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Existing “autonomous” system Sakamoto & Hagiya State transitions by molecules A transition table:{S S’} Starting from the initial state, calculate as many as possible following states according to the transition table

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Molecular implementation Each state is a ss-DNA segment Each state is a ss-DNA segment Each transition S -> S’ is a sequence of S-complementary Each transition S -> S’ is a sequence of S-complementary and S’-complementary DNA The transitions are performed in a PCR-like fashion The transitions are performed in a PCR-like fashionS0S1 S2 The rules: S0 -> S1 S1 -> S2 An “Input”

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Molecular implementation Each state is a ss-DNA segment Each state is a ss-DNA segment Each transition S -> S’ is a sequence of S-complementary Each transition S -> S’ is a sequence of S-complementary and S’-complementary DNA The transitions are performed in a PCR-like fashion The transitions are performed in a PCR-like fashionS0S1 S2 The rules: S0 -> S1 S1 -> S2

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Molecular implementation Each state is a ss-DNA segment Each state is a ss-DNA segment Each transition S -> S’ is a sequence of S-complementary Each transition S -> S’ is a sequence of S-complementary and S’-complementary DNA The transitions are performed in a PCR-like fashion The transitions are performed in a PCR-like fashionS0S1 S2 The rules: S0 -> S1 S1 -> S2

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Molecular implementation Each state is a ss-DNA segment Each state is a ss-DNA segment Each transition S -> S’ is a sequence of S-complementary Each transition S -> S’ is a sequence of S-complementary and S’-complementary DNA The transitions are performed in a PCR-like fashion The transitions are performed in a PCR-like fashionS0S1 S2 The rules: S0 -> S1 S1 -> S2

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Molecular implementation Each state is a ss-DNA segment Each state is a ss-DNA segment Each transition S -> S’ is a sequence of S-complementary Each transition S -> S’ is a sequence of S-complementary and S’-complementary DNA The transitions are performed in a PCR-like fashion The transitions are performed in a PCR-like fashionS0S1 S2 The rules: S0 -> S1 S1 -> S2

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Molecular implementation Each state is a ss-DNA segment Each state is a ss-DNA segment Each transition S -> S’ is a sequence of S-complementary Each transition S -> S’ is a sequence of S-complementary and S’-complementary DNA The transitions are performed in a PCR-like fashion The transitions are performed in a PCR-like fashionS0S1 S2 The rules: S0 -> S1 S1 -> S2

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Molecular implementation Each state is a ss-DNA segment Each state is a ss-DNA segment Each transition S -> S’ is a sequence of S-complementary Each transition S -> S’ is a sequence of S-complementary and S’-complementary DNA The transitions are performed in a PCR-like fashion The transitions are performed in a PCR-like fashionS0S1 S2 The rules: S0 -> S1 S1 -> S2 The result

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Acknowledgements Kobi Benenson Ehud Keinan Zvi Livneh Tami Paz-Elizur Irit Sagi, Ada Yonath

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From Turing Machines to Finite Automata A finite automaton is a Turing machine that can only –Move to the right –Read but not write An elementary, well-characterized class of computing devices. Computable (Turing Machines) Context-free (Stack automata) Regular (Finite Automata)

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Turing Machine and Finite Automaton

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Example Computation

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Molecular realization of Finite Automata Input: DNA S, a rest a’ Program: DNA S, a FokI Execution engine: Class-II restriction enzyme FokI, DNA Ligase, ATP

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S, a rest a’ Basic cycle of automaton Iterative processing of input until the end is reached S, a S ’ Detect the result State-symbol tag S’, a’ rest

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S0,101

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S0,101 S0,1 FokI

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S0,1 FokIS0,101

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FokI01

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FokI1S1,0

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1S1,0

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1S1,0

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Molecular realization of FA FA Alphabet: {0 = 5’- CTGGCT, 1 = 5’- CGCAGC } 1 = 5’- CGCAGC } States: {S0,S1} S0, 0 S0 S0, 1 S1 S1, 0 S1 S1, 1 S0 S0 S1 0 0 1 1 Transition Table:

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Representation of states States are not physically separated from the symbols. Subsequences of the alphabet codes represent different states {0 = 5’- CTGGCT, 1 = 5’- CGCAGC }

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Representation of states {0 = 5’- CTGGCT, 1 = 5’- CGCAGC } CTGG = a combination of S1 and 0 States are not physically separated from the symbols. Subsequences of the alphabet codes represent different states

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Representation of states {0 = 5’- CTGGCT, 1 = 5’- CGCAGC } GGCT = a combination of S0 and 0 CTGG = a combination of S1 and 0 States are not physically separated from the symbols. Subsequences of the alphabet codes represent different states

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Representation of states {0 = 5’- CTGGCT, 1 = 5’- CGCAGC } GGCT = GGCT = CTGG = CTGG = CGCA = CGCA = CAGC = CAGC = States are not physically separated from the symbols. Subsequences of the alphabet codes represent different states

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How Does it Work? Adapters = transition molecules GGATGCCTAC NNNN Fok I (9/13) recognition site S0, 0 S0 S0, 1 S1 S1, 0 S1 S1, 1 S0 3 bp 5 bp 3 bp 1 bp CCGA GTCG GACC GCGT

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Animation of experiment

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T110

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T110

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T110

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T110

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T110

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T110

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T110

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T110

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T101

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T101

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T101

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T110

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T101

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T110

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Why autonomous? Fok I and Ligase act in the same environment (NED4 buffer + 1 mM ATP, 18 o C) No interference between input molecules that are at different stages of computation Each molecule is an independent automaton. There are ~10 13 computations running in parallel

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Computation 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1,10: 50 bp ladder; 2: 101 input; 3: 010010 input; 4: S0-detector; 5: S1-detector 6: Computation result of 101 input; 7: Computation result of 010010 input 8: Computation result of 010100 input; 9: Computation result of 001000 input 150 bp 200 bp S0-result S1-result Inputdegradationproducts Reaction conditions: Environment: 120 l of NEB4 buffer + 1 mM ATP, 18 o C, 80 min Input: 2.5 pmol; Detectors: 1.5 pmol each; Transition molecules: 20 pmol each Fok I: 12 units; T4 Ligase: 120 units S0-d S1-d

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Proof of Mechanism A complete mixture: Input (010100) ; S0-detector; S1-detector; T1,T2,T3,T4; Fok I; T4 DNA Ligase The gel shows a “component removal” experiment, where each component was omitted from the complete mixture and the result was compared to the predicted outcome 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1,12: 50 bp ladder 2: complete mixture 3: No Input 4: No S0-detector 5: No S1-detector 6: No T1 7: No T2 8: No T3 9: No T4 10: No Fok I 11: No T4 DNA Ligase PredictedActual +--+------+--+-?---- Result band

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Estimation of system correctness 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Detectors are labeled with 32 P S0-result S1-result S1-detector S0-detector There are possible “wrong” bands. Their origin is currently being determined. At any rate, the correctness is >95% Exact error rate still needs to be determined Lanes: 1,7: 50 bp ladder 2: 32 P-S0-detector 3: 32 P-S1-detector 4: Computation over 010010 5: Computation over 010100 6: Computation over 001000

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