DOI:
10.1039/D5NH00459D
(Review Article)
Nanoscale Horiz., 2025, Advance Article
DNA computing: DNA circuits and data storage
Received
3rd July 2025
, Accepted 27th August 2025
First published on 27th August 2025
Abstract
Computation has consistently served as a significant indicator and direction of social development, and volume, speed, and accuracy are critical factors during development. To accelerate this computational process, various advanced technologies and constantly optimized computational methods have been developed, such as upgrading chip design and proposing quantum and photonic computing. Recently, DNA computing, as a unique computational model distinct from traditional methods, offers remarkable advantages and addresses problems that are difficult to solve with conventional computing. By designing DNA molecules and utilizing their spontaneous reactions, specific types of complex problems can be solved, such as combinatorial optimization, traveling salesman, Sudoku and other nondeterministic polynomial time (NP) problems. Based on the spontaneity of reactions, this type of computation exhibits high parallelism, making DNA computing a viable solution for high-complexity problems. This review presents an overview of the theoretical foundations of DNA computing and summarizes three distinct advantages to over traditional computing: high parallelism, efficient storage, and low energy consumption. Furthermore, based on these advantages, we assess the current state of development in two critical branches of DNA computing: DNA circuit and DNA information storage, and provide unique insights for the future development of DNA computing.
Introduction
Computing is essentially used to perform a series of operations in a set scenario to obtain specific results. In the process of computing, different conditions and operations may lead to changes in the results, but they also affect the space and time required for computing. A permanent pursuit in this field is to adopt appropriate conditions and computing processes for different problems by using small volume spaces to get the desired results quickly. However, efficient computation based on the complex models designed for particular problems remains a significant challenge, necessitating excess utilization of scarce computing resources and data storage. DNA computing provides an effective means in the field of computing in some special application scenarios. In 1994, Professor Leonard Adleman first proposed the concept of DNA computing and demonstrated the potential of DNA computing.1 The fundamental idea of DNA computing is utilizing DNA molecules as the primary components of computation, whereby varying pieces of information are loaded into the DNA sequences through the programmable property and specificity of DNA molecules, thereby realizing different conditions and computational operations by using their special chemical reactions. Since the proposal of DNA computing, different computing processes and feasibility experiments for different mathematical and logical problems have also appeared, starting a new chapter in computing.
In this review, we summarized three prominent advantages of DNA computing compared to traditional computing: high parallelism, efficient storage and low energy consumption, which is significant for the development of DNA computing. Based on these advantages, DNA computing derives two important development branches, DNA circuits and DNA information storage, which offer innovative concepts and methodologies for addressing intricate scientific challenges. We provide a comprehensive overview of the current state of development in these two domains, aiming to systematically organize and introduce the development of DNA computing and inspire researchers to further understand and reflect on its strengths and weaknesses, potentially promoting the practical application of DNA computing and breakthroughs in technology and design (Fig. 1).
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| Fig. 1 Timeline of the field of DNA computing, listing the major discoveries and developments. | |
Advantages of DNA computing
Highly parallel
High parallelism is the most significant advantage of DNA computing (1014 to 1020 operations per second compared to 108 to 1012 operations per second in modern computers2), owing to the high degree of randomness in the chemical reactions that drive DNA strand growth. This allows all the DNA strands in the system to perform simultaneous amplification, denaturation, and base-pairing, which constitute the fundamental principles of DNA computing in addressing complex non-deterministic polynomial time (NP) problems. Therefore, implementing NP-complete problems through DNA computing represents a breakthrough from verifying the correctness of polynomial-time solutions to discovering polynomial-time solutions.1,3–5 Under high parallelism, DNA computing often yields a large number of results, and one of the key aspects of DNA computing is to filter out a few correct solutions from the vast number of brute-force computational outcomes.
In 1994, professor Adleman first used DNA computing to solve the seven-vertex directed Hamiltonian path problem (HPP), marking the beginning of DNA computing (Fig. 2).1 In this computation, researchers derived all possible solutions in one step and then refined the results through purification methods. The entire experiment took about seven days. By leveraging the high parallelism of DNA computing, the generation of a solution space that would be computationally infeasible in classical electronic computing could be achieved in a single time step. However, the large number of computational results from brute-force methods would lead to an exponential increase in the solution space as the number of vertices in the Hamiltonian path problem increased. In addition to solving NP problems, the parallelism of DNA computing can also be used to simulate the rules of chess,6 and it shows potential applications in other fields, such as biomedical applications such as biosensing, diagnosis and conditional therapy.7 Early high parallelism relied on the molecular random collisions, with a limited computational scale and a propensity for signal attenuation. In 2022, the Fan Team introduced an innovative DNA-based programmable gate array, which guided the directional transfer of molecules and successfully realized 30 gate-level circuits for the first time. This technology enhanced computational reliability and minimized crosstalk, offering a viable avenue for the pursuit of high parallelism and low-energy biological computing.8 In the same year, Xiong et al. constructed a DNA computing structure of convolutional neural network algorithm, and realized the recognition of up to 32 molecular patterns with lower connectivity and complexity.9 In 2024, Lin et al. constructed a DNA computing structure which can solve simple chess and Sudoku problems.10 In addition to the exploration of computing power, DNA computing has gradually been applied in the field of pathological diagnosis in recent years, such as the diagnosis system of various pathological causes11,12 and cancer diagnosis.13,14
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| Fig. 2 (a) Illustration of the problem of directed Hamiltonian path with seven vertices. (b) Professor Adleman designed the path points and directions of the Hamiltonian path problem, where each piece of information was expressed in 20 base sequences. Parts (a) and (b) were reproduced with permission from Adlemen1 Copyright 1994, Science. | |
Efficient storage
DNA serves as a data coding carrier of biology, consisting of a random arrangement and combination of four distinct nucleotide bases. Meanwhile, the advanced synthesis methods of DNA molecules enable the precise arrangement of nucleotide bases, thereby facilitating the encoding of desired information. Moreover, the information storage density of DNA is exceptionally high (one bit per cubic nanometer, compared with three bits per 1012 nanometers in modern computers2), and the loaded data on DNA can be stored for long periods of time under suitable conditions. In essence, DNA computing is a new solution to data processing and storage that utilizes molecular-level reactions to solve complex problems. Consequently, the data storage is the ultimate outcome of DNA computing.
