Introduction

Molecular communication is one of the crucial processes essential for sustaining life activities in living organisms. Intra- and intercellular molecular interactions form a complex and coordinated molecular communication network, which is of great significance for maintaining homeostasis, adapting to the environment, and coordinating various physiological processes. Drawing inspiration from molecular communication within living organisms, molecular-level interactions have constructed artificial communication networks to achieve information transmission1,2 and even more complex tasks which enable broad application prospects in computer science3, biomedical engineering4,5,6,7, information technology8 and so on9,10. However, current research on artificially simulated communication predominantly relies on linear or cascade communication modes. The lack of the programmability, multiplexing capabilities and generalization limit their use to simulate intricate communication networks accurately11. Consequently, it is urgent to develop an innovative model that can explore more intricate networks for simulating molecular communication.

DNA molecules have created special links between biotechnology, materials science, and information technology12,13,14,15. Utilizing the structure features and interactions of DNA molecular, DNA strands have been employed for molecular computing13,16, storage17,18, and logic circuits19,20. More importantly, structural DNA nanotechnology has successfully enabled the construction of self-assembling DNA nanostructures with nanoscale addressability and programmability21,22. These DNA nanostructures can be further modified and designed with specific recognition patterns, allowing precise organization for more complex operations, which have been extensively applied in molecular computing23,24, functional nanodevices25,26, higher-order structure assembly27,28 and topology construction29,30,31. DNA origami32, as a type of DNA nanostructure, offers higher design flexibility, structural stability, programmability, and modularity—traits essential for constructing communication networks that require precise control of molecular interactions and spatial organization. However, their potential in simulating molecular communication networks is still largely unexplored, especially in addressing the challenges associated with establishing programmable, multiplexed and general communication network models.

Here, we present a DNA nanostructure recognition-based artificial molecular communication network (DR-AMCN), in which the rectangular DNA origami nanostructures are utilized as nodes with complementary connectors between them serving as edges between nodes. We initially established direct communication, series communication, parallel communication, and orthogonal communication mechanisms to demonstrate feasibility and expanded the capacity of our system by implementing the construction of bus, ring, star, tree and hybrid topology networks with to showcase its programmability and scalability. Finally, we explored the application of DR-AMCN in graph theory by traversing all paths of a seven-node Hamiltonian graph, and demonstrated the method has scalable potential. By the establishment of a node partition algorithm for path traversal based on DR-AMCN, the computational complexity of the seven-node Hamiltonian path problem is reduced and solved directly by a rate-zonal centrifugation method for the selection of the unique Hamiltonian path. This abstract model serves as a tool for comprehending and addressing problems in information and computer science, while also offering a perspectives and methodologies for investigating molecular communication mechanisms and regulatory networks.

Results

Establishment of DR-AMCN

The generic communication network model comprises two essential components: nodes and edges. Nodes serve as the fundamental units within the network which represent the communicating entities. Edges denote the lines to connect nodes and symbolize data transmission paths or communication channels, in which arrows are employed to indicate the direction of communication (Fig. 1a). We select the two-dimensional rectangular DNA origami nanostructure adapted from Rothemund’s work21 to build a node, which is formed by folding a long single-stranded scaffold with hundreds of oligonucleotide staples through a one-pot assembly. Given the programmable and addressable nature of DNA origami nanostructures, we exclude the staples located on the two shorter sides of the rectangle to establish programmable edges. The rectangular DNA origami nanostructures exhibit dimensions of ~90 nm × 60 nm with a height measuring 2 nm, and the AFM images demonstrated its well-formed structure and morphology in accordance with the design (Supplementary Fig. 1). Benefiting from the high specificity of DNA base pairing, we strategically redesigned the staples on the sides of rectangular DNA origami nanostructures to elongate 11-nt sticky ends as connectors, following the approach developed by Eyal’s group33 (differentiate by color). These connectors play a critical role in recognition during communication (all connector species used in this article were shown in Supplementary Data 1). Consequently, rectangular DNA origami nanostructures with complementary sticky ends have the potential to dimerize and establish communications between nodes when diffusing randomly in solution. Each connector consists of two pairs of edge staples intertwined and interlocked to form three complementary regions. To ensure effective communication, we investigated the dimerization efficiency using varying quantities of connectors, ranging from one to six pairs (Fig. 1b, Supplementary Figs. 2 and 4a, and Supplementary Table 1). Statistical analysis of the AFM images demonstrated that the yields of DNA origami dimers were 81.2%, 87.5%, 92.5%, 92.7%, and 92.1% for connectors ×1, ×2, ×3, ×4, and ×6, respectively (Supplementary Fig. 3). This indicated that dimerization efficiency increased with the addition of connectors but stabilized upon reaching three or more connectors. It was noteworthy that an excessive sticky ends at the ×6-group connector led to nonspecific binding and cross-linking that increased aggregate formation. Comprehensive consideration, we opted the ×3-group connector design to construct the subsequent communication network.

