Julius B. Lucks/Bibliography/Mao-Nature-407-2000

Notes on [1]

• computation using aperiodic self-assembly of DNA
  • isomorphism to Wang tiles which can act as a Turing machine
• triple-crossover molecules - 4 DNA strands that pair into 3 double helices in plane
• 8 triple-crossover molecules used
  • 2 x values representing inputs
  • 4 y values that perform the XOR corresponding to the inputs (0,0) (1,0) (0,1) (1,1)
  • 2 'corner' molecules which set up the initial conditions (bring together x_1 and y_1 for example)
• example computation (See Figure 1)
  • start with C1 and C2
  • C1 recruits y1=1, C2 recruits x1=1
  • x1 recruits x2=0
  • y2=1 can only bond to x2=0, and y1=1, therefore y2 = y1 XOR x2
  • x2 and y2 can recruit x3 and y3, respectively, thereby computing a cumulative XOR
• The calculation is read out by ligating together reporter strands on each of the tiles
  • Contains the series of inputs and intermediate steps in the calculation
• SAT problems in DNA computing context: 11, 14, 15
• Computation with DNA hairpins: 16
• 'This XOR computation can be used for executing one-time pad cryptosystem (theoretically unbreakable)': 17
• can also be used to specify the construction of nanomaterials algorithmically

References

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1. Notes