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rsta.royalsocietypublishing.org
Molecular ping-pong Game of
Life on a two-dimensional
DNA origami array
N. Jonoska1 and N. C. Seeman 2
Research
Cite this article: Jonoska N, Seeman NC. 2015
Molecular ping-pong Game of Life on a
two-dimensional DNA origami array. Phil.
Trans. R. Soc. A 373: 20140215.
http://dx.doi.org/10.1098/rsta.2014.0215
Accepted: 5 May 2015
One contribution of 13 to a Theo Murphy
meeting issue ‘Heterotic computing:
exploiting hybrid computational devices’.
Subject Areas:
nanotechnology, molecular computing
Keywords:
oscillating DNA attachments, laser
illumination assembly control, DNA origami,
DNA signals, Game of Life, cellular automata
Author for correspondence:
N. Jonoska
e-mail: [email protected]
1 Department of Mathematics and Statistics, University of South
Florida, Tampa, FL, USA
2 Department of Chemistry, New York University, New York, NY, USA
We propose a design for programmed molecular
interactions that continuously change molecular
arrangements in a predesigned manner. We introduce
a model where environmental control through laser
illumination allows platform attachment/detachment
oscillations between two floating molecular species.
The platform is a two-dimensional DNA origami
array of tiles decorated with strands that provide
both, the floating molecular tiles to attach and to pass
communicating signals to neighbouring array tiles.
In particular, we show how algorithmic molecular
interactions can control cyclic molecular arrangements
by exhibiting a system that can simulate the dynamics
similar to two-dimensional cellular automata on a
DNA origami array platform.
1. Introduction
As a discipline, computer science, or informatics, aims
to advance our lives through new information and
computation methodologies, as well as to explain
natural processes through our understanding of how
information propagates and is being computed in nature.
In the past two decades, new computing paradigms
inspired by natural processes such as biomolecular
computing have been developed. These models are
inspired by biological molecular processes and chemical
self-assembly and have been shown to advance the
nanotechnology needed for new material designs and
our understanding of biomolecular processes. DNAbased bottom-up assembly, introduced roughly 35 years
ago [1], has been explored by at least 100 laboratories in
recent years. Complex DNA motifs that entail the lateral
fusion of DNA double helices [2], such as DNA double
2015 The Author(s) Published by the Royal Society. All rights reserved.
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rsta.royalsocietypublishing.org Phil. Trans. R. Soc. A 373: 20140215
(DX), triple (TX), paranemic cross-over molecules [3,4] have been used as tiles and building blocks
for large nanoscale arrays [5,6]. In addition to the two-dimensional arrays, three-dimensional
structures such as a cube [7], a truncated octahedron [8], tetrahedron [9] and arbitrary graphs
[10–12] have been constructed from DNA duplex and junction molecules. Techniques have been
further developed for a variety of polyhedra [13–15], and the first macroscopic self-assembled
three-dimensional DNA crystals have been reported [16]. The construction of approximately
100 × 100 nm two-dimensional DNA nanostructures was significantly facilitated by Rothemund’s
DNA origami [17], where a standard single-stranded vector plasmid is used to outline a shape
while short DNA strands connect portions of the plasmid fixing its shape in a rigid form.
Since its appearance, DNA origami has been used as a seed for arranging DX tiles in an array
[18], nanotube constructions [19], three-dimensional boxes (with cargos) [20,21]. Further, DNA
origami, as templates for large DNA-based tiles, were arranged in a two-dimensional crystalline
array [22].
The informational character of DNA makes it a perfect molecule for information processing at
the nano level. Winfree [5] introduced the Tile Assembly Model and showed that two-dimensional
self-assembled arrays made of DX or TX DNA tiles can simulate the dynamics of a bounded onedimensional cellular automaton and so are capable of potentially performing computations as a
Universal Turing machine. Several successful experiments have confirmed computation by arraylike DNA self-assembly such as binary addition (simulation of XOR) using TX molecules (tiles)
[23], Sierpinski triangle assembly [24,25], and a binary counter [18] by DX molecules. Further,
transducer simulations with programmed inputs by TX DNA molecules have also been reported
[26–28]. On the other side, ‘DNA fuel’ strands introduced by Yurke et al. [29] became a base for
development of DNA strand displacement networks that have been shown to be able to perform
digital [30,31] and analogue computation [32]. Several new designs for strand displacement
computational networks attached on a two-dimensional origami platform have been theoretically
proposed [33,34].
