Abstract
Finding a large set of single DNA strands that do not crosshybridize to themselves or to their complements (so-called domains in the language of chemical reaction networks (CRNs)) is an important problem in DNA computing, self-assembly, DNA memories and phylogenetic analyses because of their error correction and prevention properties. In prior work, we have provided a theoretical framework to analyze this problem and showed that Codeword Design is NP-complete using any single reasonable metric that approximates the Gibbs energy, thus practically excluding the possibility of finding any procedure to find maximal sets exactly and efficiently. In this framework, codeword design is reduced to finding large sets of strands maximally separated in DNA spaces and, therefore, the size of such sets depends on the geometry of these spaces. Here, we introduce a new general technique to embed them in Euclidean spaces in such a way that oligos with high/low hybridization affinity are mapped to neighboring/remote points in a geometric lattice, respectively. This embedding materializes long-held mataphors about codeword design in terms of sphere packing and leads to designs that are in some cases known to be provable 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 DNA strand lengths, based on estimates of the kissing (or contact) number for sphere packings in Euclidean spaces. Conversely, we show how solutions to DNA codeword design obtained by experimental or other means can also provide solutions to difficult spherical packing geometric problems via this embedding. Finally, the reduction suggests an analytical tool to arrange the dynamics of strand displacement cascades in CRNs to effect the transformation through bounded Gibbs energy changes, and thus is potentially useful in compilers for wet tube implementation of biomolecular programs.
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Garzon, M.H., Bobba, K.C. (2012). A Geometric Approach to Gibbs Energy Landscapes and Optimal DNA Codeword Design. In: Stefanovic, D., Turberfield, A. (eds) DNA Computing and Molecular Programming. DNA 2012. Lecture Notes in Computer Science, vol 7433. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32208-2_6
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DOI: https://doi.org/10.1007/978-3-642-32208-2_6
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