DNA Computing on a Chip

1
DNA Computing on a Chip

• Mitsunori Ogihara and Animesh Ray
• Nature, vol. 403, pp. 143-144
• Cho, Dong-Yeon

2
Abstract

• In a DNA computer
• The input and output are both strands of DNA.
• A computer in which the strands are attached to
  the surface of a chip can now solve difficult
  problems quite quickly.
• Liu et al., 2000
• Liu, Q. et al., DNA computing on a chip,
  Nature, vol. 403, pp. 175-179, 2000.

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Arriving at the truth by elimination

• Problem classes
• Polynomial time or P problems
• O(1), O(n), O(nlogn), O(n2), O(n3),
• Non-deterministic polynomial time or NP problems
• Hard NP problems have running times that grow
  exponentially with the number of the variables.
• O(2n), O(3n), O(n!)
• New technology for massively parallel elimination
  Liu et al., 2000
• This algorithm harnesses the power of DNA
  chemistry and biotechnology to solve a
  particularly difficult problem in mathematical
  logic.

4
Adlemans experiments

• Hamilton path problem
• Millions of DNA strands, diffusing in a liquid,
  can self-assemble into all possible path
  configurations.
• A judicious series of molecular manoeuvres can
  fish out the correct solutions.
• Adleman, combining elegance with brute force,
  could isolate the one true solution out of many
  probability.

5
Lius experiments

• Satisfiability Problem
• Find Boolean values for variables that make the
  given formula true
• 3-SAT Problem
• Every NP problems can be seen as the search for a
  solution that simultaneously satisfies a number
  of logical clauses, each composed of three
  variables.

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Procedure

• Step 1.
• Attach DNA strings encoding all possible answers
  to a specially treated gold surface.
• Step 2.
• Complementary DNA strands that satisfy the first
  clauses are added to the solution.
• The remaining single strands are destroyed by
  enzymes.
• The surface is then heated to melt away the
  complementary strands.
• This cycle is repeated for each of the remaining
  clauses.

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• Step 3.
• The surviving strands first have to be amplified
  using the PCR.
• Their identities are then determined by pairing
  with an ordered array of strings identical to the
  original set of sequences.
• O(3k1) vs. O(1.33n), O(2n)
• k the number of clauses
• n the number of variables

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Problems

• Scaling up this technique to solve larger 3-SAT
  problems is still unrealistic.
• Correcting errors arising from the inherent
  sloppiness of DNA chemistry
• High cost of tailor-made DNA sequences
• 50-variable 3-SAT 1015 unique DNA strands
• Designing enough unique DNA strands
• Exponentially increasing number of DNA molecules
• A compromise may be achieved by reducing the
  search space through heuristics.

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Conclusions

• The ideal application for DNA computation does
  not lie in computing large NP problems
• There may be a need for fully organic computing
  devices implanted within a living body that can
  integrated signals from several sources and
  compute a response in terms of an organic
  molecular-delivery device for a drug or signal.