Biomedical Engineering Reference
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both input stimuli ( Muramatsu et al. 2006 ). This AND gate implementation could
mechanically drive biomolecular devices.
7.3
Self-Assembly Biomolecular Computing
Biomolecular computing can help build complex two- or three-dimensional self-
assembled or self-replicating structures, illustrating a bottom-up approach for
nanoscale technology. Self-assembling, as discussed in Chap. 5 , can be done with
nanometer precision. A modular way of programmable assembly of nanostructures
involves DNA tiles that have sticky ends that match the corresponding sticky ends
of other tiles. The net result is a tiling lattice ( Ezziane 2006 ). Examples of DNA
computation using self-assembled tiles are given in Feldkamp and Niemeyer ( 2006 ),
and a detailed discussion of error corrections can be found in Sager et al. ( 2008 ).
An illustration of biomolecular computation based on shape processing is the
problem of three-vertex colorability for a graph with six vertices and nine edges,
which can be solved by self-assembly of DNA strands ( Wu et al. 2009 ). In this case,
stable-branched DNA molecules are used to encrypt the solution as a nanoobject
with a connectivity resembling that of the graph and not as sets of symbols encoded
in DNA base pair sequence. The computation is performed in the presence of
enzymes, which catalyze ligation and restriction reactions. Each vertex is embodied
by a branched junction molecule with a number of arms equal to the number of
connections it must establish with its adjacent vertices. Each arm has an extended
single-strand 5 0 end, composed of 24 nt, each color being represented by different
shades of gray in Fig. 7.5 .The5 0 ends identify unambiguously each edge that
connects two neighboring vertices through three specific parts that enter their
composition.
These parts, denoted by x, y, and z, encode the edge information in the x and z
portions and the color in y, so that all three arms of a branched junction have the
same y parts on their 5 0 ends and the portions x and z on one arm of the molecule
that represent vertex i, for example, are complementary to the x and z parts of the
single-strand extensions of one of the arms representing the adjacent vortex j (their
y portions are not complementary in this case, since the colors of adjacent vertices
3
6
4
1
2
Fig. 7.5 DNA graph that
encrypts the solution of the
three-vertex colorability
problem
5
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