A Mechanical Turing Machine: Blueprint for a Biomolecular Computer

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A Mechanical Turing MachineBlueprint for a
Biomolecular Computer

• Udi Shapiro
• Ehud Shapiro

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Medicine in 2050
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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

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Medicine in 2050 Doctor in a Cell
Programmable Computer
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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

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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

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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

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A design 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

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Logical Design for an Intra-Cellular Computer
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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)

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1936 Turing had an answer...

• Hilberts 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)

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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
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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

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Configuration
State symbol and location of read/write head
Alphabet tape symbols
Initial configuration
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Example Control ProgramWell-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

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Example computation

Scan right to first )

Scan left to first (

Scan right to first )
Scan left to left paren
Stop, not accepting
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Example Control ProgramWell-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)

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Movie
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A Mechanical Turing Machine
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Device Components
Alphabet monomers
Control
Transition monomers
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Alphabet Monomers
Side group representing symbol
A
D
C
B
A
Left Link
Right Link
Alphabet Polymer
Alphabet Monomer
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Transition Molecules
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

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Transition Molecules
S
S
A
S
A
S
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
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Example Configuration
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Example Configuration
Current state
Tape polymer
A
B
C
E
S2
S0
D
S0
D
S1
S1
Trace polymer
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Example Transition Before
The device in operation Before
A
B
C
C
S3
D
S0
S0
D
S2
S2
F
E
S1
S1
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Example Transition After
The device in operation After
A
B
C
C
S3
S0
S0
D
D
S2
S2
F
E
S1
S1
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Example Control ProgramWell-formed Expressions
(

S0
S0

S2

S1
b
)
S0
S0
S0
S0

(

S0

S1
S2


S3
2
S1
S1
(
S2

S2
b

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Example Computation
We show only good random moves
Movie
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Example Trace Polymer
S
A
A
S
S
A
A
S
S
A
A
S
S
A
A
A
S
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Implementation
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Implementation
Transition Molecules
Alphabet Molecules
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A Transition
4
3
1
1
4
5
6
3
5
6
2
2
Before
After
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The Device
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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

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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

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Cellular Input
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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

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Cellular output
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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

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Ultimately...
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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...

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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

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Wanted Single recognition site, constant
distance splicer
D N bp