2. Existing “autonomous” system Sakamoto & Hagiya State transitions by molecules A transition table:{S  S’} Starting from the initial state, calculate as many as possible following states according to the transition table

3. Molecular implementation Each state is a ss-DNA segment Each state is a ss-DNA segment Each transition S -> S’ is a sequence of S-complementary Each transition S -> S’ is a sequence of S-complementary and S’-complementary DNA The transitions are performed in a PCR-like fashion The transitions are performed in a PCR-like fashionS0S1 S2 The rules: S0 -> S1 S1 -> S2 An “Input”

4. Molecular implementation Each state is a ss-DNA segment Each state is a ss-DNA segment Each transition S -> S’ is a sequence of S-complementary Each transition S -> S’ is a sequence of S-complementary and S’-complementary DNA The transitions are performed in a PCR-like fashion The transitions are performed in a PCR-like fashionS0S1 S2 The rules: S0 -> S1 S1 -> S2

5. Molecular implementation Each state is a ss-DNA segment Each state is a ss-DNA segment Each transition S -> S’ is a sequence of S-complementary Each transition S -> S’ is a sequence of S-complementary and S’-complementary DNA The transitions are performed in a PCR-like fashion The transitions are performed in a PCR-like fashionS0S1 S2 The rules: S0 -> S1 S1 -> S2

6. Molecular implementation Each state is a ss-DNA segment Each state is a ss-DNA segment Each transition S -> S’ is a sequence of S-complementary Each transition S -> S’ is a sequence of S-complementary and S’-complementary DNA The transitions are performed in a PCR-like fashion The transitions are performed in a PCR-like fashionS0S1 S2 The rules: S0 -> S1 S1 -> S2

7. Molecular implementation Each state is a ss-DNA segment Each state is a ss-DNA segment Each transition S -> S’ is a sequence of S-complementary Each transition S -> S’ is a sequence of S-complementary and S’-complementary DNA The transitions are performed in a PCR-like fashion The transitions are performed in a PCR-like fashionS0S1 S2 The rules: S0 -> S1 S1 -> S2

8. Molecular implementation Each state is a ss-DNA segment Each state is a ss-DNA segment Each transition S -> S’ is a sequence of S-complementary Each transition S -> S’ is a sequence of S-complementary and S’-complementary DNA The transitions are performed in a PCR-like fashion The transitions are performed in a PCR-like fashionS0S1 S2 The rules: S0 -> S1 S1 -> S2

9. Molecular implementation Each state is a ss-DNA segment Each state is a ss-DNA segment Each transition S -> S’ is a sequence of S-complementary Each transition S -> S’ is a sequence of S-complementary and S’-complementary DNA The transitions are performed in a PCR-like fashion The transitions are performed in a PCR-like fashionS0S1 S2 The rules: S0 -> S1 S1 -> S2 The result

10. Acknowledgements Kobi Benenson Ehud Keinan Zvi Livneh Tami Paz-Elizur Irit Sagi, Ada Yonath

11. From Turing Machines to Finite Automata A finite automaton is a Turing machine that can only –Move to the right –Read but not write An elementary, well-characterized class of computing devices. Computable (Turing Machines) Context-free (Stack automata) Regular (Finite Automata)

12. Turing Machine and Finite Automaton

13. Example Computation

14. Molecular realization of Finite Automata Input: DNA S, a rest a’ Program: DNA S, a FokI Execution engine: Class-II restriction enzyme FokI, DNA Ligase, ATP

15. S, a rest a’ Basic cycle of automaton Iterative processing of input until the end is reached S, a S ’ Detect the result State-symbol tag S’, a’ rest

16. S0,101

17. S0,101 S0,1 FokI

18. S0,1 FokIS0,101

19. FokI01

20. FokI1S1,0

21. 1S1,0

22. 1S1,0

23. Molecular realization of FA FA Alphabet: {0 = 5’- CTGGCT, 1 = 5’- CGCAGC } 1 = 5’- CGCAGC } States: {S0,S1} S0, 0  S0 S0, 1  S1 S1, 0  S1 S1, 1  S0 S0 S1 0 0 1 1 Transition Table:

24. Representation of states States are not physically separated from the symbols. Subsequences of the alphabet codes represent different states {0 = 5’- CTGGCT, 1 = 5’- CGCAGC }

25. Representation of states {0 = 5’- CTGGCT, 1 = 5’- CGCAGC } CTGG = a combination of S1 and 0 States are not physically separated from the symbols. Subsequences of the alphabet codes represent different states

26. Representation of states {0 = 5’- CTGGCT, 1 = 5’- CGCAGC } GGCT = a combination of S0 and 0 CTGG = a combination of S1 and 0 States are not physically separated from the symbols. Subsequences of the alphabet codes represent different states

27. Representation of states {0 = 5’- CTGGCT, 1 = 5’- CGCAGC } GGCT = GGCT = CTGG = CTGG = CGCA = CGCA = CAGC = CAGC = States are not physically separated from the symbols. Subsequences of the alphabet codes represent different states

28. How Does it Work? Adapters = transition molecules GGATGCCTAC NNNN Fok I (9/13) recognition site S0, 0  S0 S0, 1  S1 S1, 0  S1 S1, 1  S0 3 bp 5 bp 3 bp 1 bp CCGA GTCG GACC GCGT

29. Animation of experiment

30. T110

31. T110

32. T110

33. T110

34. T110

35. T110

36. T110

37. T110

38. T101

39. T101

40. T101

41. T101

42. T101

43. T101

44. T101

45. T110

46. T110

47. T101

48. T110

51. Why autonomous? Fok I and Ligase act in the same environment (NED4 buffer + 1 mM ATP, 18 o C) No interference between input molecules that are at different stages of computation Each molecule is an independent automaton. There are ~10 13 computations running in parallel

52. Computation 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1,10: 50 bp ladder; 2: 101 input; 3: 010010 input; 4: S0-detector; 5: S1-detector 6: Computation result of 101 input; 7: Computation result of 010010 input 8: Computation result of 010100 input; 9: Computation result of 001000 input 150 bp 200 bp S0-result S1-result Inputdegradationproducts Reaction conditions: Environment: 120  l of NEB4 buffer + 1 mM ATP, 18 o C, 80 min Input: 2.5 pmol; Detectors: 1.5 pmol each; Transition molecules: 20 pmol each Fok I: 12 units; T4 Ligase: 120 units S0-d S1-d

53. Proof of Mechanism A complete mixture: Input (010100) ; S0-detector; S1-detector; T1,T2,T3,T4; Fok I; T4 DNA Ligase The gel shows a “component removal” experiment, where each component was omitted from the complete mixture and the result was compared to the predicted outcome 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1,12: 50 bp ladder 2: complete mixture 3: No Input 4: No S0-detector 5: No S1-detector 6: No T1 7: No T2 8: No T3 9: No T4 10: No Fok I 11: No T4 DNA Ligase PredictedActual +--+------+--+-?---- Result band

54. Estimation of system correctness 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Detectors are labeled with 32 P S0-result S1-result S1-detector S0-detector There are possible “wrong” bands. Their origin is currently being determined. At any rate, the correctness is >95% Exact error rate still needs to be determined Lanes: 1,7: 50 bp ladder 2: 32 P-S0-detector 3: 32 P-S1-detector 4: Computation over 010010 5: Computation over 010100 6: Computation over 001000