LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

Methods for Constructing Coded DNA
Languages
Nataˇsa Jonoska and Kalpana Mahalingam
Department of Mathematics
University of South Florida, Tampa, FL 33620, USA
jonoska@math.usf.edu, mahaling@helios.acomp.usf.edu
Abstract. The set of all sequences that are generated by a biomolecular
protocol forms a language over the four letter alphabet ∆ = {A, G, C, T }.
This alphabet is associated with a natural involution mapping θ, A ↦→ T
and G ↦→ C whichisanantimorphismof∆ ∗ . In order to avoid undesirable
Watson-Crick bonds between the words (undesirable hybridization),
the language has to satisfy certain coding properties. In this paper we
build upon an earlier initiated study and give general methods for obtaining
sets of code words with the same properties. We show that some
of these code words have enough entropy to encode {0, 1} ∗ in a symbolto-symbol
mapping.
1 Introduction
In bio-molecular computing and in particular DNA based computations and
DNA nanotechnology, one of the main problems is associated with the design
of the oligonucleotides such that mismatched pairing due to the Watson-Crick
complementarity is minimized. In laboratory experiments non-specific hybridizations
pose potential problems for the results of the experiment. Many authors
have addressed this problem and proposed various solutions. Common approach
has been to use the Hamming distance as a measure for uniqueness [3,8,9,11,19].
Deaton et al. [8,11] used genetic algorithms to generate a set of DNA sequences
that satisfy predetermined Hamming distance. Marathe et al. [20] also used
Hamming distance to analyze combinatorial properties of DNA sequences, and
they used dynamic programing for design of the strands used in [19]. Seeman’s
program [23] generates sequences by testing overlapping subsequences to enforce
uniqueness. This program is designed for producing sequences that are suitable
for complex three-dimensional DNA structures, and the generation of suitable
sequences is not as automatic as the other programs have proposed. Feldkamp
et al. [10] also uses the test for uniqueness of subsequences and relies on tree
structures in generating new sequences. Ruben at al. [22] use a random generator
for initial sequence design, and afterwards check for unique subsequences
with a predetermined properties based on Hamming distance. One of the first
theoretical observations about number of DNA code words satisfying minimal
Hamming distance properties was done by Baum [3]. Experimental separation
of strands with “good” codes that avoid intermolecular cross hybridization was
N. Jonoska et al. (Eds.): Molecular Computing (Head Festschrift), LNCS 2950, pp. 241–253, 2004.
c○ Springer-Verlag Berlin Heidelberg 2004