DNA Storage Systems Research Articles

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.

On Levenshtein’s Reconstruction Problem Under Insertions, Deletions, and Substitutions

The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sequence reconstruction problem</i> corresponds to the model in which a sequence from some code is transmitted over several noisy channels that produce distinct outputs. Then, the channels’ outputs, received by the decoder, are used to recover the transmitted sequence, and the main problem under this paradigm is to calculate the minimum number of channels that enables unique reconstruction of the transmitted word. This problem is equivalent to finding the size of the largest intersection of channels’ outputs sets received after transmitting distinct codewords. Motivated by the error behavior observed in DNA storage systems, the present work extends the study of the reconstruction model to the case in which a binary word is transmitted over channels prone to substitutions, insertions, and deletions. Furthermore, we also study the size of the error balls generated by either one deletion and at most a fixed number of substitutions or one insertion and at most one substitution in a binary word. For the case of only substitutions, we present a decoder of optimal complexity, which improves upon a recent construction of such a decoder. Lastly, a simplification of that decoder is studied in case there are more channels than the minimum required number.

Multidimensional data organization and random access in large-scale DNA storage systems

With impressive physical density and molecular-scale coding capacity, DNA is a promising substrate for building long-lasting data archival storage systems. To retrieve data from DNA storage, recent implementations typically rely on large libraries of meticulously designed orthogonal PCR primers, which fundamentally limit the capacity and scalability of practical DNA storage. This work combines nested and semi-nested PCR to enable multidimensional data organization and random access in large DNA storage. Our strategy effectively pushes the limit of DNA storage capacity and dramatically reduces the number of orthogonal primers needed for efficient PCR random access. Our design uses only k⁎n primers to uniquely address nk data-encoding oligos. The architecture inherently supports various well-defined PCR random-access patterns that can be tailored to organize and preserve the underlying DNA-encoded data structures and relations in simple database-like formats such as rows, columns, tables, and blocks of data entries. We design in silico PCR experiments of a four-dimensional DNA storage to illustrate the mechanisms of sixteen different random-access patterns each requiring no more than two PCR reactions to selectively amplify a target dataset of various sizes. To better approximate the physical system, we formulate mathematical models based on empirical distributions to analyze the effect of pipetting, PCR bias, and PCR stochasticity on the performance of multidimensional data queries from large DNA storage.

A self-contained and self-explanatory DNA storage system

Current research on DNA storage usually focuses on the improvement of storage density by developing effective encoding and decoding schemes while lacking the consideration on the uncertainty in ultra-long-term data storage and retention. Consequently, the current DNA storage systems are often not self-contained, implying that they have to resort to external tools for the restoration of the stored DNA data. This may result in high risks in data loss since the required tools might not be available due to the high uncertainty in far future. To address this issue, we propose in this paper a self-contained DNA storage system that can bring self-explanatory to its stored data without relying on any external tool. To this end, we design a specific DNA file format whereby a separate storage scheme is developed to reduce the data redundancy while an effective indexing is designed for random read operations to the stored data file. We verified through experimental data that the proposed self-contained and self-explanatory method can not only get rid of the reliance on external tools for data restoration but also minimise the data redundancy brought about when the amount of data to be stored reaches a certain scale.

NOREC4DNA: using near-optimal rateless erasure codes for DNA storage

BackgroundDNA is a promising storage medium for high-density long-term digital data storage. Since DNA synthesis and sequencing are still relatively expensive tasks, the coding methods used to store digital data in DNA should correct errors and avoid unstable or error-prone DNA sequences. Near-optimal rateless erasure codes, also called fountain codes, are particularly interesting codes to realize high-capacity and low-error DNA storage systems, as shown by Erlich and Zielinski in their approach based on the Luby transform (LT) code. Since LT is the most basic fountain code, there is a large untapped potential for improvement in using near-optimal erasure codes for DNA storage.ResultsWe present NOREC4DNA, a software framework to use, test, compare, and improve near-optimal rateless erasure codes (NORECs) for DNA storage systems. These codes can effectively be used to store digital information in DNA and cope with the restrictions of the DNA medium. Additionally, they can adapt to possible variable lengths of DNA strands and have nearly zero overhead. We describe the design and implementation of NOREC4DNA. Furthermore, we present experimental results demonstrating that NOREC4DNA can flexibly be used to evaluate the use of NORECs in DNA storage systems. In particular, we show that NORECs that apparently have not yet been used for DNA storage, such as Raptor and Online codes, can achieve significant improvements over LT codes that were used in previous work. NOREC4DNA is available on https://github.com/umr-ds/NOREC4DNA.ConclusionNOREC4DNA is a flexible and extensible software framework for using, evaluating, and comparing NORECs for DNA storage systems.

