Information-based autonomous reconfiguration in systems of interacting DNA nanostructures

ARTICLE

Information-based autonomous recon

guration in

systems of interacting DNA nanostructures

Philip Petersen

, Grigory Tikhomirov

& Lulu Qian

2,3

The dynamic interactions between complex molecular structures underlie a wide range of

sophisticated behaviors in biological systems. In building arti

cial molecular machines out of

DNA, an outstanding challenge is to develop mechanisms that can control the kinetics of

interacting DNA nanostructures and that can compose the interactions together to carry out

system-level functions. Here we show a mechanism of DNA tile displacement that follows

the principles of toehold binding and branch migration similar to DNA strand displacement,

but occurs at a larger scale between interacting DNA origami structures. Utilizing this

mechanism, we show controlled reaction kinetics over

ve orders of magnitude and pro-

grammed cascades of reactions in multi-structure systems. Furthermore, we demonstrate the

generality of tile displacement for occurring at any location in an array in any order, illustrated

as a tic-tac-toe game. Our results suggest that tile displacement is a simple-yet-powerful

mechanism that opens up the possibility for complex structural components in arti

cial

molecular machines to undergo information-based recon

guration in response to their

environments.

https://doi.org/10.1038/s41467-018-07805-7

OPEN

Biology, California Institute of Technology, Pasadena, CA 91125, USA.

Bioengineering, California Institute of Technology, Pasadena, CA 91125, USA.

Computer Science, California Institute of Technology, Pasadena, CA 91125, USA. These authors contributed equally: Philip Petersen, Grigory Tikho

mirov

Correspondence and requests for materials should be addressed to L.Q. (email:

luluqian@caltech.edu

)

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1

1234567890():,;

M

olecular structures, such as the cell membrane, provide

compartmentalization and spatial organization key to

the functionality of natural molecular machines in

biological organisms. DNA, an information-bearing molecule, has

been used to engineer the self-assembly of prescribed nanos-

tructures

. Among various techniques, DNA origami

is parti-

cularly robust for organizing other kinds of molecules into any

desired patterns, which have been used for studying unknown

aspects of biomolecular interactions

, fabricating devices with

nanoscale features

, or functioning as a breadboard for bio-

chemical circuits

and a testing ground for molecular robots

–

Individual DNA origami structures can be programmed to create

larger structures hierarchically, recently approaching the size of a

small bacterium

. However, unlike the sophisticated dynamic

interactions between complex protein molecules, for example as

seen in alternative sigma factors recon

fi

guring the function of

RNA polymerase

, the designed interactions between DNA

origami structures have so far been limited to just binding and

unbinding.

The mechanism of DNA strand displacement

has been used

to program dynamic interactions between small DNA molecules

that give rise to sophisticated system-level behaviors

–

, owing

to the fact that a wide range of kinetics can be controlled by

varying the strength of a toehold domain

and that the toe-

hold for initiating a downstream reaction can be hidden until the

strand has been released from an upstream reaction (termed

“

toehold sequestering

”

)

. If a similar mechanism that has

these two properties governed the interactions between complex

DNA nanostructures rather than between individual DNA

strands, it would give rise to sophisticated autonomous recon

fi

guration in systems of DNA nanostructures, much like the

autonomous information processing in DNA circuits and devices.

While the fundamental principle of DNA base pairing relies on

the complementarity of Watson

–

Crick binding, a similar princi-

ple can be exploited at a much larger scale to program the

interactions between DNA origami structures

. In a DNA strand

displacement process, there are two fundamental principles:

fraying of double strands allows for an invading strand to initiate

a competition with a previously bound strand for binding to its

complementary strand; structural

fl

exibility of single strands

allows for the unbounded part of both the invading strand and

the competing strand to be pushed out of the way in order for the

branch migration to take place. If these two principles can be

satis

fi

ed in individual DNA origami structures and their com-

plexes, it will be possible to create similar displacement reactions

and use them to program dynamic system-level functions at a

much larger scale.

Here we show a mechanism of DNA tile displacement, in which

an invader DNA origami tile displaces another tile from an array

of tiles, enabled by a binding domain on the tile edge functioning

as a toehold. We measure the kinetics of tile displacement reac-

tions with varying toehold strengths, and show that the kinetics

can be controlled over a range of

fi

ve orders of magnitude,

reaching a maximum effective rate of ~4.5 × 10

−

−

. Using

this mechanism, we develop three example systems for general-

purpose recon

fi

guration in DNA nanostructures: competitive,

sequential, and cooperative tile displacement, each illustrating a

basic type of information processing within structural recon

fi

guration. Finally, we demonstrate the generality of tile displace-

ment reactions through a multi-step recon

fi

guration pathway

shown as a tic-tac-toe game, where each player has nine unique

DNA origami tiles that can be used to make nine possible moves

in any order on a 264 by 264 nanometer game board.

