Towards Autonomous Molecular Computers Masami Hagiya, Proceedings of GP, 1997

1
Towards Autonomous Molecular ComputersMasami
Hagiya, Proceedings of GP, 1997

• 2004. 11. 20.
• Nakjung Choi
• Email fomula_at_mmlab.snu.ac.kr

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Contents

• DNA computing and accompanying research problem
• Aldeman-Lipton Paradigm
• Winfrees Cellular Automata
• DNA State Machines
• From Computation to Structure Construction

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DNA Computing and Accompanying Research Problems
(1/3)

• The Adleman-Lipton Paradigm 12
• One of data-parallel computation using DNA
  molecules
• Combinational search problems by generating and
  testing paths represented by DNA molecules

4
DNA Computing and Accompanying Research Problems
(2/3)

• The Adleman-Lipton Paradigm
• In the generating step
• Candidates (about 1012) for a solution are
  randomly generated using hybridization between
  complementary sequences of DNA
• In the testing step
• Molecular biology techniques to check whether
  each candidate satisfies the conditions necessary
  for it to represent a solution (data-parallel
  computation)

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DNA Computing and Accompanying Research Problems
(3/3)

• Reliability of Experimental Results
• Physico-chemical consideration in the design of
  tube algorithms
• Optimize the tube protocols
• Problem Size
• Presently, aim only to certify the feasibility
• Remain relatively small (only 7 vertices in
  Adlemans)
• Experimental Costs
• Autonomous computation by molecular reactions

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Winfrees Cellular Automata

• A computational model 3
• Employ rectangular tiles made of DC units, each
  of which consists of four DNA molecules
• Simulate computation of one-dimensional cellular
  automata by a tiling reaction of DX units in the
  two dimensional plane
• Solve search problems such as the DHPP by having
  many tiling reactions proceed in parallel in a
  test tube (one-pot ? autonomous)

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DNA State Machines (1/5)

• Successive Localized Polymerization
• Transition table of a stat machine
• A state transition is performed by the
  polymerization of a hairpin structure formed by a
  single strand

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DNA State Machines (2/5)

• Computing Boolean Expressions
• Not only the input to the boolean expression but
  also the boolean expression itself is represented
  as a DNA molecule
• An input to a expression containing n variables

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DNA State Machines (3/5)

• Computing Boolean Expressions
• Boolean expression example

Implementation
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DNA State Machines (4/5)

• Computing Boolean Expressions
• Restriction ? each variable is allowed to occur
  only once
• If the value of xi is true, then the next stat
  could be either var2 or output--.
• Boolean expressions in which each variable occurs
  at most once are called µ-formulas.
• If variable xi occurs twice in a boolean
  expression, a copy of xi, xi must be prepared,
  and the value of xi is also given in an input
  and must be identical to that of xi

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DNA State Machines (5/5)

• Computing Boolean Expressions
• In Winfrees paper 4, not only boolean
  expressions but also binary decision diagrams can
  be implemented

The representation of µ-formulas eby computing
trans(e, output, output--)
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From Computation to Structure Construction

• Autonomous computation by molecular reactions
• A method for constructing structures on the
  molecular scale
• If one can construct complex structures out of
  DNA molecules, one can also organize other kinds
  of molecules guided by the structures of DNA

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References

• 1 Leonard M. Adleman Molecular Computation of
  Solutions to Combinatorial Problems, Science,
  Vol.266, 1994, pp.1021-1024.
• 2 Richard J. Lipton DNA Solution of Hard
  Computational Problems, Science, Vol.268 1995,
  pp.542-545.
• 3 Erik Winfree, Xiaoping Yang and Nadirian C.
  Seeman Universal Computation via Self-assembly
  of DNA Some Theory and Experiments, Second
  Annual Meeting on DNA Based Computers, June 10,
  11, 12, 1996, DIMACS Workshop, Princeton
  University, Dept. of Computer Science,
  pp.172-190.
• 4 Erik Winfree to be submitted to 4th DIMACS
  Workshop on DNA Based Computers, 1998.