LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

Digital Information Encoding on DNA 159
can be done so that the composition of the strands follows a predetermined
pattern (e.g., 60% c/g’s and 40% a/t’s). All biners are then uniformly mapped to
aDNAcodewordbythesameassignment.Theresultingcodethushasminimum
h-distance between DNA codewords no smaller than in the original BNA seed.
Fig. 2(b) shows the quality of the codes obtained by this method, to be discussed
next.
3.4 Evaluation of Code Quality
For biner codes, a first criterion is the distribution of h-distance between codewords.
Fig. 1(a) shows this distribution for the various codes generated by tensor
products. The average minimun pairwise distance is, on the average, about 33%
of the strand length. This is comparable with the minimum distance of l/3 in
template codes.
As mentioned in [2], however, the primary criterion of quality for codeword
sets is performance in the test tube. A reliable predictor of such performance is
the Gibbs energy of hybridization. A computational method to compute the
Gibbs energy valid for short oligonucleotides (up to 60 bps) is given in [8].
Code sets obtained by generate-and-filter methods using this model have been
tested in the tube with good experimental results [8,10]. The same Gibbs energy
calculation was used to evaluate and compare the quality of code sets generated
by the template and tensor product methods. According to this method, the
highest Gibbs energy allowable between two codewords must be, at the very
least, −6 Kcal/mole if they are to remain noncrosshybridizing [8].
Statistics on the Gibbs energy of hybridization are shown in Fig. 2. The template
codes of very short lengths in Fig. 2(a) remain within a safe region (above
−6 kCal/Mole), but they have too low Gibbs energies that permit crosshybridization
for longer lengths. On the other hand, although the tensor product operation
initially decreases the Gibbs energy, the Gibbs energies eventually stabilize and
remain bounded within a safe region that does not permit cross hybridization,
both on the average and minimum energies.
Fig. 3 shows a more detailed comparison of the frequency of codewords in
each of the two types of codes with a Gibbs energy prone to cross hybridization
(third bar from top). Over 80% of the pairwise energies are noncrosshybridizing
for template codes (top and middle bars), but they dip below the limit in
a significant proportion. On the other hand, all pairwise energies predict no
crosshybridization among tensor product codewords, which also exhibit more
positive energies. Finally, the number of codewords produced is larger with tensor
products, and increases rapidly when the lengths of the codewords reaches
64− and 128−mers (for which no template codes are available.)
4 Encoding Abiotic Information in DNA Spaces
This section explores the broader problem of encoding abiotic information in
DNA for storage and processing. The methods presented in the previous section