DNA Computation and Circuit Construction

1. DNA Computation and Circuit Construction Isabel Vogt 2012

2. What is computation? • 2+2=4 • RULE: 1 if and only if A=1 and B=1, else 0 Computation

3. Computer Output Inputs

4. DeoxyriboNucleicAcid (DNA)

5. How can we engineer DNA to computesolutions to problems?

6. DNA Replication = Information Transfer

8. 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 vinand ends at vout, and passes through every vertex exactly once. Vout Vin 5 1 0 4 2 3

9. Generate random paths through the graph • Keep only those paths that begin with vin and end with vout • If G has n vertices, keep only those paths that enter exactly n vertices • Keep only those paths that enter each vertex at least once • If any paths remain, say YES, if not NO 150234 05 15150234 02315 243 051515 024315 0234315 4501

10. Parallel Computing With DNA

11. Unique 20mer for each vertex • Generate random paths through the graph Mix together for all vertices vi in Gand for all edges eij Unique 20mer for every existing edge Last 10mer of Oi and first 10mer of Oj Random Path through G Splints for G-specific ligation

12. Keep only those paths that begin with vin and end with vout … … PCR copy region between (inclusive) and

13. Separate oligomers based upon size and keep only those of n(20) bases • If G has n vertices, keep only those paths that enter exactly n vertices MW 120mer

14. Keep only those paths that enter each vertex at least once Pull down for every vertex

15. Ligate G-specific paths through DNA hybridization • Run PCR with primers for and . • Separate oligomers on a gel and keep only those with length n(20) • Affinity chromatography for each vertex sequence • Amplify and run on a gel for a band • Generate random paths through the graph • Keep only those paths that begin with vin and end with vout • If G has n vertices, keep only those paths that enter exactly n vertices • Keep only those paths that enter each vertex at least once • If any paths remain, say YES, if not NO

16. 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?

18. Branch Migration No Reaction Irreversible Reaction Reversible Reaction(see-sawing) Chen and Ellington. CurrOpin Biotech, 21: 2010

19. See-sawing Reporting Thresholding

20. Reporter S6 T* S6* Input S2 Gate S6 S5 T S5 T T* S5* T*

21. Reporter S6 T* S6* S5 S6 S2 S5 T T T* S5* T*

22. Reporter S6 T* S6* Output S5 S6 T T S2 S5 T* S5* T*

23. Reporter S5 S6 T T T* S6* S2 S5 T* S5* T* “Reporting”

24. Reporter S6 T* S6* Output S5 S6 T T S2 S5 T* S5* T*

25. Reporter S6 T* S6* Input S2 S6 S5 T S5 T T* S5* T* “See-Sawing”

26. Fueled see-sawing: catalytic output release Gate:Output S6 S5 T Input S2 T* S5* T* S5 T Fuel S7 S5 XS T

27. Entropically Driven – back of the envelope calculation For Fuel strands catalyze complete release of output

28. Thresholding: Limited output release Gate:Output S6 S5 T Input S2 T* S5* T* S5 T Threshold 0.5 eq S5 No Toehold Longer Toehold S5* S2* T*

29. Irreversiblepreferential binding • Rate increases exponentially with length of toehold sequence • No toehold on the opposite side makes the reverse reaction negligible Threshold 0.5 eq S5 No Toehold Longer Toehold S5* S2* T* Zhang and Winfree. JACS,131: 2009

31. FAN OUT • Single input • If above threshold – catalytically releases all output • FAN IN • Many inputs • Stoichiometrically releases single output

33. 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

34. OR Gate • Add either x0 or x1 to indicate OFF or ON • OR Gate: OR for ON (output = 1) or AND for OFF (output =0) OFF ON

36. Why did this work? • Simplicity • Abstraction • Tolerance Temperature • A lot of careful troubleshooting! Clamps Toehold length

37. Why do we care? • Functional, useful computers? • Computation + DNA nanostructures • See-sawing in RNAi and miRNAs? • Regulation in an “RNA world”