Medium scale integration of molecular logic gates in an automaton.

Abstract

The assembly of molecular automata that perform increasingly complex tasks, such as game playing, presents an unbiased test of molecular computation. We now report a second-generation deoxyribozyme-based automaton, MAYA-II, which plays a complete game of tic-tac-toe according to a perfect strategy. In silicon terminology, MAYA-II represents the first "medium-scale integrated molecular circuit", integrating 128 deoxyribozyme-based logic gates, 32 input DNA molecules, and 8 two-channel fluorescent outputs across 8 wells.

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Medium Scale Integration of Molecular
Logic Gates in an Automaton
Joanne Macdonald,*,†Yang Li,†,§,Marko Sutovic,†,§Harvey Lederman,†,§
Kiran Pendri,†,§Wanhong Lu,†,§Benjamin L. Andrews,‡Darko Stefanovic,‡and
Milan N. Stojanovic†
National Chemical Bonding Center: Center for Molecular Cybernetics, DiVision of
Experimental Therapeutics, Department of Medicine, Columbia UniVersity, New York,
New York, and Department of Computer Science, UniVersity of New Mexico,
Albuquerque, New Mexico
Received September 1, 2006; Revised Manuscript Received September 14, 2006
ABSTRACT
The assembly of molecular automata that perform increasingly complex tasks, such as game playing, presents an unbiased test of molecular
computation. We now report a second-generation deoxyribozyme-based automaton, MAYA-II, which plays a complete game of tic-tac-toe
according to a perfect strategy. In silicon terminology, MAYA-II represents the first “medium-scale integrated molecular circuit”, integrating
128 deoxyribozyme-based logic gates, 32 input DNA molecules, and 8 two-channel fluorescent outputs across 8 wells.
Molecular computation and circuits engineering1-27using a
“silicomimetic” approach is currently focused on building
molecular networks analogous to electrical engineering
designs. These networks consist of logic gates, which
perform Boolean logical operations such as AND, NOT, and
OR on one or more inputs to produce an output. While
individual molecular gates and small networks have previ-
ously been constructed, these gates are yet to be integrated
at higher levels of complexity. Such integration in electrical
engineering arises from massive parallelism and intercon-
nections, rather than fundamental component complexity.
The ability to truly integrate molecular components remains
crucial for the construction of next-generation molecular
devices.11,14
The largest solution-phase molecular circuits previously
considered include networks combining up to 20 logic
modules.11,20On a similar scale, utilizing a full set of
deoxyribozyme-based logic gates,6,19,24we have constructed
solution-phase computing circuits such as a half-adder,7
ligase-phosphodiesterase cascades,19and most recently a full-
adder that comprises 7 logic gates in a single tube.24Systems
of greater complexity include molecular automata,4,8-10which
are capable of analyzing a series of human or environmental
inputs in a meaningful fashion. An unbiased test of automa-
ton construction is game playing, and we have focused on
tic-tac-toe: one of the simplest games of perfect information,
and yet a surprisingly complex combinatorial problem, with
2.65 × 10103nonlosing strategies for a complete version of
tic-tac-toe.28To this end, we previously constructed a
deoxyribozyme-based molecular automaton (MAYA, a mo-
lecular array of YES and AND gates) that plays a simplified
symmetry-pruned game of tic-tac-toe encompassing 19
permissible game plays, using an array of 23 logic gates
distributed over 8 wells.8
We now report the development of the first solution-phase
molecular assembly comprising over 100 molecular logic
gates, which more than quadruples the complexity performed
by any previous system. Expanding from our original
automaton, MAYA-II is a second generation molecular
automaton capable of playing a complete game of tic-tac-
toe against a human opponent, and encompasses 76 permis-
sible game plays. MAYA-II is more user-friendly than its
predecessor, as it signals both players move in a two-color
output system and imposes no constraints on the position of
the human player’s first move. However, similar to MAYA-
I, MAYA-II is constructed from three classes of stem-loop
controlled deoxyribozyme-based logic gates that are allos-
terically modulated by input oligonucleotides to produce
fluorescent output signals (Figure 1):6-8(i) YESx gates are
activated by a single input x; (ii) xANDy gates are activated
in the presence of two inputs x and y; and (iii) xANDyAND-
NOTz gates are activated in the presence of inputs x and y
only if a third inhibiting input z is absent. To play MAYA-
II, a set of deoxyribozyme-based logic gates are arranged
according to a predetermined strategy in a 3 × 3 array within
a 384-well assay plate (see Figure 2A). Oligonucleotide
inputs encoding the human moves are added successively
* To whom correspondence should be addressed. E-mail: jm2236@
columbia.edu. Address: 650 W 168th St, Box 84, New York, NY 10032.
