Biomolecular Computing - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 199

must differ). All three x, y, and z parts are encoded in 8 nt. When two arms of vertices
with the same color hybridize, they form a restriction site alloying molecule cutting
by a specific enzyme, associated to that specific color. On the contrary, when vertices
with different colors join, the y parts of the sticky ends contain despaired restriction
sites and the resulting edge is not destroyed by the restriction enzymes. The
algorithm that solves the problem of three-vertex colorability involves the operations
of annealing, during which the sticky ends hybridize, ligation, cleavage/cutting,
during which the structures with joined identical-colored vertices are destroyed by
the action of restriction enzymes, and extraction, which identifies the solution to the
problem by the size of the remaining graphs. Three copies of each vertex, one for
each color, are initially placed in solution, and the biomolecules are selected such
that the optimal temperatures for ligation and restriction are different enough so
that they take place separately as the temperature varies. The nanoobject that results
after hybridization consists of a single strand that traverses twice the graph, each
edge being a dsDNA molecule. The mathematical model of bidimensional shapes
with colored edges is called Wang tile.
Biomolecular computing can also control the reversible self-assembly of
nanoparticles into structural aggregates. For example, it is possible to couple
200-nm silica nanoparticles with pH-sensitive polymer shells with enzyme-base
logic gates ( Motornov et al. 2008 ). For pH <5, the nanoparticle dispersion is
stabilized by the charged polymer molecules, whereas for pH >5the nanoparticles
aggregate into structures with dimensions of 3m because hydrophobic interactions
between polymer chains dominate. To reversibly control the self-assembly process,
pH changes must occur as a result of enzyme-based computing systems that generate
biocatalytic reactions. If the pH-changing reaction occurs only in the presence of
two input enzymes, the system implements the AND operation, the 0 and 1 logic
states being encoded in the absence and presence, respectively, of each enzyme.
Similarly, an OR logic gate is implemented if a pH change takes place in the
presence of either one of two enzymes, which activate independent biocatalytic
reactions. After completion of these reactions, the state of the system can be reset
by another enzyme, which restores the pH value.
Other applications make use of DNA-patterned scaffolds or templates for
targeted deposition of specific biomolecules that are part of computing protocols.
Biomolecular logic circuits based on DNA self-assembly can identify femtomole
quantities of analytes, such as short nucleic acids or proteins, in solution by
encoding the optical response of arrangements of chromophores ( Pistol et al. 2010 ).
This sensor consists of a 2 80 80-nm 3 DNA grid, assembled as a 4 4-tile
motif, on which input chromophores are attached at precise locations on one tile and
the output chromophores on the neighboring tile. The resonance energy transfer of
bound chromophores generates constrained pathways for excitons, which transfer
between donors and acceptors, such that a multidonor resonance energy transfer
index due to denaturation of the gate or input excitation designates the output.
Chromophore triplets, consisting of two donors and one acceptor, are particularly
well suited for logic and sensing since their optical responses can be changed by
tuning the donor-acceptor separations.