DNA Computing by Self Assembly

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DNA Computing by Self Assembly

• Erik Winfree, Caltech

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Self Assembly of a Box
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Information and Algorithms

• Electronic microprocessors control
  electro-mechanical devices
• Biochemical circuits control molecular/chemical
  events
• General Goal design biochemical
  algorithms/circuits that are programmable and can
  perform functions

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Self Assembly Model

• Model we will investigate molecular self
  assembly of heterogeneous crystals
• Idea use periodic order of crystals to perform
  arbitrarily complex computation
• What are purposes of self assembly?
• 2 main schools of thought

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Purposes

• 1. Use massive parallelism of chemistry and lots
  of DNA at a time to solve difficult combinatorial
  optimization problems, such as SAT/TSP
• 2. Use self assembly algorithms to fabricate
  exact shapes / circuits/ patterns etc..

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Precursors

• Idea of self assembly arose from 3 ideas
• 1. DNA computing (Adleman 1994)
• 2. Tiling theory (Grun. Shep. 1986)
• 3. DNA nanotechnology (Seeman 1982)

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DNA Computing
Adleman 1994 Solved 6 node Hamiltonian Path
Problem Nodes labeled with random 20mer Edge(u,
v) last 10 BP of u first 10 BP of v
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Hamiltonian Path
Used DNA hybridization to generate random paths
through graph Added programmable binding to
impose conditions (start city, end city, num
cities, no repeats..)
1st meaningful computation by DNA Heralded as a
landmark achievement
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Steps of process

• Generate random paths (DNA molecules) through
  graph
• Use PCR to amplify all paths that start at first
  city and end at last city (use primers)
• Test if path contains city 1. Amplify paths that
  pass test. Repeat tests for cities 2 through n.
• If anything left, return YES. Else return NO.

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Tiling Theory

• Tiling arrangement of basic shapes to cover
  infinite plane
• Wang 1963 Showed infinite num of square tiles
  with 4 colored sides can create Turing machine
  history

• Wang Tiles are very powerful. Use DNA molecules
  to simulate Wang tiles in self assembly

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DNA Nanotechnology
Seeman 1982 use DNA as a building block for
nanostructures Block Four armed DNA
double-crossover molecules (DX) Label 4 arms of
DX molecules with labels like Wang tiles
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DX Molecule Wang tile
Adjacent tiles sequences at sticky ends of 2
molecules go together
Upper Right A CATAC Lower Left B GTATG
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Simplified Tile Assembly Model

• Given a set of possible tiles and possible bonds
• 4 sides of tile have bonds, bond has strength (0,
  1,2)
• 2 tiles can bond together if their bonds fit, and
  if total strength (sums of bond strengths on
  common sides) is gt threshold
• Growth starts with a seed tile

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Binary Counter
Using 3 border tiles, 2 0-bit tiles, 2 1-bit
tiles, can simulate a binary counter Power only
7 tiles required
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Experimental Demonstrations
1d array Adleman DNA Computing1994 2d array
Winfree 1998 3d array Open Next Example of
Winfree construction
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XOR Practice

• Everyone try this out.
• Start with a 1 in a sea of 0s.
• To generate next row, each tile checks its two
  neighbors, performs XOR and places the result
  below it in the next row
• XOR 00 0 110
• 01 1 101

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XORing

• 000000000010000000000
• 000000000101000000000
• 000000001000100000000
• 000000010101010000000
• 000000100000001000000
• 000001010000010100000
• 000010001000100010000
• 000101010101010101000
• 001000000000000000100
• ..

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Sierpinski Triangle
1st 2d process to be experimentally demonstrated
Sierpinski Gasket Best result so far 8 by 16
error-free triangle
Poor results due to 1-10 tile binding error
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Sample Tile Solution
Slight variant of Sierpinski Triangle
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Application 1 Solve NP hard problems

• NP-complete problems exponential number of
  solutions, hard to find correct solution, but
  easy to verify
• Idea Chemistry can generate all possible
  solutions and filter solutions quickly
• Hack Push exponential dimension of problem into
  volume of DNA needed
• 1 mL DNA 260 bits of information

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Apply self assembly

• Let massive parallelism solve problem
• In self assembly, generate input as initial set
  of tiles
• See if Yes or No tile is produced at end

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Current results

• Problems solved Hamiltonian Path,
  Satisfiability, etc..
• Assuming no errors, 40-variable SAT needs 30 mL
  DNA and several hours
• 1012 operations/second, inferior to computers
• Winfree No low hanging fruit for self assembly
  here

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Application 2 Programmable Nanofabrication

• Fabricate molecular electronic circuits
• Current technology hitting the limit soon
• Solution create molecular structures like carbon
  nanotubes.
• How to arrange tiny chemical components into
  fixed patterns?

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Nanocircuits

• Solution Use self assembly to create molecular
  components
• Small pieces such as NAND/OR gates can be created
• Hard to create large microprocessors
• Self assembly good to make circuits that have
  concise descriptions, eg recursive formulations

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DNA Circuit Picture
RAM Demultiplexer
2 bands earlier bit counter example
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Summary Achievements

• Robust, readily programmable
• Dozens of crystals have been successfully used as
  DNA tiles
• Self assembly has concrete experimental results,
  unlike other molecular computing technologies

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Summary Current Problems

• Current DNA tiles distorted, 1 positioning error
  in experiments.
• Size of tile is limited all crystals lt 10
  microns.
• 1 10 step error. eg tiles bond incorrectly
  quite often. Very big problem.
• gt New model error correcting tiles in self
  assembly

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Yet more problems

• Undesired nucleation self assembly starts by
  itself
• Problem occurs because biological system starts
  when it wants to minimize energy
• Solution Have programmable control of
  nucleation. Add energy barriers to force assembly
  to start with seed tile.

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Future Questions

• Natural question What shapes can be made by self
  assembly?
• Has parallels to Computability / Chomsky Language
  Theory
• Minimum number of steps to make a shape?
• Minimum number of tiles to make shape?

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Final Thoughts

• Although bio systems are like circuits,
  remember they
• Contain large amounts of randomness
• Have very high error rates
• Contain hidden biological processes that cannot
  be described
• So CS people dont be surprised if experimental
  results are different from theoretical predictions

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More thoughts

• Winfree We have already harnessed the electron
  to create electronic computers
• No real progress has been made on chemical or
  nano computers
• So Algorithmic self assembly systems may be best
  best at next generation computers

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Interested?

• Winfree, E. 2003. DNA Computing by Self-Assembly.
  NAE's The Bridge, 33(4)31-38
• dna.caltech.edu
• Contains a plethora of papers about numerous
  aspects of self assembly