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

Given a word \(w=w_1w_2\cdots w_n\) of length n over an ordered alphabet \(\Sigma _k\), we construct a graph \(G(w)=(V(w), E(w))\) such that V(w) has n vertices labeled \(1, 2,\ldots , n\) and for \(i, j \in V(w)\), \((i, j) \in E(w)\) if and only if \(w_iw_j\) is a scattered subword of w of the form \(a_{t}a_{t+1}\), \(a_t \in \Sigma _k\), for some \(1 \le t \le k-1\) with the ordering \(a_t<a_{t+1}\). A graph is said to be Parikh word representable if there exists a word w over \(\Sigma _k\) such that \(G=G(w)\). In this paper we characterize all Parikh word representable graphs over the binary alphabet in terms of chordal bipartite graphs. It is well known that the graph isomorphism (GI) problem for chordal bipartite graph is GI complete. The GI problem for a subclass of (6, 2) chordal bipartite graphs has been addressed. The notion of graph powers is a well studied topic in graph theory and its applications. We also investigate a bipartite analogue of graph powers of Parikh word representable graphs. In fact we show that for G(w), \(G(w)^{[3]}\) is a complete bipartite graph, for any word w over binary alphabet.

Structural Properties of Word Representable Graphs

/pdf/involution-codes-with-application-to-dna-strand-design-4ud7cbrp6x.pdf

Involution Codes with Application to DNA Strand Design

This paper discusses some algebraic properties of Parikh q-matrices. A new way of q-counting of the subwords of a given word w is introduced. It has been shown that the notion of alternating Parikh q-matrices can be characterized using the q-counting polynomials. We also show that a Minor of a Parikh q-matrix is a polynomial in q with non-negative coefficients. Further this work provides an extension of the definition of partial sum ⊕ to Parikh q-matrices. A characterization on words x and y such that the partial sum of their Parikh q-matrices is always a Parikh q-matrix is also given. We also provide some partial results for the case q = 1.

Some Algebraic Aspects of Parikh q-Matrices

We introduce an extension of the restricted shuffle operator on binary words considered by Atanasiu and Teh (2016). We then derive properties on Parikh matrix equivalence of words over a binary alp...

Properties of Parikh Matrices of Binary Words Obtained by an Extension of a Restricted Shuffle Operator

In this paper we study a generalization of the classical notions of solid codes and comma-free codes: involution solid codes (0-solid) and involution join codes (0-join). These notions are motivated by DNA strand design where Watson-Crick complementarity can be formalized as an antimorphic involution. We investigate closure properties of these codes, as well as necessary conditions for 0-solid codes to be maximal. We show how the concept of 0-join can be utilized such that codes that are not themselves θ-comma free can be split into a union of subcodes that are θ-comma free.

Kalpana Mahalingam

Papers

Structural Properties of Word Representable Graphs

Involution Codes with Application to DNA Strand Design

Some Algebraic Aspects of Parikh q-Matrices

Properties of Parikh Matrices of Binary Words Obtained by an Extension of a Restricted Shuffle Operator

Involution solid and join codes