Fig. 1: Establishment of DR-AMCN.
figure 1

a The generic communication network model. Design of node, edge, and communication of DR-AMCN. b Diagrams and corresponding AFM images of results with varying numbers of connector pairs, including one, two, three, four, and six pairs. c Encoding rule of molecular identifier and implementation with DNA nanostructure. d Diagrams and corresponding AFM images of nodes 0–6. scale bars: 50 nm.

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To distinguish different nodes, we developed molecular identifiers to label and encode the nodes to uniquely identify and differentiate the nodes in the network (Fig. 1c). A 4-bit binary encoding was employed for each node (denoted as N n, where N is the shorthand for node, and n is the decimal number of the node). The first three bits were coding bits (depicted as dark blue circle), where site 1 was specified as least significant bit (LSB) and site 3 was defined as most significant bit (MSB). Additionally, there was an odd parity bit (represented by a dark green circle) assigned to the fourth bit in order to ensure the coding accuracy. The decimal serial numbers were converted to their binary representations and encoded by adding 1, with the order from left to right corresponding to the LSB to the MSB. Taking node 2 (N 2) as an example, the serial number 2 was first converted into its binary representation (1101), followed by encoding it into a pattern based on the predefined array, and subsequently decoded into a biotin-streptavidin (B-SA) pattern on the rectangular DNA origami nanostructure (Supplementary Fig. 4b). We created 7 nodes from 0 to 6 and listed all the node encodings and SA patterns as well as the corresponding AFM images (Fig. 1d). We employed both the original encoding and the encoding with parity check for node 4, the yield statistics indicated that the parity check has improved the accuracy of the molecular identifiers compared to original encoding (Supplementary Fig. 5). Statistical analysis of the AFM images showed that the accuracy (estimated by counting the number of nanostructures with target pattern over nanostructures satisfied parity check) for node 0, 1, …, and 6 was calculated to be 99.1%, 99.2%, 95.1%, 99.6%, 94.3%, 95.8%, 95.9%, respectively (Supplementary Figs. 5–7). The assembly yield (calculated by counting the number of nanostructures with target pattern over all nanostructures) of node 0, 1, …, and 6 was estimated to be 93.9%, 94.8%, 71.5%, 94.4%, 75.6%, 81.1%, 75.3%, respectively (Supplementary Fig. 8). Certainly, by adding biotin modification sites to DNA origami, the encoding capability for molecular identifiers can be appropriately extended. For example, Supplementary Fig. 41a, b illustrates the 5-bit encoding for nodes 0–9.

