Theoretical and Experimental DNA Computation (Natural ...

62 3 Models of Molecular Computation
as proteins or DNA on a square lattice. The model extends the theory of tiling
by Wang tiles [152] to encompass the physics of self-assembly.
Within the model, computations occur by the self-assembly of square tiles,
each side of which may labelled. The different labels represent ways in which
tiles may bind together, the strength (or “stickiness”) of the binding depending
on the binding strength associated with each side. Rules within the system
are therefore encoded by selecting tiles with specific combinations of labels
and binding strengths. We assume the availability of an unlimited number of
each tile. The computation begins with a specific seed tile, and proceeds by
the addition of single tiles. Tiles bind together to form a growing complex
representing the state of the computation only if their binding interactions
are of sufficient strength (i.e., if the pads stick together in such a way that
the entire complex is stable).
1 1
1
1 1
0
L 0
S
(a)
0
0
0 1
0 0
1
2 3
R
L 0
512
L 0
0
0
0
0
256
L 0
0
0
0
0
0
0
0
0
128
L 0
0
0
0
0
0
0
0
0
0
0
64
L 0
0
0
0
0
0
0
0
0
0
0
0
0
32
L 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
(b)
L 0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
8
L 0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
4
L 0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
1
2
L 0
1 0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
R
R
R
R
R
R
R
R
R
S
0
Direction of growth
Fig. 3.6. (a) Binary counting tiles. (b) Progression of the growth of the complex
Consider the example depicted in Fig. 3.6. This shows a simple system for
counting in binary within the Tile Assembly Model. The set of seven different
9
8
7
6
5
4
3
2
1
0