DNA Codeword Design: Theory and Applications

Abstract

This is a survey of the origin, current progress and applications of a major roadblock to the development of analytic models for DNA computing (a massively parallel programming methodology) and DNA self-assembly (a nanofabrication methodology), namely the so-called CODEWORD DESIGN problem. The problem calls for finding large sets of single DNA strands that do not crosshybridize to themselves or to their complements and has been recognized as an important problem in DNA computing, self-assembly, DNA memories and phylogenetic analyses because of their error correction and prevention properties. Major recent advances include the development of experimental techniques to search for such codes, as well as a theoretical framework to analyze this problem, despite the fact that it has been proven to be NP-complete using any single concrete metric space to model the Gibbs energy. In this framework, codeword design is reduced to finding large sets of strands maximally separated in DNA spaces and, therefore, the key to finding such sets would lie in knowledge of the geometry of these spaces. A new general technique has been recently found to embed them in Euclidean spaces in a hybridization-affinity-preserving manner, i.e., in such a way that oligos with high/low hybridization affinity are mapped to neighboring/remote points in a geometric lattice, respectively. This isometric embedding materializes long-held metaphors about codeword design in terms of sphere packing and error-correcting codes and leads to designs that are in some cases known to be provably nearly optimal for some oligo sizes. It also leads to upper and lower bounds on estimates of the size of optimal codes of size up to 32–mers, as well as to infinite families of solutions to CODEWORD DESIGN, based on estimates of the kissing (or contact) number for sphere packings in Euclidean spaces. Conversely, this reduction suggests interesting new algorithms to find dense sphere packing solutions in high dimensional spheres using results for CODEWORD DESIGN previously obtained by experimental or theoretical molecular means, as well as a proof that finding these bounds exactly is NP-complete in general. Finally, some research problems and applications arising from these results are described that might be of interest for further research.