Results

Concept of DNA tile displacement

. In earlier work, we designed

a square DNA origami tile to construct arrays with combinatorial

patterns

. To form 2 by 2 arrays, we designed a single tile such

that four rotated copies can bind to each other to form a larger

square (Supplementary Fig. 1a). We explored several edge designs

and expected to obtain a high yield of the arrays only when the

edge interactions were weak enough to eliminate kinetic traps.

However, a surprisingly high yield was observed with a relatively

strong edge design (Supplementary Fig. 1b), for which we

expected the formation of arrays to take place at a temperature

where the binding between any two complementary tile edges was

largely irreversible. If the only possible reactions were just bind-

ing, then a fraction of the

fi

nal structures should be trimers

(Supplementary Fig. 1c, solid arrows), con

fl

icting with the

observed high yield of 2 by 2 arrays. There were two possible

explanations:

fi

rst, the arrays actually formed at a temperature

high enough for reversible binding. Second, a dimer and a trimer

could undergo a displacement reaction to yield a 2 by 2 array

while releasing a monomer, and two copies of trimers could also

undergo a displacement reaction to yield a 2 by 2 array while

releasing a dimer (Supplementary Fig. 1c, dotted arrows). With

displacement reactions, the lack of spontaneous unbinding will

not result in kinetic traps and all tiles will eventually self-assemble

into the desired 2 by 2 arrays (Supplementary Fig. 1c, simula-

tions). While the observation did not rule out either explanation,

or a combination of the two, the second possibility provoked us to

explore further. If it exists, displacement will affect the under-

standing of self-assembly not only in arrays with designed sizes

but also in unbounded arrays. For example, dynamic rearrange-

ment of DNA origami structures has been observed on a liquid

bilayer

, hinting at the possibility that a well-formed structure

with stronger edge interactions could displace a malformed one

with weaker edge interactions in a periodic DNA origami array.

To investigate if one DNA origami structure can displace

another from a complex of structures without any spontaneous

unbinding within the complex, we performed two experiments: at

room temperature, a complex of two square tiles were mixed

together with a triangular tile

that either has the same binding

domain as one of the squares or has an additional binding

domain that is complementary to the other square (Supplemen-

tary Fig. 1d, e). The two squares remained bound to each other in

the former experiment but one square swapped with the triangle

in the latter, suggesting that displacement indeed occurred. With

this initial evidence, we set off to explore if the desired properties

of DNA strand displacement reactions can be reproduced to

program the dynamic interactions between DNA origami

structures.

In a DNA strand displacement reaction, a single strand with a

toehold domain binds to an uncovered complementary domain in

a double-stranded complex, initiates a branch migration process,

and eventually releases the previously bound strand while

becoming part of a double strand itself (Fig.

a). Similarly, in a

DNA tile displacement reaction, an invader tile with a toehold

domain binds to a complex consisting of a cover tile and a base

tile, initiates a competition with the cover tile for binding to the

base tile, and eventually releases the cover tile while itself

becoming fully bound to the base tile (Fig.

b and Supplementary

Movie 1). Unlike a DNA strand displacement reaction, the

toehold and branch migration domains in a tile displacement

reaction consist of a set of edge staples rather than a string of

nucleotides (Fig.

c and Supplementary Fig. 1f).

Each DNA origami tile is composed of four isosceles triangles,

with bridge staples zipping together the seams between the

adjacent triangles (Fig.

c). To visualize the reactants and

products of the desired reaction by atomic force microscopy

(AFM), we labeled the invader tile with an X and the cover tile

with an O using patterns of double-stranded staple extensions. In

prior work, this origami design was used to scale up the

diversity

and complexity

of two-dimensional DNA nanos-

tructures. Here, we chose this origami design for exploring the

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full potential of tile displacement because it has a good degree of

structural

fl

exibility along all four edges to possibly allow branch

migration within complex multi-origami structures

—

it is known

that bending between adjacent helices

and near the internal

seams

is possible. Moreover, the tiles can self-assemble into

larger structures with a set of edge staples that each has a blunt-

end stacking bond and a very short sticky end

—

weak enough to

allow fraying between staple pairs.