Programmable communication mechanisms of DR-AMCN

To evaluate a range of elementary communication mechanisms, we conducted one-to-one direct interactions as well as complex interactions in one-to-many and many-to-many scenarios (Fig. 2a and Supplementary Table 2). These mechanisms formed the foundation for constructing intricate communication networks. Firstly, we constructed one-to-one directed communication between node 0 (N 0) and node 1 (N 1). By incorporating complementary connectors (blue) at the edges of nodes 0 and 1 in equal molar ratios, we observed the communication accuracy of path 0 → 1 (abbreviated as P 01) with an estimated AFM yield of 92.8% (calculated by counting the number of target nanostructures over all nanostructures satisfied the parity check, Fig. 2b). Due to the minor imperfections in the rectangular DNA origami nanostructure design, the relaxed nanostructure of the rectangle exhibited a certain degree of curvature, which accumulated during multimerization and resulted in the folding of multimers. Previous studies34 have demonstrated that an appropriate dose of UV radiation can effectively rectify these distortions in DNA nanostructures. In our study, we employed UV irradiation at a wavelength of 264 nm for 8 minutes. The results indicated that this treatment effectively flattened the nanostructures without compromising protein labeling (Supplementary Fig. 9). In the subsequent experiments, all samples were treated with UV irradiation prior to AFM characterization.

Fig. 2: Programmable communication mechanisms of DR-AMCN.
figure 2

a Diagram of basic communication mechanisms, including one-to-one, one-to-many, and many-to-many communication. b–f Schematic, representative AFM images and product statistics of the communication, including directional communication between nodes N 0 and N 1. Sample size is 112, with 104 for P 01. b orthogonal communication between nodes N 0, N 4 and nodes N 1, N 2 generating path 0 → 1 (blue) and 4 → 2 (red). Sample size is 111, with 52 for P 01 and 51 for P 42. c, d parallel communication between node N 0 with N 1 or N 2 generating path 0 → 1 (blue) and 0 → 2 (red) without bias. Sample size is 224, with 58 for P 01 and 57 for P 02. e as well as multiplexed communication for path 0 → 1 (blue), 0 → 2 (red), 4 → 1 (golden), and 4 → 2 (purple) through a common connector. Sample size is 136, with 31 for P 01, 30 for P 02, 32 for P 41 and 34 for P 42. f The x in the product statistics represents deserted reactants and other side products. The yield of each path was calculated by counting the number of target DNA nanostructures over all nanostructures. Three AFM images were counted for each DNA nanostructure, and each image was from an independent experiment. Source data are provided as a Source Data file. Scale bars, 50 nm.

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Given the intricate nature of biological systems, molecular communication often endured diverse interferences and noises, we conducted tests to evaluate its resistance against such disturbances. We introduced an interfering node 2 into the communication between nodes 0 and 1. The results showed that the communication system remained specific in the presence of interferences (Supplementary Fig. 10). This highlights the high resistance to interference of the communication system. Next, we demonstrated orthogonal communication between various nodes, wherein multiple communication processes could be carried out concurrently within a communication system. We designed four nodes (N 0, N 1, N 4, and N 2), with N 0 and N 1 interacted through the blue connectors and N 4 and N 2 interacted through the red connectors. The four nodes were subsequently mixed and annealed in equal concentration, resulting in two independent communication paths—path 0 → 1 (P 01) and 4 → 2 (P 42) without crosstalk (Fig. 2c, d and Supplementary Fig. 11). The implementation of orthogonal communication ensures the preservation of signal integrity and minimizes interference between different channels, which was crucial for multi-node communication systems.

In addition to one-to-one communication, a transmitting node could simultaneously communicate with multiple receiving nodes in parallel (one-to-many), in order to enhance communication efficiency and reduce cost. Consequently, we allocated the identical receiver to both node 1 (N 1) and node 2 (N 2), while assigning the corresponding transmitter to node 0 (N 0). Subsequently, a concentration ratio of 1:1:1 was set for nodes N 0, N 1, and N 2, followed by observation of the communication result. Statistical on the assembled products proved that the percentage of path 0 → 1 (P 01) and 0 → 2 (P 02) was 25.9% and 25.4% respectively, with redundant nodes 1 and 2 remaining as monomers (Fig. 2e and Supplementary Fig. 12). The evenly distribution of communication path indicated that our system exhibited no path bias and demonstrated load balancing and fairness, thus achieving efficient and stable communication.