Further, ‘DNA fuel’ strands were used to produce devices that were sequence-dependent
[29,35]. Such devices were incorporated in two-dimensional DNA arrays [36] as well as in
the programmable DNA transducer where simultaneous programmed molecular movements
were achieved [37,38]. The same mechanisms were used for structures that can perform simple
‘walking’ on an arranged platform [39–41]. Three later walking devices [42–44] showed a
significant robustness such that the directions and the actions of the walker were guided by a
sequence of strand displacements incorporated within the walking platform.
In many programmed structural self-assembly experiments thus far, as well as in the
theoretical Tile Assembly Model, it is assumed that the DNA motifs are predesigned and they
follow the programmed design to assemble structures, rarely reacting to environmental input. The
cooperation between the motifs is guided by sticky ends, and once a molecule appears within a
larger structure, it has no further computational interaction with its immediate environment. Such
passive roles of the motifs, and the assembled structures, seem counterintuitive to the dynamic
process of computation where programmed molecular interactions could produce continuous
structural changes and re-use of the building motifs. Here we propose an experimentally feasible
model for programmed cycles of molecular interactions that is able to continuously change
molecular arrangements. This proposed system consists of a two-dimensional DNA origami
array whose tiles serve as a transmission storage (equipped with ‘communication’ and ‘identity’
strands) and free floating tiles able to attach to their respective ‘identity’ counterparts on the
array and transmit signals to their neighbouring locations. The array tiles are divided in a
checker-board (red/green) fashion such that in an alternate manner, at each cycle, one of the
colours receives the floating tiles and computes the identity of the next cycle tiles to be attached
on the other colour tiles in the array. We suggest that environmental control of the cycles can
be achieved by equipping red (green) identity tiles with red (respectively, green) dyes whose
exposure to appropriate illumination of the appropriate wave length increases temperature
and thereby can prevent attachment or disassociate the appropriate floating tiles from
the array.
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We assume a two-dimensional array (platform) where the molecules are arranged. This platform
also allows molecular communication from one arrangement step to another. The model is closely
related to a cellular automaton, while it differs from it in two aspects: the underlying array is
partitioned into two parts and the point values alternate in their updates between these two parts.
Another difference is that at a given point, the next state value depends only on the state value of
its neighbours that belong to the other partition set, and not on its own value. Cellular automata
assume configurations on infinite arrays, which of course cannot be implemented experimentally.
We define our general model on an infinite array as well, but assume implementation on a finite
rectangular array. Let Σ be a finite set of states, which are represented by distinct molecular
shapes or markers, X = Z × Z be the integer lattice of the plane, and for a point v ∈ X let
Nv = {v + (1, 0), v + (0, 1), v + (−1, 0), v + (0, −1)} be the set of all four neighbouring points of v in
directions east, north, west and south. The neighbourhood of each array tile in this case consists
of tiles immediately up, down, left and right, also known as the von Neumann neighbourhood.
Let X = R ∪ G be a partition of the integer lattice into R = ‘red’ and G = ‘green’ points such that
each lattice point has a neighbour of different colour, v ∈ R has at least one neighbour in G, and
each v ∈ G has at least one neighbour in R. Lattice points in one of the partition sets are said to
be ‘oppositely’ coloured to those of the other set. We denote with Nvc the neighbours of v that
are oppositely coloured from v. Figure 1 depicts an example of partitioning X into a red set R
and a green set G in a checkerboard fashion. In this case Nv = Nvc . An arrangement is a partial
map σR : R → Σ (red arrangement) or a partial map σG : G → Σ (green arrangement) indicating
molecular arrangements over the red or the green points in the lattice.
The dynamics of the system are such that it alternates between red and green arrangements.
For a given arrangement σR (respectively, σG ), let σR (v) (respectively, σG (v)) be the state (type of
the molecule) of lattice point v in R (respectively, G), while σG (Nvc ) (respectively, σR (Nvc )) the states
of the oppositely coloured neighbours of v. Two types of local rules φR , φG : Σ i → Σ (i = 1, 2, 3, 4)
associate a state (molecule) in Σ to a tuple of states, representing the communication between
cells in the red and cells in the green lattice points. These rules change the state of each lattice
point according to the set of states of the oppositely coloured neighbouring points; if v ∈ R then
σR (v) = φR (σG (Nvc )) (respectively, σG (v) = φG (σR (Nvc ))).
