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Design of a biomolecular Device that executes process Algebra Urmi Majumder and John Reif Department of Computer Science Duke University DNA15, JUNE 10, 2009

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Outline Process Algebra: A model of computation motivation, challenges and goals Whiplash PCR machines for molecular Process Algebra simulation of process algebra constructs with whiplash pcr machines summary of results

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Outline Process Algebra: A model of computation motivation, challenges and goals Whiplash PCR machines for molecular Process Algebra simulation of process algebra constructs with whiplash pcr machines summary of results

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process Algebra formal semantics of concurrent communicating processes execute distinct programs in parallel communicate via handshaking protocol stochastic ∏-calculus specification of probabilities for process behavior

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main constructs 5 Secondary Constructs Sequential Composition Process execution in sequence Replication Create child processes Summation Choose from multiple possible operations Primary Constructs Interaction Delay Operation Parallel Composition Figure adopted from Artificial Biochemistry, L Cardelli, Algorithmic Bioprocesses, 2008

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Outline Process Algebra: A model of computation motivation, challenges and goals Whiplash PCR machines for molecular Process Algebra simulation of process algebra constructs with whiplash pcr machines summary of results

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goal simulate process algebraic systems with biomolecules simulate constructs with biomolecules stochastic delay operation process communication parallel composition other secondary constructs

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motivation inspiration from biology inter-cellular communication molecular communication nano-scale distributed computing nano-scale sensing

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tiling assemblies + hybridization chain reaction rfrf r b,2 rfrf rfrf r b,1 FIGURE ADOPTED FROM EVANKO, 2004

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whiplash pcr machines State S1 a i b i a i+1 b i+1 a i-1 b i-1 anbnanbn a1b1a1b1 ajbjajbj ai*ai* Current State Rule j Current state of Rule i-1 Next state of Rule i-1 n rules transition table Stopper

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whiplash pcr machines ai*ai* State S2 a i b i a i+1 b i+1 a i-1 b i-1 anbnanbn a1b1a1b1 ajbjajbj Polymerase Next state copied a i * b i * State S3 a i b i a i+1 b i+1 a i-1 b i-1 anbnanbn a1b1a1b1 ajbjajbj Heat

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whiplash pcr machines a i * b i * State S4 a i b i a i+1 b i+1 a i-1 b i-1 anbnanbn a1b1a1b1 ajbjajbj Cool a j * = b i * State S5 a i b i a i+1 b i+1 a i-1 b i-1 anbnanbn a1b1a1b1 ajbjajbj Transition from State i to State j State S2

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challenges local execution of distinct programs parallel execution no interference feature supported by tiling assemblies, hybridization chain reaction, whiplash pcr machines handshaking communication dispatch of carrier molecules insufficient needs acknowledgement exactly same two processes should communicate repeatedly

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locality & molecular process algebraic systems free-floating rule molecules compute globally no guarantee on exactly same processes communicating repeatedly communication via release + capture of carrier molecules TILING ASSEMBLIES & HCR

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locality & molecular process algebraic systems inputs and programs in close proximity guaranteeing parallel execution of distinct programs can be connected via tethering dna nanostructure allowing same two processes to communicate repeatedly WHIPLASH PCR MACHINES

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locality & molecular process algebraic systems Supporting Nanostructure P1P1 P2P2 P1P1 P2P2 Interaction Hybridization INTERPROCESS COMMUNICATION IN MOLECULAR PA SYSTEMS

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WPCR machines for molecular PA systems biochemical techniques hybridization polymerization restriction multi-temperature THERMAL CYCLE stem-loops FOR DETERMINING EXTENT OF INFORMATION EXCHANGE

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Outline Process Algebra: A model of computation motivation, challenges and goals Whiplash PCR machines for molecular Process Algebra simulation of process algebra constructs with whiplash pcr machines summary of results