Finally, we conducted a many-to-many form of communication, which contained cross communication between multiple senders and multiple receivers. We developed multiplexing of connectors in which multiple communication pathways were combined and transmitted over a single connector (Fig. 2f and Supplementary Fig. 13). Four distinct paths were established between two sender nodes (N 0 and N 1) and two receiver nodes (N 4 and N 2), namely path 0 → 1 (P 01), 0 → 2 (P 02), 4 → 1 (P 41), and 4 → 2 (P 42). Each communication instance was facilitated through the utilization of a common connector. The reaction was conducted with nodes in equal molar ratio, the statistical analysis revealed an approximate yield of the four paths, with an overall communication efficiency of 93.4% (the sum of the yields of the four paths). The technique of multiplexing facilitated the simultaneous transmission of multiple signals through a single connector, thereby enhancing channel utilization, reducing costs, and effectively conserving resources.

The programmability and scalability of DR-AMCN for complex network topologies

Having established several fundamental communication mechanisms, we next explored expanding the capacity of the communication system for implementing complex communication networks. Extracting features for topological classification of networks was an efficient research methodology that facilitated the understanding of characteristics, behavioral patterns, and performance of diverse network types. Inspired by cellular communication networks, these structures often exhibited bus-shaped (e.g., axons in the nervous system), star-shaped (e.g., function of immune cells), and tree-like branching patterns (e.g., differentiation of stem cells) features. In fact, these were also common topological structures in traditional computer networks and communication systems. Hence, we attempted to construct these three network topologies to investigate the impact of node layout and interconnection on network performance and behavior (Supplementary Table 3).

The bus topology was concatenated linear pathways in series, where all nodes established unidirectional connections with neighboring nodes individually. Firstly, the series communication of three nodes N 0, N 1, and N 2 was investigated (Supplementary Fig. 14a). This involved assigning two sets of specific connectors to the three DNA origami nanostructures, which assembled into trimeric DNA nanostructures synergistically to form a communication path 0 → 1 → 2 (P 012). The yield of trimers was ~80.2% as determined from AFM image statistics (Supplementary Fig. 14b). The construction of communication pathway with a length of three nodes following the prescribed order exhibited the potential for long-distance communication. Then, we designed and simulated a bus-like communication network with five nodes (Fig. 3a). In our design, N 0 was served as the initial node responsible for transmitting signals, while N 4 functioned as the terminal node dedicated to receiving signals. Intermediate nodes (N 1, N 2, and N 3) acted both as senders and receivers to pass on information in one direction. The complementary relationships between connectors were determined based on their location within the path, a total of four pairs of connectors were required and led to the longer communication path was generated as path 0 → 1 → 2 → 3 → 4 (P 01234). AFM images and agarose gel electrophoresis confirmed the assembly of pentameric DNA nanostructures (Fig. 3d and Supplementary Figs. 15–17). According to AFM image analysis, the pentamer exhibited an approximate assembly yield of 72.8%. Among pentamer structures, 52.1% satisfied the parity check, and a great majority of them decoded as the correct communication path, thereby confirming the construction of bus-type networks. However, in the event of a failure of any intermediate node, the communication network would be disrupted, leading to the formation of an oligomeric DNA nanostructure. When the bus topology is transformed by connecting its start and end nodes, a ring topology is formed. This design facilitates continuous information transmission within the network, allowing the path 0 → 1 → 2 → 3 → 4 to circulate repeatedly. As shown in Supplementary Fig. 18, AFM imaging confirmed the assembly of an 18-unit DNA origami multimer, in which the P 01234 was transmitted three times in full. This achievement highlights the capability of DR-AMCN to support continuous and robust information flow.

