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. Scaling the ribosome
E. Coli
1 micron
 = 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 D A T A
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. Configuration D C A B S State symbol and location of read/write head
Alphabet tape symbols D C A B S0
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. Example computation ( # # # S0 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,)  #,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 *
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Device Components
Alphabet monomers
Control
Transition monomers *

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

30. Transition Molecule for*
Transition Molecules
כ'/ניסן/תשע"ז07/16/96 S’
Transition Molecule for
A,S  S’,X A S
One side group representing target state S’
Three recognition sites: source state S, source symbol A, target symbol A’ *

31. Transition Molecules A,S  S’,X S,A  X,S’ A,S  S’,A’*
Transition Molecules
כ'/ניסן/תשע"ז07/16/96 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. Example ConfigurationD C A B S’ S

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

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

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

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

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

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

39. Implementation

40. Implementation Transition Molecules Alphabet Molecules *
כ'/ניסן/תשע"ז07/16/96
Transition Molecules
Alphabet Molecules *

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

42. The Device *
כ'/ניסן/תשע"ז07/16/96 *

43. *
כ'/ניסן/תשע"ז07/16/96 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 *
כ'/ניסן/תשע"ז07/16/96 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*
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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*
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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

51. Error Detection and Correction
Cascade several computer along history polymer
Each computer checks computation of previous computer, aborts/corrects errors
Only last computer produces visible output

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