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

A Mechanical Turing Machine:Blueprint for a Biomolecular Computer

Udi ShapiroEhud Shapiro

Medicine in 2050

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

Medicine in 2050: “Doctor in a Cell”

Programmable ComputerProgrammable Computer

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

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

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”

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

Logical Design for an Intra-Cellular Computer

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)

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)

The Turing Machine

D A T A

INFINTE TAPE

Finite Control may be in one of finitely many states S0,S1,…,Sn

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

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”

Configuration

DDCCAA BB SS

State symbol and location of read/write headState symbol and location of read/write head

Alphabet tape symbolsAlphabet tape symbols

DDCCAA BBS0S0

Initial configurationInitial configuration

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

Example Control Program:Well-formed Expressions

Example computation

####

##

Scan right to first )Scan right to first )

Scan left to first (Scan left to first (

Scan right to first )Scan right to first )

Scan left to left parenScan left to left paren

Stop, not acceptingStop, not accepting

( ( (S0

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)

Example Control Program:Well-formed Expressions

SS00

(( )) ))

MovieMovie

A Mechanical Turing Machine

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Alphabet monomersAlphabet monomers

Transition monomersTransition monomers

ControlControl

Device Components

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Alphabet Monomers

Side group representing symbolSide group representing symbol

Left LinkLeft Link Right LinkRight Link

AA DDCCBB

Alphabet PolymerAlphabet PolymerAlphabet MonomerAlphabet Monomer

AA

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Transition Molecules

S’S’

AA SS

Transition Molecule forTransition Molecule forA,S S’,X

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’

AA SS

Transition Molecule forTransition Molecule forA,S A,S S’,X S’,X

Transition Molecule forTransition Molecule forS,A X,S’

S’S’

AA SS

A Loaded Transition Molecule forA Loaded Transition Molecule forA,S S’,A’

A’A’

S’S’

AASS

Example Configuration

DDCCAA BB S’S’

AASS

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Trace polymer

AA BB CC

S0S0S0S0

S1S1

DD

S1S1

DD

EES2S2

Tape polymer

Current state

Example Configuration

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S1S1

DD

Example Transition: Before

AA

BB

CC

S0S0 S0S0

S1S1

DD

EE

S2S2 S2S2

CC

FF

S3S3

The device in operation: Before

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Example Transition: After

AA

BB

CC

S0S0 S0S0

S1S1

DD

S1S1

DD

EE

S2S2 S2S2

CC

FF

S3S3

The device in operation: After

Example Control Program:Well-formed Expressions

((

((S0S0

S0S0 ##

##S0S0

S0S0 ##

))S0S0

S1S1 ##

bbS0S0

S2S2

##

S1S1((

S0S0 ##

S1S1##

S1S122

##

S2S2##

S2S2 ##

S2S2bb

S3S3

S0

L

RR

LLS0

S0

Example Computation

MovieMovie

We show only “good” random moves

Example Trace Polymer

A’A’

S’S’

AA SS

A’A’

S’S’

AA SS

A’A’

S’S’

AA SS

A’A’

S’S’

AASS

AA

AA

AA

AA

Implementation

Implementation

Alphabet Molecules Transition Molecules

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33

55

22

22

4466

55

33

66

44

1111

BeforeBefore AfterAfter

A TransitionA Transition

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

Cellular Input

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

Cellular output

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

Ultimately...

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...

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

Wanted: Single recognition site, constant distance splicer

D = N bpD = N bp