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

/pdf/rich-words-in-the-block-reversal-of-a-word-30w6hydl.pdf

Rich words in the block reversal of a word

Mateescu et al (2001) introduced the notion of Parikh matrix of a word as an extension of the well-known concept of Parikh vector of a word. The Parikh matrix provides more numerical information about a word than given by the Parikh vector. Here we introduce the notion of M-vector of a binary word which allows us to have a linear notation in the form of a unique vector representation of the Parikh matrix of the binary word. We then extend this notion of M-vector to a binary image treating it as a binary array over a two-symbol alphabet. This is done by considering the M-vectors of the words in the rows and columns of the array. Among the properties associated with a Parikh matrix, M-ambiguity or simply ambiguity of a word is one which has been investigated extensively in the literature. Here M-ambiguity of a binary array is defined in terms of its M-vector and we obtain conditions for M-ambiguity of a binary array.

Binary images, M-vectors, and ambiguity

The concept of Parikh matrix of a word was introduced by Mateescu et al. [8] to count scattered subwords in a given word over an ordered alphabet. Motivated by a recent study of Atanasiu [3], on this notion using morphisms, we consider, in this paper, general morphisms on words and obtain various properties related to subwords, in the context of a weak-ratio property considered in [12].

Morphisms and Weak-Ratio Property.

A DNA string is a Watson-Crick (WK-)palindrome when the complement of its reverse is equal to itself. The Watson-Crick mapping θ is an involution that is also an antimorphism. In this paper, we study a generalization of conjugates of a word that incorporate the notion of WK-involution θ called θ-conjugates or WK-conjugates. We consider some general properties of the set Cθ(w), i.e., the set of θ-conjugates of a word w. We characterize words with the same set of θ-conjugates and also provide words where the set of conjugates of a word is equal to the set of θ-conjugates of the word. We study the distribution of palindromes and Watson-Crick palindromes, also known as θ-palindromes, among both the set of conjugates and θ-conjugates of a word w. We also find the structure of words that have at least one (WK-)palindrome in Cθ(w). 

Counting (Watson-Crick) palindromes in Watson-Crick conjugates

A DNA string is a Watson-Crick (WK) palindrome when the complement of its reverse is equal to itself. The Watson-Crick mapping $\theta$ is an involution that is also an antimorphism. $\theta$-conjugates of a word is a generalisation of conjugates of a word that incorporates the notion of WK-involution $\theta$. In this paper, we study the distribution of palindromes and Watson-Crick palindromes, also known as $\theta$-palindromes among both the set of conjugates and $\theta$-conjugates of a word $w$. We also consider some general properties of the set $C_{\theta}(w)$, i.e., the set of $\theta$-conjugates of a word $w$, and characterize words $w$ such that $|C_{\theta}(w)|=|w|+1$, i.e., with the maximum number of elements in $C_{\theta}(w)$. We also find the structure of words that have at least one (WK)-palindrome in $C_{\theta}(w)$.

Kalpana Mahalingam

Papers

Rich words in the block reversal of a word

Binary images, M-vectors, and ambiguity

Morphisms and Weak-Ratio Property.

Counting (Watson-Crick) palindromes in Watson-Crick conjugates

Theta palindromes in theta conjugates