Kinetics of DNA tile displacement

. The capability of controlling

reaction kinetics, making some reactions faster or slower than the

others, gives rise to complex behaviors in diverse chemical and

biological systems, for example as seen in the transient memory

in bacterial chemotaxis

and the oscillations in cell cycles

.Itis

desirable to achieve controlled reaction kinetics in engineered

systems, even if the overall behaviors only share similarities at the

abstract principle level or are a lot simpler than those seen in

Inv

off

CT:BT

Inv

2,0

Inv

2,4

Inv

2,4

:BT

Invader

tile

Base

tile

Cover

tile

Base

tile

Cover

tile

Invader

tile

Tile displacement

Strand displacement

Binding rate,

= 1

= 2

4.5 × 10

–1

2 × 10

–1

Dissociation rate,

off

= 1

= 2

Displacement rate,

2 nM

4 nM

Simulations

Experiments

Inv

Stacking bond

Sticky end

1.0

0.8

0.6

0.4

0.2

0.0

Fraction completed

Time (hours)

2nt 4Toe

2nt 3Toe

2nt 2Toe

2nt 1Toe

2nt 0Toe

1nt 4Toe

1nt 3Toe

1nt 2Toe

1nt 1Toe

1nt 0Toe

6–

–1

1 s

–1

3–2

–1

0.025 s

–1

1–1.1

–1

2.5 × 10

–1

= 2,

= 3

′

Fig. 1

Concept and kinetics of DNA tile displacement.

Domain-level diagram of a DNA strand displacement reaction. T is a short toehold domain of

typically 3 to 8 nucleotides. B is a long branch migration domain of typically 15 to 20 nucleotides. Asterisks in the domain names indicate sequence

complementarity.

Domain-level and

origami-level diagram of a DNA tile displacement reaction. Toehold and branch migration domains are composed

of 4 and 7 edge staples, respectively. Invader tile and cover tile are labeled with double-stranded staple extensions in an X and O pattern, respective

ly.

Tile displacement reactions with varying toeholds. CT is a cover tile. BT

is a base tile with

=

1 or 2 indicating the number of nucleotides in the sticky end

of each of the 4 edge staples in the toehold domain. Inv

is an invader tile with

=

0 through 4 indicating the number of edge staples in the toehold

domain. F and Q indicate a

uorophore- and quencher-labeled edge staple, respectively.

Model and rate parameters of tile displacement in comparison

with strand displacement.

is the number of nucleotides in the toehold domain of a strand displacement reaction with average DNA sequences.

Fluorescence kinetics experiments, simulations, and AFM images of the tile displacement reactions. Experiments were performed at 25 °C and AFM

images were collected after 48 h. Dotted and solid boxes highlight reactants and products, respectively. Colons in the species names indicate multi-

tile

complexes. Scale bars are 200 nm

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biology. For example, in strand displacement circuits, controlled

reaction kinetics has enabled dynamic behaviors including con-

sensus

and oscillation

. To identify the range of kinetics that

can be controlled in tile displacement reactions, we created toe-

holds with varying strengths and performed a set of

fl

uorescence

kinetics experiments to measure the reaction rates.

While keeping the number of staples and the length of sticky

ends in the branch migration domain the same, we varied the

toehold domain from 0 to 4 staples each with 1- to 2-nucleotide

sticky ends (Fig.

d). For the convenience of experiments, we kept

all 4 toehold staples in the base tile and only varied those in the

invader. At the end of the branch migration domain, two

paired staples were modi

fi

ed with a

fl

uorophore and a quencher,

respectively. While the cover tile remains bound to the base tile,

the

fl

uorophore will be quenched and result in low

fl

uorescence

signal. If the cover tile with the quencher is released, the

fl

uorescence signal will consequently increase.

Within 24 h, the

fl

uorescence trajectories essentially did not

change over time for invaders with 0 toehold staples (Fig.

f).

With 1 to 4 toehold staples, a range of reaction kinetics was

observed. Naturally, with the same length of sticky ends, more

staples resulted in faster kinetics; with the same number of

staples, longer sticky ends resulted in faster kinetics. Interestingly,

toeholds with staples that have 1-nt and 2-nt sticky ends saturated

at noticeably different rates.

To gain a quantitative understanding of the kinetics, we

utilized a simple model to analyze the tile displacement reactions

(Fig.

e), of a similar mathematical form as was used for strand

displacement reactions

. Comparing the simulations with

experimental data (Fig.

f), including additional experiments

with varying concentrations of the invader (Supplementary

Fig. 2), we found a set of parameters that explained the data

reasonably well (Fig.

e and Supplementary Note 1, Supplemen-

tary Eqs. (1) and (2)). In summary, the binding rate is roughly 10

to 100 times slower than strand displacement, depending on the

length of the sticky end. Similar to strand displacement, the

dissociation rate decreases exponentially with increasing number

of nucleotides in the toehold, which depends on both the number

of toehold staples and the length of the sticky end. The

displacement rate is roughly 40 times slower than strand

displacement. The effective rate of the overall tile displacement

reaction reached a maximum of 4.5 × 10

−

−

. At low

concentration (e.g., <50 nM), the bimolecular binding rate limits

the overall reaction rate and an increasing concentration will

result in faster tile displacement; at high concentration (e.g., >50

nM), the unimolecular displacement rate limits the overall

reaction rate and an increasing concentration will become less

signi

fi

cant and eventually saturate.

