DNA data-structure

A DNA Data Structure
Ben Shirt-Ediss & Natalio Krasnogor

The Dr. Jekyll Side of DNA
Source:
http://compbio.pbworks.com

Mr. Hide: DNA as a Dynamic Polymerdization Reactions
e of DNA hybridization reactions is the Watson-Crick DNA hybridization between two
A strands as discussed in Section 1.2.2. Two ssDNA strands can attach to each other.
o detach from one another, if the temperature is greater than the melting temperature
6). The melting temperature of a dsDNA is deﬁned as the temperature at which 50%
nverted to single stranded form.
Figure 6: DNA Denaturation Renaturation [60]
Hybridisation Toehold-Mediated
Strand Displacement
Toehold Exchange
trol of DNA Strand Displacement Kinetics A R T I C L E
Several subsequent works used Yurke’s basic reaction sequence
(a hybridization step followed by strand displacement to reverse the
effect of the initial hybridization) for controlling complex nanos-
cale structures. Simmel and Yurke34
demonstrated a nanoactuator
related to Yurke’s original tweezer design. Addition of a first input
strand pushed the two arms of the nanoactuator apart; addition of
a second input strand set them free. In further work they built a
device that could be switched between three distinct states using
two pairs of fuel strands35
. Tian and Mao36
built a device consisting
of two DNA complexes reminiscent of interlocking gears that could
be repeatedly cycled through three different states.
Reconfiguring self-assembled structures. Strand displacement
can be combined with structural self-assembly to enable dynamic
reconfiguration of larger DNA nanostructures post-assembly, and
can be used to induce ch
ple of this was describe
toehold-mediated cyclin
rotary DNA device. Th
states corresponding to
JX2 (Fig. 1b). They also
structure large enough t
scope and demonstrated
tural motif relative to th
Their device was based
nanomachine30
that resp
than DNA inputs.
Chakraborty et al.38
l
that could be switched be
Seeman39
demonstrated
2* 3*
3
1 2
22
2
3
1
5'
3'
3'
CCCTCATTCAATACCCTACG
AGAGGTA
c
a
b
32
Input A
Complex X
2. Domain 2 undergoes
branch migration
3. Strand displacement
completes
1. Toehold domains
initiate binding
Complex Y
Output B
(toehold)
(toehold)
GGGAGTAAGTTATGGGATGC
3*2*
2
1 2* 3*
3
1
2
2
3*2*
2* 3*
2 3
21
2* 3*
2
CCACATACATCATATT
1
–––
Source:
Zhang & Winfree. 2011. Nat Chem.
Source:
Zhang & Winfree. 2009

DNA: Dynamic and also Well Understood
Predictable tertiary structure
Can use methods in Mol. Bio
to quantify experimental success
Enzymatic reactions cutting/joining
DNA well characterised
Hybridisation, branch migration
and strand displacement reactions
well understood
PAGE, Fret, PCR, AFM…
xDNA model (left), with equal
has di↵erentiated major and
x with one base pair displayed.
III. INTRODUCING DIFFERENT WID
AND MINOR DNA GROOVES
B-DNA in the original oxDNA m
widths, while in reality DNA has a lar
a smaller minor groove. Having realisti
and minor grooves is equivalent to havi
tioned backbone sites in the model, an
the physical properties of many DNA
in DNA origami, antiparallel double
crossovers, for which the position of t
shown to be crucial for origami structur
is anisotropic duplex bending: the dup
bend more easily into the major groove
the groove widths are unequal.
The oxDNA nucleotide is compos
sites: the hydrogen-bonding, stacking, a
introduce di↵erent groove widths by ch
oxDNA

