DNA Computing: Mathematics with Molecules

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DNA Computing Mathematics with Molecules
Russell DeatonProfessor Comp. Sci. Engr.The
University of Arkansas Fayetteville, AR
72701 rdeaton_at_uark.edu
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What is DNA Computing (DNAC) ?
The use of biological molecules, primarily DNA,
DNA analogs, and RNA, for computational purposes.
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Why Nucleic Acids?

• Density (Adleman, Baum)
• DNA 1 bit per nm3, 1020 molecules
• Video 1 bit per 1012 nm3
• Efficiency (Adleman)
• DNA 1019 ops / J
• Supercomputer 109 ops / J
• Speed (Adleman)
• DNA 1014 ops per s
• Supercomputer 1012 ops per s

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What makes DNAC possible?

• Great advances in molecular biology
• PCR (Polymerase Chain Reaction)
• DNA Microarrays
• New enzymes and proteins
• Better understanding of biological molecules
• Ability to produce massive numbers of DNA
  molecules with specified sequence and size
• DNA molecules interact through template matching
  reactions

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What is a the typical methodology?

• Encoding Map problem instance onto set of
  biological molecules and molecular biology
  protocols
• Molecular Operations Let molecules react to
  form potential solutions
• Extraction/Detection Use protocols to extract
  result in molecular form

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PHYSICAL STRUCTURE OF DNA
20 Å
3 OH
5 C
Minor Groove
34 Å
5
3
Sugar-Phosphate Backbone
Major Groove
5
3
Nitrogenous Base
C 5
3 0H
Central Axis
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What is an example?

• Molecular Computation of Solutions to
  Combinatorial Problems
• Adleman, Science, v. 266, p. 1021.

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Algorithm

• Generate Random Paths through the graph.
• Keep only those paths that begin with vin and end
  with vout.
• If graph has n vertices, then keep only those
  paths that enter exactly n vertices.
• Keep only those paths that enter all the vertices
  at least once.
• In any paths remain, say Yes otherwise, say
  No

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INTER-STRAND HYDROGEN BONDING
()
(-)
()
(-)
to Sugar-Phosphate Backbone
to Sugar-Phosphate Backbone
Adenine
Thymine
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STRAND HYBRIDIZATION
100 C
HEAT
COOL
OR
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DNA LIGATION
?
?
?
?
?
?
?
?
?
?
Ligase Joins 5' phosphate to 3' hydroxyl
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Encoding
GCATGGCC
0
CCGGTCGA
1
CCGGTACC
AGCTTAGG
2
ATGGCATG
0
0
2
1
GCATGGCCATGGCATG CCGGTACC
GCATGGCCAGCTTAGG CCGGTCGA
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Massively Parallel Search
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Algorithm

• Generate Random Paths through the graph.
• Keep only those paths that begin with vin and end
  with vout.
• If graph has n vertices, then keep only those
  paths that enter exactly n vertices.
• Keep only those paths that enter all the vertices
  at least once.
• In any paths remain, say Yes otherwise, say
  No

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DNA Polymerase
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POLYMERASE CHAIN REACTION
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Start V0, Stop V6
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Algorithm

• Generate Random Paths through the graph.
• Keep only those paths that begin with vin and end
  with vout.
• If graph has n vertices, then keep only those
  paths that enter exactly n vertices.
• Keep only those paths that enter all the vertices
  at least once.
• In any paths remain, say Yes otherwise, say
  No

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GEL ELECTROPHORESIS - SIZE SORTING
Electrode
Samples
Slower
Gel
Buffer
Electrode
Faster
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Right Length
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Algorithm

• Generate Random Paths through the graph.
• Keep only those paths that begin with vin and end
  with vout.
• If graph has n vertices, then keep only those
  paths that enter exactly n vertices.
• Keep only those paths that enter all the vertices
  at least once.
• In any paths remain, say Yes otherwise, say
  No

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ANTIBODY AFFINITY
Add oligo with Biotin label

B
GTGGTACACTG
Anneal
Heat and cool
Add Paramagnetic-Streptavidin Particles

B
GTGGTACACTG
Bind
Isolate with Magnet
GTGGTACACTG
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Every Vertex
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Algorithm