Cooperative sequence clustering and decoding for DNA storage system with fountain codes.

In DNA storage systems, there are tradeoffs between writing and reading costs. Increasing the code rate of error-correcting codes may save writing cost, but it will need more sequence reads for data retrieval. There is potentially a way to improve sequencing and decoding processes in such a way that the reading cost induced by this tradeoff is reduced without increasing the writing cost. In past researches, clustering, alignment and decoding processes were considered as separate stages but we believe that using the information from all these processes together may improve decoding performance. Actual experiments of DNA synthesis and sequencing should be performed because simulations cannot be relied on to cover all error possibilities in practical circumstances. For DNA storage systems using fountain code and Reed-Solomon (RS) code, we introduce several techniques to improve the decoding performance. We designed the decoding process focusing on the cooperation of key components: Hamming-distance based clustering, discarding of abnormal sequence reads, RS error correction as well as detection and quality score-based ordering of sequences. We synthesized 513.6 KB data into DNA oligo pools and sequenced this data successfully with Illumina MiSeq instrument. Compared to Erlich's research, the proposed decoding method additionally incorporates sequence reads with minor errors which had been discarded before, and thus was able to make use of 10.6-11.9% more sequence reads from the same sequencing environment, this resulted in 6.5-8.9% reduction in the reading cost. Channel characteristics including sequence coverage and read-length distributions are provided as well. The raw data files and the source codes of our experiments are available at: https://github.com/jhjeong0702/dna-storage.

Minimum Free Energy Coding for DNA Storage.

With the development of information technology, huge amounts of data are produced at the same time. How to store data efficiently and at low cost has become an urgent problem. DNA is a high-density and persistent medium, making DNA storage a viable solution. In a DNA data storage system, the first consideration is how to encode the data effectively into code words. However, DNA strands are prone to non-specific hybridization during the hybridization reaction process and are prone to errors during synthesis and sequencing. In order to reduce the error rate, a thermodynamic minimum free energy (MFE) constraint is proposed and applied to the construction of coding sets for DNA storage. The Brownian multi-verse optimizer (BMVO) algorithm, based on the Multi-verse optimizer (MVO) algorithm, incorporates the idea of Brownian motion and Nelder-Mead method, and it is used to design a better DNA storage coding set. In addition, compared with previous works, the coding set has been increasing by 4%-50% in size and has better thermodynamic properties. With the improvement of the quality of the DNA coding set, the accuracy of reading and writing and the robustness of the DNA storage system are also enhanced.

DNA-Based Storage: Models and Fundamental Limits

Due to its longevity and enormous information density, DNA is an attractive medium for archival storage. In this work, we study the fundamental limits and trade-offs of DNA-based storage systems by introducing a new channel model, which we call the noisy shuffling-sampling channel. Motivated by current technological constraints on DNA synthesis and sequencing, this model captures three key distinctive aspects of DNA storage systems: (1) the data is written onto many short DNA molecules; (2) the molecules are corrupted by noise during synthesis and sequencing and (3) the data is read by randomly sampling from the DNA pool. We provide capacity results for this channel under specific noise and sampling assumptions and show that, in many scenarios, a simple index-based coding scheme is optimal.

Design of Nonbinary Error Correction Codes With a Maximum Run-Length Constraint to Correct a Single Insertion or Deletion Error for DNA Storage

Due to the advantages of high information densities and longevity, DNA storage systems have begun to attract a lot of attention. However, common obstacles to DNA storage are caused by insertion, deletion, and substitution errors occurring in DNA synthesis and sequencing. In this paper, we first explain a method to convert binary data into general maximum run-length $r$ sequences with specific length construction, which can be used as the message sequence of our proposed code. Then, we propose a new single insertion/deletion nonbinary systematic error correction code and its corresponding encoding algorithm. For the proposed code, we design the fixed maximum run-length $r$ in the parity sequence of the proposed code to be three. Additionally, the last parity symbol and the first message symbol are always different. Hence, the overall maximum run-length $r$ of the output codeword is guaranteed to be three when the maximum run-length of the message sequence is three. Finally, we determine the feasibility of the proposed encoding algorithm, verify successful decoding when a single insertion/deletion error occurs in the codeword, and present the comparison results with relevant works.