DNA Computing
ime study of the dynamics of a single mol-
ule and the chemical and biochemical re-
tions that such a molecule may undergo in
lution.
REFERENCES AND NOTES
. W. E. Moerner, Science 265, 46 (1994), and refer-
ences therein.
. M. Orrit, J. Bernard, R. I. Personov, J. Phys. Chem.
97,10256(1993).
. F. GOttler, T. Irngartinger, T. Plakhotnik, A. Renn, U.
P. Wild, Chem. Phys. Lett. 217, 393 (1994).
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Brenner, Jpn. J. Appl. Phys. 33,1571 (1994).
. E. Betzig and R. J. Chichester, Science 262, 1422
(1993).
. J. K. Trautman, J. J. Macklin, L. E. Brus, E. Betzig,
Nature 369, 40 (1994).
. D. C. Nguyen, R. A. Keller, J. H. Jett, J. C. Martin,
Anal. Chem. 59, 2158 (1987).
. K. Peck, L. Stryer, A. N. Glazer, R. A. Mathies, Proc.
Natl. Acad. Sci. U.S.A. 86, 4087 (1989).
. W. B. Whitten, L. M. Ramsey, S. A. Arnold, B. V.
Bronk, Anal. Chem. 63,1027 (1991); K. C. Ng, W. B.
Whitten, S. A. Arnold, L. M. Ramsey, ibid. 64, 2914
(1992).
. M. Eigen and R. Rigler, Proc. Natl. Acad. Sci. U.S.A.
91, 5740 (1994).
. In fluorescence correlation spectroscopy, the inten-
sity recorded at time t is multiplied by that recorded
at t + At and the product is integrated over a finite
period of time; see D. E. Koppel, Phys. Rev. A 10,
1938 (1974).
. T. T. Perkins, D. E. Smith, S. Chu, Science 264, 819
(1994); T. T. Perkins, S. R. Quake, D. E. Smith, S.
Chu, ibid., p. 822.
. S. B. Smith, L. Finzi, C. Bustamante, ibid. 258,1122
(1992); C. Bustamante, Annu. Rev. Biophys. Bio-
phys. Chem. 20, 415 (1991).
. M. Washizu and 0. Kurosawa, IEEE Trans. Ind. Appl.
26,1165 (1990).
. S. B. Smith, P. K. Aldridge, J. B. Callis, Science 243,
203 (1989).
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194, 278 (1991).
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(1981).
. I. Auzanneau, C. Barreau, L. Salome, C. R. Acad.
Sci. Paris 316, 459 (1993).
. H. Kabata et al., Science 262, 1561 (1993).
. D. A. Schafer, J. Gelles, M. P. Sheetz, R. Landick,
Nature 352, 444 (1991).
. Laser excitation at 488.0 and 514.5 nm was provided
by an argon ion laser (Lexel Lasers, Fremont, CA). The
laser beam entered the microscope through a back
port and was directed to an oil-immersion objective
(x100, NA = 1.3, Nikon Instrument Group, Melville,
NY) by a dichroic beamsplitter (505DRLP02 or
22. M. B. Schneider and W. W. Webb, Appl. Opt. 20,
1382 (1981).
23. R. Rigler, U. Mets, J. Widengren, P. Kask, Eur. Bio-
phys. J. 22,169 (1993).
24. W. Feller, An Introduction to Probability Theory and
its Applications (Wiley, New York, ed. 3, 1968).
25. S. A. Soper, H. L. Nutter, R. A. Keller, L. M. Davis, E.
B. Shera, Photochem. Photobiol. 57, 972 (1993).
34. W. P. Ambrose, P. M. Goodwin, J. C. Martin, R. A.
Keller, ibid., p. 364.
35. S.N. acknowledges the Whitaker Foundation for a
young investigator award. D.T.C. is a Beckman Cell
Science Scholar of Stanford University. This work
was supported by Beckman Instruments, Inc.
18 July 1994; accepted 19 September 1994
Molecular Computation of Solutions to
Combinatorial Problems
Leonard M. Adleman
The tools of molecular biology were used to solve an instance of the directed Hamiltonian
path problem. A small graph was encoded in molecules of DNA, and the "operations" of
the computation were performed with standard protocols and enzymes. This experiment
demonstrates the feasibility of carrying out computations at the molecular level.
In 1959, Richard Feynman gave a visionary
talk describing the possibility of building
computers that were "sub-microscopic" (1).
Despite remarkable progress in computer
miniaturization, this goal has yet to be
achieved. Here, the possibility of comput-
ing directly with molecules is explored.
A directed graph G with designated ver-
tices vn and vout is said to have a Hamilto-
nian path (2) if and only if there exists a
sequence of compatible "one-way" edges el,
e2, ... ., e, (that is, a path) that begins at in,
ends at v., and enters every other vertex
exactly once. Figure 1 shows a graph that
for vn = 0 and v01u = 6 has a Hamiltonian
path, given by the edges 0-*1, 1->2, 2->3,
3---4, 4->5, 5->6. If the edge 2->3 were
removed from the graph, then the result-
ing graph with the same designated verti-
ces would not have a Hamiltonian path.
Similarly, if the designated vertices were
changed to vin = 3 and vout = 5 there
Department of Computer Science and Institute for Molec-
ular Medicine and Technology, University of Southern Cal-
ifornia, 941 West 37th Place, Los Angeles, CA 90089,
USA.
SCIENCE * VOL. 266 * 11 NOVEMBER 1994
would be no Hamiltonian path (because,
for example, there are no edges entering
vertex 0).
There are well-known algorithms for de-
ciding whether an arbitrary directed graph
with designated vertices has a Hamiltonian
path or not. However, all known algorithms
for this problem have exponential worst-case
complexity, and hence there are instances of
modest size for which these algorithms re-
quire an impractical amount of computer
time to render a decision. Because the direct-
ed Hamiltonian path problem has been
proven to be NP-complete, it seems likely
that no efficient (that is, polynomial time)
algorithm exists for solving it (2, 3).
The following (nondeterministic) algo-
rithm solves the directed Hamiltonian path
problem:
Step 1: Generate random paths through the
graph.
Step 2: Keep only those paths that begin with vin
and end with v,,f.
Step 3: If the graph has n vertices, then keep
only those paths that enter exactly n vertices.
Step 4: Keep only those paths that enter all of
1021
onFebruary25,2016DownloadedfromonFebruary25,2016DownloadedfromonFebruary25,2016DownloadedfromonFebruary25,2016Downloadedfrom
Science
1994
02 TATCGG&TCGGTATATCCGA
0 GCTATTCGAQCTTAAAGCTA
04 GGCTAGGTACCAGCATGT
02-3 GTATATCCQGACTATTCQG
03-4 CTTA&AGCTAQGCTAQGTAC
03 CG&TA&GCTCGA.&TTTCG&T
0,),
Fig. 1. Directed graph. When vi, = 0 and v,,t = 6,
a unique Hamiltonian path exists: 0-s1, 1 -s2,
2-s3, 3->4, 4-s5, 5-s6.
03,4
start stop
A unique hamiltonian path exists:
0>1,1>2,2>3,3>4,4>5,5>6
C
-150
-100
-50
1 2 3 4 5 6
-150
-100
-50
1 2 3 4 5 6 7
-150
-100
-50
1 2 3 4 5 6 7
illonis ----
Formation of DNA molecules encode possible paths
PCR & cut gel to select paths starting at 0, ending at 6
DNA paths entering all vertices found by
6 washings with magnetic beads
7 days of lab work