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Whiplash PCR

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Outline Process Algebra: A model of computation motivation, challenges and goals Whiplash PCR machines for molecular Process Algebra simulation of process algebra constructs with whiplash pcr machines summary of results

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STochastic delay operation

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a i1 a i2 x a i2 * a i3 b i a i1 * a i3 * a i2 * a i2 x* STATE 1 COOL (to T 1 ) a i1 a i2 x a i2 * a i3 b i a i1 * a i2 * a i2 x* a i3 * STATE 2 POLYMERASE BINDS

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STochastic delay operation a i1 a i2 x a i2 * a i3 b i a i1 * a i2 * a i2 x* a i3 * STATE 3 a i1 a i2 x a i2 * a i3 b i a i1 * a i2 * a i2 x* a i3 * bi*bi* STATE 4 HEAT (to T 0 )

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STochastic delay operation a i1 bi bi a i3 a i2 * x a i2 a i1 * a i2 * a i2 x* a i3 * bi*bi* a j1 *a j2 *x*a j2 ya j3 * STATE 5 a i2 * a i3 a i1 * a i3 * a i2 * a i2 x* a i1 a i2 x bibi a j2 * a j3 a j1 a j2 x bjbj x* a j2 * a j2 a j1 * STATE 6 a j3 * STATE 3 COOL (to T 1 )

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Parallel Composition

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PARALLEL Composition x a 22 * a 23 b 2 a i1 a i2 x a i2 * a i3 b i x a n2 * a n3 b n a i1 * x* a i2 a i3 * a i2 * a’ 12 x’ a’ 12 * a’ 13 b’ 1 a’ i1 a’ i2 x’ a’ i2 * a’ i3 b’ i x’ a’ n2 * a’ n3 b’ n a’ n1 * x’* a’ n2 * a’ n3 * a’ n2 * CASE: A a’ n1 a n1 a n2 a 21 a 22 a’ 11 a’ n2 DIFFERENT TRANSITION RULES DIFFERENT CURRENT STATES

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PARALLEL Composition x a 22 * a 23 b 2 a i1 a i2 x a i2 * a i3 b i x a n2 * a n3 b n a i1 * x* a i2 a i3 * a i2 * a 11 a 12 x a 12 * a 13 b 1 a i1 a i2 x a i2 * a i3 b i a n2 x a n2 * a n3 b n a n1 * x* a n2 * a n3 * a n2 * CASE: B a n1 a n2 a 21 a 22 SAME TRANSITION RULES DIFFERENT CURRENT STATES

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interprocess communication

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a wpcr machine simulating interprocess communication DELAY IN PROCESS INTERACTION = max(time required by interacting processes to reach appropriate state) SIMULATE COMPLEMENTARY SYNCHRONOUS INTERACTION P1’S CURRENT STATE CANNOT BIND WITH ANY OF ITS TRANSITION RULES AFTER M TRANSITIONS P2’S CURRENT STATE CANNOT BIND WITH ANY OF ITS TRANSITION RULES AFTER N TRANSITIONS EACH CAN RESUME STOCHASTIC DELAY OPERATION AFTER MUTUAL INTERACTION AND MODIFICATION

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a wpcr machine simulating interprocess communication HOW TO IMPLEMENT COMMUNICATION BETWEEN PROCESSES P1 AND P2? ENCODE IN P1’S CURRENT STATE (3’ END) THE CURRENT STATE OF ONE OF THE TRANSITION RULES OF P2 ENCODE IN P2’S CURRENT STATE (3’ END) THE CURRENT STATE OF ONE OF THE TRANSITION RULES OF P1 ALLOW THE CURRENT STATES OF P1 AND P2 TO HYBRIDIZE USING A WATSON CRICK COMPLEMENTARY REGION COPY THE DESIRED CURRENT STATES PREVENT COPYING OF EXTRA SYMBOLS BY USING STEM-LOOPS AND NON-STRAND-DISPLACING POLYMERASE RESUME STOCHASTIC DELAY OPERATION FOR EACH PROCESS