A system of interactive molecular arrangement is a tuple S = (R ∪ G, Σ, φR , φG , σR0 ), where σR0
is the seed arrangement. A computation of S is a sequence of alternating coloured arrangements
σR0 , σG0 , σR1 , σG1 , . . . such that the state at each lattice point of an arrangement in this sequence
is obtained according to the corresponding local rule applied to its oppositely coloured
neighbouring states of the predecessor arrangement.
Consider the interactive molecular arrangement system whose lattice partition is the checker
board partition of the plane, where R = {(i, j) | i + j is odd } and G = {(i, j) | i + j is even } (figure 1).
The system has two states, 0 and 1, and the two types of rules φR and φG are the same providing
state value 1 to a given lattice point if and only if there are two or three oppositely coloured
neighbours of value 1. These rules are similar to the Conway’s GoL cellular automaton rule where
each cell in the plane lattice assumes value 1 if and only if it has two or three neighbours of value 1.
Except, in GoL all cells are updated simultaneously and each cell has eight neighbours instead of
four defined with Nv . We call this system GoL-like. An example of a 5 × 5 segment of the board
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2. Cycles of interactive molecular arrangements
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We also initiate a theoretical model for cooperative molecular interactions on a given
platform that allows cycles of programmed molecular arrangements and dynamical information
processing to be experimentally feasible; moreover, through the proposed signal transmission and
molecular interactions on the predesigned array we show how to implement two-dimensional
cellular automata like iterative arrangements, thereby providing a ‘modus operandi’ for cyclic
molecular cooperation. We have chosen a Game of Life-like (GoL-like) cellular automaton rule
[45], where a cell assumes a value 1 if and only if two or three of its neighbours also have a value
1, otherwise, the cell assumes a value 0.
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Figure 2. Iterations of the GoL-like interactive molecular arrangement system on a 5 × 5 grid. (Online version in colour.)
with arrangements of 0’s and 1’s is depicted in figure 2, top row. The far left (red) arrangement is
the seed arrangement σR0 . The local rule φG associates 1 with all green points that are surrounded
by two, or three 1’s in the red seed arrangement. The next arrangement σG0 consists of a green
pattern of 0’s and 1’s after application of φG , while σR1 is the red arrangement obtained from σG0
after applying φR which in this case equals φG . In the second row, the arrangements σRi and σGi
are shown under a single arrangement of σ i for i = 0, 1.
Given a finite n × n array size, and the initial σR0 seed arrangement, for any rules φR , φG , the
arrangement sequence σ 0 , σ 1 , . . . is eventually periodic. This follows from the fact that there are
only a finite number of configurations and the transitions between the iterations are deterministic.
For the seed σ 0 of figure 2, and the GoL-like system the sequence becomes periodic after the
first three iterations (figure 3). However, the GoL-like system seems to exhibit quite complicated
dynamics. Our initial experimentation on a 15 × 15 grid, as well as a 25 × 25 grid shows periodic
behaviour after hundreds (respectively, thousands) of iterations for some seeds.
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s 0R
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Figure 1. An example of a checkerboard type of a red–green partition of the plane lattice points. In this case, tile
neighbourhoods coincide with the oppositely coloured tile neighbourhoods. (Online version in colour.)
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Figure 3. The arrangement sequence of GoL-like system on a 5 × 5 grid. (Online version in colour.)
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Figure 4. Shapes obtained from cross-linking tiles with value 1 following GoL-like rules with initial configuration σ 0 . (Online
version in colour.)
One can think of the system as a ‘factory’ of shapes. The arrangement of a given set of symbols
in each σ i can be used to cross-link parts of the arrangement such that when the floating tiles
are disassociated from the the platform, they assume a shape defined by those symbols. For the
example above, by cross-linking tiles with label 1, there are three shapes (figure 4) that can be
obtained from a 5 × 5 grid initialized with σ 0 and the above GoL-like rules.
