DNA Codewords Research Articles

Construction of DNA Codes From Composite Matrices and a Bio-Inspired Optimization Algorithm

In this work, we present a new construction method for reversible codes. We employ composite matrices derived from group rings and show how to construct these matrices so that they are also reversible. Also in this work, we give an algorithm for calculating conflict free DNA codes that satisfy the Hamming distance, the reverse, the reverse-complement, the GC-content constraints with each DNA codeword being free from reverse complement sub-strings. By employing our construction method for reversible codes and our algorithm, we construct a number of DNA codes that satisfy the above constraints. Many of the codes we obtain have better parameters than some known DNA codes and many have parameters that are new to the literature.

DNA Linear Block Codes: Generation, Error-Detection, and Error-Correction of DNA Codeword

In modern age, the increasing complexity of computation and communication technology is leading us towards the necessity of new paradigm. As a result, unconventional approach like DNA coding theory is gaining considerable attention. The storage capacity, information processing and transmission properties of DNA molecules stimulate the notion of DNA coding theory as well as DNA cryptography. In this paper we generate DNA codeword using DNA (n, k) linear block codes which ensures the secure transmission of information. In the proposed code design strategy DNA-based XOR operation (DNAX) is applied for effective construction of DNA codewords which are quadruples generated over the set of alphabets, . By worked out examples we explain the use of generator matrix and parity check matrix in encryption and decryption of coded data in the form of short single stranded DNA sequences. The newly developed technique is capable of detecting as well as correcting error in transmission of DNA codewords from sender to the intended receiver.

DNA codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4

Abstract A one to one correspondence between the elements of a finite local Frobenius non-chain ring of length 5 and nilpotency index 4, and k-tuples of DNA codewords is established. Using this map the structure of DNA codes over these rings is determined, the length of the code is relatively prime to the characteristic of the residue field of the ring.

Fractal construction of constrained code words for DNA storage systems

The use of complex biological molecules to solve computational problems is an emerging field at the interface between biology and computer science. There are two main categories in which biological molecules, especially DNA, are investigated as alternatives to silicon-based computer technologies. One is to use DNA as a storage medium, and the other is to use DNA for computing. Both strategies come with certain constraints. In the current study, we present a novel approach derived from chaos game representation for DNA to generate DNA code words that fulfill user-defined constraints, namely GC content, homopolymers, and undesired motifs, and thus, can be used to build codes for reliable DNA storage systems.

DNA codes over finite local Frobenius non-chain rings of length 4

A one to one correspondence between the elements of a finite local Frobenius non-chain ring of length 4 and k-tuples of DNA codewords is established. Using this map the structure of DNA codes over finite local Frobenius non-chain rings of length 4 is determined, the length of the code is relatively prime to the characteristic of the residue field of the ring.

Correcting a Single Indel/Edit for DNA-Based Data Storage: Linear-Time Encoders and Order-Optimality

An indel refers to a single insertion or deletion, while an edit refers to a single insertion, deletion or substitution. In this article, we investigate codes that correct either a single indel or a single edit and provide linear-time algorithms that encode binary messages into these codes of length n. Over the quaternary alphabet, we provide two linear-time encoders. One corrects a single edit with ⌈log n⌉+ O(loglog n) redundancy bits, while the other corrects a single indel with ⌈log n⌉+2 redundant bits. These two encoders are order-optimal. The former encoder is the first known order-optimal encoder that corrects a single edit, while the latter encoder (that corrects a single indel) reduces the redundancy of the best known encoder of Tenengolts (1984) by at least four bits. Over the DNA alphabet, we impose an additional constraint: the GC-balanced constraint and require that exactly half of the symbols of any DNA codeword to be either C or G. In particular, via a modification of Knuth's balancing technique, we provide a linear-time map that translates binary messages into GC-balanced codewords and the resulting codebook is able to correct a single indel or a single edit. These are the first known constructions of GC-balanced codes that correct a single indel or a single edit.

On conflict free DNA codes

DNA storage has emerged as an important area of research. The reliability of DNA storage system depends on designing the DNA strings (called DNA codes) that are sufficiently dissimilar. In this work, we introduce DNA codes that satisfy a special constraint. Each codeword of the DNA code has a specific property that any two consecutive sub-strings of the DNA codeword will not be the same (a generalization of homo-polymers constraint). This is in addition to the usual constraints such as Hamming, reverse, reverse-complement and $GC$-content. We believe that the new constraint will help further in reducing the errors during reading and writing data into the synthetic DNA strings. We also present a construction (based on a variant of stochastic local search algorithm) to calculate the size of the DNA codes with all the above constraints, which improves the lower bounds from the existing literature, for some specific cases. Moreover, a recursive isometric map between binary vectors and DNA strings is proposed. Using the map and the well known binary codes we obtain few classes of DNA codes with all the constraints including the property that the constructed DNA codewords are free from the hairpin-like secondary structures.