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interprocess communication a i1 bi bi a i3 a i2 * x a i2 a i1 * a i2 * a i2 x* a i3 * P1: STATE 1 a’ i1 b’ i a’ i3 a’ i2 * x’ a’ i2 P2: STATE 1 P2P2 a’ i1 * a’ i3 * a’ i2 x’* a’ i2 * MULTIPLE STATE TRANSITIONS a m1 bm bm a m3 a m2 * x a m2 a k1 * a k2 * a k2 x* P1: STATE N a’ m1 b’ m a’ m3 a’ m2 * x’ a’ m2 P2: STATE M P2P2 a’ k1 * a’ k2 x’* a’ k2 * d1d1 c1c1 c2c2 d2d2 c1*c1* c2*c2* x’*a’ m2 a’ m3 * x*a m2 a m3 * COOL (to T 2 )

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interprocess communication a m2 * a m3 a k1 * d 1 c 1 a k2 * a k2 a m1 a m2 x bmbm c2c2 a’ m2 * a’ m3 a’ k1 * c* 2 d 2 a’ k2 * a’ k2 a’ m1 a’ m2 x’ b’ m c* 1 P2P2 P1P1 (P1, P2) : STATE 1 x* x’* a m2 * a m3 a k1 * d 1 c 1 a k2 * a k2 a m1 a m2 x bmbm c2c2 a’ m2 * a’ m3 a’ k1 * c* 2 d 2 a’ k2 * a’ k2 a’ m1 a’ m2 x’ b’ m c* 1 P2P2 P1P1 x* x’* (P1, P2) : STATE 2 POLYMERIZE

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interprocess communication a m2 * a m3 a k1 * d 1 c 1 a k2 * a k2 a m1 a m2 x bmbm c2c2 a’ m2 * a’ m3 a’ k1 * c* 2 d 2 a’ k2 * a’ k2 a’ m1 a’ m2 x’ b’ m c* 1 P2P2 P1P1 x’* x* (P1, P2) : STATE 3 HEAT (to T 0 ) a m1 bm bm a m3 a m2 * x a k1 * a k2 * a k2 x* P1: STATE N+1 a’ m1 b’ m a’ m3 a’ m2 * x’ a’ m2 P2: STATE M+1 P2P2 a’ k1 * a’ k2 x’* a’ k2 * d1d1 c1c1 c2c2 d2d2 c1*c1* c2*c2* d1*d1* d2*d2* a m2

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interprocess communication COOL (to T 1 ) Stochastic Delay Operation MULTIPLE STATE TRANSITIONS x’ a’ m2 * a’ m3 b’ m a’ k2 * a’ k2 x’* P2: STATE M+2 P2P2 x a m2 * a m3 b m a k2 * a k2 x* P1: STATE N+2 P1P1 a’ m2 a’ m1 d2d2 c1*c1* c2*c2* d1*d1* d1d1 c2c2 c1c1 d2*d2* a m1 a m2

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limitations of Wpcr simulation of pa LIMITATIONS OF ORIGINAL WPCR MACHINE: BACK-HYBRIDIZATION Figure from Displacement Whiplash PCR: Optimized Architecture and Experimental Validation, DNA 10, LNCS 4287, pgs: 393-403, 2006 Back-hybridization is a phenomenon where a hairpin with a longer double stranded (ds) DNA region is preferentially formed over one with a shorter ds-DNA region.

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Outline Process Algebra: A model of computation motivation, challenges and goals Whiplash PCR machines for molecular Process Algebra simulation of process algebra constructs with whiplash pcr machines summary of results

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summary process algebra run processes in parallel (concurrency) send and receive data along a communication channel (interaction) Wpcr machines input and program local to the machine concurrent processes in original wpcr machine our modification allows interaction open question can we remove thermal cycles?

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Questions?

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Sequential composition

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restricted replication

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summation

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