LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

156 Max H. Garzon, Kiranchand V. Bobba, and Bryan P. Hyde
rate 1, and are therefore more efficient for a given encoding length. The result of
the computation only needs to re-interpreted in terms of the assigned mapping
used to transduce the original problem’s input into DNA strands. Therefore,
given the nature of the inspiring biochemistry, analogous codes for hybridization
distance are more appropriately called error-preventing codes, because the minimum
separation in terms of hybridization distance prevents errors, instead of
enabling error detection and correction once they have occurred.
2.3 Gibbs Energy
Ideally, the Gibbs energy released in the hybridization process between strand
pairs is the most appropriate criterion of quality for a code set for experiments in
vitro. Although hybridization reactions in vitro are governed by well established
rules of local interaction between base pairings, difficulties arise in trying to
extend these rules to even short oligonucleotides (less than 150-mers) in a variety
of conditions [28]. Hence an exhaustive search of strand sets of words maximally
separated in a given coding space is infeasible, even for the small size of oligonucleotides
useful in DNA computing.
Computation of the Gibbs energy thus relies on approximations based on
various assumptions about the type of interactions between neighboring bonds.
Various models have been proposed for the range of oligonucleotides used in
DNA-based computing, major among which are the nearest-neighbor model and
the staggered-zipper model [28]. We use an extension of the nearest neighbor
model proposed by [8] that computes optimal alignments between DNA oligonucleotides
using a dynamic programming algorithm. There is evidence that this
calculation of the Gibbs energy, while not as computationally efficient as the
h-distance, is a good predictor of actual hybridization in the range of 20- to
60-mers in PCR reactions in vitro [5].
3 Error-Preventing Codes
Codes designs can now be described based on the tensor product operation and
compared with codes obtained using the template method [2]. Both types of
codes are obtained by first finding good biner sets (a template or a seed set)
which is then used to generate a set of BNA strings. These codes are then
transformed into code sets for DNA computation in real test tubes, so the basic
question becomes how they map to codeword sets in DNA and how their quality
(as measured by the parameter τ) maps to the corresponding reaction conditions
and DNA ensemble behavior.
3.1 The Template Method
The template method requires the use of a template n-biner T which is as far
from itself as possible in terms of h-measure, i.e., |T,T| >> 0, and an errorcorrecting
code C with words of length n. The bits are mapped to DNA words