The concept of DNA as a data carrier can be traced back to the mid-1960s. However, DNA synthesis and sequencing technology were not mature at that time. The initial experimental demonstration occurred in 1988, as evidenced by the studies conducted by Davis.15 He encoded the light and dark pixels of the image through 0 and 1, and then converted the data into a DNA strand with 28 bases and inserted it into E. coli. After nearly 25 years of slow development, DNA information storage technology saw a breakthrough in 2012 when Church's team successfully encoded a 659 kB book using a method called short chain DNA.16 In 2013, Goldman's team achieved groundbreaking progress in DNA data storage by successfully encoding 739 kB of data.17 In 2024, Preuss used short sequence combination coding to significantly improve the density of information storage, achieving a DNA information storage density of 1.6 picobits (PB) per gram.18 In the same year, DNA information storage also began to be effectively integrated with DNA computing on a large scale, developing the capability to repeatedly write, read, erase, reload and compute specific data.10 At the same time, with the development of random access technology for DNA data storage, the practicability and reliability of DNA storage have also improved.19,20
Low-energy
DNA computing is a low-energy computing method. Unlike traditional electronic computers, DNA computing leverages the spontaneous behavior of DNA molecules in chemical reactions, using specific processes such as self-assembly and molecular recognition through enzymatic reactions to perform computational tasks. These reactions typically occur at room temperature, eliminating the need for complex energy supply systems, and the energy consumption of these chemical reactions is significantly lower than that of the electronic operations in traditional computers. Therefore, DNA-mediated computing is more energy-efficient than modern computers. A typical DNA strand reaction in DNA computing consumes 5 × 10−20 joules of energy, compared to 10−9 joules in silicon-based computers.2
DNA computing has the natural advantage of low energy consumption. By optimizing the operational processes and mechanisms of DNA computing, it can become even more energy efficient. By designing DNA switches and DNA molecular logic gates, the computing amount is reduced to constructing more convenient logic circuit optimization21,22 (Table 1).
Table 1 The difference between silicon-based computing and DNA computing. The table was reproduced with permission from Shu et al.2 Copyright 2023, American Chemical Society
Characteristics |
Silicon-based |
DNA-mediated |
Information storage |
1 bit per 1012 nm3 |
1 bit per nm3 |
Processing speed |
108 to 1012 operations per second |
1014 to 1020 operations per second (ligation) |
Energy efficiency |
109 operations per Joule |
2 × 1019 operations per Joule |
Computing architecture |
Effective for single operation; multiple cores of CPU for multiple operations at one time (up to six operations) |
Ineffective for single operation; naturally effective for massive parallel operations |
Advances in DNA computing
The above three major advantages have laid the foundation for the advancement of DNA computing, which confirm the potential for the functional and application development. By drawing upon the established framework of traditional electronic computing development, DNA computing has successfully harnessed these advantages to create a range of new functionalities and applications. Traditional electronic computers realize various operations through different combinations of electronic logic gates to receive and process electronic input signals and produce output signals. Therefore, various logic gates based on DNA molecules in DNA computing are the basis of their development, and the DNA-based computing structure using logic gates has become the core architecture of DNA computing. In order to realize the logic gate function of different scenarios, DNA circuits currently have four construction methods: only composed of DNA chains, composed of a series of enzymatic reactions, based on DNA nanostructure circuits and compartmentalized DNA circuit structures based on other materials.
Enzyme-free DNA logic circuits
The enzyme-free DNA logic circuit is a kind of computing method developed based on traditional DNA computing, executing complete complex computing operations only through the interaction of DNA molecules. The core idea of the enzyme-free DNA logic circuit is to design specific DNA sequences and reaction steps, so that DNA molecules can spontaneously complete logic operations driven by molecular thermodynamics without enzyme catalysis. The realization of an enzyme-free DNA logic circuit is usually based on two basic strategies of DNA molecular exchange and DNA molecular recognition. In molecular exchange, DNA molecules can spontaneously react with each other through the energy difference of designed base pairing to exchange specific nucleotide pairs and finally realize the exchange of DNA chains. In molecular recognition, the transmission of signals is formed through specific DNA molecular recognition, and the continuous DNA strand displacement controls the output result of the entire circuit (Fig. 3a).23 Based on the above two strategies, the combination of specially designed DNA sequences that enables DNA computing to perform the same operations as in an electronic computer, such as Boolean logic, is implemented by using a molecular exchange strategy (Fig. 3b),24,25 and arithmetic operation is implemented by using a molecular recognition strategy (Fig. 3c)26 and a series of neural network functions.27 With the development of complex DNA computing systems, more DNA logic circuits are being applied to improve the energy efficiency, computing rate and the stability of computing. In 2018, Wang Boya et al. introduced redundant sequences to generate entropy changes that are unfavorable for reaction occurrence, thus constructing an error correction circuit that makes unnecessary reactions less likely to occur.28 In 2020, Wang Fei et al. simulated the switching circuit used in electronic computing to enable DNA circuits to perform operations in a modular and high-speed manner.23 With the increasing complexity of DNA circuits, higher levels of logic statements have been designed through the cross-design and application of molecular exchange and molecular recognition strategies, such as oscillating,29 probabilistic switching,30 buffering31 and time control.32
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| Fig. 3 (a) Schematic diagram of DNA signal conduction in a simple circuit. Using four steps, the circuit process using molecular exchange and molecular recognition strategies is realized through a specially designed DNA sequence. The figure was reproduced with permission from Wang et al.16 Copyright 2020, Nature Publishing Group. (b) Some basic Boolean logic operations are implemented by the specific design of the DNA sequence, which are Translator gates, NOT operation and signal restoration from top to bottom. The figure was reproduced with permission from Seelig et al.17 Copyright 2006, The American Association for the Advancement of Science. (c) Boolean matrix multiplication was performed by the combination and replacement of DNA, and 12 different combinations of products were calculated using the presence or absence of specific DNA chains to represent true (1) and false (0). The figure was reproduced with permission from Genot et al.19 Copyright 2012, John Wiley and Sons. | |
In the enzyme-free DNA logic circuit, the circuit structure and experimental operation are simple with high system stability. However, due to the single strategy of calculation steps, the computational efficiency and flexibility are limited when dealing with complex tasks. The enzymatic DNA logic circuit compensates for these deficiencies to some extent.
