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A Mechanical Turing Machine: Blueprint 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” 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

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

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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

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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

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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”

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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

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Logical Design for an Intra-Cellular Computer

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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)

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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)

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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

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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”

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

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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

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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 ((( S0

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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

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S0()) Movie

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A Mechanical Turing Machine

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Alphabet monomers Transition monomers Control Device Components

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

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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’

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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

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Example ConfigurationDCABS’ AS

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

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

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

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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

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Example Computation Movie We show only “good” random moves

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

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Implementation

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Alphabet Molecules Transition Molecules

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3 5 2 2 4 6 5 3 6 4 1 1 BeforeAfter A Transition

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The Device

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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

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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

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Cellular Input

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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

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Cellular output

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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

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Ultimately...

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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...

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Related work n C. H. Bennett 1970- “Assignment considered (thermodynamically) harmful” Reversible computation is the answer “Hypothetical Enzymatic Turing machine” n L.M. Adelman et al. 1994- DNA Computing “Biological steps” (outside intervention) Self-assembly (tiling) n 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

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