LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

164 Max H. Garzon, Kiranchand V. Bobba, and Bryan P. Hyde
for relatively short bases are complete for simple discriminating tasks that may
suffice for many applications.
5 Summary and Conclusions
A new approach (tensor product) has been introduced for the systematic generation
of sets of codewords to encode information in DNA strands for computational
protocols so that undesirable crosshybridizations are prevented. This is
a hybrid method that combines analytic techniques with a combinatorial fitness
function (h-distance [18]) based on an abstract model of complementarity in
binary strings. A new way to represent digital information has also been introduced
using such sets of noncrosshybrizing codewords (possibly in solution, or
affixed to a DNA-chip) and some properties of these representations have been
explored.
An analysis of the energetics of codeword sets obtained by this method show
that their thermodynamic properties are good enough for acceptable performance
in the test tube, as determined the Gibbs energy model of Deaton et al.
[8]. These results also confirm that the h-distance is not only a computationally
tractable model, but also a reliable model for codeword design and analysis. The
final judge of the quality of these code sets is, of course, the performance in the
test tube. Preliminary evidence in vitro [5] shows that these codes are likely to
perform well in wet tubes.
A related measure of quality is what can be termed the coverage of the code,
i.e., how well spread the code is over the entire DNA space to provide representation
for every strand. This measure of quality is clearly inversely related to
the error-preventing quality of the code. it is also directly related to the capacity
of DNA of a given length to encode information, which is given by a quantity
that could be termed dimension of the space of DNA strands of length n, although
properties analogous to the concept of dimension in euclidean spaces are
yet to be assessed. Finally, determining how close tensor product codes come to
optimal size is also a question worthy of further study.
Acknowledgements
Much of the work presented here has been done in close collaboration with the
molecular computing consortium that includes Russell Deaton and Jin Wu (The
U. of Arkansas), Junghuei Chen and David Wood (The U. Delaware). Support
from the National Science Foundation grant QuBic/EIA-0130385 is gratefully
acknowledged.
References
1. L. Adleman (1994), Molecular computation of solutions of combinatorial problems.
Science 266, 1021-1024.