Enzymatic DNA logic circuits
In synthetic biology, DNA structures that are constructed through simple enzymatic reactions exhibit enhanced specificity and superior catalytic capability compared to pure DNA systems.33,34 Therefore, learning from these successful experiences, DNA logic circuit introduces the enzyme to make DNA computing have a simpler circuit structure to achieve efficient computing and faster computing speed.22,35 In enzyme-free DNA logic circuits, one of the severe challenges is leakage, caused by multiple strand complexes resulting from defects in sequence design and synthesis errors. In the enzyme-promoted DNA circuit, due to the catalysis of an enzyme, the leakage problem is significantly alleviated by allowing simpler structures to be used as logical statements. For example, Song et al. used chain replacement DNA polymerase to achieve signal replacement output through primer polymerization.22 In his design, the circuit functions of the OR gate (Fig. 4a) and AND gate (Fig. 4b) are realized successfully, and the result can be detected by using a fluorescence signal. The selection of enzymes is one of the most important steps in the enzymatic logic circuit, and the commonly used enzymes include DNA polymerase or splicing enzyme. There are also some promising DNA computing enzymes such as RecA (recognition and excision enzyme), deoxyribozyme, and Cas nucleases.35 Milligan et al. used the RecA in 2015 to increase the reaction rate of DNA circuits by nearly 9 times (Fig. 4c).36 Cas nucleases can bind to RNA with a complementary base, thus recognizing DNA sequences specifically through specific RNA sequences. Therefore, based on this characteristic of the Cas nuclease, various applications can be achieved by the rational design of different guide RNA and DNA circuits. In 2007, Barrangou et al. were able to control the activity of Cas nucleases through DNA circuits to regulate gene expression in living cells.37 Simultaneously, specific Cas nucleases would exhibit indiscriminate nuclease activity upon binding, leading to non-selective cleavage of all single-stranded nucleic acids. By taking advantage of this indiscriminate catalytic capacity, Cas nucleases can be used to activate fluorescent single-stranded DNA reporters and be integrated with DNA circuits for sensitive molecular diagnostics.38,39 At the same time, various combinations of polymerases, restriction endonucleases, ligase and nucleases have been gradually integrated into DNA circuits. For example, Kim and Winfree used T7 RNA polymerase to create various types of transcriptional oscillators to produce RNA and used RNaseH to destroy it (Fig. 4d).40 The addition of enzymes not only brings more strategic choices to DNA circuits in addition to molecular exchange and molecular recognition, but also enables enzymatic DNA circuits to have complex and efficient structures by using the specificity and catalytic control of enzymes.
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| Fig. 4 (a) The design and testing of OR gate DNA polymerase enzymatic DNA circuits, which involve two types of DNA hybridization (DH) and polymerization (PO) reactions in the OR gate. (b) The design and testing of AND gate DNA polymerase enzymatic DNA circuits, which involve two types of DNA hybridization and polymerization reactions in the AND gate to generate output strands. The above two figures were reproduced with permission from Song et al.15 Copyright 2019, Nature Research. (c) The use of RecA, a molecular sliding enzyme, to form catalytic complexes with DNA, enhancing the reaction rate in DNA circuit reactions. The figure was reproduced with permission from Milligan et al.29 Copyright 2015, Royal Society of Chemistry. (d) The design and construction of a bistable negative feedback oscillator using T7 RNA polymerase and RNaseH. The figure was reproduced with permission from Kim et al.33 Copyright 2011, European Molecular Biology Organization. | |
Logic circuits for DNA nanostructures
Whether enzyme-free or enzyme-containing, the stability of DNA circuits primarily depends on the precise pairing and interaction between DNA molecules. This makes them more susceptible to interference or failure when exposed to environmental changes or require precise reactions. In contrast, DNA nanostructures are designed with a certain level of structural stability and redundancy, allowing them to maintain strong stability under specific environmental conditions. In the 1980s, professor Seeman first proposed the scheme to self-assemble DNA strands from the bottom up.41 In the following 40 years, DNA nanostructures were gradually improved by the initial tiles, extending to DNA brick and DNA origami structures, which can lead to construction of DNA structures with controllable geometry and topology.42
At the same time, compared with DNA molecules, a major advantage of DNA nanostructures is that the spatial structure of DNA circuits can be predetermined. Chatterjee realized DNA circuits with predetermined reaction paths by constructing DNA hairpins with certain spatial structures on DNA origami scaffolds (Fig. 5a and b).43 This highly precise and stable self-assembly design, along with modular DNA circuits, can address specific tasks, such as cargo sorting,44 maze solving,45 building limited-state machine46 and cryptography.47 Among them, a promising DNA computing device is the DNA origami register, which is designed and manufactured using the addressable characteristics of the DNA nanostructure. This structure can temporarily store the intermediate data of the computing and guide the asynchronous computing of the cascade circuit, thus increasing the scale and circuit depth of the liquid phase DNA digital computing.8 By designing solid-state DNA origami registers and surface-to-solution adapters to form a heterogeneous integrated architecture, the signal transmission speed between sequential cascaded circuits is improved, realizing high-speed sequential DNA computing (Fig. 5c).48 Apart from DNA origami registers, DNA nanostructure itself can also be used as a unit of DNA computing. The carefully designed DNA nanostructure can be used to interact with biomolecules, and the computing can simulate Boolean logic in living cells in vitro.49–51 In addition to programming a single DNA nanostructure, it is also possible to organize and coordinate multiple nanostructures to form DNA circuits, and then construct complex self-assembly circuits for DNA computing. DNA computing circuits can be constructed through the interaction between DNA nanostructures, such as Petersen et al. constructed DNA circuits by the displacement of DNA tiles in 2018 (Fig. 5d).52 In addition to building DNA circuits, the nuclease resistance of the DNA nanostructure may be used to realize the long-term stable DNA circuit in cells, so as to realize the living application of DNA computing. Whether it is an enzyme-free or enzyme-containing DNA circuit or a logic circuit of DNA nanostructure, there are always biological molecules diffusing and mixing in the solution, so it is difficult to control the inherent random collision of molecules.53 To deal with this problem, researchers proposed a method to construct compartmentalized DNA circuit using other materials.