3. Experimental implementation
In this section, we describe the experimental process for implementing interactive molecular
arrangements systems. There are several recent experimental advances that make implementing
cyclic programmable molecular choreography feasible. DNA origami tiles assemble in twodimensional arrays [22], while incorporated signalling strands within DNA origami have
programmed a walking robot to pick-up cargo [42]. Recently, we have achieved controlled stepby-step tile assembly through signal activated sticky ends [46]. This is in contrast to the passive
form of self-assembly where molecules can assemble as soon as their sticky ends find their
complements, and in order to accomplish cooperative interaction (necessary for computation)
one has to calibrate the temperature of the reaction very carefully. In [46], a series of five DX
DNA tiles were assembled in an active cascade process. Each DX tile contains an activation
site on one end, whose binding releases a signal consisting of a long intramolecular strand that
releases a protecting strand on the other end, about 18 nm away. Another experimental advance
that supports the feasibility of of the interactive molecular arrangements is the cyclic replication,
through selection, of DNA origami dimers controlled by laser illumination and temperature.
In [47], a process and a system was designed made of DNA origami tiles that exponentially
replicate a seed pattern, doubling the copies in a series of diurnal-like cycles of temperature
and UV illumination (for cross-linking), producing more than 7 million copies in 24 cycles. This
system was used to demonstrate exponential growth and selection: two similarly growing subpopulations, one with a ‘red’ dye incorporated, the other with a ‘green’ dye, can be controlled
by coloured light. The light heats one species reducing its replication rate. The progeny of
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(a) Tiles and signalling
(i) Platform and floating tiles
The proposed system consists of two parts: a platform (n × n array) assembled from tiles in a
checkerboard arrangement and floating tiles that perform the cyclic arrangements by assembling
on the platform. We propose to use DNA origami tiles [17] shown in figure 5 that have room
to incorporate the necessary signalling and binding elements. It has been shown that these are
capable of producing two-dimensional arrays [22]. The tile is constructed by a standard M13
single-stranded vector plasmid used to outline a shape while short DNA strands connect pieces
of the plasmid, fixing its shape in a rigid form. The basic tile unit is a square cross structure
approximately 100 nm in width and height. The helices on the horizontal part of the the cross lie
on top of the vertical portion of the cross.
The edges of the tile consist of the ends of six pairs of DNA double helices. The platform tiles
have binding sites that are single-stranded portions contained in these helices, so that two tiles
that bind would have their edge helices aligned, bound at specific helices through single-stranded
overlaps. The remaining edge interactions can be mediated by favourable helix stacking between
aligned helices [48]. As DNA origami can assume a variety of shapes [17], imposing geometrically
complementary edges by altering the lengths of the edge helices is another method to promote
correct edge matching and discourage incorrect binding.
Platform. The platform consists of two species of origami tiles, ‘red’ and ‘green’ tiles arranged in
a checkerboard fashion. The checkerboard assembly of the array can be imposed by the sequence
design of the edge sticky ends. Each tile is connected with oppositely coloured tiles (figure 6). The
two types of tiles distinguish by the sticky ends on the two types of strands, ‘communication’ and
‘identity’ strands, attached on top of each tile (§3b), perpendicular to its plane.
Floating tiles. Although the floating tiles could have different geometry than the platform tiles,
we show the same shape as the platform tiles for simplicity. These tiles have no sticky ends on
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the non-absorbing species replicate preferentially and take over the system. All these advances
provide a basis for the design described below.
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Figure 5. Basic DNA origami tile. (Online version in colour.)
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(b) Signal mechanism from one species to the neighbouring locations
(i) Platform strand extensions
Each platform tile is equipped with single stranded extensions, two pairs on each edge (figure 7).
One of the edge extensions is the ‘communication’ signal and the other is the ‘identity’ strands.
The red (respectively, green) communication signals on the red (respectively, green) platform
tiles, when triggered, interact with the green (respectively, red) identity strands on the green
(respectively, red) platform tiles at the neighbouring locations. The labels on the strands indicate
distinct sequences encoding that label. Barred symbols indicate Watson–Crick complements. The
primed symbols 0’, 1’, etc., on the green tile indicate distinct sequences encoding the equivalent
role values as 0 and 1 on the red tile. The arrows in figure 6 show the communication between
the two types of tiles. The red tiles send red signals to the green tiles, and the green tiles send
green signals to the red tiles. The default setting of the identity strands on the platform tiles is 0
(as depicted in figure 7). If a tile of value 1 is attached to the platform, then the identity strands of
the neighbouring locations assume value 1.