Algorithms for Reconstruction Over Single and Multiple Deletion Channels

Recent advances in DNA sequencing technology and DNA storage systems have rekindled the interest in deletion channels. Multiple recent works have looked at variants of sequence reconstruction over a single and over multiple deletion channels, a notoriously difficult problem due to its highly combinatorial nature. Although works in theoretical computer science have provided algorithms which guarantee perfect reconstruction with multiple independent observations from the deletion channel, they are only applicable in the large blocklength regime and more restrictively, when the number of observations is also large. Indeed, with only a few observations, perfect reconstruction of the input sequence may not even be possible in most cases. In such situations, maximum likelihood (ML) and maximum aposteriori (MAP) estimates for the deletion channels are natural questions that arise and these have remained open to the best of our knowledge. In this work, we take steps to answer the two aforementioned questions. Specifically: 1. We show that solving for the ML estimate over the single deletion channel (which can be cast as a discrete optimization problem) is equivalent to solving its relaxation, a continuous optimization problem; 2. We exactly compute the symbolwise posterior distributions (under some assumptions on the priors) for both the single as well as multiple deletion channels. As part of our contributions, we also introduce tools to visualize and analyze error events, which we believe could be useful in other related problems concerning deletion channels.

Low cost DNA data storage using photolithographic synthesis and advanced information reconstruction and error correction

Due to its longevity and enormous information density, DNA is an attractive medium for archival storage. The current hamstring of DNA data storage systems—both in cost and speed—is synthesis. The key idea for breaking this bottleneck pursued in this work is to move beyond the low-error and expensive synthesis employed almost exclusively in today’s systems, towards cheaper, potentially faster, but high-error synthesis technologies. Here, we demonstrate a DNA storage system that relies on massively parallel light-directed synthesis, which is considerably cheaper than conventional solid-phase synthesis. However, this technology has a high sequence error rate when optimized for speed. We demonstrate that even in this high-error regime, reliable storage of information is possible, by developing a pipeline of algorithms for encoding and reconstruction of the information. In our experiments, we store a file containing sheet music of Mozart, and show perfect data recovery from low synthesis fidelity DNA.

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.

Error Rate-Based Log-Likelihood Ratio Processing for Low-Density Parity-Check Codes in DNA Storage

Due to the advantages of high storage densities and longevity, DNA storage has become one of the attractive technologies for future data storage systems. However, the writing/reading cost is still high and more efficient techniques for DNA storage are required. In this paper, we propose improved log-likelihood ratio (LLR) processing schemes based on observed statistics for low-density parity-check (LDPC) code decoding to reduce reading cost while encoding schemes are kept unchanged. Due to the mismatch between the real channel and the observed statistics and also the limit of maximum decoder input value, scaling the magnitude of LLR can lead to a better error correcting performance. Therefore, we propose two strategies: 1) directly scaling LLRs and 2) scaling pairwise substitution error rates, which changes the magnitude of LLRs. We also suggest the relation between substitution error rate and scaling values in the strategies by using curve fitting methods. Simulation results show that the error correcting performance from the proposed LLR calculation is better than that from the conventional scheme. Finally, we verify that the proposed LLR methods can be generally applied in DNA storage systems, and present practical methods to calculate error rates.

A Characterization of the DNA Data Storage Channel

Owing to its longevity and enormous information density, DNA, the molecule encoding biological information, has emerged as a promising archival storage medium. However, due to technological constraints, data can only be written onto many short DNA molecules that are stored in an unordered way, and can only be read by sampling from this DNA pool. Moreover, imperfections in writing (synthesis), reading (sequencing), storage, and handling of the DNA, in particular amplification via PCR, lead to a loss of DNA molecules and induce errors within the molecules. In order to design DNA storage systems, a qualitative and quantitative understanding of the errors and the loss of molecules is crucial. In this paper, we characterize those error probabilities by analyzing data from our own experiments as well as from experiments of two different groups. We find that errors within molecules are mainly due to synthesis and sequencing, while imperfections in handling and storage lead to a significant loss of sequences. The aim of our study is to help guide the design of future DNA data storage systems by providing a quantitative and qualitative understanding of the DNA data storage channel.

Construction of Bio-Constrained Code for DNA Data Storage

With extremely high density and durable preservation, DNA data storage has become one of the most cutting-edge techniques for long-term data storage. Similar to traditional storage which impose restrictions on the form of encoded data, data stored in DNA storage systems are also subject to two biochemical constraints, i.e., maximum homopolymer run limit and balanced GC content limit. Previous studies used successive process to satisfy these two constraints. As a result, the process suffers low efficiency and high complexity. In this letter, we propose a novel content-balanced run-length limited code with an efficient code construction method, which generates short DNA sequences that satisfy both constraints at one time. Besides, we develop an encoding method to map binary data into long DNA sequences for DNA data storage, which ensures both local and global stability in terms of satisfying the biochemical constraints. The proposed encoding method has high effective code rate of 1.917 bits per nucleotide and low coding complexity.

Driving the Scalability of DNA-Based Information Storage Systems.