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| Fig. 5 (a) An abstract logic circuit (left) is implemented using DNA hairpin components arranged on the DNA origami, and a top view (middle and bottom) of the circuit on the origami shows that there are four basic hairpins in the circuit, which is tested experimentally to test the structure of the circuit (right). (b) The reaction mechanism of the four basic DNA hairpins on DNA origami. The above two figures were reproduced with permission from Chatterjee et al.36 Copyright 2017, Nature Research. (c) The left figure shows the sequential calculation of data exchange between liquid circuit and solid-state DNA origami register, while the right figure shows the molecular details of the DNA origami record that can work on the surface. The gray box shows the molecular details of the storage unit. The figure was reproduced with permission from Zhang et al.41 Copyright 2024, American Chemical Society. (d) Schematic diagram of the three scenarios of DNA chain replacement reaction at the level of DNA strand, domain and DNA nanostructure are realized by DNA tiles. The figure was reproduced with permission from Petersen et al.45 Copyright 2019, Nature Publishing Group. | |
Compartmentalized DNA circuit
The compartmentalized DNA circuit is a strategy to provide an alternative for the positioning of DNA circuits by using other materials or structures besides DNA nanostructures, such as colloid, lipid, protein, vesicle, etc., so as to reduce the accidental crosstalk in the solution system after the attachment or encapsulation of DNA circuit. For example, Kim and colleagues constructed DNA logic circuits by loading DNA-functionalized nanoparticles onto lipid bilayers, using the hybrid state of these nanoparticles as a signal (Fig. 6a).54 However, the reaction rate is slow, especially between particles, due to the very small amount of DNA on such 2D surfaces.55 This issue can be addressed by encapsulating DNA circuits in vesicles or oil-in-water droplets. For vesicle encapsulation, the vesicle membrane is modified with nanopores to create a compartmentalized space for single-stranded DNA (Fig. 6b)56 or absorbable aggregates.57 For oil-in-water droplet encapsulations, the signal changes are determined by the random distribution of key components such as internal enzymes,58 making them ideal for optimizing DNA circuits in a large parameter space. Additionally, the small volume of the droplets enables single-molecule level DNA computations, making them suitable for constructing highly sensitive sensing devices.59
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| Fig. 6 (a) Three types of DNA-modified nanoparticles, memory, floating and reporting, are attached to the lipid bilayer. Memory and reporting nanoparticles are fixed, while floating nanoparticles can diffuse and react with DNA in the solution to change the hybridization state of nanoparticles. The figure was reproduced with permission from Kim et al.47 Copyright 2020, American Association for the Advancement of Science. (b) By inserting cholesterol-tagged DNA origami signal units (DOSUs) into the surface of the vesicles, a transmission channel through which fluorescent molecules can be transported was constructed. The figure on the right shows the vesicles containing DOSUs (first row) and those without DOSUs (second row) in a fluorescent solution. The figure was reproduced with permission from Jahnke et al.49 Copyright 2024, Wiley. (c) Oil-in-water droplets containing DNA can be prepared using protein polymer conjugates and streptavidin for DNA computing. The figure was reproduced with permission from Joesaar et al.54 Copyright 2019, Nature Research. | |
Currently, compartmentalized DNA circuits have not been widely applied in the construction of DNA computing. Their potential to achieve computational reaction specificity by attaching or encapsulating DNA circuits remains to be explored. This approach could lead to a breakthrough in the flexibility of DNA computing by preventing unnecessary interactions (Fig. 6c).60 In such a system, the diffusion of biomolecules no longer causes circuit crosstalk; instead, it facilitates circuit operation. Theoretically, this system allows for the construction of complex DNA computations using only identical and simple circuits.61
DNA computing structure
Currently, DNA logic circuits have been successfully constructed using different reaction principles and basic structures. When constructing DNA computing systems using these different DNA logic circuits, there are typically two approaches. The first approach involves achieving specific functions through the unique recognition capabilities of DNA. A prime example is the development of various DNA-based sensors that detect changes in parameters such as fluorescence, current, or absorbance intensity. These sensors achieve high sensitivity by designing specific DNA sequences to target molecules. To date, nearly infrared voltage sensors,62 magnetic sensors,63 cisplatin sensors based on fluorescent DNA,64 and a series of enzyme sensors have been successfully developed.65 In the field of bioengineering, DNA biosensors are widely used in environmental monitoring and clinical diagnosis. However, most DNA computations currently focus on the outside of cell membranes, with applications within cells limited to relatively simple circuits.66 Therefore, developing DNA biosensors that can function normally in living cells is crucial for further advancements. First, it is necessary to develop DNA circuits with long-term stability, such as using DNA nanostructures to enhance the stability of DNA circuits in living cells.67 The second type is an integrated DNA computing structure designed for large-scale parallel computing and problem-solving. In 2001, the Benenson's team constructed a programmable finite automaton using DNA and DNA polymerase.68 In 2018, Cherry et al. developed a winner-take-all neural network based on DNA strand displacement reactions and an extended seesaw DNA gate motif,25,69 which enabled information memory and utilization.70 In 2023, Fan et al. designed a highly scalable DNA-based programmable gate array (DPGA) and integrated three layers of DPGA to create a universal DNA integrated circuit (DIC) capable of solving binary equations, thus overcoming the limitations of circuit scale and depth in DNA molecular computing.8
Progress in DNA data storage
The DNA circuit is the main framework of DNA computing. Its development is very important, but as the input signals and output signals of the ends of computing, information storage is also a key component that cannot be avoided in the development of a DNA computer. The rapid development of DNA data storage began in 2012, when the Church Team first realized large-scale data storage in DNA molecules.16 After nearly 12 years of development, DNA data storage has made impressive achievements in the design of data coding algorithms and data storage modes.