DNA Computing
lution.
ences therein.
97,10256(1993).
(1993).
Nature 369, 40 (1994).
Anal. Chem. 59, 2158 (1987).
Natl. Acad. Sci. U.S.A. 86, 4087 (1989).
(1992).
91, 5740 (1994).
1938 (1974).
Chu, ibid., p. 822.
phys. Chem. 20, 415 (1991).
26,1165 (1990).
203 (1989).
194, 278 (1991).
(1981).
Sci. Paris 316, 459 (1993).
Nature 352, 444 (1991).
1382 (1981).
phys. J. 22,169 (1993).
Leonard M. Adleman
3---4, 4->5, 5->6. If the edge 2->3 were
USA.
vertex 0).
problem:
graph.
and end with v,,f.
1021
Science
1994competing
with silicon
embedding
control in
molecular systems
and cells

DNA Computing
lution.
ences therein.
97,10256(1993).
(1993).
Nature 369, 40 (1994).
Anal. Chem. 59, 2158 (1987).
Natl. Acad. Sci. U.S.A. 86, 4087 (1989).
(1992).
91, 5740 (1994).
1938 (1974).
Chu, ibid., p. 822.
phys. Chem. 20, 415 (1991).
26,1165 (1990).
203 (1989).
194, 278 (1991).
(1981).
Sci. Paris 316, 459 (1993).
Nature 352, 444 (1991).
1382 (1981).
phys. J. 22,169 (1993).
Leonard M. Adleman
3---4, 4->5, 5->6. If the edge 2->3 were
USA.
vertex 0).
problem:
graph.
and end with v,,f.
1021
Science
1994
AND/OR
logic gates Source:
Qian & Winfree 2011
saw gate with a few wires can create a catalytic
cycle in which input transforms free fuel into free
output without being consumed in the process
(Fig. 1D and fig. S1, B and C). Initially, the output
signal is bound to the right side of the gate; the
input and fuel signals are free (in our analogy, the
output is riding on the right side of the seesaw
board; the input and fuel are wandering around).
The input signal first releases the output signal and
binds to the gate instead (the input jumps onto the
left side of the board and makes the output jump
off). The fuel signal then displaces the input signal
by binding to the gate in the same way (the fuel
pushes off the input). A catalytic cycle has been
completed. In general, a free signal on one side of
a seesaw gate can catalyze the exchange of signals
on the other side, and this exchange will not hap-
pen without the catalyst. These reactions are driv-
en forward by the entropy of equilibration for the
seesawing reactions. A small amount of free input
can catalyze the release of a large amount of free
output (fig. S2).
Thresholding can be directly combined with a
seesaw catalyst to support a digital abstraction—
which is the basic principle underlying digital
logic in electronics—by pushing the intrinsically
analog signal toward either the ideal ON or OFF
value. Fluorescence kinetics experiments (Fig. 1E)
demonstrated the circuit in Fig. 1A connected to
the reporter in Fig. 1B. The input-versus-output
relationship (plotted in Fig. 1F) reveals a sharp
threshold, ideal for signal restoration.
A cascade of two seesaw gates can compute
the logic function OR or AND. To explain this,
we introduce two composable seesaw compo-
nents for digital circuits. We first define the
gross production of signal X as the total amount
eventually released from the gate:
〈X〉 ¼ ∫
þ∞
0
Xprod
ðtÞdt ð1Þ
Motivated by sequence design constraints (figs. S3
and S4), we then define two types of feedforward
seesaw gates, each assuming an irreversible down-
stream drain. The first type is called an amplifying
gate. It has a threshold and fuel. If the gross
production of its input is greater than the initial
amount of threshold, the output will keep being
released catalytically until it reaches the max-
imum, which is the initial amount of bound
arrives at the gate (negative number). A reporter
that transforms a DNA signal into a fluorescence
signal is represented by half a node with a zigzag
arrow (Fig. 1B), with its initial relative concen-
tration written similar to a threshold.
Each signal is a single-stranded DNA mole-
cule that has two recognition domains identify-
ing the two gates it connects, one on either side
of a central toehold domain. Each gate is asso-
ciated with a gate base strand that has (the com-
plement of ) one recognition domain flanked by
two toehold domains. When a signal strand is
bound to a gate, it forms a gate:signal complex
with the gate’s base strand. At any given mo-
ment (not counting the transient states during
reactions shown in fig. S1C), a gate base strand
always has a signal strand bound to one side,
leaving the toehold on the other side uncovered.
There are three basic reactions involved in
a seesaw network (Fig. 1C and fig. S1C). The
first one is seesawing: A free signal on one side
of a gate can release a signal bound on the other
side of the gate by toehold-mediated strand dis-
placement. The process starts with the free signal
strand (e.g., w2,5) hybridizing to the gate:signal
complex (e.g., G5:5,6) at the uncovered toehold
domain (e.g., T*) and then undergoing branch mi-
gration through the recognition domain (e.g., S5).
The previously bound signal will fall off when it
is attached to the gate base strand only by the
short toehold. The resulting gate:signal complex
(e.g., G2,5:5) will have an uncovered toehold on
the other side, and therefore the now-free signal
(e.g., w5,6) can reverse the process symmetrically.
The second reaction is thresholding: A thresh-
old species associated with a gate and an imping-
ing signal can react with the signal by means
of a longer toehold (e.g., s2*T*), producing
only inert waste species that have no exposed
toehold. Thresholding is much faster than see-
sawing because the toehold-mediated strand dis-
placement rate grows exponentially with toehold
length for short toeholds (7, 8). As a result, see-
sawing effectively only happens when the input
signal exceeds the threshold. The third reaction
is reporting: A reporter species similar to a thresh-
old, but modified with a fluorophore and quench-
er pair, can absorb an impinging signal while
generating a fluorescence signal. Unlike thresh-
binds to the gate instead (the input jumps onto the
left side of the board and makes the output jump
off). The fuel signal then displaces the input signal
by binding to the gate in the same way (the fuel
pushes off the input). A catalytic cycle has been
completed. In general, a free signal on one side of
a seesaw gate can catalyze the exchange of signals
on the other side, and this exchange will not hap-
pen without the catalyst. These reactions are driv-
en forward by the entropy of equilibration for the
seesawing reactions. A small amount of free input
can catalyze the release of a large amount of free
output (fig. S2).
Thresholding can be directly combined with a
seesaw catalyst to support a digital abstraction—
which is the basic principle underlying digital
we introduce two composable seesaw comp
nents for digital circuits. We first define th
gross production of signal X as the total amou
eventually released from the gate:
〈X〉 ¼ ∫
þ∞
0
Xprod
ðtÞdt ð
Motivated by sequence design constraints (figs. S
and S4), we then define two types of feedforwa
seesaw gates, each assuming an irreversible dow
stream drain. The first type is called an amplifyin
gate. It has a threshold and fuel. If the gro
production of its input is greater than the initi
amount of threshold, the output will keep bein
released catalytically until it reaches the ma
imum, which is the initial amount of boun
Fig. 2. Digital logic gates implemented with the seesaw DNA motif. (A) Abstract diagram of

