Theoretical and Experimental DNA Computation (Natural ...

110 5 Physical Implementations
not to provide definitive answers ...but rather to show that a number of seemingly
disparate questions must be connected to each other in a fundamental
way.” [46]
In [45], Conrad expanded on this work, showing how the information processing
capabilities of organic molecules may, in theory, be used in place of
digital switching components (Fig. 5.1a). Enzymes may cleave specific substrates
by severing covalent bonds within the target molecule. For example,
as we have seen, restriction endonucleases cleave strands of DNA at specific
points known as restriction sites. In doing so, the enzyme switches the state of
the substrate from one to another. Before this process can occur, a recognition
process must take place, where the enzyme distinguishes the substrate from
other, possibly similar molecules. This is achieved by virtue of what Conrad
refers to as the “lock-key” mechanism, whereby the complementary structures
of the enzyme and substrate fit together and the two molecules bind strongly
(Fig. 5.1b). This process may, in turn, be affected by the presence or absence
of ligands. Allosteric enzymes can exist in more than one conformation (or
“state”), depending on the presence or absence of a ligand. Therefore, in addition
to the active site of an allosteric enzyme (the site where the substrate
reaction takes place) there exists a ligand binding site which, when occupied,
changes the conformation and hence the properties of the enzyme. This
gives an additional degree of control over the switching behavior of the entire
molecular complex.
In [17], Arkin and Ross show how various logic gates may be constructed
using the computational properties of enzymatic reaction mechanisms (also
see [34] for a review of this work). In [34], Bray also describes work [79, 80]
showing how chemical “neurons” may be constructed to form the building
blocks of logic gates.
5.3 Initial Set Construction Within Filtering Models
All filtering models use the same basic method for generating the initial set
of strands. An essential difficulty in all filtering models is that initial multisets
generally have a cardinality which is exponential in the problem size. It
would be too costly in time, therefore, to generate these individually. What
we do in practice is to construct an initial solution, or tube, containing a
polynomial number of distinct strands. The design of these strands ensures
that the exponentially large initial multi-sets of our model will be generated
automatically. The following paragraph describes this process in detail.
Consider an initial set of all elements of the form p1k1,p2k2,...,pnkn. This
may be constructed as follows. We generate an oligonucleotide (commonly
abbreviated to oligo) uniquely encoding each possible subsequence piki where
1 ≤ i ≤ n and 1 ≤ ki ≤ k. Embedded within the sequence representing pi is
our chosen restriction site. There are thus a polynomial number, nk,ofdistinct
oligos of this form. The task now is how to combine these to form the desired