DNA data coding algorithm
The first key point of data storage is the coding of data. In the coding design of data, the storage capacity and recoverability of data are mainly considered. However, there are some special obstacles in the DNA data storage due to the synthesis and nature of DNA, including base mutation, sequence loss, sequence duplication, and generating unsatisfactory secondary structures. Therefore, in the development of DNA data storage there is an urgent need for algorithm optimization. In 2015, Grass et al. first introduced the Reed–Solomon code for error correction in the data field into the DNA data storage system (Fig. 7a),71 thus successfully solving the error problems such as base mutation and sequence loss, laying the foundation for DNA data storage applications. From this advance, DNA storage started to develop towards storage capacity. In 2017, Erlich and Zielinski introduced the fountain code, successfully achieving a high data density of 1.57 bits per nucleotide (Fig. 7b).72 In 2022, Ping et al. used two sets of coding rules to encode and convert two binary messages, with their intersection forming the final sequence (Fig. 7c).73 This coding scheme realized high density and high stability of information storage, and increased the storage density to 1.778 bits per nucleotide. The algorithm of Yin–Yang dual encoding realizes high density and high stability of data storage, and the storage density per nucleotide reached 1.778 bits. Meanwhile, the data recovery rate of Yin–Yang dual encoding was nearly two orders of magnitude higher than that of the fountain code. In 2024, Esra Satır proposed a lossless compression method based on spatial coding, which encoded and decoded the vectors of DNA bases in each two-bit space domain to improve the efficiency and density of data storage, achieving a storage density increase of 1.99 bits.74 Recently, DNA storage systems predominantly utilize a substantial quantity of short DNA strands within a DNA pool. The process of data writing is dependent on the synthesis of DNA array, while data reading is facilitated through DNA sequencing technologies. Therefore, the faster speed and greater density of data writing and reading are apparently the further development of DNA data storage technology. In recent years, with the advancement of DNA nanostructure technology, which can write data at multiple sites in three-dimensional space and provides a larger storage capacity, DNA nanostructures have emerged as a new type of DNA information storage medium, avoiding the data read/write limitations associated with short-strand DNA.
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| Fig. 7 (a) As illustrated in the figure above, two letters or bytes from the text file are mapped to three elements of a Galois field, which is 47 in size, through a base conversion (from the square of 256 to the cube of 47). The Reed–Solomon (RS) code, as illustrated in the middle figure, is used to add redundancy A to each block. Each column is indexed, and redundancy B is generated through a second (internal) RS encoding step. Finally, by mapping GF (47) to the DNA encoding wheel depicted below, each element is mapped to three nucleotides, ensuring that no base is repeated more than three times. The figure was reproduced with permission from Grass et al.65 Copyright 2015, John Wiley and Sons. (b) The 32-bit small file uses the fountain code to divide into eight four-bit segments, and introduces a two-digit seed code, used only for display purposes. The figure was reproduced with permission from Erlich et al.66 Copyright 2017, The American Association for the Advancement of Science. (c) As shown in the left figure, the YYC code is used to split and compile the same information by combining two sets of Yin and Yang coding strategies. The process of realizing the right figure is shown by YYC coding. The figure was reproduced with permission from Ping et al.67 Copyright 2022, Nature Research. | |
Data storage in DNA nanostructures
DNA nanostructures provide the potential to optimize these problems through the three-dimensional multi-site writing and more macroscopic data storage space. The main types of DNA nanostructures in current DNA information storage technologies are linear DNA, DNA origami, and other structures. Linear DNA structures encode information through differences in DNA nodes, such as using enzymes to create deletions at specific sites (Fig. 8a),75 designing DNA sequences to create dumbbell hairpin structures (Fig. 8b)76 or using biotin for modification.77 Such linear DNA structures store information via nanopore reading. The key feature of using DNA origami for information storage compared to linear DNA is that the information can be stored not just in the DNA sequences but directly in the three-dimensional origami structure, where information is encoded through the deformation or asymmetry of the origami structure. Additionally, under this storage model, more cost-effective methods like fluorescence microscopy can be used to read the information. Lin et al. achieved asymmetric labeling on nanorods using multicolor fluorescence, which exponentially increases coding capacity with the number of fluorophores and labeled regions, while also enabling information reading with super-resolution microscopy (Fig. 8c).78 Pan et al. similarly labeled DNA nanorods with fluorescence and introduced varying amounts of fluorophores as an intensity variable, enhancing its coding capability.79 Moreover, DNA can also form unique structures on other substrates for information storage, such as fluorescently modified DNA strands loaded onto electrode arrays (Fig. 8d)80 and DNA chains are wound around carbon nanotubes (CNTs) to form tubular nucleic acids (TNAs).81 At the same time, the characteristics of self-assembly of DNA nanostructures endows them with unique advantages in data encryption. The self-assembly properties of DNA nanostructures provide unique advantages in information encryption. Many information storage systems that utilize DNA nanostructures have achieved information encryption. By removing or replacing key elements, the self-assembly structure of DNA nanostructures can become more complex and secure. For example, Zhu used linear DNA structures to store information by reserving specific ends at each site, allowing for the addition of invasion chains to alter specific information and achieve encryption.82 Talbot used DNA switches to create small DNA loops within linear DNA structures, achieving both information storage and encryption.83
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| Fig. 8 (a) Different numbers of DNA dumbbell structures were inserted into a segment of the long DNA chain, resulting in different current signals under the same potential in the nanopore. The torsion angle between each DNA dumbbell unit was 34.3°. The process of realizing the right figure is shown by YYC coding. The figure was reproduced with permission from Tabatabaei et al.69 Copyright 2020, Nature Publishing Group. (b) The DNA-guided programmable restriction enzyme Pyrococcus furiosus Argonaute (PfAgo) creates gaps at specific sites on linear DNA as sites for information storage. The figure was reproduced with permission from Bell et al.70 Copyright 2016, Nature Research. (c) Different sites that can be loaded with fluorescein were extended on the DNA nanorods, and barcodes based on DNA nanorods were created by introducing a variable number or type of fluorescein. The figure was reproduced with permission from Lin et al.72 Copyright 2012, Nature Research. (d) Three different types of information were recorded on a single electrode array unit, with different bits represented by different fluorophores. The figure on the right shows the fluorescence readings for the three different bits. The figure was reproduced with permission from Song et al.74 Copyright 2018, Nature Publishing Group. | |
In recent years, research studies on DNA information storage have primarily focused on the development of static systems. When storing information, the inability to precisely control individual bases in DNA makes it difficult to modify its structure, thus the stored data is fixed at that moment. Further developing DNA computing may require dynamic information storage systems capable of reading, erasing, and writing information.