DNA Computing
lution.
ences therein.
97,10256(1993).
(1993).
Nature 369, 40 (1994).
Anal. Chem. 59, 2158 (1987).
Natl. Acad. Sci. U.S.A. 86, 4087 (1989).
(1992).
91, 5740 (1994).
1938 (1974).
Chu, ibid., p. 822.
phys. Chem. 20, 415 (1991).
26,1165 (1990).
203 (1989).
194, 278 (1991).
(1981).
Sci. Paris 316, 459 (1993).
Nature 352, 444 (1991).
1382 (1981).
phys. J. 22,169 (1993).
Leonard M. Adleman
3---4, 4->5, 5->6. If the edge 2->3 were
USA.
vertex 0).
problem:
graph.
and end with v,,f.
1021
Science
1994
a
b
11 *
5*
6*
4
3*
2*
1*
76*3*
4
1 1
52
1
1
1*
5*2*
1*
Track base
Track base Track base Track base
1*1
7 2*
3*
1*1
6
7
11*
5*
1
5
6*3
4
11*
2*
1
2
3*6
7
11*
5*
1
5
6*
7*
1*
4*
1* 1*
7*
1
7*5
6
Walker
Hairpin H1 Hairpin H2
1*
2* 5*
1*1
25
11
4
3* 6* 7 2*
3* 3*
2*76*3*
1
52
1 1*
5*2*
1* 1
4
1
2
33
4
11*
2* 5*
1*1
2 5
1
3* 6* 7 2*
3*
1
2
1 1*1 1*1
1*
4*
Expended track Fresh track
Direction
of motion
3
2 4*
1*1
1*
3
2 4*
REVIEW ARTICLENATURE CHEMISTRY DOI: 10.1038/NCHEM.957
Source:
Omabegho, T., Sha, R. & Seeman, N. C. 2009
Molecular
walkers

DNA Computing
lution.
ences therein.
97,10256(1993).
(1993).
Nature 369, 40 (1994).
Anal. Chem. 59, 2158 (1987).
Natl. Acad. Sci. U.S.A. 86, 4087 (1989).
(1992).
91, 5740 (1994).
1938 (1974).
Chu, ibid., p. 822.
phys. Chem. 20, 415 (1991).
26,1165 (1990).
203 (1989).
194, 278 (1991).
(1981).
Sci. Paris 316, 459 (1993).
Nature 352, 444 (1991).
1382 (1981).
phys. J. 22,169 (1993).
Leonard M. Adleman
3---4, 4->5, 5->6. If the edge 2->3 were
USA.
vertex 0).
problem:
graph.
and end with v,,f.
1021
Science
1994
Universal substrate for
reaction kinetics
DNA as a universal substrate for chemical kinetics
David Soloveichika,1
, Georg Seeliga,b,1
, and Erik Winfreec,1
a
Department of Computer Science and Engineering, University of Washington, Seattle, WA 98195; b
Department of Electrical Engineering, University of
Washington, Seattle, WA 98195; and c
Departments of Computer Science, Computation and Neural Systems, and Bioengineering, California Institute of
Technology, Pasadena, CA 91125
Edited by José N. Onuchic, University of California San Diego, La Jolla, CA, and approved January 29, 2010 (received for review August 18, 2009)
Molecular programming aims to systematically engineer molecular
and chemical systems of autonomous function and ever-increasing
complexity. A key goal is to develop embedded control circuitry
within a chemical system to direct molecular events. Here we show
that systems of DNA molecules can be constructed that closely ap-
proximate the dynamic behavior of arbitrary systems of coupled
chemical reactions. By using strand displacement reactions as a
primitive, we construct reaction cascades with effectively unimole-
cular and bimolecular kinetics. Our construction allows individual
reactions to be coupled in arbitrary ways such that reactants can
participate in multiple reactions simultaneously, reproducing the
desired dynamical properties. Thus arbitrary systems of chemical
equations can be compiled into real chemical systems. We illustrate
our method on the Lotka–Volterra oscillator, a limit-cycle oscillator,
a chaotic system, and systems implementing feedback digital logic
and algorithmic behavior.
molecular programming ∣ mass-action kinetics ∣ strand displacement
cascades ∣ chemical reaction networks ∣ nonlinear chemical dynamics
Chemical reaction equations and mass-action kinetics provide
a powerful mathematical language to describe and analyze
chemical systems. For well over a century, mass-action kinetics
has been used to model chemical experiments and to predict
and explain their dynamical properties. Both biological and non-
biological chemical systems can exhibit complex behaviors such as
oscillations, memory, logic and feedback control, chaos, and pat-
tern formation—all of which can be explained by the correspond-
ing systems of coupled chemical reactions (1–4). Whereas the use
wire the components to achieve particular functions. Attempts to
systematically understand what functional behaviors can be ob-
tained by using such components have targeted connections to
analog and digital electronic circuits (10, 18, 19), neural networks
(20–22), and computing machines (15, 20, 23, 24); in each case,
complex systems are theoretically constructed by composing
modular chemical subsystems that carry out key functions, such
as boolean logic gates, binary memories, or neural computing
units. Despite its apparent difficulty, we directly targeted CRNs
for three reasons. First, shoehorning the design of synthetic
chemical circuits into familiar but possibly inappropriate comput-
ing models may not capture the natural potential and limitations
of the chemical substrate. Second, there is a vast literature on
the theory of CRNs (25, 26) and even on general methods to im-
plement arbitrary polynomial ordinary differential equations as
CRNs (27, 28). Third, as a fundamental model that captures
the essential formal structure of chemistry, implementation of
CRNs could provide a useful programming paradigm for mole-
cular systems.
Here we propose a method for compiling an arbitrary CRN
into nucleic-acid-based chemistry. Given a formal specification
of coupled chemical kinetics, we systematically design DNA mo-
lecules implementing an approximation of the system scaled to an
appropriate temporal and concentration regime. Formal species
are identified with certain DNA strands, whose interactions are
mediated by a set of auxiliary DNA complexes. Nonconserving
CRNs can be implemented because the auxiliary species implic-
itly supply energy and mass.
OGY
Soloveichik et al. 2010
1:
12:
3:
2
3
buffering module
time (hrs)
concentration(nM)
unscaled
1.5
1
1
5.105 /M/s
1/300 /s
1/300 /s
scaled
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
5
10
15
20
A B CIdeal chemical reactions DNA reaction modules Simulation of ideal and DNA reactions
ideal DNA