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the edge helices and do not interact with the others except through single-stranded extensions
perpendicular to the plane of the tile. These extensions bind to the platform identity strands and
send signals to the neighbouring locations on the platform. There are two species of floating
tiles, ‘red’ and ‘green’ species that can bind to the ‘red’ (respectively, ‘green’) tiles on the
platform. The two species are distinguished by the IR Dyes attached on their ‘identity’ and ‘signal
initiation’ strands (figure 8). The red (respectively, green) floating tiles will have IR Dyes 800
(respectively, IR Dyes 700) attached that generate heat when exposed to a 785 nm laser beam
(respectively, 685 nm). The heat then both prevents hybridization in its vicinity and disassociates
previously hybridized duplex. As mentioned, current experimental findings show that iterative
hybridization of appropriately labelled single floating origami tiles to a system of duplex origami
tiles equipped with dye labelled single strands can be controlled with laser beams [47]. Each
species of floating tiles can be hairpin decorated on the opposite side of the plane from the
extension strands to indicate their values (whether 0 or 1).
rsta.royalsocietypublishing.org Phil. Trans. R. Soc. A 373: 20140215
Figure 6. Communication signals: the arrows indicate the direction of the communication. The red tiles communicate their
identity value with the red arrows to the green tiles. (Online version in colour.)
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Figure 7. Extension strands on the platform. The default value of the identity strands is 0, as both 0̄ and 0̄ sequences are
exposed on the red and green identity tiles (ID). If a red tile of value 1 attaches to the platform, 0̄ and ȳ will initiate strand
displacement on the floating tile (figure 8) exposing segment B̄ on the red communication duplex (CM). This will allow the free
segment B on the green identity duplex to interact with the newly freed B̄ and expose 1̄ on the green identity tile as that green
edge value in the next cycle. (Online version in colour.)
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Figure 8. Extension strands on the platform and on the floating tiles. (Online version in colour.)
(ii) Floating tile extensions
Each edge of a floating tile is equipped with an identity strand. Each identity strand hybridizes
to an identity strand on the platform (there are four such strands on the platform tile) and
‘recognizes’ the value of the neighbouring tile. The combination of the four identity strands
determines the value of the tile (i.e. in our case, if there are 2 or 3 identity strands with value
1, then the floating tile has value 1, otherwise it has a value 0). The value of the tile is indicated
with hairpin labelling on the other side of the tile. Only tiles of value 1, when attached to the
platform, transmit signals to the neighbouring locations indicating their value 1. Tiles of value 0
do not transmit their value. In figure 8, an edge on a red tile with identity attachment strand 1 is
depicted. An identity attachment strand 0 on a tile of value 1 has a similar construction, except in
that case the single stranded portion is 0 instead of 1.
(c) Cyclic communication on the platform
We propose that the signalling across and between tiles be accomplished with a combination
similar to the reversible strand exchange mechanism [30,31] (figure 9). This method is based on
the toehold-mediated strand exchange introduced by Yurke et al. [29] and was also used by the
authors for designing a programmable input for finite-state automata with output. It is closely
related to the Omabegho et al. [43] autonomous cascade walker. The essence of the method is in
the following: if in a solution containing two strands ab and cb̄, where b and b̄ form a duplex, a
third strand āb̄ complementary to ab is introduced, the strand cb̄ is replaced in the duplex by āb̄.
In this case, the sequence a is said to be a ‘toehold’.
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Figure 9. Red floating tile attachment cycle. (a) Attachment of a red tile of value 1 with an edge value 1 (red platform tile
identity strands had segments 1̄ · 0̄ · ȳ exposed). Green laser beam is active, the green tiles are disassociated. The middle
duplex with complementary x̄ · x starts forming. (b) Middle duplex x̄ · ȳ on the red floating tile is formed and the red signal
strand Ā · B̄ · 1̄ is exposed. (c) Toehold A from the red communication strand interacts with the red signal strand on the
floating tile forming the duplex Ā · B̄ · 1̄ and freeing the toehold B on the green identity tile to interact with B̄ segment
on the newly formed single strand of the communication duplex. This exposes 1̄ · 0̄ · ȳ on the green identity tile. (d) Green
laser beam stops and green floating tile whose corresponding edge value is 1 is being attached (indicated with a small green
square for clarity). (e) Red laser beam is activated and duplexes formed with strands containing the red dye are disassociated. If
the attached green floating tile has value 1, signal transmission equivalent to (a–c) on the red floating tile is initiated but is not
depicted. (f ) The red tile detaches and toeholds A and 0̄ in the middle duplex start reacting with the single-stranded portions
with dyes bringing the strands on the red floating tile edge in the original form. (Online version in colour.)
