Solution of a 20-Variable 3-SAT Problem on a DNA Computer

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Solution of a 20-Variable 3-SAT Problem on a DNA
Computer

• Ravinderjit S. Braich, Nickolas Chelyapov, Cliff
  Johnson,
• Paul W. K. Rothemund, and Leonard Adleman
• Science vol. 296 19 April 2002
• Summarized by Jiyoun Lee

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Introduction

• The Boolean formula
• 20 variable with 24-clause 3-conjunctive normal
  form (3-CNF) formula, F
• F was designed to have a unique satisfying truth
  assignment
• Sticker model
• Mix and split for half-library generation
• Polymerase extension method for full-length
  library generation
• Graduate PCR to read the answer

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Sticker model

• Sticker model
• Library Sticker
• Operations
• Combine
• Separation
• Setting
• Cleaning
• Separation based on subsequence ? use only
• Application of stickers
• Random access memory that requires no strand
  extension, uses no enzyme, and (at least in
  theory) its materials are reusable

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Separation operation

• Separation using AcryditeTM phosphoamidite for
  modifying DNA molecules at 5-end during chemical
  synthesis
• Covalently linking the probes to the gel matrix
• Gives one benefits of solid-support-based system
  while still remaining characteristics of a
  solution-based system
• Separation
• Oligonucleotide probes immobilized in
  polyacrylamide gel-filled glass modules
• Capture with immobilized probes and release at a
  higher temperature

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Attachment of oligonucleotides to solid

• Various methods are available to attach
  oligonucleotides to solid surfaces such as
  microarray slides, microtiter plates or magnetic
  beads, including
• Biotin-oligo non-covalently complexed with
  Streptavidin.
• SH-oligo covalently linked via a disulfide bond
  to a SH-surface.
• Amine-oligo covalently linked to an activated
  carboxylate or an aldehyde group.
• Phenylboronic acid (PBA)-oligo complexed with
  salicylhydroxamic acid (SHA)

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AcryditeTM

• Enables covalent attachment of oligonucleotides
  and other macromolecules to surfaces via acrylic
  linkages.
• An oligonucleotide derivatized with Acrydite
  group can polymerize with acrylamide monomer to
  form polyacrylamide or can react with thiol or
  silane surfaces. This chemistry is also
  compatible for attachment to polymer surfaces.
• 2D ? 3D immobilization

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An acrylic acid group can be directly attached to
the 5'-end of an oligonucleotide (with a 6-carbon
linker arm) at the time of synthesis using
Acrydite, an acrylic- phosphoramidite developed
by Mosaic Technologies
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The library I

• XkT, XkF 15 base value sequences, 2N library
  strands
• Constraints
• Library sequences contain only A, T, C ? less
  secondary structure
• All library and probe sequences have no
  occurrence of 5 or more consecutive identical
  nucleotides
• Every probe sequence has at least 4 mismatches
  with all 15 base alignment of any library
  sequence
• Every 15 base subsequence of a library sequence
  has at least 4 mismatches with all 15 base
  alignment of itself or any library sequence
• No probe sequence has a run of more than 7
  matches with any 8 base alignment of any library
  sequence
• No library sequence has a run of more than 7
  matches with any 8 base alignment of itself or
  any other library sequence
• Every probe sequence has 4, 5, or 6 Gs in its
  sequence
• ? Discourage intra- and interlibrary strand
  hybridization and unintended probe-library strand
  hybridization

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The library II

• XkZ, 5-end Acrydite-modified oligonucleotides
• Used as probes
• Synthesis of long molecules
• Synthesis of two half-libraries x0 through x10
  (left half-library), x11 through x20 (right
  half-library)
• Half-libraries a mix-and split combinatorial
  synthesis technique was used
• The 300-oligomer (300-mer) full library was
  created from the two half-libraries using a
  polymerase extension method

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Mix and split

• Combinatorial DNA library construction
  (half-library)
• During synthesis

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Polymerase extension method

• Assembly PCR method for the synthesis of long DNA
  sequences from large numbers of oligonucleotides
• Does not rely on DNA ligase but instead relies on
  DNA polymerase to build increasingly longer DNA
  fragments during the assembly process
• Derived from DNA shuffling

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5
3
5
3
Left half (110) 150 mer
Right half (1120) 150 mer
10 pmole
X11 X10
2 pmole each
5
3
? Final volume 20 ml in 1X T4 DNA ligase buffer,
incubate at RT for 2 hrs
Mixture 0.5 ml Primer X1T, X1F,
Acrydite-modified X20T, X20F
1 ml aliquot, PCR again
Band extraction, creat stock solution
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The computer and the computational protocol

• Step 1 Insert the library module into the hot
  chamber of the electrophoresis box and the first
  clause module into the cold chamber of the box.
  Begin electrophoresis.
• Step 2 Remove both modules from the box. Discard
  the module from the hot chamber. Wash the box and
  add new buffer. Insert the module from the cold
  chamber into the hot chamber and the module for
  the next clause into the cold chamber. Begin
  electrophoresis.
• Step 3 Repeat Step 2 for each of the remaining
  22 clauses.
• Step 4 Extract the answer strands from the final
  clause module, PCR-amplify, and read the answer.

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0.5cm thick plexiglass
Probe layer (releasing)
Probe layer (capturing)
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A clause module
3.2 cm
4.5 cm
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Detection of the answer

• Graduate PCR

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Capture-release efficiency