A Mechanical Turing Machine Blueprint for a Biomolecular

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 = 0. 25 micron in Pentium II 1 micron E. Coli

Scaling the ribosome

Scaling the ribosome 1)Mbyte(

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 05/12/2020

1900 Hilbert Posed a Problem n n 23 rd: 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) 05/12/2020

1936 Turing had an answer. . . n n n Hilbert’s 23 rd 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 n and established its universality (Church-Turing thesis) 05/12/2020

The Turing Machine INFINTE TAPE D AT A Read/Write Head may read and/or write a symbol, and move one cell to the left or to the right S 7 Tape Cell may contain one symbol of a given tape alphabet Finite Control may be in one of finitely 05/12/2020 many states S 0, S 1, …, Sn

Transitions n n n 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” 05/12/2020

Configuration A B S C D State symbol and location of read/write head Alphabet tape symbols S 0 A Initial configuration 05/12/2020 B C D

Example Control Program: Well-formed Expressions n n n Accept well-formed expressions over “(“ and “)“ (), (()), ()(), (())() are well-formed, ((), )(, ()), ()()(, are not. States: • S 0: Scanning right, seeking right parenthesis • S 1: Right paren found, scan left seeking left paren. • S 2: Right end of string found, scan left, accept if no excess parens found. • S 3: Accept 05/12/2020

Example computation S 0 ) # ) ) # Scan right to first ) Scan left to first ( # Scan right to first ) Scan left to left paren Stop, not accepting 05/12/2020

Example Control Program: Well-formed Expressions n n n n S 0, ( (, S 0, # , #, S 0, ) #, S 1 (erase right paren and enter S 1) S 0, blank #, S 2 (end of string, enter S 2) (, S 1 S 0, # (erase left paren and enter S 0) , #S 1 S 1, # #, S 2, # blank, S 2 S 3, # (end of string, enter S 3) 05/12/2020

S 0 Movie ) ( (

A Mechanical Turing Machine 05/12/2020

Device Components Alphabet monomers Transition monomers Control

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

Transition Molecules S’ Transition Molecule for A, S S’, X A n n S One side group representing target state S’ Three recognition sites: source state S, source symbol A, target symbol A’

Transition Molecules S’ S’ A S S Transition Molecule for A, S S’, X S, A X, S’ S’ A’ A S A Loaded Transition Molecule for A, S S’, A’

Example Configuration A B S’ S A C D

Example Configuration Current state Tape polymer A B C S 2 E D D S 1 Trace polymer S 0

The device in operation: Before Example Transition: Before A B S 0 D D S 1 C C S 3 S 2 F E

The device in operation: After Example Transition: After A B S 0 D S 1 C C S 3 S 2 F E

Example Control Program: Well-formed Expressions ) S 0 # S 1 S 0 ) S 0 # S 2 ( S 0 b S 3 # b S 2 # S 1 # S 2 # ) S 1 # S 2 2 S 0

Example Computation We show only “good” random moves Movie

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

Implementation

Implementation Alphabet Molecules Transition Molecules

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

The Device

A 4 3 1 5 2

B 1 a 2 a 1 b 2 b 3 a 5 a 4 a 3 b 5 b Front 4 a 4 b 3 a 5 a 5 b 4 b Back 3 b

Device ~ Ribosome n n n 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 n n 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 n n n 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 n n n 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 n n n 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 n n n 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 n Cascade several computer along history polymer Each computer checks computation of previous computer, aborts/corrects errors Only last computer produces visible output

Related work n n n 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