Tel: +1-212-342-5610. Fax: +1-212-305-3475.
†Columbia University.
‡University of New Mexico.
§NSF-funded high school internship program.
NANO
LETTERS
2006
Vol. 6, No. 11
2598-2603
10.1021/nl0620684 CCC: $33.50
Published on Web 10/07/2006
© 2006 American Chemical Society

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to the wells and trigger the automaton’s next move. After
each input addition, the well-plate is analyzed using a
fluorescent plate reader which follows accumulation of two
fluorescent oligonucleotide outputs: display of the human
move is observed in the “green” fluorescein output channel,
and the automaton’s response to the human input addition
is observed in the “red” tetramethylrhodamine (TAMRA)
output channel. An example game is shown in Figure 2B.
The game strategy for MAYA-II (Figure 2A and Sup-
porting Information) is considerably different from MAYA-
I. The automaton still moves first into the middle square (well
5) controlled by a constitutively active deoxyribozyme added
immediately prior to the beginning of the game. However
successive automaton moves are constructed as a hierarchical
cascade of AND gates, with YES gates responding to the
first human move (NOT loops are included to prevent
secondary activation in already played wells or are redundant
and included to minimize cumulative nondigital behavior in
side wells over several moves). In doing this, MAYA-II is
a step toward programmable and generalizable MAYAs that
are trainable to play any game strategy. Our strategy required
32 input oligonucleotides, encoding both the position and
timing of a human move. These inputs are named INM
wherein N is the position of the move (wells 1-4 or 6-9),
and M is the timing of the move (1 for the first move, 2 for
the second move, etc.). For example, input I62 would be
added to every well when a human would like to indicate to
the automaton they are moving into square 6 as their second
move. This strategy was translated into Boolean logic
amenable to deoxyribozyme-based implementation (Figure
2) using a custom computer program, resulting in 96 logic
gates for automaton move calculations and an additional 32
logic gates to display human moves. We stress that,
considering traditional difficulties in selecting nucleic acids
suitable for computation29,30and the relatively high concen-
tration of individual gates needed to accomplish readable
outputs, it was far from certain at the outset of this project
that such a number of inputs and gates could be coordinated
in solution.
The 32 input oligonucleotide sequences (Table 1) were
chosen to investigate both the inherent generality of our logic
gate design, and our ability to derive inputs using computer
assistance (akin to previous system designs31). In contrast
to MAYA-I, where a smaller number of inputs meant trial-
and-error substitution of inputs was feasible, we used an
algorithm specifically devised for this purpose: (1) A
theoretical library of stem-loop structures (containing a stem
of 5 base-pairs and a loop of 15 nucleotides) was generated
by applying a search algorithm, based on simple combina-
torial constraints,32where loops containing stronger internal
structures of more than two base-pairs were eliminated; (2)
of the 10 795 generated sequences, a set of 32 15-mer loop
sequences with no more than four nucleotides in common
in a continuous stretch were selected for trial as oligonucle-
otide inputs and randomly assigned to human move and order
positions; (3) these sequences were inserted into deoxyri-
bozyme gate structures and analyzed using mfold;32(4) input
sequences inducing gate misfolding were discarded and
replaced with the next inputs from our library; (5) canonical
gates and their reverse complement 15-mer input sequences
were custom-synthesized and tested in solution-phase for
digital gate behavior; (6) inputs and gates failing to show
expected digital behavior were substituted with the next input
from our collection. Tested input sequences are listed in
Table 1. Out of the initial set of 32 inputs only three were
rejected and substituted. Thus, while there is still space for
improvement in the design of our algorithm, it led to
minimization of trial-and-error from the input selection.
All automaton response gates were constructed from
deoxyribozyme E67,24,33(Figure 1), which cleaves oligo-
nucleotide substrate STto produce product PTand an increase
in “red channel” TAMRA (T) fluorescence. Variable signal
intensity was detected in some gates, and signal optimization
was achieved by manipulating the 5′ or 3′ ends of the gate
molecule, reversing the input loop sequences, or removing
redundant NOT loops (summarized in Table 1, sequences
Figure 1. Automaton move gates and logic gate structures: (A)
Automaton move gates were designed from E6 deoxyribozyme-
based logic gates.7,24,33Upon addition of activating input, these gates
cleave substrate STto produce PTand an increase in TAMRA (T)
fluorescence. YESx gates are activated by a single input x. (B)
xANDy gates are activated in the presence of two inputs x and y.
(C) xANDyANDNOTz gates are activated in the presence of inputs
x and y only if a third inhibiting input “z” is not present. Inserts
show a truth table of logic gate behavior.