Family of Constrained Codes for Archival DNA Data Storage

DNA-based data storage systems have evolved as a solution to accommodate data explosion. In this letter, some properties of DNA codewords that are essential for an archival DNA storage are considered for the design of codes. Constraint-based DNA codes, which avoid runs of nucleotides, have fixed GC-weight, and a specific minimum distance is presented. An altruistic algorithm that enumerates DNA codewords with the above constraints is provided. A theoretical bound on such DNA codewords is obtained. This bound is tight when there is no minimum distance constraint.

An Improved Non-dominated Sorting Genetic Algorithm-II (INSGA-II) applied to the design of DNA codewords

DNA codewords design is critical for many research fields, from DNA computing, to DNA hybridization arrays, to DNA nanotechnology. Results in the literature rely on a wide variety of design criteria adapted to the particular requirements of each application. Since DNA codewords design can be regarded as a multi-objective optimization problem, and nondominated sorting genetic algorithm II (NSGA-II) has been demonstrated as one of the most efficient algorithms for multi-objective optimization problems, in this paper, we proposed an improved nondominated sorting genetic algorithm II (INSGA-II) for the design of DNA codewords. The novelty of our method is that introduced the constraints to the non-dominated sorting process. The performance of our method is compared with other DNA codewords design methods, and the experiment results in silico showed that the INSGA-II has a higher convergence speed and better population diversity than those of other algorithms, and can provide reliable and effective codewords for the controllable DNA computing.

Testing DNA code words properties of regular languages

One aspect of DNA Computing is the possibility of using DNA molecules for solving some “complicated” computational problems. In this context, the DNA code word design problem assumes a fundamental role: given a problem encoded in DNA strands and biochemical processes, the final computation is a concatenation of the input DNA strands that must allow us to recover the solution of the given problem in terms of the input (unique decipherability). Thus the initial set of DNA strands must be a code. In addition, it should satisfy some restrictions, called here DNA properties, in order to prevent them from interacting in undesirable ways. So a new interest towards the design of efficient algorithms for testing whether a language X is a code, has arisen from (wet) DNA Computing, but, as far as we know, only when X is a finite set. In this paper we provide an algorithm for testing whether an infinite but regular set of words is a code that avoids some DNA properties among unwanted intermolecular and intramolecular hybridizations.

Insertion and deletion correcting DNA barcodes based on watermarks.

BackgroundBarcode multiplexing is a key strategy for sharing the rising capacity of next-generation sequencing devices: Synthetic DNA tags, called barcodes, are attached to natural DNA fragments within the library preparation procedure. Different libraries, can individually be labeled with barcodes for a joint sequencing procedure. A post-processing step is needed to sort the sequencing data according to their origin, utilizing these DNA labels. The final separation step is called demultiplexing and is mainly determined by the characteristics of the DNA code words used as labels.Currently, we are facing two different strategies for barcoding: One is based on the Hamming distance, the other uses the edit metric to measure distances of code words. The theory of channel coding provides well-known code constructions for Hamming metric. They provide a large number of code words with variable lengths and maximal correction capability regarding substitution errors. However, some sequencing platforms are known to have exceptional high numbers of insertion or deletion errors. Barcodes based on the edit distance can take insertion and deletion errors into account in the decoding process. Unfortunately, there is no explicit code-construction known that gives optimal codes for edit metric.ResultsIn the present work we focus on an entirely different perspective to obtain DNA barcodes. We consider a concatenated code construction, producing so-called watermark codes, which were first proposed by Davey and Mackay, to communicate via binary channels with synchronization errors. We adapt and extend the concepts of watermark codes to use them for DNA sequencing. Moreover, we provide an exemplary set of barcodes that are experimentally compatible with common next-generation sequencing platforms. Finally, a realistic simulation scenario is use to evaluate the proposed codes to show that the watermark concept is suitable for DNA sequencing applications.ConclusionOur adaption of watermark codes enables the construction of barcodes that are capable of correcting substitutions, insertion and deletion errors. The presented approach has the advantage of not needing any markers or technical sequences to recover the position of the barcode in the sequencing reads, which poses a significant restriction with other approaches.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0482-7) contains supplementary material, which is available to authorized users.