The extreme density of DNA presents a compelling advantage over current storage media; however, to reach practical capacities, new systems for organizing and accessing information are needed. Here, we use chemical handles to selectively extract unique files from a complex database of DNA mimicking 5 TB of data and design and implement a nested file address system that increases the theoretical maximum capacity of DNA storage systems by five orders of magnitude. These advancements enable the development and future scaling of DNA-based data storage systems with modern capacities and file access capabilities.

Nucleic Acid Databases and Molecular-Scale Computing.

DNA outperforms most conventional storage media in terms of information retention time, physical density, and volumetric coding capacity. Advances in synthesis and sequencing technologies have enabled implementations of large synthetic DNA databases with impressive storage capacity and reliable data recovery. Several robust DNA storage architectures featuring random access, error correction, and content rewritability have been constructed with the potential for scalability and cost reduction. We survey these recent achievements and discuss alternative routes for overcoming the hurdles of engineering practical DNA storage systems. We also review recent exciting work on in vivo DNA memory including intracellular recorders constructed by programmable genome editing tools. Besides information storage, DNA could serve as a versatile molecular computing substrate. We highlight several state-of-the-art DNA computing techniques such as strand displacement, localized hybridization chain reactions, and enzymatic reaction networks. We summarize how these simple primitives have facilitated rational designs and implementations of in vitro DNA reaction networks that emulate digital/analog circuits, artificial neural networks, or nonlinear dynamic systems. We envision these modular primitives could be strategically adapted for sophisticated database operations and massively parallel computations on DNA databases. We also highlight in vivo DNA computing modules such as CRISPR logic gates for building scalable genetic circuits in living cells. To conclude, we discuss various implications and challenges of DNA-based storage and computing, and we particularly encourage innovative work on bridging these two areas of research to further explore molecular parallelism and near-data processing. Such integrated molecular systems could lead to far-reaching applications in biocomputing, security, and medicine.

Asymptotically Optimal Codes Correcting Fixed-Length Duplication Errors in DNA Storage Systems

A (tandem) duplication of length $ k $ is an insertion of an exact copy of a substring of length $ k $ next to its original position. This and related types of impairments are of relevance in modeling communication in the presence of synchronization errors, as well as in several information storage applications. We demonstrate that Levenshtein's construction of binary codes correcting insertions of zeros is, with minor modifications, applicable also to channels with arbitrary alphabets and with duplication errors of arbitrary (but fixed) length $ k $. Furthermore, we derive bounds on the cardinality of optimal $ q $-ary codes correcting up to $ t $ duplications of length $ k $, and establish the following corollaries in the asymptotic regime of growing block-length: 1.) the presented family of codes is optimal for every $ q, t, k $, in the sense of the asymptotic scaling of code redundancy; 2.) the upper bound, when specialized to $ q = 2 $, $ k = 1 $, improves upon Levenshtein's bound for every $ t \geq 3 $; 3.) the bounds coincide for $ t = 1 $, thus yielding the exact asymptotic behavior of the size of optimal single-duplication-correcting codes.

Codes in the Space of Multisets—Coding for Permutation Channels With Impairments

Motivated by communication channels in which the transmitted sequences are subject to random permutations, as well as by certain DNA storage systems, we study the error control problem in settings where the information is stored/transmitted in the form of multisets of symbols from a given finite alphabet. A general channel model is assumed in which the transmitted multisets are potentially impaired by insertions, deletions, substitutions, and erasures of symbols. Several constructions of error-correcting codes for this channel are described, and bounds on the size of optimal codes correcting any given number of errors derived. The construction based on the notion of Sidon sets in finite Abelian groups is shown to be optimal, in the sense of the asymptotic scaling of code redundancy, for any "error radius" and any alphabet size. It is also shown to be optimal in the stronger sense of maximal code cardinality in various cases.

Models and Information-Theoretic Bounds for Nanopore Sequencing

Nanopore sequencing is an emerging new technology for sequencing DNA, which can read long fragments of DNA (~50,000 bases) in contrast to most current short-read sequencing technologies which can only read hundreds of bases. While nanopore sequencers can acquire long reads, the high error rates (20%-30%) pose a technical challenge. In a nanopore sequencer, a DNA is migrated through a nanopore and current variations are measured. The DNA sequence is inferred from this observed current pattern using an algorithm called a base-caller. In this paper, we propose a mathematical model for the "channel" from the input DNA sequence to the observed current, and calculate bounds on the information extraction capacity of the nanopore sequencer. This model incorporates impairments like (non-linear) inter-symbol interference, deletions, as well as random response. These information bounds have two-fold application: (1) The decoding rate with a uniform input distribution can be used to calculate the average size of the plausible list of DNA sequences given an observed current trace. This bound can be used to benchmark existing base-calling algorithms, as well as serving a performance objective to design better nanopores. (2) When the nanopore sequencer is used as a reader in a DNA storage system, the storage capacity is quantified by our bounds.