Nano Lett., Vol. 6, No. 11, 20062599

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and graphs in Supporting Information). For human move
visualization we used 8-17-based deoxyribozyme logic
gates,7,24,34which cleave substrate SFto produce product PF
and an increase in “green channel” fluorescein (F) fluores-
cence. However, only two input sequences were found to
be active, and the underlying enzyme was re-engineered by
lengthening the substrate binding region (Figure 3A) leading
to the perfect digital behavior of all inputs (Figure 3B). After
individual testing and optimization, gates were mixed ac-
cording to the MAYA-II algorithm (Figure 2) and retested
for digital behavior to exclude the possibility of undesirable
cross reactivity. Results were expressed as the slope of
Figure 2. Schematic representation of MAYA-II. One-, two-, and three-input deoxyribozyme-based logic gates are allosterically modulated
by 32 human-operated input oligonucleotides: 96 logic gates and one constitutively active deoxyribozyme distributed across nine wells
calculate automaton moves, and 32 gates (boxed) display human moves by implementation of a two-color fluorogenic output system.
Green loops denote positive regulation, and red loops denote negative regulation. (B) A representative game. Gates and active deoxyribozyme
(final conditions listed in the Supporting Information) were mixed with 0.5 µM SF, 1 µM STand dispensed into nine wells of a 384-well
plate. Inputs (1 µM) were added in sequence into each well to signal the human players move, and both fluorescein (F) and TAMRA (T)
fluorescence was measured every 15 min for 60 min in between each move. Results are expressed as the slope of signal increase over time
(dF min-1).
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Nano Lett., Vol. 6, No. 11, 2006

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fluorescence change over time (∆F min-1, Figure 2).
Automaton move gates with slopes greater than 3000 ∆F
min-1were considered positive, and signals smaller than
2000 δF min-1were discounted as background noise. Human
move gates tended to give higher signals and rates of reaction
over time and were thus included at lower concentrations.
Even so, these gates typically gave a positive reaction of
greater than 5000 ∆F min-1, and reactions smaller than 4000
∆F min-1were considered noise. While most gates were
not adversely affected within the mixtures, variable signal
intensity was observed for some automaton move gates, and
these were optimized either as described above, or by altering
the concentration of individual gates within the mix. Interest-
ingly, a directly proportional signal to concentration ratio
was not observed for every gate, as some gates were inhibited
by increasing concentrations within the mix (Supporting
Information).
Upon establishment of the final conditions (Supporting
Information), MAYA-II was constructed as a set of eight
tubes (the Well 5 tube containing active deoxyribozyme was
sometimes omitted), and all 76 tic-tac-toe games were
repeatedly tested. MAYA-II was able to play perfectly a
general tic-tac-toe game by successfully signaling both
human and automaton moves. Small immediate increases of
fluorescence upon input addition, most likely the result of a
conformational change of a gate complexed with substrate,
were occasionally observed at the first measurement (the first
15 min of reaction); however this was distinguishable from
positive signals as the fluorescence did not continue to
increase. Thus, digital behavior could be reliably confirmed
within 30 min of input addition. An example game is shown
in Figure 2, and the results from all 76 games are provided
in the Supporting Information.
The success of MAYA-II indicates the maturity of our
deoxyribozyme-based logic gate system as a “plug and play”
integrated logic gate system. MAYA-II integrates 128
molecular logic gates, 32 oligonucleotide inputs, and 8 two-
channel fluorescent outputs across 8 wells. It could be argued
Table 1.