To compare the reaction completion levels from

fl

uorescence

kinetics experiments with AFM experiments, we analyzed the

number of products over the total number of products and

reactants in 5 by 5

μ

m images that contained on average more

than 40 tile complexes. All samples were taken directly from the

kinetics experiments and imaged at 48 h. We found 3.8 ± 0.5%

and 96.2 ± 3.7% reacted tile complexes for invader without and

with a 2-nt 4-staple toehold, respectively (Supplementary Fig. 3a).

Similarly, 5.1 ± 0.8% and 93.0 ± 3.3% of tile complexes reacted

with an invader without and with a 1-nt 4-staple toehold,

respectively. The observations from both types of experiments

were in agreement with each other.

Competitive recon

fi

guration

. With the ability to control kinetics

over

fi

ve orders of magnitude, it is now possible to create system-

level behaviors that exploit the rate differences among multiple

tile displacement reactions. For example, competition can be

created to allow a basic type of information-based structural

recon

fi

guration: a sigmoidal function in response to a signal

concentration. This function is one of the essential building

blocks for digital logic computation

in strand displacement and

other synthetic circuits. To demonstrate this function, we

designed two competing tile displacement reactions triggered by

the same invader, one at a much faster rate than the other

(Fig.

a). The invader tile has a 2-nt 4-staple toehold, expected to

interact with two types of cover:base tile complexes, one with a

matching toehold and the other with a 1-nt 4-staple toehold. For

the latter, based on the kinetics measurements, the effect of a

single dangling nucleotide should be insigni

fi

cant here. We expect

the overall rate of the faster reaction to be approximately 18 times

that of the slower reaction (Supplementary Fig. 2). Two distinct

fl

uorophores were used to monitor the two products

simultaneously.

When the invader concentration was less than 2 nM (1×), it

preferentially triggered the faster reaction and the concentration

of the product from the slower reaction remained low (Fig.

b).

However, when the invader concentration exceeded 1×, the faster

reaction was quickly saturated and the excess invader was

available to also trigger the slower reaction. With the same model

and rate constants shown in Fig.

e (Supplementary Eqs. (3) and

(4)), we were able to predict the kinetics of the competition

reasonably well. Looking at the completion levels of the two

competing reactions at 24 h, the product of the faster reaction

increased linearly in response to the invader concentration, until

reaching its maximum, while the product of the slower reaction

exhibited a sigmoidal function (Fig.

c). The faster reaction

functioned as a threshold for the slower reaction. By tuning the

concentration of the cover:base tile complex in the faster reaction,

one can in principle tune the value of the threshold and thus shift

the sigmoidal function as desired.

We chose two representative samples with an invader

concentration below and above the threshold to visualize the

recon

fi

guration results using AFM (Fig.

b). In the

fi

rst case, most

tile complexes were unreacted with a cover tile (labeled with an

O) bound to the base tile (labeled with a line for one type and left

unlabeled for the other). Largely, only one type of product from

the faster reaction was observed, in which the cover tile was

replaced by an invader labeled with an X. In the second case,

nearly no unreacted tile complexes were present and both types of

recon

fi

gured products were found. Using 5 by 5

μ

m images that

contained at least 90 tile complexes, the percentage of reactants

that were converted to products for the slower and faster

recon

fi

guration pathways were quanti

fi

ed to be 8.7 ± 0.8% and

57.0 ± 3.6%, respectively, with 0.6× invaders, and 97.7 ± 2.3% and

100%, respectively, with 3× invaders (Supplementary Fig. 3b).

Again, the results were consistent between AFM and

fl

uorescence

kinetics experiments.

Sequential recon

fi

guration

. Next, we explored if the mechanism

of toehold sequestering can be implemented in tile displacement

to allow for cascades of structural recon

fi

gurations and thus more

sophisticated system behaviors. We designed a 2 by 2 array of tiles

in which a

fi

rst invader can displace one tile while revealing a

previously protected toehold, and sequentially a second invader

consisting of two tiles can displace two other tiles from the same

array (Fig.

a). The

fl

uorophore and quencher were placed near

the end of the second branch migration domain to monitor the

completion of the two-step recon

fi

guration. From initial experi-

ments, we learned that displacement across tile corners could be

slow and intermediate states of displacement should be con-

sidered for possible spurious reactions (Supplementary Fig. 4 and

Supplementary Note 2). With this understanding, the design

shown in Fig.

a ensures that spontaneous dissociation only

occurs for toehold domains and no intermediate states should

lead to any undesired products.

