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

One of the main research topics in DNA computing is associated with the design of information encoding single or double stranded DNA strands that are “suitable” for computation. Double stranded or partially double stranded DNA occurs as a result of binding between complementary DNA single strands (A is complementary to T and C is complementary to G). This paper continues the study of the algebraic properties of DNA word sets that ensure that certain undesirable bonds do not occur. We formalize and investigate such properties of sets of sequences, e.g., where no complement of a sequence is a prefix or suffix of another sequence or no complement of a concatenation of n sequences is a subword of the concatenation of n + 1 sequences. The sets of code words that satisfy the above properties are called θ – prefix, θ-suffix and θ-intercode respectively, where θ is the formalization of the Watson-Crick complementarity. Lastly we develop certain methods of constructing such sets of DNA words with good properties and compute their informational entropy.

DNA codes and their properties

In this paper we study a generalization of the classical notions of bordered and unbordered words, motivated by DNA computing. DNA strands can be viewed as finite strings over the alphabet {A, G, C, T}, and are used in DNA computing to encode information. Due to the fact that A is Watson-Crick complementary to T and G to C, DNA single strands that are Watson-Crick complementary can bind to each other or to themselves in either intended or unintended ways. One of the structures that is usually undesirable for biocomputation, since it makes the affected DNA string unavailable for future interactions, is the hairpin: If some subsequences of a DNA single string are complementary to each other, the string will bind to itself forming a hairpin-like structure. This paper studies a mathematical formalization of a particular case of hairpins, the Watson-Crick bordered words. A Watson-Crick bordered word is a word with the property that it has a prefix that is Watson-Crick complementary to its suffix. More generall...

Involutively bordered words

The Parikh vector of a word enumerates the symbols of the alphabet that occur in the word. The Parikh matrix of a word which has been recently introduced, is an extension of the notion of Parikh vector and gives more numerical information about the word in terms of certain subwords. Intensive investigation on various theoretical properties of Parikh matrices has taken place. This paper deals with the problem of finding properties of words so that their Parikh matrices commute.

Product of parikh matrices and commutativity

The study of hairpin-free words has been initiated in the context of DNA computing. DNA strands that, theoretically speaking, are finite strings over the alphabet {A, G, C, T} are used in DNA computing to encode information. Due to the fact that A is complementary to T and G to C, DNA single strands that are complementary can bind to each other or to themselves in either intended or unintended ways. One of the structures that is usually undesirable for biocomputation, since it makes the affected DNA string unavailable for future interactions, is the hairpin: if some subsequences of a DNA single string are complementary to each other, the string will bind to itself forming a hairpin-like structure. This paper continues the theoretical study of hairpin-free languages. We study algebraic properties of hairpin-free words and hairpins. We also give a complete characterization of the syntactic monoid of the language consisting of all hairpin-free words over a given alphabet and illustrate it with an example using the DNA alphabet.

/pdf/the-syntactic-monoid-of-hairpin-free-languages-nkcbz0egbe.pdf

The syntactic monoid of hairpin-free languages

A two-dimensional word (2D) is a rectangular finite array of letters from the alphabet \(\varSigma \). A 2D word is said to be a 2D palindrome if it is equal to its reverse image. In this paper, we study some combinatorial properties of 2D palindromes. In particular, we provide a sufficient condition under which a 2D word is said to be a 2D palindrome, discuss the necessary and sufficient condition under which a 2D word can be decomposed into 2D palindromes, and find the relation between the set of all 2D palindromes and the set of all 2D primitive words. We also show that the set of all 2D palindromes is not a recognizable language, and study a special class of 2D palindromes, namely 2D palindrome square words.

Kalpana Mahalingam

Papers

DNA codes and their properties

Involutively bordered words

Product of parikh matrices and commutativity

The syntactic monoid of hairpin-free languages

Two-Dimensional Palindromes and Their Properties