Fig. 3: The programmability and scalability of DR-AMCN for complex network topologies.
figure 3

a–c, Diagrams of network topology, DNA nanostructure design, and communication paths with corresponding cropped AFM images for the bus (a), star (b), and tree (c) topology, respectively. Scale bars, 50 nm. d–f, Large range AFM image of the bus (d), star (e), and tree (f) topology, respectively. Scale bars, 200 nm. The distinct paths were indicated by boxes with distinct colors. In the bus topology, a DNA nanostructure pentamer represents P 012345. In the star topology, four types of DNA nanostructure dimers encode P 01 (blue), P 02 (red), P 03 (purple), and P 04 (golden), respectively. In the tree topology, four types of DNA nanostructure trimers encode P 013 (blue), P 014 (red), P 025 (purple), and P 026 (golden), respectively.

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The star topology represented an extension of parallel communication, wherein a central node functioned as the core, and other terminal nodes were directly connected to the central node simultaneously. We designed and simulated a star network graph comprising five nodes (Fig. 3b). N 0 was served as the central node, while N 1, N 2, N 3, and N 4 were acted as terminal nodes. Then, we defined DNA origami nanostructures as the nodes and their communications in the star network. The network consisted of four distinct communication paths, namely path 0 → 1 (blue), 0 → 2 (red), 0 → 3 (purple), and 0 → 4 (golden) (Fig. 3b, e). To investigate the impact of signal competition between communities on transmission efficiency, we first set the molar ratios of nodes N 0, N 1, N 2, N 3, and N 4 at 1:1:1:1:1 (Supplementary Fig. 19). Although AFM images revealed the even distribution of four communication paths, mismatches occurred in the connectors of randomly distributed terminal monomers resulting in an error rate of approximately 39%. Because central node accommodated all terminals for each communication path, a sufficient number of node 0 may maintain the communications. Hence, the molar ratios of nodes N 0, N 1, N 2, N 3, and N 4 of 2:1:1:1:1 and 4:1:1:1:1 were tested which generated a reduced error rate with 16.7% and 4.3%, respectively. Furthermore, dimer proportions reached up to 88.5%, which was closely approaching assembly yield levels for DNA origami dimers (Supplementary Figs. 20 and 21). The gel electrophoresis also verified the dimerization yield increased with the increase in the molar ratio (Supplementary Fig. 22). The further statistical analysis of the path distribution showed that it still exhibited communication load balancing, which complied with the conclusion obtained in parallel communication between two paths mentioned above. This finding demonstrated that communication efficiency within star networks did not diminish with increasing complexity. Therefore, the performance within star networks was directly related to the characteristics and behavior of the central node itself—a key factor determining their functionality. Star networks offer an insight into how competition for signals between communities could impact signal transmission.

Then we moved to a more intricate network structure named tree topology, comprising a root node and multiple child nodes, which could further connect additional child nodes to form a multi-level hierarchy. In this study, we designed and implemented a three-layer tree communication network graph consisting of seven nodes (Fig. 3c). The first layer represented the root node (N 0), which could communicate with two parallel child nodes (N 1 or N 2) in the second layer. Similarly, in the third layer, child node N 1 could communicate with leaf nodes N 3 or N 4 in parallel, while child node N 2 could also establish parallel communication with leaf nodes N 5 or N 6. The corresponding DNA nanostructure design illustrated the assembly of trimeric DNA nanostructure and traversal of communication paths 0 → 1 → 3 (blue), 0 → 1 → 4 (red), 0 → 2 → 5 (purple), and 0 → 2 → 6 (golden), which were verified by AFM images and agarose gel electrophoresis (Fig. 3c, f and Supplementary Figs. 23 and 24). To investigate the communication efficiency of each type of node, we maintained a ratio of root node to child node to leaf node at 1:1:1 and 4:2:1. We observed the same phenomenon including evenly distribution of four communication paths and an impressive yield of the DNA origami trimers up to 82.8% under a sufficient number of node N 0 (Supplementary Fig. 25). The construction of a tree topology served as further evidence supporting our strategy’s capability to build extensive communication networks. Different types of basic network topologies can be combined to form hybrid topologies to create more complex communication networks. Building on the principles of both bus and star topologies, we further carried out a 6-nodes Star/Bus hybrid topology. As demonstrated in Supplementary Fig. 26, the resulting DNA origami communication system was assembled into four types of DNA origami tetramers, each corresponding precisely to the designed communication paths. This implementation underscores the versatility of DR-AMCN in constructing highly customizable complex networks.