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The

fl

uorescence kinetics experiments showed that with both

invaders, the two-step recon

fi

guration successfully took place

(Fig.

b, yellow trajectory). As expected, the two-step cascade was

slower than the second step alone (green trajectory). Lacking the

fi

rst invader, the second invader alone triggered only a small

fraction of spurious reactions (blue trajectory). We revised the

model to include a branch migration step across the corners of

adjacent tiles (Supplementary Eqs. (5) and (6)). Comparing the

data with simulations, we estimated that the displacement rate

across corners is roughly 100 times slower than that within the

same tile edge.

AFM experiments con

fi

rmed that the 2 by 2 arrays remained

unreacted, labeled as a frown, with the second but not the

fi

rst

invader, and recon

fi

gured into a smile with the presence of both

invaders (Fig.

b and Supplementary Fig. 5a). With increased

complexity of the reactants, imperfect stoichiometry of tiles in the

self-assembly process and spurious interactions between tiles with

active edges become more signi

fi

cant and thus interpreting the

structures in AFM images become more challenging. Using the

two types of products (a 2 by 2 array and a two-tile complex), the

yield of sequential tile displacement (i.e. the percentage of

reactants that were converted to products) was estimated as 83.3

± 9.8% and 90.5 ± 6.1% at 48 h, respectively. The difference of the

two estimates is within the statistical error, indicating that the

estimates are not perfectly accurate but still reasonable.

The sequential tile displacement system not only demonstrated

the principle of toehold sequestering and cascades, but also

enabled another basic type of information-based structural

recon

fi

guration: response to more than one environmental signal

that indicate given instructions or available resources, represented

as two types of invaders. Functionally, the

fi

rst invader could

arrive much earlier than the second and the structure would still

be recon

fi

gured as expected. In the next example system, we ask:

can structural recon

fi

guration be programmed to take place only

when two types of signals are simultaneously present?

Cooperative recon

fi

guration

. Similar to the principle of coop-

erative hybridization

, we designed two invader tiles that each

bind to one side of a 2 by 2 array (Fig.

c). If only one tile is

present, it should branch migrate to the center of the array.

However, without a second tile, the process should be reversible

and the invader will dissociate again. When both tiles are present,

the two branch migration processes should meet at the center of

the array, resulting in a cooperative tile displacement. Because it

is effectively a trimolecular reaction with all three reactants at a

relatively low concentration, for the overall reaction to take place

at a reasonable rate, the binding and branch migration should be

suf

fi

ciently fast and the dissociation should be suf

fi

ciently slow.

With these considerations, we chose a 2-nt 3-staple toehold for

each invader (Fig.

d), which was shown to be almost as fast as a

2-nt 4-staple toehold in the kinetics experiments but also rever-

sible enough to allow for toehold dissociation.

fl

uorescence kinetics experiments, when the 2 by 2 array was

mixed together with one or the other invader, the

fl

uorescence

signal remained low (Fig.

d, blue and green trajectories). But

when both invaders were present, the signal went high (yellow

trajectory). We simulated the cooperative reactions with all

possible binding, dissociation, and displacement steps (Supple-

mentary Eqs. (7) and (8)). Despite that the completion level was

different, the half completion time of the experiment roughly

agreed with the simulation. In AFM experiments, the 2 by 2

arrays remained unreacted (labeled as a frown) with only one

invader, but 68.0 ± 7.7% of them recon

fi

gured into a smile with

both invaders (Supplementary Fig. 5b). We observed a higher

Inv:BT1

Inv:BT2

BT1

Inv

BT1

Inv

BT2

Inv

BT2

2 nM (1×)

CT:BT1

Inv

CT:BT2

2 nM (1×)

Simulations

Experiments

1.0

0.8

0.6

0.4

0.2

0.0

Fraction completed

1.0

0.8

0.6

0.4

0.2

0.0

Fraction completed

1.0

0.8

0.6

0.4

0.2

0.0

Fraction completed

Time (hours)

Inv:BT1

Inv

3.0×

2.2×

1.8×

1.4×

0.6×

0.4×

0.2×

0.0×

Inv

3.0×

2.2×

1.8×

1.4×

0.6×

0.4×

0.2×

0.0×

Inv:BT2

Invader concentration (×)

01234

Inv:BT2

Inv:BT1

Fig. 2

Competitive recon

guration.

Domain-level diagram of two competing tile displacement reactions. BT1 and BT2 are base tiles with 1-nt and 2-nt

sticky end in 4 toehold staples, respectively. They are labeled with two distinct

uorophores for the two reactions to be monitored simultaneously.

and

are effective rates of the two reactions, respectively.