DNA Computing
NAM data
storage
lution.
ences therein.
97,10256(1993).
(1993).
Nature 369, 40 (1994).
Anal. Chem. 59, 2158 (1987).
Natl. Acad. Sci. U.S.A. 86, 4087 (1989).
(1992).
91, 5740 (1994).
1938 (1974).
Chu, ibid., p. 822.
phys. Chem. 20, 415 (1991).
26,1165 (1990).
203 (1989).
194, 278 (1991).
(1981).
Sci. Paris 316, 459 (1993).
Nature 352, 444 (1991).
1382 (1981).
phys. J. 22,169 (1993).
Leonard M. Adleman
3---4, 4->5, 5->6. If the edge 2->3 were
USA.
vertex 0).
problem:
graph.
and end with v,,f.
1021
Science
1994
commentary
Nucleic acid memory
Victor Zhirnov, Reza M. Zadegan, Gurtej S. Sandhu, George M. Church and William L. Hughes
Nucleic acid memory has a retention time far exceeding electronic memory. As an alternative storage
media, DNA surpasses the information density and energy of operation offered by ﬂash memory.
I
nformation and communication
technologies generate vast amounts of
data that will far eclipse today’s data flows
In this Commentary, we discuss
the information retention, density and
energetics of NAM — specifically related to
unfathomable technological advances —
such as those from the Human Genome
Project — with the scaling expertise of the
Zhirnov et al. 2016
10cm
10cm
10cm

Abstract Data Types
Container
List
Associative array
Multimap
Set
Stack
Queue
Double-ended queue
Priority queue
Tree
Graph

DNA Molecular Stack Recorder
Record occurence of events in a cell
Interfere with cellular mRNA in an
ordered way
Release a “trigger” signal for
downstream processes after certain
cellular events have transpired
……

b'
aa'
d'c'
g'
ff'
e'
b
c a
a'
b
d e
hh'
lk
x
c'
push write-X
pop
b
a'a
dc
g
f'f
e
report
x'm
0 1
GAAG
U
G
U
G
U
G
CGGGAGAU
G
G C
U C U C C C G
A
A
G U G G U
G
U
C C G C C G
G G
C
A
GCGGCGG
U
U
G
G
U
C
UCCC
b'
aa'
d'c'
g'
ff'
e'
c a
a'
b
d e
hh'
lk
x
push write-X
pop
b
a'a
dc
g
f'f
e
report
x'm
0 1
G
G
G
AG
A
C
C
A
A
CCGCCGC
U
G
C C
C G G C G G
A
C
A C C A C
U
U
C G G G A G A
G C
C
AUCUCCCG
C
A
C
A
C
ACUUC
d' c'e'
start push
read pop
b
a'a
dc
g
f'f
e
0 1
GA
A
G
U
G
G
U
G U
U
U
G
G
U
C U
C
C
C
G
A
A G
U
G
U
G
U
G
C
DNA Bricks
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
0 1
GGGAGAG
C
C A
U C U C C C
G C A
C
A
C
A
CUU
C
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
start push write-X
b g
0 1
G
G
G
AG
A
G
C
C
A
UCUCCCG
C
AC
A
C
A
C U U
C G G G A G A
C
C
A A
A
U
U
A
G
U
A
G
G
U
A G
A
C
A
A
A
A
A
A A G A C
C
G
C
U
A
A
A
C
UCUAA
U
C
A
CA
C
C
U
A
C
U
A
A
U
A
C
A
C
C
ACUUC
(27nt)
(31nt)
(64nt)
(64nt)
(98nt)

