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

“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.

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

Scaling the ribosome

Scaling the ribosome (1Mbyte)

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

Scaling the Ribosome 25 nm

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

Transfer RNA

Ribosome Components

A Loaded Ribosome

Protein construction (0)

Protein construction (1)

Protein construction (2)

Protein construction (3)

Ribosomes in operation

The Turing Machine

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 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

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

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

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

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)

S0 ( ) ) Movie

A Mechanical Turing Machine

Device Components Alphabet monomers Control Transition monomers * כ'/ניסן/תשע"ז07/16/96 Device Components Alphabet monomers Control Transition monomers *

Side group representing symbol * Alphabet Monomers כ'/ניסן/תשע"ז07/16/96 Side group representing symbol A A B C D Left Link Right Link Alphabet Monomer Alphabet Polymer *

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’ *

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’ *

Example Configuration D C A B S’ S

Example Configuration * כ'/ניסן/תשע"ז07/16/96 Example Configuration Current state Tape polymer A B C S2 E D S0 S0 D S1 S1 Trace polymer *

Example Transition: Before * כ'/ניסן/תשע"ז07/16/96 The device in operation: Before Example Transition: Before A B C C S3 S0 S0 D D S2 S2 F E S1 S1 *

Example Transition: After * כ'/ניסן/תשע"ז07/16/96 The device in operation: After Example Transition: After A B C C S3 S0 S0 D D S2 S2 F E S1 S1 *

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

Example Computation We show only “good” random moves Movie

Example Trace Polymer A S’ A’ A S A S’ A’ A S A S’ A’ A S A S’ A’ S A

Implementation

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

A Transition 4 3 1 1 4 5 6 3 5 6 2 2 Before After * כ'/ניסן/תשע"ז07/16/96 A Transition 4 3 1 1 4 5 6 3 5 6 2 2 Before After *

The Device * כ'/ניסן/תשע"ז07/16/96 *

* כ'/ניסן/תשע"ז07/16/96 A 4 3 5 2 1 *

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 *

Device ~ Ribosome Both operate on two polymers symultaneously * כ'/ניסן/תשע"ז07/16/96 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 *

Device is unlike the Ribosome * כ'/ניסן/תשע"ז07/16/96 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 *

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

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

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

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

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

Related work C. H. Bennett 1970- * Related work כ'/ניסן/תשע"ז07/16/96 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 *