Fluorescence kinetics experiments, simulations, and AFM images of competitive tile displacement.

1× corresponds to a standard concentration of 2 nM. Dotted and two types of solid boxes highlight reactants and two types of products, respectively. Sc

ale

bars are 200 nm.

Completion level of competitive tile displacement at 24 h (bars) overlaid with simulations (lines). It is clear from the kinetics trajectories

shown in

that the completion levels for Inv:BT2 with invader concentration from 1.4× through 3.0× have reached maximum reaction completion, and that

the difference in these completion levels re

ects the noise in the experimental measurements. Thus, error bars correspond to the standard deviation of

these four completion levels, scaled proportionally to each of the 16 completion levels

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fraction of invaders that spuriously formed dimers in these AFM

images, suggesting a possible explanation for the lower comple-

tion level. By adding the dimerization reactions into the model

(Supplementary Eq. (9)), the completion level in simulation better

agreed with the experiment (Fig.

d, lighter yellow trajectory).

Generality of DNA tile displacement

. With the three example

systems, we have demonstrated two key properties of DNA tile

displacement reactions as well as using them for information-

based autonomous recon

fi

guration in systems of multiple inter-

acting DNA origami structures. The properties of controlled

kinetics with varying toehold strengths and cascades through

toehold sequestering, which have enabled sophisticated dynamic

behaviors in DNA circuits and robots, are now proven to exist at

a much larger scale in complex DNA nanostructures. However, to

what extent tile displacement reactions can be used to create

increasingly powerful system behaviors depends on the generality

of these reactions for taking place at any location in an array.

To explore this generality, we designed a 3 by 3 array that

allows nine unique tile displacement reactions to take place in any

desired order (Fig.

a). There are three types of reactions:

displacing a corner tile, an edge tile, and a center tile, which

complete the set of possible reactions for displacing a tile with any

number of neighbors in arrays of any size. Along the exterior of

the array, we placed one toehold between any two adjacent tiles,

resulting in 8 unique toeholds. Half of them were used to initiate

a corner tile displacement, where an invader with the matching

toehold binds to the edge tile adjacent to the corner tile, branch

migrates within a tile edge and then across a 90 degree corner,

releasing the previously bound corner tile and integrating itself

into the array. The other half of the toeholds were used to initiate

an edge tile displacement. These toeholds are present both in the

original corner tiles and their invaders. Thus, regardless of

T1a2a34

T2b

T1a2b34

T1b2c

1202×

0012×

1002×

T2b

T1a

T2a

T1a

T2b

T2a

T1b

T2c

T1a

T2b

T1b

T2c

T1b2c

T1a2a34

T1a2b

T1b2c34

T2a

T2b

T1b

T1a

T2a

T1b

T2b

T1a

T2a

T1a2a34

T1b

T2b

122×

120×

102×

T1a2a34

T1b2b34

T1a2a

T1b

T2b

Simulations

Experiments

Simulations

Experiments

1.0

0.8

0.6

0.4

0.2

0.0

Fraction completed

Time (hours)

1.0

0.8

0.6

0.4

0.2

0.0

Fraction completed

Time (hours)

Fig. 3

Sequential and cooperative recon

guration.

Domain-level diagram of two reactions that take place in a cascade to

rst displace a single tile and

then displace two tiles from a 2 by 2 array. Toehold and branch migration domains with unique sets of edge staples are in distinct colors. Arrows with

black-

lled and white-

lled arrowheads indicate the forwards and backwards directions of a reaction step, respectively.

Fluorescence kinetics

experiments, simulations, and AFM images of sequential tile displacement. Species names of multi-tile complexes are abbreviated by omitting colon

s and

repeated Ts (e.g., T1a2a34 indicates T1a:T2a:T3:T4). Some structures in the AFM images are spurious dimers of invaders (T1b2c) or products (T1a2b),

due

to non-speci

c binding of the stacking bonds or sequence similarity of the sticky ends. Imperfect stoichiometry in assembling the reactants leads to small

excess of some tiles, which could further introduce aggregates between structures with active edges. A few example diagrams for interpreting these

spurious structures are shown in Supplementary Fig. 5.

Domain-level diagram of two invader tiles cooperatively displacing two tiles from a 2 by 2 array.

Fluorescence kinetics experiments, simulations, and AFM images of cooperative tile displacement. In simulations, the lighter yellow trajectory

corresponds to a model that includes invader dimerization. The standard concentration (1×) in all experiments was 2 nM. In all AFM images, dotted and

solid boxes highlight reactants and products, respectively. Scale bars are 200 nm

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whether the adjacent corner tile has been displaced yet, an edge

tile invader can bind to the matching toehold, branch migrate

through three tile edges across two corners, and release the

previously bound edge tile.