Input Sequences for MAYA-II and Modifications Required for Human Move Gates
5′ AND3′ AND
Modified Modified
inputs and sequencea
YES/Mtotal
+-
Rtotal
+-
RNOT/x
I11
I12
I13
I14
I21
I22
I23
I24
I31
I32
I33
I34
I41
I42
I43
I44
I61
I62
I63
I64
I71
I72
I73
I74
I81
I82
I83
I84
I91
I92
I93
I94
Totals:
AACGACTGCACCACG
CTCTCCCTGTACCCA
ACCCCTCTCGCTCTT
TTCTGCCTTGATCCG
TGTTGTCTTATCCAT
TCAGATGCTACGTGT
ACCGTACTCGACCTA
TCGGATCTCGGTTTC
TACACGCTGGTCAAT
CACTATCTCGAATCA
GCGTGACTGCGGCAT
GTTGGTCTTGTAGGA
GCTAGGCTATCGCGT
TAATACCTGAGCGGG
TACCCCCTAGTCTGC
AACGGACTTCAACAG
CGGGATCTCGTCGGT
ATCGCTCTCCATGCA
ATCTATCTCGTTCCG
ACTCCGCTCGACTTA
GGATCACTTACGTAT
GGTAGCCTTTTATCG
CATTGCCTCGATATC
CCAGACCTTTCAAGT
TGCGTACTTTGGGTC
TCAGGGCTACGCAAG
TAATTACTGTTTCAC
GGATGCCTGGCGTCT
TGCTATCTCGACAAG
CTCAGGCTGTGTATT
CAGAGCTATACGGAG
GCTACTCTGGGTGCT
16
2
1
3/x3
25
6
1
1
7
3
1
1
7
6
1
-41
15
6
-41
2
3
10
-1
-1
15
-413
+5
1
-11
1/-16
7
1
1
6
8
2
3
10
-2
-1
-1
6
2
+2
1
1
-1
1
+23
10/x10
-45
1
1
2
-1
1/+16
+13
7
5
1
+4
2
-1
16
7
1
1
6
3
10
-66
2
+1
+2
-31
-11
1
+13
7
5
1
88
+4
2
-1
8/+1/-1 88
+4
-23 7
+18
-14 7 64/x13
aInputs rejected: r11,TGTCCACTGTCAGGG; r22,ATAATAGAGGACGGA, r93,TGAGCTCTTCCAGGT. Key: YES, number of Human move YES
gates modified; 5′ AND, number of 5′ AND loops modified; 3′ AND, number of 3′ AND loops modified; NOT, number of NOT loops modified; Modified
(M), Number of modified human move gate loops; +, Number of loops with 5′ and 3′ terminal nucleotides added; -, number of loops with 5′ and 3′
terminal nucleotides removed; R, number with 5′ and 3′ loops reversed; x, number with NOT loop removed.
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that by integrating more than 100 molecular logic gates in a
single system, MAYA-II represents the first “medium-scale
integrated molecular circuit” in solution. This increased
complexity of MAYA-II has enabled refinement of our
deoxyribozyme logic gate model, allowing the development
of design principles for optimizing digital gate behavior35
and the generation of a library of known input sequences
(Table 1). Because our gates are made from DNA, we also
expect them to be amenable to evolutionary methods for
development.36Our symmetrical game strategy enabled the
entire game to be essentially encoded as a series of YES
and AND gates, which take into account only two human
moves: the current and preceding. We propose that a total
of 152 gates could be used to encode any symmetrical game
strategy into any automaton using the above-defined 32
inputs and allowing for subsequent additional activation in
already played wells. We are currently constructing the full
set of gates for the development of selection procedures to
obtain fully trainable automata.
The practical applications of this massive parallel integra-
tion are more likely in oligonucleotide analysis rather than
competition with silicon in high-speed computing. For
example, the ability to detect and analyze combinations of
multiple DNA sequences within minutes has direct applica-
tions in microarray style diagnostics. Automata the size of
MAYA-II analyze the space of 232possible subsets of the
32 input oligonucleotides and partition it into equivalence
classes signaled by unique two-color, eight-well patterns, for
a total of up to 216) 65 536 patterns. Based on MAYA-II,
we are currently developing several systems for multiplex
SNP detection and viral lineage attribution. Moreover, the
versatility of the input and output system allows coupling
of logic gate processing to both upstream and downstream
events, such as the detection and release of small molecules
and the inhibition of enzymatic activity.37We are investigat-
ing the depth to which serial connectivity can be achieved
and are considering a reset function to allow gates to perform
multiple tasks. These developments should allow for the
application of deoxyribozyme logic gate technology in
bidirectional signaling events and pave the way for the next
generation of fully autonomous molecular devices.
Acknowledgment. This material is based upon work
supported by the National Science Foundation under Grants
IIS-0324845, CCF-0523317, and CHE-0533065, Searle Fel-
lowship to M.N.S., and NSF CAREER Grant 0238027 to
D.S. The authors wish to thank Donald Landry for support,
and the corresponding author gratefully acknowledges An-
drew Macdonald for thoughtful discussions and encourage-
ment.
Supporting Information Available: Detailed experi-
mental methods, additional figures, all logic gate sequences,
and results from all 76 games. This material is available free
of charge via the Internet at http://pubs.acs.org.
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Figure 3. Human move gates: (A) Human move gates were
designed from 8.17 deoxyribozyme-based logic gates.7,24,34Upon
addition of activating input, these gates cleave substrate SF to
produce product PFand an increase in fluorescein fluorescence (F).
Lengthening of the substrate binding region created 8.17.1, with
more reliable enzyme activity. The insert shows a truth table of
logic gate behavior. (B) Raw fluorescence activity (F) of 8.17 and
8.17.1-based gates (20 nM) using 1 µM SF in the presence
(triangles) or absence (stars) of 1 µM inputs. Gates derived from
8.17 were variably active, as demonstrated here by Yes 13 (active)
and Yes 81 (not active), whereas gates derived from 8.17.1 were
always active, as displayed for Yes 13.1 and Yes 81.1
2602
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