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

From OpenWetWare

# 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