DNA Computing Leonard Adlemans Algorithm

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DNA Computing Leonard Adlemans Algorithm

• Lars Schäfer
• University of Stuttgart

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Motivation

• Limited parallelism of electronic computers
• Silicon close to physical limits
• Speed
• Size

• New approaches
• Quantum computing
• Optical computing
• DNA computing

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DNA Computing

• DNA can perform computations
• Stores information (up to 108 TByte in 1 liter)
• Allows manipulation
• DNA is tiny and "fast"
• New computing paradigm
• Try all possible solutions (parallel)
• Remove wrong solutions

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Outline

• DNA structure
• Biochemical processes
• Electrophoresis
• Ligation
• Polymerase Chain Reaction (PCR)
• Adlemans algorithm
• Conclusion

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Outline

• DNA structure
• Biochemical processes
• Electrophoresis
• Ligation
• Polymerase Chain Reaction (PCR)
• Adlemans algorithm
• Conclusion

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DNA Structure
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4
1
3
2
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DNA Structure - Single Strand

• 4 Bases
• Adenine (A)
• Thymine (T)
• Cytidine (C)
• Guanine (G)

• Distinctive ends
• 5 (5-prime) end
• 3 end
• Sequence
• 5-ATCG-3

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DNA Structure Double Strand

• Annealing
• G lines up with C
• 3 hydrogen bonds
• A lines up with T
• 2 hydrogen bonds

• Watson-Crick complement
• 5-ATCG-3
• 3-TAGC-5
• "Double Helix"
• 2 intertwined strands

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Outline

• DNA structure
• Biochemical processes
• Electrophoresis
• Ligation
• Polymerase Chain Reaction (PCR)
• Adlemans algorithm
• Conclusion

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Biochemical Processes - Electrophoresis

• Separation of DNA depending on
• Size
• Electrical charge
• Fill with agarose gel (0.5 5)
• Load slots with samples and ladder
• Apply current
• Identify and extract

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Biochemical Processes Ligation

• Enzyme T4 DNA ligase
• Anneal
• Overhanging complementary ends (sticky ends)
• Hydrogen bonds
• Ligate
• Covalently bond 3 and 5 ends

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Biochemical Processes Polymerase Chain Reaction

• Replication of DNA
• Polymerase enzym
• Complementary copy of template strand
• Primer signals starting point

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Outline

• DNA structure
• Biochemical processes
• Electrophoresis
• Ligation
• Polymerase Chain Reaction (PCR)
• Adlemans algorithm
• Conclusion

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Directed Hamiltonian Path Problem
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• Find Path, which
• Starts at vin
• Ends at vout
• Passes every vertex exactly once
• vin0 and vout6
• 0?1 ? 2 ? 3 ? 4 ? 5 ? 6
• NP-Complete
• No polynomial time algorithm known

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1
6
0
2
5
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Graph Encoding with DNA

• Vertex i
• Random 20-mer DNA sequences Oi
• Watson-Crick complement Oi
• Edge i ? j
• 3 10-mer of Oi (For i 0 take all of O0)
• 5 10-mer of Oj (For j 6 take all of O6)
• Preserves edge orientation

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Adlemans Algorithm

• Try all possible solutions, then remove wrong
  solutions
• Generate random paths through the graph
• Keep only those paths that begin with vin and end
  with vout
• Keep only those paths that enter exactly n
  vertices
• Keep only those paths that enter all of the
  vertices at least once

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Step 1

• Generate random paths
• For each vertex i (except 0 and 6)
• 50 pmol of Oi
• For each edge i ? j
• 50 pmol of Oi ? j
• Ligation of Oi ? j with Oi as "connectors"

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Step 2

• Amplify paths with vin 0 and vout 6
• Polymerase Chain Reaction
• Number of other paths is negligible

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Step 3

• Keep only paths that enter exactly n vertices
• Agarose gel electrophoresis
• Extract 140 base-pair (bp) band

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Step 4

• Keep only paths that enter all vertices
• Produce single stranded DNA
• Affinity separate
• Conjugate Oi to metal beads
• Oi anneals to path containing Oi
• Magnetic field retains Oi
• Drop other paths
• Repeat for all Oi
• Electrophorese
• If 140 base-pair band is present
• Hamiltonian path exists

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Algorithm Summary

• First molecular computation
• Brute force
• Massively parallel
• Complexity
• Linear complexity in bio steps
• Exponential complexity in DNA strands
• 70 vertices require 1025 kg DNA
• Attempt to repeat experiment failed
• Ambiguous results
• Protocols error prone
• Sensitive to impurities

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Conclusion

• Still basic research (only 8 years)
• Better protocols
• Better DNA algorithms
• Feasibility of DNA computing
• Advantages
• Extremely high information density
• Massive parallelism

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Thank You!
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DNA Structure