LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

160 Max H. Garzon, Kiranchand V. Bobba, and Bryan P. Hyde
Fig. 2. Gibbs energies of (a = above) template codes; and (b = below) tensor
product codes.
could possibly be used to encode symbolic information (strings) in DNA single
strands. A fundamental problem is that the abiotic nature of the information
would appear to require massive synthesis of DNA strands proportional to the
amount to be encoded. Current methods produce massive amounts of DNA
copies of the same species, but not of too many different species. Here, some
theoretical foundation and experimental results are provided for a new method,
described below. Theis method can be regarded as a new implementation of Tom
Head’s idea of aqueous computing for writing on DNA molecules [22,?], although
in through simpler operations (only hybridization.)
4.1 A Representation Using a Non-crosshybridizing Basis
Let B be a set of DNA molecules (the encoding basis, or “stations” in Head’s
terminology [22], here not necessarily bistable), which is assumed to be finite
and noncrosshybridizying according to some parameter τ (for example, the Gibbs
energy, or the h-distance mentioned above.) For simplicity, it is also assumed that
the length of the strands in B is a fixed integer n,andthatB contains no hairpins.
If τ =0andtheh-distance is the hybridization criterion, a maximal such set
B can be obtained by selectiong one strand from every (non-palindromic) pair
of Watson-Crick complementary strands. If τ = n, a maximal set B consists of
only one strand of length n, to which every other strand will hybridize under