Considering that it may be dif

fi

cult to initiate a center tile

displacement because of limited toehold accessibility near

the interior of an array, 4 additional toeholds between the center

tile and its neighbors were used to collectively initiate the reaction

(1,3)

(1,1)

(3,1)

(2,2)

(3,3)

(2,3)

(3,2)

Day 0

Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

Simulations

Experiments

T1b

T5b

T2b

T1b

T2b

T1b

T2b

T5b

T1-9

T1b

T1b-9

T1-4b-9

T4b

T1-5b-9

T5b

1.0

0.8

0.6

0.4

0.2

0.0

Fraction completed

Time (hours)

Center

Edge

Corner

Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

Yield (%)

Center

Edge

Corner

Fig. 4

Generality of DNA tile displacement.

Three types of tile displacement reactions, shown in a cascade, in 3 by 3 arrays. 12 toehold and 12 branch

migration domains with unique sets of edge staples are in distinct colors. Toeholds used to initiate each reaction are highlighted in boxes.

Fluorescence

kinetics experiments, simulations, and AFM images of three example reactions, one of each type, performed separately. All three reactions have the s

ame

array as a reactant at 4 nM and distinct invader tiles at 8 nM. In AFM images, dotted and solid boxes highlight reactants and products, respectively. Spe

cies

names of multi-tile complexes are further abbreviated by replacing continuous tile numbers with a dash (e.g., T1-9 indicates T123456789). Scale bar

s are

200 nm.

Design diagram, AFM images, and yield estimation of a tic-tac-toe game. Two players each have 9 tiles labeled with X or O, each of which is

designed to displace one speci

c tile from the array. (

) indicates the position of the tile to be displaced is in row

and column

. Scale bar is 100 nm.

Yield was estimated as the number of desired products (shown in the design diagram and representative AFM image for each day) divided by the total

number of all 3 by 3 arrays in 10 by 10

μ

m AFM images. The standard error was calculated as

ffiffiffiffiffiffiffiffiffiffi

=

ffiffiffi

, where

is the estimated yield and

is the total

number of arrays, treating the yield as a Bernoulli probability.

=

54, 82, 39, 37, 29, 22, and 12 for days 1 through 7. Error bars correspond to the standard

error of the yield

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7

(Fig.

a). Similar to the other types of reactions, these toeholds are

also present both in the original edge tiles and their invaders.

With 4 toeholds on a center tile invader, any of the toeholds can

bind to an edge tile and branch migrate to disconnect one edge of

the center tile. When all four edges of the original center tile have

been disconnected, it will be fully displaced by the invader.

To create 12 unique toeholds and branch migration domains,

we reduced the number of staples in a toehold but increased the

number of nucleotides in each sticky end. With 5-nt 2-staple

toeholds, whose strength should be similar to 2-nt 4-staple

toeholds, 9 staples are now available for creating coded branch

migration domains in which speci

fi

c sets of edge staples are left

out. We designed three unique edge codes, each consisting of

6 staples (Supplementary Fig. 7a).

We modeled the three types of tile displacement reactions,

considering the branch migration steps within a tile edge and

across a tile corner (Supplementary Eqs. (10) and (11)).

Comparing the simulations with experimental data, we estimated

that the displacement rate for coded branch migration domains is

roughly 25 times slower than that for branch migration domains

with continuous edge staples. As predicted by simulations,

fl

uorescence kinetics data showed that the center tile displace-

ment was the fastest and the edge tile displacement was the

slowest (Fig.

b). A simple explanation is that the overall reaction

rate depends on the total number of branch migration steps

across a tile corner, which is the slowest reaction step for

completing a displacement. Unlike what the simulations

predicted, the completion level of the corner tile displacement

is much lower than that of the center tile displacement. We

attribute it to the impurity of the molecules: similar to how

synthesis errors in unpuri

fi

ed DNA strands could signi

fi

cantly

affect the completion level of a strand displacement circuit

given the complexity of the molecules, tile displacement reactions

could be even more prone to synthesis errors. Moreover, missing

staples

, especially those in the toeholds, could also signi

fi

cantly affect the completion level of tile displacement reactions.

Thus, the fraction of arrays that are fully reactive

—

those with

neither synthesis errors in edge staples nor missing edge staples

—

would decrease quickly with an increasing number of branch

migration domains per toehold. This hypothesis is re

fl

ected in the

order of completion levels of the center, corner, and edge tile

displacement: it agrees with the number of toeholds per branch

migration domain

—

1, 1/2, and 1/3, respectively.