Discussion
The emergence of DNA computing offers a new approach to the field of computation. By leveraging its high parallelism and efficient information storage, DNA computing demonstrates superior efficiency in solving large-scale complex problems compared to electronic computing. Additionally, due to its high-specific programmability, DNA computing can also achieve functional designs such as biological monitoring. Based on the scale of application, DNA computing can be divided into two main development directions: one is the integrated DNA computing system designed for large-scale complex operations, and the other is the small-scale DNA computing structure designed for specific functions. Regardless of the direction chosen, the core focus remains on the customized design of DNA circuits and the flexible use of DNA information storage. In the design of DNA circuits and DNA information storage, DNA origami has demonstrated unique advantages. When constructing DNA computing structures, biomolecular components diffuse and mix in a solution, and the inherent random collisions of molecules,53 which are difficult to control, hinder the development of scalable and programmable biological computing devices. To address this issue, DNA origami registers have been developed, offering a possibility for large-scale and even small-scale ordered DNA computing.8,48 Currently, the development of DNA origami structures is still focused on the self-assembly of superstructures84–86 and biomedical applications such as drug loading and targeted recognition.87,88 However, the multi-site and three-dimensional spatial structure of DNA origami structures in DNA circuits and DNA information storage indicates greater potential for development.
Challenges and prospects
The high programmability and biocompatibility of DNA computing, among other features, make its potential for development undeniable. However, practical applications face significant challenges due to the high costs of DNA synthesis and sequencing, the low computational efficiency compared to electronic computing, and the instability of computational results. The large-scale application of DNA computing still faces numerous challenges. The development of DNA computing shares similarities with traditional electronic computing, including the need to explore new computational models, optimize computational processes, and enhance DNA circuit design. Additionally, it has its unique direction, which involves adapting to the characteristics of DNA by upgrading and iterating DNA synthesis and sequencing technologies, thereby breaking the limitations on information reading and writing.
In the face of the potential of DNA computing, we need to face up to the gap with traditional electronic computing and explore its advantages. We need to accurately identify the location of DNA computing to fully realize its potential capabilities. The excellent biocompatibility of DNA computing provides a solid foundation for biological detection. At present, most of the DNA computing concentrates on the cell membrane and the outside of the cell, and the intracellular application is only relatively simple circuit, so the development of DNA circuits that can function in living cells is the key to further development, which needs to improve long-term stability for DNA circuit in the cells. Additionally, compared to traditional computing, DNA computing has very high computational power, but due to the limited read and write speeds, this potential has been difficult to fully explore. Therefore, the data read and write potential of DNA nanostructure should be further developed, and the enhanced programmability of the system should be leveraged to develop a DNA data storage solution characterized by high data storage density and the capability for data modification.
DNA computing is still a long way from developing into an integrated computer. For a real computer, circuits form its fundamental framework, and information storage marks the beginning and end of its computations. However, integrating DNA circuits with DNA information storage has been a significant challenge in DNA computing. The primary issue is the limited controllability of DNA. Although DNA is highly programmable, accurately controlling individual bases within it remains a significant challenge after synthesis. Consequently, it is difficult to overwrite DNA circuits and information storage at the single-base or short-chain level. Although a functional DNA computer structure capable of storing, retrieving, computing, erasing, and rewriting DNA data is preliminarily constructed, this system still has vast potential for improvement in terms for speed and information capacity, and further advancements are needed to integrate DNA circuits with DNA information storage.
In the case that the breakthrough of DNA computing to electronic computing cannot be realized in the short term, the combination of DNA computing and electronic computing and the efficient conversion of DNA computing and data signals are the greatest possibility for the practical investment of DNA computing. In the future, by making full use of the advantages of DNA computing and the combination with electronic computing or living organisms, for example, enhancing the directionality and speed of DNA computing by activating different small-scale segmented DNA circuits with electrical signals, or achieving comprehensive and efficient detection by combining the biocompatibility and diversity of DNA sensors with the conversion between DNA signals and electrical signals, we may see a huge technological upgrade.
Author contributions
Conceptualization and supervision: H. X., Y. Y., and Y. T. Investigation, resources, and visualization: H. X. and Y. Y. Writing – original draft: H. X. Writing – review and editing: H. X., Y. Y., X. Y., Z. Z., P. L., S. L., and Y. T.
Conflicts of interest
There are no conflicts to declare.
Data availability
No primary research results, software or code have been included and no new data were generated or analysed as part of this review.
Acknowledgements
This work is supported by the National Natural Science Foundation of China (grant no. 22372077 and 92356304).
References
- L. M. Adlemen, Molecular computation of solutions to combinatorial problems, Science, 1994, 266, 1021–1024 CrossRef.
- J. J. Shu, et al., Programmable biomolecule-mediated processors, J. Am. Chem. Soc., 2023, 145, 25033–25042 CrossRef CAS.
- R. J. Lipton, DNA solution of hard computational problems, Science, 1995, 268, 542–545 CrossRef CAS.
- D. F. Li, Is DNA computing viable for 3-sat problems?, Theor. Comput. Sci., 2003, 290, 2095–2107 CrossRef.
- M. Darehmiraki and H. M. Nehi, A surface-based DNA algorithm for the solving binary knapsack problem, Appl. Math. Comput., 2007, 188, 1991–1994 CrossRef.
- X. Chen, et al., Massively parallel DNA computing based on domino DNA strand displacement logic gates, ACS Synth. Biol., 2022, 11, 2504–2512 CrossRef CAS.
- S. S. Jia, et al., DNA-based biocomputing circuits and their biomedical applications, Nat. Rev. Bioeng., 2025, 3, 535–548 CrossRef.
- H. Lv, et al., DNA-based programmable gate arrays for general-purpose DNA computing, Nature, 2023, 622, 292–300 CrossRef CAS PubMed.
- X. W. Xiong, et al., Molecular convolutional neural networks with DNA regulatory circuits, Nat. Mach. Intell., 2022, 4, 625–635 CrossRef.
- K. N. Lin, et al., A primordial DNA store and compute engine, Nat. Nanotechnol., 2024, 19, 1654–1664 CrossRef CAS.
- Q. Ma, et al., An automated DNA computing platform for rapid etiological diagnostics, Sci. Adv., 2022, 8, eade0453 CrossRef CAS.
- L. H. Zhang, et al., A multi-input molecular classifier based on digital DNA strand displacement for disease diagnostics, Adv. Mater., 2025, 37, 2413198 CrossRef CAS.
- D. R. Kong, et al., DNA logical computing on a transistor for cancer molecular diagnosis, Angew. Chem., Int. Ed., 2024, 63, e202407039 CrossRef CAS PubMed.
- H. Y. Zhao, et al., DNA molecular computing with weighted signal amplification for cancer mirna biomarker diagnostics, Adv. Sci., 2025, 12, 2416490 CrossRef CAS.
- J. Davis, Microvenus, Art J., 1996, 55, 70–74 CrossRef.