Figure 9 shows a schematic view of the cascading signal transmission on the platform upon
attachment of a red tile of value 1 with edge identity strand of value 1. With each strand
displacement, there is a gain of some base pairs (we anticipate 4 base pair gain). Figure 9a
shows an edge of a red tile attached to the platform. Due to the 685 nm laser beam emission,
the green tiles are not attached. Upon hybridization of the portion 1 · 0 · y on the identity strands,
the portion x · y in the middle duplex of the floating tile forms, and disassociates the segment A
from the side strand containing A · B · 1 with the red dye. This process ensures that there is no
communication on the platform before the floating tile is being attached, and the strand migration
process leaves a time lapse between the attachment of the red tile and the release of the toehold
A (figure 9b). The toehold A on the communication strand of the platform is free to interact with
the corresponding complementary signal initiation strand on the floating tile (figure 9c). This
interaction leaves toehold B to interact with the identity strands on the green tile leaving ȳ · 0̄ · 1̄
free to ‘identify’ a green tile. As soon as the green laser beam is stopped, the green dyes stop
emitting heat and the green floating tiles are free to attach to the platform (figure 9d). In figure 9d,
the green tile is depicted with a small green square for clarity of the figure. If the attached green
tile has value 1, the strand interactions on the green tile appears, similarly to the red floating tile
depicted in figure 9a,b but is not pictured.
When the red 785 nm laser beam is activated, both red and green floating tiles are attached on
the platform but only the red dyes on the red floating tiles start emitting heat and disassociate the
labelled strands from their complements (figure 9e). The amount of heat is proportional with the
reciprocal value of the distance r, i.e. T(r) = T0 + T(R/r), where T0 is the ambient temperature
and T is the change in temperature over distance r with heat source of radius R. This means that
.........................................................
(f)
x–
y–
–
C
y
y–
–
0– 0
1 1
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D
–
C–
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0–tile
1–tile
0
0
0 0
1
0
1
0
1
1
1
0
0
10
1
1
1
1
0
1
0
1
1
0
1
1
0
Figure 10. Tile types needed for GoL-like implementation.
at distance 28–30 nm there is a change of 1◦ C when a sphere of the DNA duplex size (3.5 nm) is
heated by 8◦ C. The origami tile allows for more than 30 nm distance between the red and green
monochromatic duplexes in (figure 9d), hence the effect of the heat emitting red dye on the green
duplexes can be kept on less then 1◦ C. With the application of 785 nm laser beam, the floating red
tile is not attached to the platform any more and is free to float in the solution. The energetically
favourable base pair gain (i.e. increased favourability of G) eventually brings the identity and
signal initiation strands of the floating tile to their original condition and leaves the identity and
the communication duplex on the platform red tile in the same condition as when no red tile was
attached figure 9f. If the attached green tile has value 1, then its attachment (equivalently to the
red tile) would communicate its value to the red identity strand on the red platform tile, such that
when the red 785 nm laser beam is stopped, the red floating tiles can attach to the platform and
the cycle can continue from situation (a).
(d) Game of Life-like implementation
Tile types. For the implementation of the interactive molecular arrangement system that simulates
the GoL-like function, we need six types of floating tiles in each species of red and green tiles.
Because the origami tiles are symmetric and the function that we propose depends on only the
number of neighbouring tiles being 1 or 0, and not on their locations (north, south, east or west),
there are three types of 0-tiles and three types of 1-tiles. The schematic of the tiles is depicted in
figure 10. The values of the edges of the tiles indicate the values of the identity strands attached
on the floating tiles, and according to their values, the tile takes the identity 0 or 1. The edges of
the 1-tiles are also equipped with signal initiation strands such that upon their attachment they
communicate through the platform with the neighbouring locations.
