Computing with DNA

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Computing with DNA
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Overview

• Basic premise computers need not be complex
  mechanical, electro-mechanical, or electronic
  devices
• Proof Turing machine and Churchs Thesis

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Background

• Churchs Thesis
• Every function which would naturally be regarded
  as computable can be computed by a Turing
  machine.
• naturally regarded as computable means that we
  can specify an algorithm

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Background

• Computational complexity

• NP is the set of problems for which we have not
  yet found deterministic, polynomial time
  algorithms
• Nor have we proved that a deterministic,
  polynomial time algorithm does not exist
• Thus, NP P? remains an open question amongst
  computer scientists

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Background

• Within the class NP exists called NP-Complete
• A problem is considered NP-Complete if
• It is in the class NP
• It is NP-Hard (meaning all other problems in NP
  is reducible to it)
• Reducible means that there is a deterministic
  algorithm that maps one algorithm to another and
  runs in polynomial time

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Background

• Of interest in this work are
• Problems of the class NP-Complete
• Because they are naturally difficult to solve
• The concept of reducibility
• Because this is basically how Adleman initially
  visualized the use of DNA for computing

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Overview

• Utilizing chemical processes at the molecular
  level (specifically, DNA processes) problems of
  the class NP-Complete can be solve very fast
• This doesnt mean the NPP? question has been
  solved this isnt a polynomial time algorithm,
  its just a novel massively parallel approach
• It does mean that if one NP-Complete problem can
  be solved via DNA processes then they all can be
  solved via DNA processes

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DNA

• Strings of four bases
• A adenine
• T thymine
• G guanine
• C cytosine
• An enzyme
• Polymerase creates complementary strands of
  bases (C?G, A?T)
• Allows DNA to reproduce which ultimately leads to
  human reproduction

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Polymerase

• A nano-machine that runs along a strand of DNA
  and makes a complementary copy

• What does this have to do with computation?

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Adlemans Vision

• Recall the Turing Machine

• Adleman saw the similarities between a Turing
  Machine and the Polymerase process

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DNA Tools

• Watson-Crick pairing
• Two complementary strands of DNA will anneal
  (join together)
• Polmerases
• Copies one molecule to another (complementary)
• Ligases
• Bind molecules together (end-to-end)
• Nucleases
• Cut strands of DNA as specified places (bases)
• Gel electrophoresis
• A gel where shorter strands of DNA will move more
  quickly than longer strands
• DNA synthesis
• You specify the sequence of bases you want, write
  a check, and a lab will create molecules of DNA
  for you

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The Problem

• Hamiltonian Path Problem
• Given
• A graph of cities and paths between them
• A start city
• An end city
• Is there a path from start to end that passes
  through every city exactly one time?
• Note we dont want to find the path, we just
  want to know that one exists

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The Algorithm

• Generate a set of random paths through the graph
• For each path
• Remove all paths that do not have the proper
  start and end
• Remove all paths that do not pass through the
  proper number of cities
• For each city
• Remove paths that do not pass through the city
• If the resultant set of paths (from step 2) is
  not empty, then there exists a Hamiltonian path.
  If it is empty, then there is no Hamiltonian path
• If the initial set of random paths is large
  enough and random enough then the probability of
  obtaining a correct answer is high

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The Mapping to DNA

• This is where the magic takes place
• By mapping each city to a DNA sequence of bases
  and
• generating the Watson-Crick complements and
• mapping each link in the graph to a DNA sequence
  of bases related to the city mappings and
• applying the DNA tools to a batch of DNA
  molecules representing the mappings
• the problem can be solved chemically!

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The Set-up

• Get a test-tube full of DNA molecules
  representing the city complements and the links
  between cities
• Add some water, ligase, salt and a few other
  things found inside cells
• Shake it up
• And presto! The answer is in your hand
• You just have to find it

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The Set-up
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Post Processing

• All that has to be done is weed out all the
  paths in the test-tube that are not Hamiltonian
  paths
• Using polymerase with primers representing part
  of the start and end cities lots and lots of
  copies of those strands with proper start and end
  cities are created
• All the rest were barely duplicated or not
  duplicated at all
• This completes the first part of step 2

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Post Processing

• Now you just need to get rid of strands that
  are not the proper length
• Using gel electrophoresis strands of various
  lengths could be sorted
• This completes the second part of step 2

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Post Processing

• Now you only need check if all cities are present
  in the remaining DNA strands
• This involves putting DNA probes on little iron
  balls
• The probes (one for each city) will attach
  themselves to strands with that city thus also
  attaching the little iron balls to the strand
• Using a magnet these strands could be separated
  from the rest
• This is done sequentially for each intermediate
  (non start/end cities)
• This completes the third part of step 2

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All Thats Left is the Glory

• If there are any DNA strands remaining in the
  test-tube, they represent Hamiltonian paths
• If there are not, then the problem does not
  contain a Hamiltonian path

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Interesting Bits

• This process is massively parallel
• Adlemans solution was analogous to reducing one
  NP problem to another
• Its all in the data representation and mapping
• Not all that different from programming a
  parallel processor
• This is clearly not feasible for large problems,
  at least not yet
• One cubic centimeter of DNA can store as much
  information as approximately one trillion CDs
• Overcoming the momentum of investment in
  electronic computation will be difficult

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End Notes

• Leonard Adleman
• Computer Scientist UC Berkeley
• Mathematician MIT
• Theoretical Computer Scientist USC
• Co-inventor of RSA encryption
• Possibly the inventor of the computer virus
• Self-made biologist
• Renaissance man? At least a visionary.