With a unique label on a corner tile, AFM experiments

con

fi

rmed that all three types of invaders were incorporated into

the designed locations in the array, and the percentage of

reactants that were converted to products was estimated as 78.4 ±

6.0%, 52.8 ± 6.0%, and 100% for the corner, edge, and center tile

displacement, respectively (Supplementary Fig. 6).

With an understanding of the three types of tile displacement

reactions, we proceeded with a tic-tac-toe game that demon-

strated all 9 possible reactions in cascades. In this game, the 3 by 3

array with all original plain tiles was used as a nanoscale game

board (Supplementary Fig. 7a). Each of the two players was given

9 invader tiles labeled with an O or X. Making a move simply

corresponded to adding a tile to the test tube containing the game

board. Each subsequent move was made after 24 h. Representative

AFM images showed that the game board was piece-by-piece

recon

fi

gured in response to the signals given by the players, in all

three games that we played (Fig.

c and Supplementary Fig. 7d,

e). The yield of the correctly recon

fi

gured arrays incorporating all

target moves mostly decreased with an increasing number of

moves. However, because the desired reactions continue to

approach completion after 24 h, if the new move is fast enough,

some arrays could incorporate a previous move and a current

move within the same day, recovering the yield. This was seen

when a center piece was played. By the end of the game, the yield

was estimated to be 8.3 ± 2.3% (Fig.

c). Because the number of

possible distinct arrays increases quickly with the number of

moves played (Supplementary Fig. 8) and spurious interactions

between all structures also increase quickly with an increasing

excess of invaders and displaced monomers, the analysis became

much rougher toward the end of the game (Supplementary

Figs. 9

–

15).

Discussion

We have shown that tile displacement is a simple-yet-powerful

mechanism for programming dynamic behaviors in systems of

interacting DNA nanostructures. A few challenges need to be

addressed for scaling up tile displacement systems, including the

yield of DNA origami arrays before displacement (Supplementary

Fig. 16), aggregation of invaders, and spurious reactions involving

intermediate products (Supplementary Discussion). Nonetheless,

in principle, displacement allows for tiles at any desired locations

in larger arrays to be recon

fi

gured (Supplementary Fig. 17a).

Increasing the number of toeholds along each tile edge could lead

to faster reaction kinetics and higher completion levels (Supple-

mentary Fig. 17b). With stacking bonds and sticky end sequences

fully dependent on the M13 scaffold sequence, there is not

enough speci

fi

city within the branch migration domains when the

edge staples are continuous (Supplementary Fig. 17c). However,

this speci

fi

city can be increased by using coded edges (as shown

in Fig.

b), sticky ends with varying lengths, and different com-

binations of extensions and truncations at both ends of the sta-

ples. Furthermore, extended edges

could be used to remove the

sequence dependence and create a much larger library of unique

toehold and branch migration domains with more precisely

controlled binding energies. Importantly, there is already enough

speci

fi

city in the toeholds (Supplementary Fig. 17c) that could

allow for recon

fi

guration of DNA origami arrays even if the tiles

have common edges for binding to each other and the arrays are

assembled using hierarchical approaches

In this work, tile displacement experiments were performed at

a much lower concentration compared to typical strand dis-

placement systems (2 nM vs. 100 nM). Using a mass-production

method

, DNA origami structures could be assembled at a much

higher concentration and a much lower cost, making tile dis-

placement systems much faster for practical applications.

Conceptually, tile displacement provides a new understanding

of how complex molecular structures could interact with each

other and how system-level recon

fi

guration behaviors could

occur. Along the tile edges within a two-dimensional (2D)

structure, square or any other shape, information can be encoded

into several functionally independent domains. Depending on

which domains are protected and which are revealed, the struc-

ture could interact with various other structures and exchange

which ones they are bound to at different times. The dynamic

interactions between 2D structures directed by these

“

smart

edges

”

could be extended to that between 3D structures, especially

the

fl

exible ones

, directed by

“

smart surfaces

”

with

information-bearing 2D domains, resulting in more general

forms of

“

structure displacement

”

. Compared to the previously

known binding and unbinding interactions between complex

DNA nanostructures, displacement allows isothermal recon

fi

guration in non-equilibrium structures and thus much more

interesting dynamic behaviors with lower energy barriers.

Practically, tile displacement provides several unique advan-

tages for controlling structural recon

fi

guration, including ef

fi

ciently swapping in and out complex functional components that

are pre-fabricated on DNA origami surfaces, programming cas-

cades of autonomous recon

fi

guration events within a network of

interacting complex molecular structures, and creating parallel

recon

fi

guration behaviors unique to the information embedded

within each molecular structure (Supplementary Discussion).

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