A Mechanical Turing Machine: Blueprint for a Biomolecular Computer

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

2. Medicine in 2050

3. Medicine in 2050: “Doctor in a Cell” • A genetically modified cell that can operate in the human body • with an intra-cellular computer • that receives input from signal transduction pathways • and, based on its program, produces output to protein synthesis and secretion pathways • effecting any desired molecular medical treatment

4. Medicine in 2050: “Doctor in a Cell” Programmable Computer

5. Possible types of molecular output • Drugs (proteins and small molecules) synthesized on-command by the cell • Stress signals detectable by external devices • Encoded “status report” messages decipherable by external devices

6. Possible types of molecular treatment • Simple stimulus-response • Output multiple drugs based on multiple signals and a decision procedure • Feedback-controlled drug output (titration, negative control) • Any repetitive, programmable combination of the above

7. Possible types of “cellular doctors” • “Generalists” that circulate in the blood and lymphatic vessels • “Specialists” that reside in specific organs (heart, liver, kidney, bone marrow) • All use the same intra-cellular computer, each with different “software”

8. Adesign for an intra-cellular computer should be • Implementable from biomolecules (biopolymers) • that utilize standard operations of biomolecular machines (polymer cleavage, ligation, elongation, movement along a polymer, control via allosteric conformational changes), and can • sense biomolecular input, and • synthesize biomolecular output

9. Logical Design for an Intra-Cellular Computer

10. 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)

11. 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)

12. 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

13. 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”

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

15. 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

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

17. 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)

18. S0 ( ) ) Movie

19. A Mechanical Turing Machine

20. Device Components Alphabet monomers Control Transition monomers

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

22. 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

23. 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’

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

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

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

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

28. 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 #

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

30. A A A Example Trace Polymer S’ A’ A S S’ A’ A S S’ A’ A S A S’ A’ S A

31. Implementation

32. Implementation Transition Molecules Alphabet Molecules

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

34. The Device

35. 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

36. 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

37. Cellular Input

38. Computer 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

39. Cellular output

40. Computer 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

41. Ultimately...

42. Ultimately... • Universal programmable computing device that can operate in vivo • Can interact with biochemical environment • Can be “sent on a mission” • Can diagnose, prescribe, synthesize, and deliver...

43. Related work • C. H. Bennett 1970- • “Assignment considered (thermodynamically) harmful” • Reversible computation is the answer • “Hypothetical Enzymatic Turing machine” • L.M. Adelman et al. 1994- • DNA Computing • “Biological steps” (outside intervention) • Self-assembly (tiling) • S. A. Kurtz et al. 1997 • Hypothetical modified ribosome implements string rewriting on RNA

44. Wanted: Single recognition site, constant distance splicer D = N bp