DR-AMCN-driven path traversal on a Hamiltonian graph

Graph theory has been used to study the topology of complex communication networks. As the DR-AMCN path traversal was proved unbiased, we further utilized it to exhibit solving hard problems in graph theory. A Hamiltonian path is a path that visits each node of the graph once exactly. The problem of determining a Hamiltonian path for a graph is classified as an NP-complete problem, for which no algorithm has been discovered to solve it within polynomial time in the field of computer science. Excitedly, DNA-based molecular computation has been demonstrated to address the problem13,35,36. Nevertheless, the computational complexity introduced by operations including amplification, digestion, extraction, sequencing and decoding remains problematic. With the aim of solving this problem, we introduced the communication mechanism and topological network in DR-AMCN into molecular computation, establishing a node partition algorithm for path traversal.

As a representative example, we constructed a model of a directed Hamiltonian graph G with seven nodes (0, 1, …, 6) and eleven edges (Fig. 4a). The adjacency matrix shows the adjacency relation between nodes, where the existence of an edge between the nodes was recorded as 1, otherwise it was recorded as 0. Noteworthy, the graph contains two loops including 1 ↔ 2 and 2 ↔ 3. This should be avoided because the repeated visit for nodes must be an infinite loop. In our algorithm, we first analyzed and partitioned all seven nodes in G based on the incoming nodes (I) and outgoing nodes (O) of each node. The possible communication mechanisms between each node and its adjacent incoming and outgoing nodes, including one-to-one, one-to-many, and many-to-one communications was illustrated (Supplementary Fig. 27a). For a node n (N n) in the graph, which has i incoming nodes (namely I1, I2,…, Ii-1, Ii) and j outgoing nodes (namely O1, O2,…, Oj-1, Oj), we defined the node as N \(n_{O_1,O_2,...,O_{j-1},O_j}^{I_1,I_2,...,I_{i-1},I_i}\) (n, Ii, Oj ∈ {0, 1, 2, 3, 4, 5, 6}). Further, we subdivided the communication from incoming to outgoing for each center node n into a three-node communication path (I → n → O), then the node N \(n_{O_1,O_2,...,O_{j-1},O_j}^{I_1,I_2,...,I_{i-1},I_i}\) was partitioned into multiple corresponding nodes N \({n}_{O}^{I}\) (Supplementary Fig. 27b). In particular, when the incoming and outgoing nodes of N n were identical, it inevitably leads to a loop, and blocking the outgoing path of N n was an effective solution strategy (in such case, node n was denoted as N \({n}^{I}\)). As an example, N 1 demonstrated its analysis and partition process (Fig. 4b). The result of node partition of seven nodes in G was exhibited in a table (Fig. 4c).

Fig. 4: Node partition algorithm for path traversal.
figure 4

a The representation, adjacency matrix, and definition of nodes of the seven-node Hamilton graph G. The number of nonzero elements in the corresponding row is the outdegree (OD), and the number of nonzero elements in the corresponding column is the indegree (ID). b The node analysis and node partition of N 1. The red cross indicates the blocking the outgoing path. c Table of the node partition result for G. d The flow chart of node partition algorithm for graph traversal. e The path traversal tree for G.