DNA Codeword Design: Theory and Applications

This is a survey of the origin, current progress and applications of a major roadblock to the development of analytic models for DNA computing (a massively parallel programming methodology) and DNA self-assembly (a nanofabrication methodology), namely the so-called CODEWORD DESIGN problem. The problem calls for finding large sets of single DNA strands that do not crosshybridize to themselves or to their complements and has been recognized as an important problem in DNA computing, self-assembly, DNA memories and phylogenetic analyses because of their error correction and prevention properties. Major recent advances include the development of experimental techniques to search for such codes, as well as a theoretical framework to analyze this problem, despite the fact that it has been proven to be NP-complete using any single concrete metric space to model the Gibbs energy. In this framework, codeword design is reduced to finding large sets of strands maximally separated in DNA spaces and, therefore, the key to finding such sets would lie in knowledge of the geometry of these spaces. A new general technique has been recently found to embed them in Euclidean spaces in a hybridization-affinity-preserving manner, i.e., in such a way that oligos with high/low hybridization affinity are mapped to neighboring/remote points in a geometric lattice, respectively. This isometric embedding materializes long-held metaphors about codeword design in terms of sphere packing and error-correcting codes and leads to designs that are in some cases known to be provably nearly optimal for some oligo sizes. It also leads to upper and lower bounds on estimates of the size of optimal codes of size up to 32–mers, as well as to infinite families of solutions to CODEWORD DESIGN, based on estimates of the kissing (or contact) number for sphere packings in Euclidean spaces. Conversely, this reduction suggests interesting new algorithms to find dense sphere packing solutions in high dimensional spheres using results for CODEWORD DESIGN previously obtained by experimental or theoretical molecular means, as well as a proof that finding these bounds exactly is NP-complete in general. Finally, some research problems and applications arising from these results are described that might be of interest for further research.

Geometric Approaches to Gibbs Energy Landscapes and DNA Oligonucleotide Design

DNA codeword design has been a fundamental problem since the early days of DNA computing. The problem calls for finding large sets of single DNA strands that do not crosshybridize to themselves, to each other or to others' complements. Such strands represent so-called domains, particularly in the language of chemical reaction networks (CRNs). The problem has shown to be of interest in other areas as well, including DNA memories and phylogenetic analyses because of their error correction and prevention properties. In prior work, a theoretical framework to analyze this problem has been developed and natural and simple versions of Codeword Design have been shown to be NP-complete using any single reasonable metric that approximates the Gibbs energy, thus practically making it very difficult to find any general procedure for finding such maximal sets exactly and efficiently. In this framework, codeword design is partially reduced to finding large sets of strands maximally separated in DNA spaces and, therefore, the size of such sets depends on the geometry of these spaces. Here, the authors describe in detail a new general technique to embed them in Euclidean spaces in such a way that oligonucleotides with high (low, respectively) hybridization affinity are mapped to neighboring (remote, respectively) points in a geometric lattice. This embedding materializes long-held metaphors about codeword design in analogies with error-correcting code design in information theory in terms of sphere packing and leads to designs that are in some cases known to be provably nearly optimal for small oligonucleotide sizes, whenever the corresponding spherical codes in Euclidean spaces are known to be so. It also leads to upper and lower bounds on estimates of the size of optimal codes of size under 20-mers, as well as to a few infinite families of DNA strand lengths, based on estimates of the kissing (or contact) number for sphere codes in high-dimensional Euclidean spaces. Conversely, the authors show how solutions to DNA codeword design obtained by experimental or other means can also provide solutions to difficult spherical packing geometric problems via these approaches. Finally, the reduction suggests a tool to provide some insight into the approximate structure of the Gibbs energy landscapes, which play a primary role in the design and implementation of biomolecular programs.

A DNA assembly model of sentence generation

Recent results of corpus-based linguistics demonstrate that context-appropriate sentences can be generated by a stochastic constraint satisfaction process. Exploiting the similarity of constraint satisfaction and DNA self-assembly, we explore a DNA assembly model of sentence generation. The words and phrases in a language corpus are encoded as DNA molecules to build a language model of the corpus. Given a seed word, the new sentences are constructed by a parallel DNA assembly process based on the probability distribution of the word and phrase molecules. Here, we present our DNA code word design and report on successful demonstration of their feasibility in wet DNA experiments of a small scale.

