.5, 0.5)
(0.5, 0.5)
(0.5, 0.5)
(0.5, 0.5)
(0.5, 0.5)
(0.5, 1.0)
(0.3, 1.0)
(1.0, 0.5)
(1.0, 0.3)
A B
C
c
RQ
ROX
tc* c*
i tc
c trtr rb trb tb
DNA implementation
a
b
c
Kinetics equivalent in ‘CRN regime’
Mechanistic model
(strand displacement)
k1
k2
A + Join
AB
Join
AB
−1 +
a tb
CRN specification
k
A + B C
d[A]/dt = −k[A][B]
d[B]/dt = −k[A][B]
d[C]/dt = k[A][B]
d[A]/dt = −k1[A][Join
AB
]
+ k2[Join
AB
−1][a tb]
Figure 4 | Tuning the rate of the bimolecular reaction A 1 B C. a, Approximating the bimolecular rate law . The CRN pr ogr am is executed by a DNA
architectu r e that can be quantitativ ely modelled at a mechanistic level. We view strand displacement reactions (for example, A þ Join
AB
Join
AB
21 þ katbl,
see Fig. 1b for component names) as the elementary reactio n steps and the formal bimolecular rea cti on (f or example, A þ B C) as the complex reaction
pathw a y decomposed into these elementary rea ctions. In the ‘CRN regime’ (see text) the mechanistic model closely appro ximates the dynamics of the target
program. The ra te constant k of the formal sys tem can be tuned by changing the concentr ati ons of gates and auxiliary strands. b, Reactions with varying
concentr a tions of the backw ard auxiliary str ands katbl and kbtrl . The data (solid traces) show the time ev olution of C; purple trac es (0× katbl and kbtrl),
blue (1×), green (3×), olive green (6×), orange (9×)andred(13×), wher e 1× ¼ 40 nM. Gates were at 3× and the initial concentra tions of signals A and B
are indicated in each panel. Black dashed lines are fits to the bimolecular rate law in a. Best-fit rate constants to the bimolecular rate law are indicated in each
panel. Black crossed lines are fits to the mechanistic str and displacement-le v el model. c, Fitted bimolecular rate constant versus analytic predicti on. The solid
line is obtained from an analytic prediction for the dependence of the expected rate constant on the concentrations of the ba ckward auxiliary strands katbl
and kbtrl (equation (8) in Supplementary Section S5). The colour ed dots show the rate cons tants k obtained from fitting the experimental data from b.
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