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Next, we integrated all communication possibilities among the nodes to facilitate graph traversal through construction of the traverse tree (Fig. 4d). As the indegree of node 0 was zero, it was considered as the root node of the tree to start the traversal. The traversal consists of three main operations: searching, recording, and checking. As a consequence, a traversal tree containing five paths was obtained by traversing all possible paths in the Hamiltonian graph model with node 0 as the root node (Fig. 4e and Supplementary Fig. 28). Additionally, we developed a python program to execute our algorithm, which proved the feasibility of our algorithm (Supplementary Fig. 29).

According to the strategy mentioned above, Hamiltonian graph required a total of 15 sets of connectors and 20 different DNA origami nanostructures after nodes partition (Supplementary Figs. 30 and 31, and Supplementary Table 4). Then, the DR-AMCN was performed the path traversal of the Hamiltonian graph after encoded and assigned connectors to the corresponding DNA origami nanostructures (Fig. 5a and Supplementary Fig. 32). Firstly, the 20 DNA nanostructures were individually assembled in test tubes through one-pot annealing. Secondly, all DNA nanostructures were mixed in a test tube. Finally, an additional annealing step was performed over 12 hours, gradually reducing the temperature from 45 degrees to room temperature. Ultimately, as confirmed by AFM imaging, the DR-AMCN produced a mixture composed of various paths from the graph. Five cyclic-free paths were identified: 0 → 3 → 2 → 1, 0 → 3 → 4 → 5 → 6, 0 → 3 → 4 → 1 → 2, 0 → 1 → 2 → 3 → 4 → 5 → 6, and 0 → 6 conformity to our design (Fig. 5b, c and Supplementary Fig. 33).

Fig. 5: DR-AMCN-driven path traversal on a Hamiltonian graph.
figure 5

a Experimental protocol and implementation of the path traversal. b Schematic diagram and representative AFM image for five paths in the Hamiltonian graph. Scale bars, 50 nm. c Example of a multiplexed AFM image chosen to highlight parallel DNA computing of DR-AMCN. The left side of the display showed a large range AFM image, while the cropped images highlight specific regions corresponding to the numbers in large range AFM image with recognizable paths marked.

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Overall, the workflow of DR-AMCN-driven path traversal can be summarized as follows. First, the node partitioning algorithm effectively eliminating redundant loop and reduce computational complexity. Next, a traversal tree is constructed using the searching, recording, and checking operations to map all potential Hamiltonian paths and optimize the design of the corresponding DNA origami structures. Finally, a one-pot annealing algorithmic self-assembly completes the computation by generating all possible paths within the graph. This simple three-step operation reduced the complexity of the computation, streamlines the computational process due to the advantages introduced by communication mechanisms, nodes partition, network topologies of DR-AMCN.

Solving the Hamiltonian path problem

Having established the five distinct paths for Hamiltonian path problem, we asked whether the correct path could be selected from other paths. As the Hamiltonian path traverses all nodes in the graph without repetition, its length (L) must be equal to the total number (N) of nodes in the graph, thus L = N = 7 (Fig. 6a). Experimentally, we noted that the outcome of path traversal yields diverse and hierarchical DNA nanostructures. Disregarding mismatch and aggregation, the Hamiltonian path behaved as highest-order DNA origami heptamers. Conversely, other paths and paths trapped in intermediates exhibited lower-order DNA origami nanostructures ranging from monomer to hexamer. To get desired DNA origami heptamers, we applied rate-zonal centrifugation37,38 which has been used to separation according to their mass and shape to sort the goal structures from the mixture.

Fig. 6: Solving the Hamiltonian path problem.
figure 6

a Schematic illustration of rate-zonal centrifugation selection for separation of heptamer DNA nanostructure from mixed DNA nanostructures. b Experimental protocol of rate-zonal centrifugation. The mixed sample was loaded onto glycerin with a concentration gradient and centrifuged to collect 23 DNA fractions from top to bottom, which were subsequently analyzed by gel electrophoresis. c Gel analysis of products after centrifugation. Band 1–23 were DNA fractions, the band C represented mixed sample before centrifugation. d Large range and zoom-in AFM image of the band 15 from gel analysis. Four typical heptamer structures were marked with orange boxed and extracted to show the Hamiltonian path 0 → 1 → 2 → 3 → 4 → 5 → 6. Scale bars, 200 nm. Source data are provided as a Source Data file.