An Efficient Genetic Algorithm Based on the Cultural Algorithm Applied to DNA Codewords Design

An Efficient Genetic Algorithm Based on the Cultural Algorithm Applied to DNA Codewords Design

DNA Code Word Design for DNA Computing with Real-Time Polymerase Chain Reaction

Problem statement: A number of DNA computing models to solve mathematical graph problem such as the Hamiltonian Path Problem (HPP), Traveling Salesman Problem (TSP), and the Shortest Path Problem (SPP), have been proposed and demonstrated. Normally, the DNA sequences used for the computation should be critically designed in order to reduce error that could occur during a computation. We have proposed a DNA computing readout method tailored specifically to HPP in DNA computing using real-time Polymerase Chain Reaction (PCR). The DNA sequences were designed based on a procedure and DNASequenceGenerator was employed to generate the sequences required for the experiment. The drawback of the previous approach is that a pool of DNA sequences need to be generated by DNASequenceGenerator before the selection is done manually, based on several design constraints. Hence, an automatic and systematic approach is needed to generate the DNA sequences based on design constraints. Approach: In this study, a generate-and-test approach was proposed for the same problem subjected to several design constraints. The generate-and-test algorithm consists of two main levels. The first level considered the basic constraints of DNA sequence design, which were melting temperature, GC-percentage, similarity, continuity, hairpin, and H-measure. This was followed by the second level that includes specific constraints formulated based on five rules, which had been used in previous study. A generated sequence was chosen only if the sequence satisfies all the basic and specific constraints. Results: Sequences designed by generate-and-test approach have higher H-measure value than sequences generated by DNASequenceGenerator. However, the generated sequences show lower value for similarity as well as for additional constraints compared to sequences designed by DNASequenceGenerator. Conclusion: The generated DNA sequences were better compared to the sequences, obtained from DNASequenceGenerator.

DNA Code Word Design for DNA Computing with Real-Time Polymerase Chain Reaction

DNA Code Word Design for DNA Computing with Real-Time Polymerase Chain Reaction

Secondary Structure Prediction of Interacting RNA Molecules

Computational tools for prediction of the secondary structure of two or more interacting nucleic acid molecules are useful for understanding mechanisms for ribozyme function, determining the affinity of an oligonucleotide primer to its target, and designing good antisense oligonucleotides, novel ribozymes, DNA code words, or nanostructures. Here, we introduce new algorithms for prediction of the minimum free energy pseudoknot-free secondary structure of two or more nucleic acid molecules, and for prediction of alternative low-energy (sub-optimal) secondary structures for two nucleic acid molecules. We provide a comprehensive analysis of our predictions against secondary structures of interacting RNA molecules drawn from the literature. Analysis of our tools on 17 sequences of up to 200 nucleotides that do not form pseudoknots shows that they have 79% accuracy, on average, for the minimum free energy predictions. When the best of 100 sub-optimal foldings is taken, the average accuracy increases to 91%. The accuracy decreases as the sequences increase in length and as the number of pseudoknots and tertiary interactions increases. Our algorithms extend the free energy minimization algorithm of Zuker and Stiegler for secondary structure prediction, and the sub-optimal folding algorithm by Wuchty et al. Implementations of our algorithms are freely available in the package MultiRNAFold.

RNA CODEWORDS AND PROTEIN SYNTHESIS. THE EFFECT OF TRINUCLEOTIDES UPON THE BINDING OF SRNA TO RIBOSOMES.

A rapid, sensitive method is described for measuring C(14)-aminoacyl-sRNA interactions with ribosomes which are specifically induced by the appropriate RNA codewords prior to peptide-bond formation. Properties of the codeword recognition process and the minimum oligonucleotide chain length required to induce such interactions are presented. The trinucleotides, pUpUpU, pApApA, and pCpCpC, but not dinucleotides, specifically direct the binding to ribosomes of phenylalanine-, lysine-, and proline-sRNA, respectively. Since 5'-terminal, 3'-terminal, and internal codewords differ in chemical structure, three corresponding classes of codewords are proposed. The recognition of each class in this system is described. The template efficiency of trinucleotide codewords is modified greatly by terminal phosphate. Triplets with 5'-terminal phosphate are more active as templates than triplets without terminal phosphate. Triplets with 3'- or 3' (2')-terminal phosphate are markedly less active as templates. These findings are discussed in relation to the probable functions of terminal codewords. The modification of RNA and DNA codewords, converting sense into missense or nonsense codewords, is suggested as a possible regulatory mechanism in protein synthesis.