b'
aa'
d'c'
g'
ff'
e'
b
c a
a'
b
d e
hh'
lk
x
c'
push write-X
pop
b
a'a
dc
g
f'f
e
report
x'm
0 1
GAAG
U
G
U
G
U
G
CGGGAGAU
G
G C
U C U C C C G
A
A
G U G G U
G
U
C C G C C G
G G
C
A
GCGGCGG
U
U
G
G
U
C
UCCC
b'
aa'
d'c'
g'
ff'
e'
c a
a'
b
d e
hh'
lk
x
push write-X
pop
b
a'a
dc
g
f'f
e
report
x'm
0 1
G
G
G
AG
A
C
C
A
A
CCGCCGC
U
G
C C
C G G C G G
A
C
A C C A C
U
U
C G G G A G A
G C
C
AUCUCCCG
C
A
C
A
C
ACUUC
DNA Bricks
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
0 1
GGGAGAG
C
C A
U C U C C C
G C A
C
A
C
A
CUU
C
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
start push write-X
b g
0 1
G
G
G
AG
A
G
C
C
A
UCUCCCG
C
AC
A
C
A
C U U
C G G G A G A
C
C
A A
A
U
U
A
G
U
A
G
G
U
A G
A
C
A
A
A
A
A
A A G A C
C
G
C
U
A
A
A
C
UCUAA
U
C
A
CA
C
C
U
A
C
U
A
A
U
A
C
A
C
C
ACUUC
(27nt)
(64nt)
(64nt)
(98nt)
Genetic Algorithm - MOO
Find a set of brick sequences such that:
Individual bricks have the required
secondary structure (e.g. hairpins and ss/ds segments)
Desired brick-pair reactions have a
maximally negative Gibbs free energy of binding
Undesired brick-pair reactions have
close to 0 or positive Gibbs free energy of binding

c a
a*
b
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
*
b
RECORDING
Start
UCNC2016, Annunziata Lopiccolo – Newcastle University
stack
empty
Recording signals

c a
a*
b
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
*
b
c a
a*
b
c*a* a
b*
d*f* f
g*
e*
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
Start
Push
stack
empty
Recording signals

c a
a*
b
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
b
Push binds by toehold
stack
empty
Recording signals

c a
a*
b
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
Branch migration
stack
empty
Recording signals

c a
a*
b
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
a*
b
c*a* a
b*
d*f* f
g*
e*
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f*
d e c a
a*
b
c a b a* d e c a b a* d
X
stack
empty
X
Recording signals

c a
a*
b
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
b
X
Hybridisation
1 signal
on stack
X
Recording signals

c a
a*
b
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
b
c a
a*
b
c*a* a
b*
d*f* f
g*
e*
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f e*
Push
X
1 signal
on stack
X
Recording signals

ca a*
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
X
1 signal
on stack
X
Recording signals

c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
X
Branch migration
1 signal
on stack
X
Recording signals

c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
a*
b
c*a* a
b*
d*f* f
g*
e*
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f*
g
d e c a
a*
b
c a b a*
c* a* b* a d*f*
g
d
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f*
g
d
c a b a*
c* a* b* a d*f*
g
d
d e c a
a*
b
c a b a* d
X
Y
Signal Y
1 signal
on stack
X
Y
Recording signals

c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
b
X Y
Hybridisation
2 signals
on stack
X
Y
Recording signals

c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
b
c a
a*
b
c*a* a
b*
d*f* f
g*
e*
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d
Push
X Y
2 signals
on stack
X
Y
Recording signals

c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
X Y
2 signals
on stack
X
Y
Recording signals

c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
Branch migration
X Y
2 signals
on stack
X
Y
Recording signals

c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*a* a
b*
d*f* f
g*
e*
ca
c*a
c
c*
d e c a
a*
b
c
c*
c*a* a
b*
d*f* f
g*
e*
c
c*
c
c*
d e c a
a*
b
c
c*
X Y
X
Signal X
2 signals
on stack
X
Y
X
Recording signals

c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
X Y X
Hybridisation
3 signals
on stack
X
Y
X
Recording signals

c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
X Y X
Hybridisation
3 signals
on stack
X
Y
X
Popping signals

c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
ac
Y XX
c a
c* a*
d* e* c*
c a
c* a*
c a
Read
3 signals
on stack
X
Y
X
Popping signals

c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
Y XX
Read binds by toehold,
Branch migration follows
3 signals
on stack
X
Y
X
Popping signals

b a*
b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
b a*
b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
b a*
b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
b a*
b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
b a*
b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
b a*
b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
Y
X
X Strand displacement
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
Signal X released
2 signals
on stack
X
Y
X
Popping signals

DNA Molecular Stack Recorderd* e* c*
c
c*
c
c*
ca a*
b
df f*
g
e
c
c*
c
c*
d* e* c*
c
c*
c
d*f* f
g*
e* c* a* b* a d*f* f
g*
e* a*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
d*f* f
g*
e*
d e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
d e c a
Y
X
X
Pop
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
2 signals
on stack
X
Y
Popping signals

c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
d*f* f
g*
g*
e* a*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
d*f* f
g*
e*
d e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
d e c a
Y
X
X
Pop binds by toehold,
2 signals
on stack
X
Y
Popping signals

c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
ac
d*f* f
g*
g*
e* a*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
d*f* f
g*
e*
d e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
d e c a
Y
X
X Hairpin
reforms
*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
Pop-Push
double strand
2 signals
on stack
X
Y
Popping signals