• Generate Random Paths through the graph.
• Keep only those paths that begin with vin and end
  with vout.
• If graph has n vertices, then keep only those
  paths that enter exactly n vertices.
• Keep only those paths that enter all the vertices
  at least once.
• In any paths remain, say Yes otherwise, say
  No

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Hamiltonian Path
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Mismatches
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DNA Word Design

• Importance of Template-Matching Hybridization
  Reactions in DNA Computing (DNAC)
• Sequence design should implement DNAC
  architecture.
• Planned Hybridizations
• Problem Size
• Subsequent Processing Reactions
• Designed sequences should minimize unplanned
  cross-hybridizations.
• Consequences of Bad Designs Errors and Poor
  Efficiency

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DNA Word Design

• Design problem is hard.
• As number of sequences required to represent the
  problem increases, this constraints increasingly
  conflicts with the requirement of
  non-crosshybridization.
• How much of DNA sequence space is available for
  computation?

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Why In Vitro?

• In Vitro Selection and Evolution
• PCR as tool for selection
• Ability to synthesis huge, random starting
  populations
• Mutagenesis
• Oligos manufactured under conditions for use
• Use massive parallelism of DNAC to solve word
  design problem

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Protocol Outline

• Start with huge population of random sequences
  with attached primers.
• Anneal rapidly to quench oligos in mismatched
  configurations.
• Using temperature as a control, melt most
  mismatched pairs.
• Amplify and purify
• Repeat

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Experimental Results
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Experimental Results
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Latest Results
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DNA Memories
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Overview
Input DNAs (Unknown Seq.)
Sequences Comple- mentary to Input DNAs
New Unknown Input DNAs
Labeled Tag Sequence Complements
Tag1
Random Probe
Learning
Recall
Output
Memory DNA Strands (With the 3 end
Comple- mentary to the Input DNAs)
Separates Memory DNA Strands that Match
or Partially Match the New Inputs from
Those That Dont Match
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Learning

• Learning Information acquired from examples
  rather than programmed
• Protocol to store input DNAs (possibly of unknown
  sequence)
• Higher level representation of the input
  sequences
• Not individual sequence memories but whole
  populations
• Clustering of input sequences in vitro
• Massively random and parallel copying or sampling
  depending on number of inputs and probes

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Base-by-Base Amplification
Input DNA
Tag
Probe
Extension
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Sampling
Input DNA
Tag
Probe
Extension
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Energy Surface Manipulation through Learning
Before Learning
After Learning
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Tags

• Non-Crosshybridizing Sequences
• Convenient for Input/Output in absence of input
  sequence information
• Manipulate memory without input sequences
• Implement DNA2DNA Computations (Landweber and
  Lipton, DNA 3)

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Recall

• Hybridization to retrieve memories
• Similar sequences patterns matched
• Pattern matching done against whole memory
• Single memory associated with single tags
• Memory composite of output on multiple tags

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Experiments

• Test learning and recall with plasmid
• Test of sensitivity in concentration
• Test coverage of input sequence space with
• Plasmids (5k bp)
• E. Coli (5M bp)
• Test sequence resolution of protocols

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Learning
Input 1 is a 3 kb linear DNA (pBluescript)
Input 2 is a 5 kb linear DNA (?x 174)
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Recall
Plasmid inputs learned, similar sequences
recalled, and dissimilar not matched.
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Concentration Sensitivity

• Plasmids digested with Hpa II
• 1 ?g pBluescript
• 10ng - 800ng ?x 174
• Blotted with ?x 174 memory
• 1 ?x 174 detected in background of pBluescript

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Input Space Coverage

• Randomly digested input
• Learning on both inputs
• Blots nearly identical

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E. coli

1. E. coli digested
2. 219bp fragment of ?x 174 added
3. Learning with and without fragment
4. Fragment distinguished when learned

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Application
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Team

• Russell Deaton, University of Arkansas, Computer
  Science and Engineering
• Junghuei Chen, University of Delaware, Chemistry
  and Biochemistry
• Hong Bi, University of Delaware, Chemistry and
  Biochemistry
• Max Garzon, University of Memphis, Computer
  Science
• Harvey Rubin, University of Pennsyvania, School
  of Medicine
• David Wood, University of Delaware, Computer and
  Information Science

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Acknowledgement

• This work was supported by the NSF QuBIC program,
  award number EIA-0130385