Sticky-free and overhang-free DNA languages

Kari, Lila; Konstantinidis, Stavros; Losseva, Elena; Wozniak, Geoff

doi:10.1007/s00236-003-0118-7

Cited by 36 publications

(39 citation statements)

References 21 publications

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“…It can be shown that also Lev d,k is a similarity relation, with parameters (d, d + k) -see [17]. We note that for most of the DNA language properties considered in [9,15,16] the above problem is undecidable for context-free languages. As the (θ, sim)-bond-free property seems to be rather general, it might be surprising that the same problem is decidable.…”

Section: Definition 1 a Binary Relation Sim Is Called A Similarity Rmentioning

confidence: 89%

Bond-Free Languages: Formalizations, Maximality and Construction Methods

2005

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Abstract. The problem of negative design of DNA languages is addressed, that is, properties and construction methods of large sets of words that prevent undesired bonds when used in DNA computations. We recall a few existing formalizations of the problem and then define the property of sim-bond-freedom, where sim is a similarity relation between words. We show that this property is decidable for context-free languages and polynomial-time decidable for regular languages. The maximality of this property also turns out to be decidable for regular languages and polynomial-time decidable for an important case of the Hamming similarity. Then we consider various construction methods for Hamming bond-free languages, including the recently introduced method of templates, and obtain a complete structural characterization of all maximal Hamming bond-free languages. This result is applicable to the θ-k-code property introduced by Jonoska and Mahalingam.

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Section: Definition 1 a Binary Relation Sim Is Called A Similarity Rmentioning

confidence: 89%

Bond-Free Languages: Formalizations, Maximality and Construction Methods

2005

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“…1 (a), and intermolecular, (b) and (c). The following properties of a DNA language L ⊆ Σ + preventing such a hybridization have been defined in [4,8,10].…”

Section: Undesirable Bonds In Dna Languagesmentioning

confidence: 99%

“…Solid languages are also used in [10] as a tool for constructing error-detecting DNA languages that are invariant under bio-operations. We refer to [6,10,11] for further examples and for mutual relations between classes of a DNA languages satisfying these properties.…”

Section: Undesirable Bonds In Dna Languagesmentioning

confidence: 99%

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Preventing Undesirable Bonds Between DNA Codewords

2005

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Abstract. The input data for DNA computing must be encoded into the form of single or double DNA strands. As complementary parts of single strands can bind together forming a double-stranded DNA sequence, one has to impose restrictions on these sets of DNA words (=languages) to prevent them from interacting in undesirable ways. We recall a list of known properties of DNA languages which are free of certain types of undesirable bonds. Then we introduce a general framework in which we can characterize each of these properties by a solution of a uniform formal language inequation. This characterization allows us among others to construct (i) a uniform algorithm deciding in polynomial time whether a given DNA language possesses any of the studied properties, and (ii) in many cases also an algorithm deciding whether a given DNA language is maximal with respect to the desired property.

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“…On the other hand, in vitro biomolecular computing often considers them as disadvantages because it is very likely that the secondary structure formation of a DNA/RNA strand will prevent it from interacting with other DNA/RNA strands in the expected, pre-programmed way. Thence, many studies exist on how to free sequence sets from secondary structures [4], [5], [6], [7], [8], [9], [10].…”

Section: Introductionmentioning

confidence: 99%

Towards the Sequence Design Preventing Pseudoknot Formation

Kari

Seki

2009

Natural Computing

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Abstract. This paper addresses a pseudoknot-freeness problem of DNA and RNA sequences, motivated by biomolecular computing. WatsonCrick (WK) complementarity forces DNA strands to fold into themselves and form so-called secondary structures, which are usually undesirable for biomolecular computational purposes. This paper studies pseudoknot-bordered words, a mathematical formalization of a common secondary structure, the pseudoknot. We obtain several properties of WK-pseudoknot-bordered and -unbordered words. One of the main results of the paper is that a sufficient condition for a WK-pseudoknotunbordered word u to result in all words in u + being WK-pseudoknotunbordered is for u not to be a primitive word.

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Sticky-free and overhang-free DNA languages

Cited by 36 publications

References 21 publications

Bond-Free Languages: Formalizations, Maximality and Construction Methods

Bond-Free Languages: Formalizations, Maximality and Construction Methods

Preventing Undesirable Bonds Between DNA Codewords

Towards the Sequence Design Preventing Pseudoknot Formation

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