A Mechanical Turing Machine: Blueprint for a Biomolecular Computer

1. A Mechanical Turing Machine:Blueprint for a Biomolecular Computer Udi Shapiro Ehud Shapiro

2. “One can imagine the eventual emergence of a general purpose computer consisting of nothing more than a single macromolecule conjugated to a ribosomelike collection of enzymes that act on it”. --- Len Adelman, 1994.

3. 1 micron E. Coli Scaling the ribosome  = 0.25 micron in Pentium II

4. Scaling the ribosome

5. Scaling the ribosome (1Mbyte)

6. Scaling the ribosome Ribosomes translate RNA to Proteins RNA Polymerase transcribes DNA to RNA

7. Scaling the Ribosome 25 nm

8. Ribosomes in operation (= protein) Computationally: A stateless string transducer from the RNA alphabet of nucleic acids to the Protein alphabet of amino acids

9. Transfer RNA

10. Ribosome Components

11. A Loaded Ribosome

12. Protein construction (0)

13. Protein construction (1)

14. Protein construction (2)

15. Protein construction (3)

16. Ribosomes in operation

17. The Turing Machine

18. 1900 Hilbert Posed a Problem • 23rd: Find a method for deciding the truth or falsity of any statement of predicate calculus (decision procedure) • Part of larger program to establish all of mathematics on solid formal foundation, by proving every mathematical theorem mechanically from “first principles” (first order logic and elementary set theory)

19. 1936 Turing had an answer... • Hilbert’s 23rd problem has no solution, i.e., there is no such procedure • The proof required to formalize the notion of a procedure • So Turing defined a “pencil-and-paper” computation device, now called the Turing Machine • and established its universality (Church-Turing thesis)

20. The Turing Machine INFINTE TAPE D A T A Read/Write Head may read and/or write a symbol, and move one cell to the left or to the right Tape Cell may contain one symbol of a given tape alphabet S7 Finite Control may be in one of finitely many states S0,S1,…,Sn

21. Transitions • If the control is in state S and the read/write head sees symbol A to the left [right], then change state to S’, write symbol A’, and move one cell to the left [right]. • S,A A’,S’ or • A,S S’,A’ where A can be “blank”

22. A B S C D S0 A B C D Configuration State symbol and location of read/write head Alphabet tape symbols Initial configuration

23. Example Control Program:Well-formed Expressions • Accept well-formed expressions over “(“ and “)“ • (), (()), ()(), (())() are well-formed, ((), )(, ()), ()()(, are not. • States: • S0: Scanning right, seeking right parenthesis • S1: Right paren found, scan left seeking left paren. • S2: Right end of string found, scan left, accept if no excess parens found. • S3: Accept

24. ( ( ( S0 Example computation # Scan right to first ) # Scan left to first ( # Scan right to first ) Scan left to left paren Stop, not accepting

25. Example Control Program:Well-formed Expressions • S0,(  (,S0 • S0,# ,  #,S0 • S0,)  #,S1 (erase right paren and enter S1) • S0,blank  #,S2 (end of string, enter S2) • (,S1  S0,# (erase left paren and enter S0) • #,S1  S1,# • #,S2  S2,# • blank,S2  S3,# (end of string, enter S3)

26. S0 ( ) ) Movie

27. A Mechanical Turing Machine

28. Device Components Alphabet monomers Control Transition monomers

29. Alphabet Monomers Side group representing symbol A A B C D Left Link Right Link Alphabet Monomer Alphabet Polymer

30. Transition Molecules • One side group representing target state S’ • Three recognition sites: source state S, source symbol A, target symbol A’ S’ Transition Molecule for A,S  S’,X A S

31. Transition Molecules S’ S’ A S S A Transition Molecule for A,S  S’,X Transition Molecule for S,A  X,S’ S’ A’ A S A Loaded Transition Molecule for A,S  S’,A’

32. A B S’ C D S A Example Configuration

33. Example Configuration Current state Tape polymer A B C S2 E D S0 S0 D S1 S1 Trace polymer

34. The device in operation: Before Example Transition: Before A B C C S3 S0 S0 D D S2 S2 F E S1 S1

35. The device in operation: After Example Transition: After A B C C S3 S0 S0 D S2 S2 F D E S1 S1

36. Example Control Program:Well-formed Expressions ( # S0 S0 S2 # # S1 b S0 ) S0 S0 # S0 ( # S0 S1 # S2 # # S3 2 S1 S1 ( S2 # S2 b #

37. Example Computation We show only “good” random moves Movie

38. A A A Example Trace Polymer S’ A’ A S S’ A’ A S S’ A’ A S A S’ A’ S A

39. Implementation

40. Implementation Transition Molecules Alphabet Molecules

41. A Transition 4 3 1 1 4 5 6 3 5 6 2 2 Before After

42. The Device

43. A 4 3 5 2 1

44. B 1a 2a 3a 1b 2b 4a 3a 5a 4a 5a 4b 3b 5b 5b 3b 4b Front Back

45. Device ~ Ribosome • Both operate on two polymers symultaneously • Tape polymer ~ messenger RNA • Transition molecule ~ transfer RNA • Trace polymer ~ Polypeptide chain • Move one cell per transition ~ Move one codon per transition

46. Device is unlike the Ribosome • Read/write tape vs. Read-only tape • Transition molecule with side group vs. transfer RNA without side group • Move in both directions vs. Move in one direction • Trace polymer made of transition monomers vs. Polypeptide chain made of amino acids

47. Interaction: Input • Device suspends if needed molecules are not available • Non-deterministic choices can be affected by availability of molecules • Hence device can be sensitive to chemical environment

48. Interaction: Output • Device extended with transition that cleaves the tape polymer and releases one part to the environment • Hence device can synthesize any computable polymer of alphabet molecules • If alphabet monomers are ribonucleic acids, cleaved segment can be used as messenger RNA

49. Applications • Universal programmable computing device that can operate in vivo • Can interact with biochemical environment, be part of biochemical pathways • Can be “sent on a mission”, detect and respond

50. Reversibility • No “erase” operation; displaced alphabet monomers are kept in the history tape • Computer can be made reversible • Answers Bennett’s requirements