Existing autonomous system

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Existing autonomous system
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
Sakamoto Hagiya
2
Molecular implementation

• Each state is a ss-DNA segment
• Each transition S -gt S is a sequence of
  S-complementary
• and S-complementary DNA
• The transitions are performed in a PCR-like
  fashion

An Input
The rules S0 -gt S1 S1 -gt S2
3
Molecular implementation

• Each state is a ss-DNA segment
• Each transition S -gt S is a sequence of
  S-complementary
• and S-complementary DNA
• The transitions are performed in a PCR-like
  fashion

The rules S0 -gt S1 S1 -gt S2
4
Molecular implementation

• Each state is a ss-DNA segment
• Each transition S -gt S is a sequence of
  S-complementary
• and S-complementary DNA
• The transitions are performed in a PCR-like
  fashion

The rules S0 -gt S1 S1 -gt S2
5
Molecular implementation

• Each state is a ss-DNA segment
• Each transition S -gt S is a sequence of
  S-complementary
• and S-complementary DNA
• The transitions are performed in a PCR-like
  fashion

The rules S0 -gt S1 S1 -gt S2
6
Molecular implementation

• Each state is a ss-DNA segment
• Each transition S -gt S is a sequence of
  S-complementary
• and S-complementary DNA
• The transitions are performed in a PCR-like
  fashion

The rules S0 -gt S1 S1 -gt S2
7
Molecular implementation

• Each state is a ss-DNA segment
• Each transition S -gt S is a sequence of
  S-complementary
• and S-complementary DNA
• The transitions are performed in a PCR-like
  fashion

The rules S0 -gt S1 S1 -gt S2
8
Molecular implementation

• Each state is a ss-DNA segment
• Each transition S -gt S is a sequence of
  S-complementary
• and S-complementary DNA
• The transitions are performed in a PCR-like
  fashion

The result
The rules S0 -gt S1 S1 -gt S2
9
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
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Basic cycle of automaton
Iterative processing of input until the end is
reached
S, a

a

rest


ltS, nilgt

S, a
S
S, a
Detect the result

rest

State
-
symbol tag
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FokI
0
1
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FokI
1
S1,0
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1
S1,0
21
1
S1,0
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Molecular realization of FA
Alphabet 0 5- CTGGCT, 1 5- CGCAGC
States S0,S1
FA
Transition Table
0
0
1
S0, 0 ? S0 S0, 1 ? S1 S1, 0 ? S1 S1, 1 ? S0
S1
S0
1
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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
States are not physically separated from the
symbols. Subsequences of the alphabet codes
represent different states
CTGG a combination of S1 and 0
0 5- CTGGCT, 1 5- CGCAGC
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Representation of states
States are not physically separated from the
symbols. Subsequences of the alphabet codes
represent different states
CTGG a combination of S1 and 0
0 5- CTGGCT, 1 5- CGCAGC
GGCT a combination of S0 and 0
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Representation of states
States are not physically separated from the
symbols. Subsequences of the alphabet codes
represent different states
CTGG ltS1, 0gt
CGCA ltS1, 1gt
0 5- CTGGCT, 1 5- CGCAGC
GGCT ltS0,0gt
CAGC ltS0,1gt
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How Does it Work?
Adapters transition molecules
Fok I (9/13) recognition site
GGATG CCTAC
NNNN
S0, 0 ? S0
3 bp
CCGA
S0, 1 ? S1
5 bp
GTCG
S1, 0 ? S1
3 bp
GACC
S1, 1 ? S0
1 bp
GCGT
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Animation of experiment
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T
1
1
0
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T
1
1
0
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T
1
1
0
32
T
1
1
0
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T
1
1
0
34
T
1
1
0
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T
1
1
0
36
T
1
1
0
37
T
1
0
1
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T
1
0
1
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T
1
0
1
40
T
1
0
1
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T
1
0
1
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T
1
0
1
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T
1
0
1
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T
1
1
0
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T
1
1
0
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T
1
0
1
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T
1
1
0
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Why autonomous?

• Fok I and Ligase act in the same environment
  (NED4 buffer 1 mM ATP, 18 oC)
• No interference between input molecules that are
  at different stages of computation
• Each molecule is an independent automaton. There
  are 1013 computations running in parallel

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Computation
1 2 3 4 5 6 7 8 9 10
S1-result
S0-result
Input degradation products
S1-d
200 bp
S0-d
150 bp
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
Reaction conditions Environment 120 ml of NEB4
buffer 1 mM ATP, 18 oC, 80 min Input 2.5 pmol
Detectors 1.5 pmol each Transition molecules
20 pmol each Fok I 12 units T4 Ligase 120 units
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Proof of Mechanism
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
A complete mixture Input (010100) S0-detector
S1-detector T1,T2,T3,T4 Fok I T4 DNA Ligase
Result band
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
Predicted
Actual
- - - - - - - -
- - - ? - - - -
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Estimation of system correctness
1 2 3 4 5 6 7
Detectors are labeled with 32P
S1-result
Lanes 1,7 50 bp ladder 2 32P-S0-detector 3
32P-S1-detector 4 Computation over 010010 5
Computation over 010100 6 Computation over 001000
S0-result
S1-detector
S0-detector
There are possible wrong bands. Their origin is
currently being determined. At any rate, the
correctness is gt95 Exact error rate still needs
to be determined