DNA Computation and Circuit Construction
Isabel Vogt2012
What is computation?
• 2+2=4• RULE: 1 if and only if A=1 and B=1, else 0
A B Output
0 0 0
1 0 0
0 1 0
1 1 1
Computation
Computer
Inputs
Output
DeoxyriboNucleic Acid (DNA)
How can we engineer DNA to computesolutions to problems?
DNA Replication = Information Transfer
The Hamiltonian Path Problem
A directed graph G with vertices vin and vout has a directed Hamiltonian path iff there exists a sequence of one-way edges e1…ei that begins at vin and ends at vout, and passes through every vertex exactly once.
Vin
Vout
2
3
1
4
05
1. Generate random paths through the graph
2. Keep only those paths that begin with vin and end with vout
3. If G has n vertices, keep only those paths that enter exactly n vertices
4. Keep only those paths that enter each vertex at least once
5. If any paths remain, say YES, if not NO
150234
15150234
243
024315
4501
05
02315
051515
0234315
Parallel Computing With DNA
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O i
€
Oi
€
O 1
€
O 2
€
O1
€
O2
€
O1
€
O2€
O 1
€
O 2
1. Generate random paths through the graph
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Oi
Unique 20mer for each vertex
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Oi→ j
Unique 20mer for every existing edge
Last 10mer of Oi and first 10mer of Oj
Mix together for all vertices vi in Gand for all edges eij
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O i
€
Oi→ j
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O0→2
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O2→4€
O 0
€
O 2
€
O 4
Splints for G-specific ligation
Random Path through G
2. Keep only those paths that begin with vin and end with vout
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O 0
€
O 2
€
O 6… …
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O0
€
O 6
PCR copy region between (inclusive) and
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O 0
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O 6
3. If G has n vertices, keep only those paths that enter exactly n vertices
MW
120mer
Separate oligomers based upon size and keep only those of n(20) bases
4. Keep only those paths that enter each vertex at least once
€
O i
€
Oi
Pull down for every vertex
1. Generate random paths through the graph
2. Keep only those paths that begin with vin and end with vout
3. If G has n vertices, keep only those paths that enter exactly n vertices
4. Keep only those paths that enter each vertex at least once
5. If any paths remain, say YES, if not NO
1. Ligate G-specific paths through DNA hybridization
2. Run PCR with primers for and .
3. Separate oligomers on a gel and keep only those with length n(20)
4. Affinity chromatography for each vertex sequence
5. Amplify and run on a gel for a band
€
Oin
€
Oout
• Truly parallel computation• Applicability:
– # oligomeric sequences grows linearly with # edges
– Amount of oligomer scales exponentially
• Efficiency:– Approximately 1020 ligation reaction per second– ΔG ≈ -8 kcal mol-1
– 2 x 1019 reactions for 1 J– 2nd Law of Thermodynamics: 34 x 1019
irreversible rxns per J
The future of computation?
Branch Migration
No Reaction
Irreversible Reaction
Reversible Reaction(see-sawing)
Chen and Ellington. Curr Opin Biotech, 21: 2010
See-sawingReporting
Thresholding
S6*
S6
T*
T*T* S5*
S5 T
S6S5T
S2Input
Gate
Reporter
T*T* S5*
S5 T
S6S5
T
S2
S6*
S6
T*
Reporter
T*T* S5*
S5
S6S5T
S2
T
S6*
S6
T*
Reporter
Output
S6*T*
T*T* S5*
S5
S6S5T
S2
Reporter
T
“Reporting”
T*T* S5*
S5
S6S5T
S2
T
S6*
S6
T*
Reporter
Output
S6*
S6
T*
T*T* S5*
S5 T
S6S5T
S2Input
Reporter
“See-Sawing”
T*T* S5*
S5 T
S6
S5T
S2Input
Fueled see-sawing: catalytic output release
S5 T
S7
Gate:Output
Fuel
XS
Entropically Driven – back of the envelope calculation
€
W0 ≈M!
N!(M −N)!
W1 ≈M!
(N − k)!k!(M −N)!
For
€
N!> (N − k)!k!
⇒ W1 >W0€
k <N
2
Fuel strands catalyze complete release of output
T*T* S5*
S5 T
S6
S5T
S2Input
Thresholding: Limited output release
Gate:Output
Threshold
0.5 eq
S2* T* S5*
S5
Longer Toehold No Toehold
Threshold
0.5 eq
S2* T* S5*
S5
Longer Toehold No Toehold
Irreversiblepreferential binding
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ΔGbinding(kcal /mol)•Rate increases exponentially with length of toehold sequence
•No toehold on the opposite side makes the reverse reaction negligible
Zhang and Winfree. JACS,131: 2009
FAN OUT
•Single input
•If above threshold – catalytically releases all output
FAN IN
•Many inputs
•Stoichiometrically releases single output
Dual-Rail Logic
•Makes use of two different sequences, one for ON and one for OFF
•Each OR, AND, ANDNOT, NAND, NOR gate is constructed by two gates
•Prevents computation before sequences are added
OR Gate
OFF
ON
•Add either x0 or x1 to indicate OFF or ON
•OR Gate: OR for ON (output = 1) or AND for OFF (output =0)
Why did this work?
•Simplicity•Abstraction•Tolerance
Clamps
Toehold length
Temperature
•A lot of careful troubleshooting!
Why do we care?
•Functional, useful computers?
•Computation + DNA nanostructures
•See-sawing in RNAi and miRNAs?
•Regulation in an “RNA world”