- G. M. Church, et al., Next-generation digital information storage in DNA, Science, 2012, 337, 1628 CrossRef CAS.
- N. Goldman, et al., Towards practical, high-capacity, low-maintenance information storage in synthesized DNA, Nature, 2013, 494, 77–80 CrossRef CAS.
- I. Preuss, et al., Efficient DNA-based data storage using shortmer combinatorial encoding, Sci. Rep., 2024, 14, 7731 CrossRef CAS.
- Y. Zhou, et al., Advances and challenges in random access techniques for in vitro DNA data storage, ACS Appl. Mater. Interfaces, 2024, 16, 43102–43113 CrossRef CAS.
- S. Yang, et al., DNA as a universal chemical substrate for computing and data storage, Nat. Rev. Chem., 2024, 8, 179–194 CrossRef PubMed.
- P. J. Shi, et al., Ph-controlled DNA switching circuits with multi-state responsiveness for logic computation and control, Chem. – Eur. J., 2025, 31, e202404541 CrossRef CAS PubMed.
- T. Q. Song, et al., Fast and compact DNA logic circuits based on single-stranded gates using strand-displacing polymerase, Nat. Nanotechnol., 2019, 14, 1075–1081 CrossRef CAS PubMed.
- F. Wang, et al., Implementing digital computing with DNA-based switching circuits, Nat. Commun., 2020, 11, 121 CrossRef CAS PubMed.
- G. Seelig, et al., Enzyme-free nucleic acid logic circuits, Science, 2006, 314, 1585–1588 CrossRef CAS.
- L. Qian and E. Winfree, Scaling up digital circuit computation with DNA strand displacement cascades, Science, 2011, 332, 1196–1201 CrossRef CAS.
- A. J. Genot, et al., Combinatorial displacement of DNA strands: application to matrix multiplication and weighted sums, Angew. Chem., Int. Ed., 2013, 52, 1189–1192 CrossRef CAS PubMed.
- L. Qian, et al., Neural network computation with DNA strand displacement cascades, Nature, 2011, 475, 368–372 CrossRef CAS.
- B. Wang, et al., Effective design principles for leakless strand displacement systems, Proc. Natl. Acad. Sci. U. S. A., 2018, 115, E12182–E12191 CrossRef CAS.
- N. Srinivas, et al., Enzyme-free nucleic acid dynamical systems, Science, 2017, 358, eaal2052 CrossRef.
- D. Wilhelm, et al., Probabilistic
switching circuits in DNA, Proc. Natl. Acad. Sci. U. S. A., 2018, 115, 903–908 CrossRef CAS.
- Dominic Scalise, et al., DNA strand buffers, J. Am. Chem. Soc., 2018, 140, 12069–12076 CrossRef CAS PubMed.
- A. P. Lapteva, et al., DNA strand-displacement temporal logic circuits, J. Am. Chem. Soc., 2022, 144, 12443–12449 CrossRef CAS.
- J. Kim, et al., Construction of an in vitro bistable circuit from synthetic transcriptional switches, Mol. Syst. Biol., 2006, 2, 68 CrossRef PubMed.
- K. Montagne, et al., Programming an in vitro DNA oscillator using a molecular networking strategy, Mol. Syst. Biol., 2011, 7, 466 CrossRef.
- H. M. Su, et al., High-efficiency and integrable DNA arithmetic and logic system based on strand displacement synthesis, Nat. Commun., 2019, 10, 5390 CrossRef PubMed.
- J. N. Milligan and A. D. Ellington, Using reca protein to enhance kinetic rates of DNA circuits, Chem. Commun., 2015, 51, 9503–9506 RSC.
- R. Barrangou, et al., Crispr provides acquired resistance against viruses in prokaryotes, Science, 2007, 315, 1709–1712 CrossRef CAS.
- K. Shi, et al., A crispr-cas autocatalysis-driven feedback amplification network for supersensitive DNA diagnostics, Sci. Adv., 2021, 7, eabc7802 CrossRef CAS PubMed.
- J. J. Shen, et al., Sensitive detection of a bacterial pathogen using allosteric probe-initiated catalysis and crispr-cas13a amplification reaction, Nat. Commun., 2020, 11, 267 CrossRef CAS.
- J. Kim and E. Winfree, Synthetic in vitro transcriptional oscillators, Mol. Syst. Biol., 2011, 7, 465 CrossRef PubMed.
- N. C. Seeman, Nucleic-acid junctions and lattices, J. Theor. Biol., 1982, 99, 237–247 CrossRef CAS.
- P. W. K. Rothemund, Folding DNA to create nanoscale shapes and patterns, Nature, 2006, 440, 297–302 CrossRef CAS PubMed.
- G. Chatterjee, et al., A spatially localized architecture for fast and modular DNA computing, Nat. Nanotechnol., 2017, 12, 920–927 CrossRef CAS PubMed.
- A. J. Thubagere, et al., A cargo-sorting DNA robot, Science, 2017, 357, eaan6558 CrossRef.
- J. Chao, et al., Solving mazes with single-molecule DNA navigators, Nat. Mater., 2019, 18, 273–279 CrossRef CAS PubMed.
- L. Liu, et al., A localized DNA finite-state machine with temporal resolution, Sci. Adv., 2022, 8, eabm9530 CrossRef CAS.
- Y. N. Zhang, et al., DNA origami cryptography for secure communication, Nat. Commun., 2019, 10, 5469 CrossRef.
- Q. Zhang, et al., High-speed sequential DNA computing using a solid-state DNA origami register, ACS Cent. Sci., 2024, 10, 2285–2293 CrossRef CAS.
- S. M. Douglas, et al., A logic-gated nanorobot for targeted transport of molecular payloads, Science, 2012, 335, 831–834 CrossRef CAS PubMed.
- B. Groves, et al., Computing in mammalian cells with nucleic acid strand exchange, Nat. Nanotechnol., 2016, 11, 287–294 CrossRef CAS.
- Y. J. Chen, et al., DNA nanotechnology from the test tube to the cell, Nat. Nanotechnol., 2015, 10, 748–760 CrossRef CAS PubMed.
- P. Petersen, et al., Information-based autonomous reconfiguration in systems of interacting DNA nanostructures, Nat. Commun., 2019, 9, 5362 CrossRef.
- Y. Benenson, Biomolecular computing systems: principles, progress and potential, Nat. Rev. Genet., 2012, 13, 455–468 CrossRef CAS.