c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
ac
d*f* f
g*
g*
e* a*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
d*f* f
g*
e*
d e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
d e c a
Y
X
X
c a b a*
c* a* b* a d*f* f
g*
e*
d e c
c*
d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c
c*
c a b a* d e c
Read
2 signals
on stack
X
Y
d e c a
a*
b
d* e* c*
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
Popping signals

c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a b a* d e c a
b
c a b a*
d*f* f
g*
g*
e* a*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
d*f* f
g*
e*
d e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
d e c a
Y
X
X
2 signals
on stack
X
Y
d e c a
a*
b
d* e* c*
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
Popping signals

a b a*
* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
a b a*
* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
a b a*
* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
a b a*
* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
a b a*
* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
a b a*
* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
c a b a* d e c a
d*f* f
g*
e* a*
d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
d*f* f
g*
e*
d e c a
a*
b
d* e* c*
d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
d e c a
Y
X
X
Strand displacement
Signal Y released
1 signal
on stack
X
Y
d e c a
a*
b
d* e* c*
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
Popping signals

* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
* f
g*
e*
e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
* f
g*
e*
e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
c a b a* d e c a
*
e* a*
*
e*
e c a
a*
b
c*e*
d*
*
e*
d e c a
a*
b
d* e* c*
*
e*
e f*
g
fd a*
b
ac
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
d e c a
Y
X
X
f*
d* e* c*
c a b a*
c* a* b* a d*f*
d
c a b a*
c* a* b* a d*f*
d
ca a*
b
df f*
g
e
c a b a*
c* a* b* a d*f*
d
c a b a*
c* a* b* a d*f*
d
d* e* c*
c a b a*
c* a* b* a d*f*
d
c a b a* d
Pop
1 signal
on stack
X
d e c a
a*
b
d* e* c*
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
Popping signals

c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a* d e c a
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
* f
g*
e*
e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
* f
g*
e*
e c a
a*
b
c*e*
d*
*
e* a*
*
e*
e c a
a*
b
c*e*
d*
*
e*
d e c a
a*
b
d* e* c*
*
e*
e f*
g
fd a*
b
ac
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
d e c a
Y
X
X
Pop binds by toehold,
1 signal
on stack
X
d e c a
a*
b
d* e* c*
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
Popping signals

* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
* f
g*
e*
e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
* f
g*
e*
e c a
a*
b
c*e*
d*
*
e* a*
*
e*
e c a
a*
b
c*e*
d*
*
e*
d e c a
a*
b
d* e* c*
*
e*
e f*
g
fd a*
b
ac
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
d e c a
Y
X
X
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
ac
Hairpin
reforms
** f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
** f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
** f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
** f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
** f
g*
e*
e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
** f
g*
e*
e c a
a*
b
c*e*
d*
Pop-Push
double strand
1 signal
on stack
X
d e c a
a*
b
d* e* c*
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
Popping signals

* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
* f
g*
e*
e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
* f
g*
e*
e c a
a*
b
c*e*
d*
*
e* a*
*
e*
e c a
a*
b
c*e*
d*
*
e*
d e c a
a*
b
d* e* c*
*
e*
e f*
g
fd a*
b
ac
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
d e c a
Y
X
X
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
ac
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c
c*
d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c
c*
c a b a* d e c a b a* d e c
Read
1 signal
on stack
X
d e c a
a*
b
d* e* c*
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
d*f* f
g*
e*
d e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
Popping signals

DNA Molecular Stack Recorderc a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*d* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
* f
g*
e*
e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
* f
g*
e*
e c a
a*
b
c*e*
d*
*
e* a*
*
e*
e c a
a*
b
c*e*
d*
*
e*
d e c a
a*
b
d* e* c*
*
e*
e f*
g
fd a*
b
ac
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
d e c a
Y
X
X
1 signal
on stack
X
d e c a
a*
b
d* e* c*
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
d*f* f
g*
e*
d e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
Popping signals

b a*
b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
b a*
b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
b a*
b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
b a*
b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
b a*
b* a d*f* f
g*
e*
d e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
* f
g*
e*
e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
* f
g*
e*
e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
* f
g*
e*
e c a
a*
b
c*e*
d*
*
e* a*
*
e*
e c a
a*
b
c*e*
d*
*
e*
d e c a
a*
b
d* e* c*
*
e*
e f*
g
fd a*
b
ac
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
d e c a
Y
X
X
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
ad* e* c*
c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a
a*
b
c a b a*
c* a* b* a
Strand displacement Signal X released
stack
empty
X
d e c a
a*
b
d* e* c*
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*e*
d*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
d* e* c*
d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
d*f* f
g*
e*
d e c a
a*
b
c a b a* d f g f* e
c* a* b* a d* f* g* f e*
Popping signals

Naive Chemical View
S + P + Xb'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm

Real Well-Mixed Chemistry
S + P + Xb'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
— partly formed complexes
— partially bound complexes
— unintended side reactions
— DNA complexes have ﬁnite diffusion
and reaction rates

+ P b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
+ Xb'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
S
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Real Well-Mixed Chemistry
Required: Rule-based stochastic
model to rigorously capture the
reactions happening in-vitro
To know if stack chemistry
is operating correctly:

core
reactions
Which Rules? — Reaction Space
all reactions
with full domains
bound
all possible reactions,
including partially bound
complexes
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm

core
reactions
all reactions
with full domains
bound
all possible reactions,
including partially bound
complexes
Microsoft DSD 2.0
Multi-strand
thermodynamic
prediction software
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm

core
reactions

pop
push
read
X…stack
stack…push
stack…X…stack
stack…Xpush
stack…push
stack…push
Core Reactions: 1-Step Rules
stack…
…stack
start push
X
readRate parameters
pop
start
…stack
push
X…stack
+
+
+
(1)
(2)
(3)
(4) +
…stack + X
…stack +
…stack + poppush
Recording
Popping
kf(h)
⌦
kr
kf(h+b)
⌦
kr
kf(h+b)
⌦
kr
!
!
kf(h) = 106
M 1
s 1
kf(h+b) = 105
M 1
s 1
core
reactions
(5)
kf(s1) = 105
M 1
s 1
kf(s2) = 104
M 1
s 1
kf(s2)
kf(s1)
kr = 0 (No ring complexes allowed)

