Digital production, transmission and storage have revolutionized how we access and use information but have also made archiving an increasingly complex task that requires active, continuing maintenance of digital media. This challenge has focused some interest on DNA as an attractive target for information storage because of its capacity for high-density information encoding, longevity under easily achieved conditions and proven track record as an information bearer. Previous DNA-based information storage approaches have encoded only trivial amounts of information or were not amenable to scaling-up, and used no robust error-correction and lacked examination of their cost-efficiency for large-scale information archival. Here we describe a scalable method that can reliably store more information than has been handled before. We encoded computer files totalling 739 kilobytes of hard-disk storage and with an estimated Shannon information of 5.2 × 10(6) bits into a DNA code, synthesized this DNA, sequenced it and reconstructed the original files with 100% accuracy. Theoretical analysis indicates that our DNA-based storage scheme could be scaled far beyond current global information volumes and offers a realistic technology for large-scale, long-term and infrequently accessed digital archiving. In fact, current trends in technological advances are reducing DNA synthesis costs at a pace that should make our scheme cost-effective for sub-50-year archiving within a decade.

Towards practical, high-capacity, low-maintenance information storage in synthesized DNA

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Molecular Biology of the Gene.

: Significant progress has been made with solution of location problems and in preprocessing and decomposition for discrete optimization. There has also been research on the application of techniques from combinational optimization to nonlinear problems.

http://www.dtic.mil/dtic/tr/fulltext/u2/a273552.pdf

Discrete Applied Mathematics

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Computation in Living Cells: Gene Assembly in Ciliates

This paper provides an overview of existing approaches to encoding information on DNA strands for biocomputing, with a focus on the notion of Watson---Crick (WK) palindromes. We obtain a closed form for, as well as several properties of WK palindromes: The set of WK-palindromes is dense, context-free, but not regular, and is in general not closed under catenation and insertion. We obtain some properties that link the WK palindromes to classical notions such as that of primitive words. For example we show that the set of WK-palindromic words that cannot be written as the product of two nonempty WK-palindromes equals the set of primitive WK-palindromes. We also investigate various simultaneous Watson---Crick conjugate equations of words and show that the equations have, in most cases, only Watson---Crick palindromic solutions. Our results hold for more general functions, such as arbitrary morphic and antimorphic involutions.

Watson---Crick palindromes in DNA computing

We define a new relation on words by a finite series of insertions and/or deletions of palindromic subwords. In particular we concentrate on insertion or deletion of Watson---Crick palindromes. We show that the new relation ~? is, in fact, an equivalence relation where ? is any arbitrary antimorphic involution that is not the identity on the letters of the alphabet. We also show that the set of all ?-palindromic free words defined in (Daley et al. in preparation) is ~?-independent. Using the relation we define a new subclass of primitive words which we call as ~?-primitive words and show that the class of all ~?-primitive words is closed under circular permutations. We also define ~?-conjugates and ~?-commutativity and study the properties of such words and show that they are similar to that of conjugate words and words that commute.

A relation by palindromic subwords

The notion of extending Parikh q-matrix with respect to a word instead of an ordered alphabet is introduced. Some basic properties of this extending Parikh q-matrices have been investigated. Also it has been shown that the extending Parikh q-matrix mapping can be obtained as a composition of a Parikh q-matrix mapping and a word substitution morphism.

/pdf/extending-parikh-q-matrices-3aysjj5yza.pdf

Extending Parikh q-matrices

AbstractIn this paper we define and investigate the binary word operation of strong-\(\theta \)-catenation (denoted by \(\otimes \)) where \(\theta \) is an antimorphic involution modelling the Watson-Crick complementarity of DNA single strands. When iteratively applied to a word u, this operation generates all the strong-\(\theta \)-powers of u (defined as any word in \(\{u, \theta (u)\}^+\)), which amount to all the Watson-Crick powers of u when \(\theta = \theta _{DNA}\) (the antimorphic involution on the DNA alphabet \(\varDelta = \{A, C, G, T\}\) that maps A to T and C to G). In turn, the Watson-Crick powers of u represent DNA strands usually undesirable in DNA computing, since they attach to themselves via intramolecular Watson-Crick complementarity that binds u to \(\theta _{DNA}(u)\), and thus become unavailable for other computational interactions. We find necessary and sufficient conditions for two words u and v to commute with respect to the operation of strong-\(\theta \)-catenation. We also define the concept of \(\otimes \)-primitive root pair of a word, and prove that it always exists and is unique.KeywordsDNA computingMolecular computingBinary word operationsAlgebraic properties 

Watson-Crick Powers of a Word

P systems with graph productions were introduced by Freund in 2004. It was shown that such a variant of P system can generate any recursively enumerable language of weakly connected graphs. In this paper, we consider such P systems where the input is any connected graph and each graph production is labelled over an alphabet. We name the system as Process Guided P System where the computation is guided by a string over the set of labels. The set of all strings over the label alphabet which results in the halting computation of the system forms a guiding language of the system. We compare such guiding languages with Chomsky hierarchy. Two direct applications of this variant are also given.

Labelled graph rules in P systems

A new discontinuous model of computation called one-way jumping finite automata was defined by H. Chigahara et. al. This model was a restricted version of the model jumping finite automata. These automata read an input symbol-by-symbol and jump only in one direction. A generalized linear one-way jumping finite automaton makes jumps after deleting a substring of an input string and then changes its state. These automata can make sequence of jumps in only one direction on an input string either from left to right or from right to left. We show that newly defined model is powerful than its original counterpart. We define and compare the variants, generalized right linear one-way jumping finite automata and generalized left linear one-way jumping finite automata. We also compare the newly defined models with Chomsky hierarchy. Finally, we explore closure properties of the model.

Kalpana Mahalingam

Papers

A relation by palindromic subwords

Extending Parikh q-matrices

Watson-Crick Powers of a Word

Labelled graph rules in P systems

Generalized Circular One-Way Jumping Finite Automata.