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DNA Computation and Circuit Construction Isabel Vogt 2012

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What is computation? 2+2=4 RULE: 1 if and only if A=1 and B=1, else 0 ABOutput 000 100 010 111 Computation

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Computer Inputs Output

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DeoxyriboNucleic Acid (DNA)

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How can we engineer DNA to compute solutions to problems?

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DNA Replication = Information Transfer

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The Hamiltonian Path Problem A directed graph G with vertices v in and v out has a directed Hamiltonian path iff there exists a sequence of one-way edges e 1 …e i that begins at v in and ends at v out, and passes through every vertex exactly once. V in V out 2 3 1 4 0 5

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1.Generate random paths through the graph 2.Keep only those paths that begin with v in and end with v out 3.If G has n vertices, keep only those paths that enter exactly n vertices 4.Keep only those paths that enter each vertex at least once 5.If any paths remain, say YES, if not NO 150234 15150234 243 024315 4501 05 02315 051515 0234315

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Parallel Computing With DNA

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1.Generate random paths through the graph Unique 20mer for each vertex Unique 20mer for every existing edge Last 10mer of O i and first 10mer of O j Mix together for all vertices v i in G and for all edges e ij Splints for G-specific ligation Random Path through G

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2.Keep only those paths that begin with v in and end with v out … … PCR copy region between (inclusive) and

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3.If G has n vertices, keep only those paths that enter exactly n vertices MW 120mer Separate oligomers based upon size and keep only those of n(20) bases

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4.Keep only those paths that enter each vertex at least once Pull down for every vertex

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1.Generate random paths through the graph 2.Keep only those paths that begin with v in and end with v out 3.If G has n vertices, keep only those paths that enter exactly n vertices 4.Keep only those paths that enter each vertex at least once 5.If any paths remain, say YES, if not NO 1.Ligate G-specific paths through DNA hybridization 2.Run PCR with primers for and. 3.Separate oligomers on a gel and keep only those with length n(20) 4.Affinity chromatography for each vertex sequence 5.Amplify and run on a gel for a band

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Truly parallel computation Applicability: – # oligomeric sequences grows linearly with # edges – Amount of oligomer scales exponentially Efficiency: – Approximately 10 20 ligation reaction per second – ΔG ≈ -8 kcal mol -1 – 2 x 10 19 reactions for 1 J – 2 nd Law of Thermodynamics: 34 x 10 19 irreversible rxns per J The future of computation?

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Branch Migration No Reaction Irreversible Reaction Reversible Reaction (see-sawing) Chen and Ellington. Curr Opin Biotech, 21: 2010

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See-sawing Reporting Thresholding

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S6* S6 T* S5* S5 T S6 S5 T S2 Input Gate Reporter

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T* S5* S5 T S6 S5 T S2 S6* S6 T* Reporter

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T* S5* S5 S6S5 T S2 T S6* S6 T* Reporter Output

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S6* T* S5* S5 S6S5 T S2 Reporter T “Reporting”

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T* S5* S5 S6S5 T S2 T S6* S6 T* Reporter Output

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S6* S6 T* S5* S5 T S6 S5 T S2 Input Reporter “See-Sawing”

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T* S5* S5 T S6 S5 T S2 Input Fueled see-sawing: catalytic output release S5 T S7 Gate:Output Fuel XS

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Entropically Driven – back of the envelope calculation For Fuel strands catalyze complete release of output

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T* S5* S5 T S6 S5 T S2 Input Thresholding: Limited output release Gate:Output Threshold 0.5 eq S2* T* S5* S5 Longer Toehold No Toehold

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Threshold 0.5 eq S2* T* S5* S5 Longer Toehold No Toehold Irreversible preferential binding Rate increases exponentially with length of toehold sequence No toehold on the opposite side makes the reverse reaction negligible Zhang and Winfree. JACS,131: 2009

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FAN OUT Single input If above threshold – catalytically releases all output FAN IN Many inputs Stoichiometrically releases single output

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Dual-Rail Logic Makes use of two different sequences, one for ON and one for OFF Each OR, AND, ANDNOT, NAND, NOR gate is constructed by two gates Prevents computation before sequences are added

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OR Gate OFF ON Add either x 0 or x 1 to indicate OFF or ON OR Gate: OR for ON (output = 1) or AND for OFF (output =0)

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Why did this work? Simplicity Abstraction Tolerance Clamps Toehold length Temperature A lot of careful troubleshooting!

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Why do we care? Functional, useful computers? Computation + DNA nanostructures See-sawing in RNAi and miRNAs? Regulation in an “RNA world”

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