Initialization and computation. As the default values of the platform identity strands is 0, one can
establish the control between the attachment and detachment cycles with all values 0 first. For a
platform initialized σR0 as in figure 2, a platform can be constructed by first hybridizing a red
floating tile of the appropriate value to the red platform tile at the appropriate location, and
then the duplex of red tiles would be used together with the green platform tiles to assemble
the initialized platform. Each platform tile can have its location specified by the location designed
sticky ends; therefore, the platform tile of the red duplex of platform-floating tile can take its
place in the array at the appropriate location guided by its and neighbouring green platform
tile sticky ends. As the platform is initialized, the communication signals on the platform will
interact with the green platform tiles. The situation at that stage is as in figure 9b. Subsequently,
the cyclic molecular arrangement continues as described in §3c. A robust error control used in [49]
can be applied to prevent attachments of partially matched floating tiles while allowing complete
matching of the floating tiles.
4. Concluding remarks
The proposed laser illumination technique introduces ‘clock’ controlled programmed dynamics
in molecular arrangements, and the platform/floating tile signals introduce molecular
.........................................................
0
1
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0
0
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11
Competing interests. We declare we have no competing interests.
Funding. This research has been supported by grant no. CCF-1117210 from the National Science Foundation to
N.J. and N.C.S.; the NIH grant no. R01GM109459-01 to N.J. and the following grants to N.C.S.: GM-29554 from
NIGMS, grant nos. CMMI-1120890, CCF-1117210 and EFRI-1332411 from the NSF, MURI W911NF-11-1-0024
from ARO, grant nos. N000141110729 and N000140911118 from ONR, grant nos. 3849 from the Gordon and
Betty Moore Foundation.
Acknowledgements. We thank Paul Chaikin for advice on heat dissipation.
.........................................................
communication for cyclic molecular arrangements thereby providing a controlled molecular
choreography over a predesigned array. There are many examples of incorporating signaltransmission strands on a DNA origami, and most of these models are based on the Yurke
et al. [29] design for a strand-displacement mechanism using toeholds. These signals are used
for either static control of tile assemblies [50–52], or for designs of pathways simulating logic
gates (e.g. [33,34]). In the first case, the assembled structure is static once assembled; while in
the latter case, there are no arrangements except signal propagation throughout the system of
logic gates. The use of environmental control (laser beam) to move from one arrangement cycle to
another, introduces time steps in an intrinsically asynchronous system of molecular assemblies.
A clocked control is an essential part of information processing, so many new models where
molecular interactions follow a step-by-step dynamics could be designed. Here we have shown
one such model where the molecular arrangements represent the time-step development of a
two-dimensional cellular automaton like function thereby initiating the study of such systems.
Our suggestion of using two types of IR Dyes to control the clock is only one way for such clock.
It has been observed that other materials attached to DNA can produce heat locally upon laser
illumination such as small gold nanoparticles (1.4 nm gold particle melting a 7 base duplex [53])
and different shapes of particles (coated gold ‘nanorods’ and ‘nanobones’ absorbing and melting
DNA at two different wavelengths [54]). Further experimentation will examine the limitations
and possibilities of these approaches.
The theoretical limits of the proposed new approach to molecular arrangements are not yet
known. It is well known that the GoL has universal computational power. It is also known that
predicting the value of a cell in n iterations of the GoL is P-complete [55]. The finiteness of the
implemented system (finite platform) restricts the power significantly, so its actual computational
capability warrants further investigations. The computation in the proposed system also depends
on the type of partition that is assigned to the plane lattice. Some possibilities are depicted in
figure 11. There are patterns that can be obtained over one partition, but could not be acquired
over others, hence investigation of these questions is of interest. Furthermore, an experimental
confirmation of the cyclic dynamic algorithmic arrangement would be the first demonstration
of programmed cyclic molecular movements that can be seen as an incarnation of nucleic acid
robots (nubots) acting on a platform. Although there are theoretical models for nubots (e.g. [56]),
there are no experimental suggestions for their development. While the last years’ robotics
breakthroughs [57,58] were achieved with electronic components, the proposed system opens
doors for advancing such designs at a molecular level.
rsta.royalsocietypublishing.org Phil. Trans. R. Soc. A 373: 20140215
Figure 11. Different possibilities for lattice partitions. (Online version in colour.)
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