- S. Kim, et al., Nanoparticle-based computing architecture for nanoparticle neural networks, Sci. Adv., 2020, 6, eabb3348 CrossRef CAS PubMed.
- S. Piranej, et al., Chemical-to-mechanical molecular computation using DNA-based motors with onboard logic, Nat. Nanotechnol., 2022, 17, 514–523 CrossRef CAS.
- K. Jahnke, et al., DNA origami signaling units transduce chemical and mechanical signals in synthetic cells, Adv. Funct. Mater., 2024, 34, 2301176 CrossRef CAS.
- T. Mashima, et al., DNA-mediated protein shuttling between coacervate-based artificial cells, Angew. Chem., Int. Ed., 2022, 61, e202115041 CrossRef CAS PubMed.
- M. Weitz, et al., Diversity in the dynamical behaviour of a compartmentalized programmable biochemical oscillator, Nat. Chem., 2014, 6, 453 CrossRef CAS.
- G. Gines, Isothermal digital detection of micrornas using background-free molecular circuit, Sci. Adv., 2020, 6, eaay5952 CrossRef CAS.
- A. Joesaar, et al., DNA-based communication in populations of synthetic protocells, Nat. Nanotechnol., 2019, 14, 369–378 CrossRef CAS PubMed.
- R. Carlson, The pace and proliferation of biological technologies, Biosecurity Bioterrorism, 2003, 1, 203–214 CrossRef.
- G. Giammanco, et al., DNA-based near-infrared voltage sensors, ACS Sens., 2023, 8, 3680–3686 CrossRef CAS.
- P. J. Hore, A DNA-based magnetic sensor, ACS Cent. Sci., 2018, 4, 318–320 CrossRef CAS PubMed.
- T. Jantarat, et al., A label-free DNA-based fluorescent sensor for cisplatin detection, Sens. Actuators, B, 2021, 326, 128764 CrossRef CAS.
- N. Dai and E. T. Kool, Fluorescent DNA-based enzyme sensors, Chem. Soc. Rev., 2011, 40, 5756–5770 RSC.
- J. Li, Engineering nucleic acid structures for programmable molecular circuitry and intracellular biocomputation, Nat. Chem., 2017, 9, 1056–1067 CrossRef CAS PubMed.
- A. R. Chandrasekaran, Nuclease resistance of DNA nanostructures, Nat. Rev. Chem., 2021, 5, 225–239 CrossRef CAS.
- Y. Benenson, et al., Programmable and autonomous computing machine made of biomolecules, Nature, 2001, 414, 430–434 CrossRef CAS.
- A. J. Thubagere, et al., Compiler-aided systematic construction of large-scale DNA strand displacement circuits using unpurified components, Nat. Commun., 2017, 8, 14373 CrossRef CAS.
- K. M. Cherry and L. L. Qian, Scaling up molecular pattern recognition with DNA-based winner-take-all neural networks, Nature, 2018, 559, 370–376 CrossRef CAS PubMed.
- R. N. Grass, et al., Robust chemical preservation of digital information on DNA in silica with error-correcting codes, Angew. Chem., Int. Ed., 2015, 54, 2552–2555 CrossRef CAS PubMed.
- Y. Erlich and D. Zielinski, DNA fountain enables a robust and efficient storage architecture, Science, 2017, 355, 950–953 CrossRef CAS PubMed.
- Z. Ping, et al., Towards practical and robust DNA-based data archiving using the yin-yang codec system, Nat. Comput. Sci., 2022, 2, 234–242 CrossRef.
- E. Satir, A DNA data storage method using spatial encoding based lossless compression, Entropy, 2024, 26, 1116 CrossRef CAS.
- S. K. Tabatabaei, et al., DNA punch cards for storing data on native DNA sequences via enzymatic nicking, Nat. Commun., 2020, 11, 1742 CrossRef CAS.
- N. A. W. Bell and U. F. Keyser, Digitally encoded DNA nanostructures for multiplexed, single-molecule protein sensing with nanopores, Nat. Nanotechnol., 2016, 11, 645–651 CrossRef CAS PubMed.
- K. K. Chen, et al., Nanopore-based DNA hard drives for rewritable and secure data storage, Nano Lett., 2020, 20, 3754–3760 CrossRef CAS.
- C. X. Lin, et al., Submicrometre geometrically encoded fluorescent barcodes self-assembled from DNA, Nat. Chem., 2012, 4, 832–839 CrossRef CAS.
- V. Pan, et al., Monochromatic fluorescent barcodes hierarchically assembled from modular DNA origami nanorods, ACS Nano, 2021, 15, 15892–15901 CrossRef CAS.
- Y. Song, et al., DNA multi-bit non-volatile memory and bit-shifting operations using addressable electrode arrays and electric field-induced hybridization, Nat. Commun., 2018, 9, 281 CrossRef PubMed.
- Y. Y. Zhang, et al., Encoding carbon nanotubes with tubular nucleic acids for information storage, J. Am. Chem. Soc., 2019, 141, 17861–17866 CrossRef CAS PubMed.
- J. B. Zhu, et al., Image encoding using multi-level DNA barcodes with nanopore readout, Small, 2021, 17, 2100711 CrossRef CAS PubMed.
- H. Talbot, et al., Encoding, decoding, and rendering information in DNA nanoswitch libraries, ACS Synth. Biol., 2023, 12, 978–983 CrossRef CAS PubMed.
- X. H. Yan, et al., Dynamically reconfigurable DNA origami crystals driven by a designated path diagram, J. Am. Chem. Soc., 2023, 145, 3978–3986 CrossRef CAS.
- Y. F. Yu, et al., Fast synthesis of DNA origami single crystals at room temperature, Chem. Sci., 2025, 16, 793–801 RSC.
- Z. Y. Zhou, et al., Phase behavior modulation of a unary DNA origami system through allosteric stimuli, Nano Lett., 2024, 24, 12263–12270 CrossRef CAS.
- L. Z. Dai, et al., DNA origami: an outstanding platform for functions in nanophotonics and cancer therapy, Analyst, 2021, 146, 1807–1819 RSC.
- X. X. Hu, et al., Tunable multivalent aptamer-based DNA
nanostructures to regulate multiheteroreceptor-mediated tumor recognition, J. Am. Chem. Soc., 2024, 146, 2514–2523 CrossRef CAS PubMed.
Footnote |
† These authors contributed equally to this work. |
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