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

€

O i

€

Oi

€

O 1

€

O 2

€

O1

€

O2

€

O1

€

O2€

O 1

€

O 2

1. Generate random paths through the graph

€

Oi

Unique 20mer for each vertex

€

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

€

O i

€

Oi→ j

€

O0→2

€

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

€

O 0

€

O 2

€

O 6… …

€

O0

€

O 6

PCR copy region between (inclusive) and

€

O 0

€

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

€

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”