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

Medicine in 2050

Medicine in 2050: “Doctor in a Cell” n A genetically modified cell that can operate in the human body n with an intra-cellular computer n that receives input from signal transduction pathways n and, based on its program, produces output to protein synthesis and secretion pathways n effecting any desired molecular medical treatment

Medicine in 2050: “Doctor in a Cell” Programmable Computer

Possible types of molecular output n Drugs (proteins and small molecules) synthesized on-command by the cell n Stress signals detectable by external devices n Encoded “status report” messages decipherable by external devices

Possible types of molecular treatment n Simple stimulus-response n Output multiple drugs based on multiple signals and a decision procedure n Feedback-controlled drug output (titration, negative control) n Any repetitive, programmable combination of the above

Possible types of “cellular doctors” n “Generalists” that circulate in the blood and lymphatic vessels n “Specialists” that reside in specific organs (heart, liver, kidney, bone marrow) n All use the same intra-cellular computer, each with different “software”

A design for an intra-cellular computer should be n Implementable from biomolecules (biopolymers) n that utilize standard operations of biomolecular machines (polymer cleavage, ligation, elongation, movement along a polymer, control via allosteric conformational changes), and can n sense biomolecular input, and n synthesize biomolecular output

Logical Design for an Intra-Cellular Computer

1900 Hilbert Posed a Problem n 23 rd : Find a method for deciding the truth or falsity of any statement of predicate calculus (decision procedure) n 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... n Hilbert’s 23 rd problem has no solution, i.e., there is no such procedure n The proof required to formalize the notion of a procedure n So Turing defined a “pencil-and-paper” computation device, now called the Turing Machine n and established its universality (Church-Turing thesis)

The Turing Machine DATA 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 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]. n S,A  A’,S’ or n A,S  S’,A’ where A can be “blank”

Configuration DCABS State symbol and location of read/write head Alphabet tape symbols DCABS0 Initial configuration

n Accept well-formed expressions over “(“ and “)“ n (), (()), ()(), (())() are well-formed, ((), )(, ()), ()()(, are not. n 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 left to first ( Scan right to first ) Scan left to left paren Stop, not accepting ((( S0

n S0,(  (,S0 n S0,#,  #,S0 n S0,)  #,S1 (erase right paren and enter S1) n S0,blank  #,S2 (end of string, enter S2) n (,S1  S0,# (erase left paren and enter S0) n #,S1  S1,# n #,S2  S2,# n blank,S2  S3,# (end of string, enter S3) Example Control Program: Well-formed Expressions

S0()) Movie

A Mechanical Turing Machine

Alphabet monomers Transition monomers Control Device Components

Alphabet Monomers Side group representing symbol Left Link Right Link ADCB Alphabet Polymer Alphabet Monomer A

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

Transition MoleculesS’ AS Transition Molecule for A,S  S’,X Transition Molecule for S,A  X,S’ S’ AS A Loaded Transition Molecule for A,S  S’,A’ A’ S’ AS

Example ConfigurationDCABS’ AS

Trace polymer ABC S0 S0 S1 D S1 D ES2 Tape polymer Current state Example Configuration

S1 D Example Transition: Before A B C S0S0 S1 D E S2S2 C F S3 The device in operation: Before

Example Transition: After A B C S0S0 S1 D S1 D E S2S2 C F S3 The device in operation: After

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

Example Computation Movie We show only “good” random moves

Example Trace PolymerA’ S’ AS A’ S’ AS A’ S’ AS A’ S’ AS A A A A

Implementation

Alphabet Molecules Transition Molecules

BeforeAfter A Transition

The Device

Device ~ Ribosome n Both operate on two polymers symultaneously n Tape polymer ~ messenger RNA n Transition molecule ~ transfer RNA n Trace polymer ~ Polypeptide chain n Move one cell per transition ~ Move one codon per transition

Device is unlike the Ribosome n Read/write tape vs. Read-only tape n Transition molecule with side group vs. transfer RNA without side group n Move in both directions vs. Move in one direction n Trace polymer made of transition monomers vs. Polypeptide chain made of amino acids

Cellular Input

Computer Input n Device suspends if needed molecules are not available n Non-deterministic choices can be affected by availability of molecules n Hence device can be sensitive to chemical environment

Cellular output

Computer Output n Device extended with transition that cleaves the tape polymer and releases one part to the environment n Hence device can synthesize any computable polymer of alphabet molecules n If alphabet monomers are ribonucleic acids, cleaved segment can be used as messenger RNA

Ultimately...

n Universal programmable computing device that can operate in vivo n Can interact with biochemical environment n Can be “sent on a mission” n Can diagnose, prescribe, synthesize, and deliver...

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

Wanted: Single recognition site, constant distance splicer D = N bp