Characterization of Non-crosshybridizing DNA Oligonucleotides Manufactured in vitro

Chen, J.; Deaton, Russell; Garzón, Max H.; Kim, J. W.; Wood, David Murakami; Bi, Hong; Carpenter, Dylan; Wang, Y. Z.

doi:10.1007/s11047-005-4460-2

Cited by 18 publications

(13 citation statements)

References 17 publications

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“…For more details we refer the reader e.g. to [5,12,13]. Here we apply the formal language approach which has been used in [2,7,8,10,11] and others.…”

Section: Introductionmentioning

confidence: 99%

Hairpin Structures in DNA Words

et al. 2006

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Abstract. We formalize the notion of a DNA hairpin secondary structure, examining its mathematical properties. Two related secondary structures are also investigated, taking into the account imperfect bonds (bulges, mismatches) and multiple hairpins. We characterize maximal sets of hairpin-forming DNA sequences, as well as hairpin-free ones. We study their algebraic properties and their computational complexity. Related polynomial-time algorithms deciding hairpin-freedom of regular sets are presented. Finally, effective methods for design of long hairpinfree DNA words are given.

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“…For more details we refer the reader e.g. to [5,12,13]. Here we apply the formal language approach which has been used in [2,7,8,10,11] and others.…”

Section: Introductionmentioning

confidence: 99%

Hairpin Structures in DNA Words

et al. 2006

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“…Thermodynamical methods such as those in [30,33] provide the most precise results but are computationally the most expensive. Experimental studies trying to construct DNA codes in vitro with the help of the PCR operation can be found, e.g., in [16,31]. An opposite approach relying solely on the WK complementarity allows for fastest but least precise methods (see, e.g., [54,60,65] as examples).…”

Section: Dna Encoding: Problem Setting and Notationmentioning

confidence: 99%

DNA Computing — Foundations and Implications

Kari

Seki

Sosík

2012

Handbook of Natural Computing

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“…Previous attempts to construct noncrosshybridizing sets in silico using various methods such as templates and error-correcting codes (Arita et al, 2002) or heuristic search (Tulpan et al, 2005) tended to produce relatively small sets, likely far from optimal. Other methods to create noncrosshybridizing sets in vitro (Chen et al, 2006) are attractive for being able to produce a maximal physical set. However, they suffer from the challenge of identifying precisely its size and, more importantly, the composition of the sequences, hence little is learned for a more principled understanding of the complexity of DNA codeword design and, more importantly, the structure of the Gibbs energy landscapes.…”

Section: Dna Codes Gibbs Energies and Dna Spacesmentioning

confidence: 99%

“…This Codeword Design problem has seen some progress in the last decade in at least two subareas. First, in searching and/or building such DNA code sets Deaton et al, 2006;Tulpan et al, 2005;Chen et al, 2006), in which the size of feasible computational problems or self-assembled nanostructures is usually directly related to the largest ensemble of DNA molecules that satisfy a given set of crosshybridization and noncrosshybrization constraints. The second and perhaps more important area deals with developing the appropriate theoretical framework to understand and analyze this type of problems, organize the knowledge about the subject in a systematic manner, and explore the power and limitations of biomolecules at large.…”

Section: Introductionmentioning

confidence: 99%

“…Solutions to finding large sets of short oligonucleotides with noncrosshybridizing (nxh) properties have been produced by several groups, particularly the PCR Selection (PCRS) protocol used below (Garzon et al, 2009;Deaton et al, 2006;Tulpan et al, 2005;Chen et al, 2006). In prior work , a theoretical framework was provided to analyze this problem.…”

Section: Introductionmentioning

confidence: 99%

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Geometric Approaches to Gibbs Energy Landscapes and DNA Oligonucleotide Design

Garzón

Bobba

2011

International Journal of Nanotechnology and Molecular Computation

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DNA codeword design has been a fundamental problem since the early days of DNA computing. The problem calls for finding large sets of single DNA strands that do not crosshybridize to themselves, to each other or to others' complements. Such strands represent so-called domains, particularly in the language of chemical reaction networks (CRNs). The problem has shown to be of interest in other areas as well, including DNA memories and phylogenetic analyses because of their error correction and prevention properties. In prior work, a theoretical framework to analyze this problem has been developed and natural and simple versions of Codeword Design have been shown to be NP-complete using any single reasonable metric that approximates the Gibbs energy, thus practically making it very difficult to find any general procedure for finding such maximal sets exactly and efficiently. In this framework, codeword design is partially 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, the authors describe in detail a new general technique to embed them in Euclidean spaces in such a way that oligonucleotides with high (low, respectively) hybridization affinity are mapped to neighboring (remote, respectively) points in a geometric lattice. This embedding materializes long-held metaphors about codeword design in analogies with error-correcting code design in information theory in terms of sphere packing and leads to designs that are in some cases known to be provably nearly optimal for small oligonucleotide sizes, whenever the corresponding spherical codes in Euclidean spaces are known to be so. It also leads to upper and lower bounds on estimates of the size of optimal codes of size under 20-mers, as well as to a few infinite families of DNA strand lengths, based on estimates of the kissing (or contact) number for sphere codes in high-dimensional Euclidean spaces. Conversely, the authors show how solutions to DNA codeword design obtained by experimental or other means can also provide solutions to difficult spherical packing geometric problems via these approaches. Finally, the reduction suggests a tool to provide some insight into the approximate structure of the Gibbs energy landscapes, which play a primary role in the design and implementation of biomolecular programs.

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Characterization of Non-crosshybridizing DNA Oligonucleotides Manufactured in vitro

Cited by 18 publications

References 17 publications

Hairpin Structures in DNA Words

Hairpin Structures in DNA Words

DNA Computing — Foundations and Implications

Geometric Approaches to Gibbs Energy Landscapes and DNA Oligonucleotide Design

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