Simulation Results
Recording signals
t = 5 min t = 1 hour
S
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'mP
200nM
c a
a*
b
c*a* a
b*
d*f* f
g*
e*
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
d e c a b a*
sp
sp
p

Simulation Results
Recording signals
S
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'mP
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
X
200nM
c*a* a
b*
d*f* f
g*
e*
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
d e c a b a*
d e c a
a*
b
spx
spxpx
spx

Simulation Results
Recording signals
S
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'mP
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
X
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'mP
200nM
spx spxpxp
spxp
p
sp
spxp
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a

Simulation Results
Recording signals
S
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'mP
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
X
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'mP
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
X
200nM
spx
spxpx
spxpxpx
spxpxpxpx
spxpx
spxpxpx
g*
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b

Simulation Results
Recording signals
S
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'mP
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
X
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'mP
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
X
200nM
P
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
g* g*
e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
p
spxp
spxpx
spxpxp
spxpxpx
spxpxpxp
spxpxpxpxp
spxpxp
spxpxpxp

Simulation Results
Recording signals
S
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'mP
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
X
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'mP
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
X
200nM
P
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'mX
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
g* g*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
spxpxpx
spxpx spxpxpxpx
spxpxpxpxpx
spxpxpxpxpxpx
spxpxpx
spxpxpxpxspxpx

Simulation Results
R
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Popping signals
[xr]
spxp
spxpx
spxpxp spxpxp
spxpxpx
spxpxpxp
spxpxpxpx
spxpxpxpxp
[xr]
spxp spxpxpxp
g* g*
e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b

Simulation Results
R
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Q
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Popping signals
g*
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
q
[xr]
spx
spxp
spxpx
spxpxp
spxpxpx
spxpxpxp
spxpxpxpx
spxpxpxpxp
[xr]
[pq]
[pq]
spxpx
spxpxp
spxpxpx

Simulation Results
R
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Q
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
R
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Popping signals
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
r
q
sp
[xr]
[pq]
spxp
spxpx
spxpxp
spxpxpxp
spxpxpxpxp
sp
[xr]
[pq]
spxp
spxpxp

Simulation Results
R
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Q
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
R
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Q
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Popping signals
[xr]
[pq]
[xr]
[pq]
c*a* a
b*
d*f* f
g*
e*
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
d e c a b a*
d e c a
a*
b
spx
spx
spxp
spxpx
spxpxp
spxpxpx
spxpxpxp
spxpxpxpxp spxp
spxpx

Simulation Results
R
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Q
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
R
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Q
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
R
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Popping signals
c a
a*
b
c*a* a
b*
d*f* f
g*
e*
ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c a b a*
c* a* b* a d*f* f
g*
e*
d e c a
a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
c* a* b* a d*f* f
g*
e*
d e ca a*
b
c*a* a
b*
d*f* f
g*
e*
c a b a*
d e c a b a*
[xr]
[pq]
sp
[xr]
[pq]
spxp spxpxp
spxpxpxp
sp spxp

Simulation Results
R
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Q
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
R
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Q
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
R
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Q
200nM
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
Popping signals
g*
ca a*df f* e
c a b a*
c* a* b* a d*f* f
g*
e*
e f*
g
fd a*
b
ac
c a
a*
b
s
q
sp
[xr]
[pq]
[xr]
[pq]
s
q
sp spxp spxpxp
spxpxpxp

Experimental Results
●But results are hard to interpret because of the superposition of stacks.
●Concentration of read and pop needs to be controlled.
1 signal 2 signals 3 signals 1 signal2 signals
SPX
SPXP
SPXPX
SPXPXP
SPXPXPX
P RX PQ
Reading and Popping
Recording Popping
Selected bioanalyzer results qualitatively show same pattern as simulations
PAGE gel results still pose some questions…!
P
P P P P
X X
X X
XP
S S
P P P
S S S
S dimer
S dimer
S
SP SP SP SP SP
SPP?
SSP?
S
S dimer
P
SP
SSP?
X
SPP?
XP
P+X S+P+X+P S+PS+X+P+P

Simulation Results
Brick order matters!
t = 1 hour t = 1 hour
S
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
P
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
X
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
P
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
X
spxpx
spxpxpx
S
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
X
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
X
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
P
b'
aa'
d'c'
g'
ff'
e'c a
a'
b
c a
a'
b
d e
hh'
lk
x
d' c'e'
start push write-X
read pop
b
a'a
dc
g
f'f
e
report
x'm
P
In order Out of order
spxpx
spxpxpx
spx
s
spxpxpxpx
spxpxpxpxpx
spxpxpxpxpxpx
spxpxpxpxpxpxpx

Challenges Establishing In-Silico/In-Vitro Equivalence
CHEMISTRY
MODEL
spxpxpx
spxpxpx
EXPERIMENT
“a qualitative
agreement exists”
“pure” output:
all species and
concentrations known
“proxy” output:
chemistry state encoded
by indirect variables
y scale: nt
y scale: migration time

Challenges Establishing In-Silico/In-Vitro Equivalence
CHEMISTRY
MODEL
DETECTOR 
MODEL
spxpxpx
spxpxpx
EXPERIMENT
y scale: nt
y scale: migration time

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