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

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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


  1. Mao C, LaBean TH, Relf JH, and Seeman NC. Logical computation using algorithmic self-assembly of DNA triple-crossover molecules. Nature. 2000 Sep 28;407(6803):493-6. DOI:10.1038/35035038 | PubMed ID:11028996 | HubMed [Mao-Nature-407-2000]