Molecular Computing Machine

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Molecular Computing Machine Uses its Input as
Fuel
Kobi Benenson
Joint work with Rivka Adar, Tamar Paz-Elizur, Zvi
Livneh and Ehud Shapiro
Department of Computer Science and Applied Math
Department of Biological Chemistry Weizmann
Institute of Science, Rehovot, Israel
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Information destruction in electronic computers
bit reset to zero (Landauer, Bennett)
0yz
Free energy
W Tkln2
xyz
Entropy decreasing and hence free
energy-consuming operation, which is avoided in
reversible computing
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Information destruction in biology physical
degradation of the bit sequence (string to
multiset)
xyz
gt 40kT
Free energy
x, yz
Entropy increasing and energy-releasing
operation, which can be exploited to avoid the
demand for external energy source
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• Input destruction can be used as a source of
  energy
• If output is smaller than input (e.g. yes/no
  questions), computation can be accomplished
  without external energy
• We realized this theoretical possibility

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Finite automaton an example
An even number of as
a
S0, a ? S1 S0, b ? S0 S1, a ? S0 S1, b ? S1
b
b
S0
S1
a
Two-states, two-symbols automaton
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Automaton A1
An even number of as
S0, a ? S1 S0, b ? S0 S1, a ? S0 S1, b ? S1
a
b
a
S0
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Automaton A1
An even number of as
S0, a ? S1
S0, a ? S1 S0, b ? S0 S1, a ? S0 S1, b ? S1
S0
a
b
a
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Automaton A1
An even number of as
S0, a ? S1 S0, b ? S0 S1, a ? S0 S1, b ? S1
S1
b
a
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Automaton A1
An even number of as
S1, b ? S1
S0, a ? S1 S0, b ? S0 S1, a ? S0 S1, b ? S1
S1
b
a
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Automaton A1
An even number of as
S0, a ? S1 S0, b ? S0 S1, a ? S0 S1, b ? S1
S1
a
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Automaton A1
An even number of as
S1, a ? S0
S0, a ? S1 S0, b ? S0 S1, a ? S0 S1, b ? S1
S1
a
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Automaton A1
An even number of as
S0, a ? S1 S0, b ? S0 S1, a ? S0 S1, b ? S1
S0
The output
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Previous molecular finite automaton
Benenson, Paz-Elizur, Adar, Keinan, Livneh
Shapiro, Nature 414, 430 (2001)
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(No Transcript)
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A new molecular automaton

• Key differences
• No Ligase, hence no ATP
• Software reuse molecule not consumed during
  transition
• Hence a fixed amount of hardware and software
  molecules may process input of any length without
  external source of energy

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A new molecular automaton

• Significant improvement of yields and performance

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Modifications in the molecular design
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Problems of the previous design

• Evidence of Ligase-free computation, but
  inefficient
• Often FokI cuts only one input DNA strand
• Computation stalled after a few steps

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Modifications in the molecular design
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Modifications in the molecular design
The software molecules
Shortest possible spacers between the FokI site
and the ltstate, symbolgt recognition sticky ends
0-, 1- and 2-bp
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Experimental implementation
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The automata
A1 even number of as
A2 even number of symbols
A3 ends with b
The inputs
I5 baaaabb I6 baaaabba I7 abbbbabbabb I8
abbbbaaaabba
I1 abb I2 abba I3 babbabb I4 babbabba
GGCTGCCGCAGGGCCGCAGGGCCGCAGGGCCGCAGGGCCTGGCTGCCTGG
CTGCCTGGCTGCCTGGCTGCCGCAGGGCCGCAGGGCCTGGCTGCCGTCGG
TACCGATTAAGTTGGA CGGCGTCCCGGCGTCCCGGCGTCCCGGC
GTCCCGGACCGACGGACCGACGGACCGACGGACCGACGGCGTCCCGGCGT
GGCGGACCGACGGCAGCCATGGCTAATTCAACC
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Single step proof
Ia
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P-O-GGCT CA G-32P
Ib
22
H-O-GGCT CA G-32P
Phosphorylated and non-phosphorylated
single-symbol input
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Single step proof
Phosphorylated and non-phosphorylated transition
molecule (T1)
Ta
Tb
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Single step proof

• All possible combinations are mixed with FokI
  (No Ligase and No ATP in all the reactions)
• We prove that there is no Ligase and ATP
  contamination in the FokI batch

FokI
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Single step proof
Ia
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P-O-GGCT CA G-32P
Ib
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H-O-GGCT CA G-32P
Ta
Tb
FokI
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Computation capabilities
A set of 8 inputs was tested with 3 software
programs, at standard conditions 4 mM FokI 4 mM
software 1 mM input 8 oC 20 min
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Computation capabilities
Direct output detection by denaturing PAGE
A1
Automaton
A2
A3
Expected output S
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
1 0 0 1 0 1 1 0
S1
S0
Input I
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
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Computation capabilities

• All the runs allowed correct major results with
  minor byproducts
• Only small ratio of the byproducts represent
  computation error

A1
Automaton
A2
A3
Expected output S
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
1 0 0 1 0 1 1 0
S1
S0
Input I
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
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Software recycling

• Automaton A1
• Input I8
• Each software molecule 0.075 molar ratio to the
  input
• T2, T5 and T8 performed on the average 29, 21 and
  54 transitions each.

time
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Optimization the fastest computation

• 4 mM software, 4 mM hardware and 10 nM input
• Rate 20 sec/operation/molecule
• 50-fold improvement over the previous system

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Optimization the best parallel performance

• 10 mM software, 10 mM hardware and 5 mM input
• Combined rate 6.646x1010 operations/sec/ml
• 8000-fold improvement over the previous system

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Conclusions

• Our experiments demonstrate
• 3x1012 automata/ml (240-fold improvement)
• Performing 6.6x1010 transitions/sec/ml
  (8000-fold improvement)
• With transition fidelity of 99.9 (2-fold
  improvement)
• Dissipating 1.02x10-8 W/ml as heat at ambient
  temperature

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Conclusions
We developed a molecular finite automaton that
realizes the theoretical possibility using the
input as the sole source of energy
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Thanks for your attention!