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Prior to embarking on the separation of the Hamiltonian path, we initially explored the potential of rate-zonal centrifugation in segregating samples comprising DNA origami polymers ranging from monomer to octamer (Supplementary Fig. 34). For the purpose of sorting nanostructures with varying sizes, we employed a linear quasi-continuous glycerol gradient (50%–70%). The DNA nanostructure sample was loaded onto the top of the glycerol and the tube was centrifuged at 320,000 g for 80 minutes, followed by collecting fractions from the top to bottom of the tube carefully (100 μL, per fraction, 23 fractions were collected in this experiment) and analyzed by gel electrophoresis (Supplementary Fig. 35a). The bands 1–23 were DNA origami polymers, while the band C represented the mixture before centrifugation (Supplementary Fig. 35b). The upward shift of the band indicated that DNA origami polymers were separated after centrifugation and distributed in solution as distinct layers. The DNA origami polymers were recycled according to the gel band and AFM characterization. The results revealed a stratified distribution of DNA origami polymers in fractions 7–15, wherein the size of the DNA origami polymers exhibited a gradual increase with increasing depth of fractions (Supplementary Fig. 35c). Notably, the predominant range for heptamer distribution was observed within fractions 14–15. Moreover, fractions deeper than 15 were demonstrated as aggregates (Supplementary Fig. 36).

After establishing the rate-zonal centrifugation protocol, we further employed it for solving the Hamiltonian path (Fig. 6b). The agarose gel electrophoresis obtained a similar result of band upward shift as the product of path traversal was extended (Fig. 6c). The DNA fraction indicated by band 15 was recovered and subjected to AFM characterization (Fig. 6d and Supplementary Fig. 37). A representative AFM image was revealed that three structures exhibited the correct Hamilton path of P 0123456. Therefore, we demonstrated the success of this strategy, confirming the solving of the Hamiltonian path problem. Compared to previous DNA-based approaches for solving the Hamiltonian path problem, our strategy introduced a node partitioning algorithm, which preemptively eliminated erroneous and cyclic paths and reduced computational complexity. We also designed a 10-nodes Hamiltonian graph with 17 edges and derived a traversal tree with 8 sub-paths using the node partitioning algorithm, and completed the path traversal with DR-AMCN (Supplementary Figs. 38–42). This method could be applied to more complex graphs in theory, potentially serving as a general computational method.

Discussion

In conclusion, we have employed a DNA nanostructure recognition strategy to establish an artificial communication network, named DR-AMCN, which was extensible and programmable for user-customized network topology. In DR-AMCN, rectangular DNA origami nanostructures served as nodes in the network, and nodes were labeled and encoded using molecular identifiers, while complementary sticky ends designed at the sides of rectangular DNA origami nanostructures were used to create edges in the network. We have implemented various communication mechanisms, including serial, parallel, orthogonal, and multiplexing, demonstrating the feasibility, programmability, and scalability of different communication mechanisms and systems. These mechanisms could be applied to construct various communication network topologies, including bus, ring, star, tree, and hybrid structures. Finally, we have explored their applications in graph theory which has reduced the computational complexity of the seven-node Hamiltonian path problem through nodes partition and solved the problem by a rate-zonal centrifugation method. We demonstrated the scalability of the method, providing evidence of DR-AMCN’s potential applications in computational science.

Given the flexibility and designability of DNA origami nanostructures and connectors, we envision that DR-AMCN will contribute to a deeper understanding of the mechanisms underlying molecular communication. For example, abstracting the molecular communication process into a graph, where nodes represent the molecules itself, intracellular signal sensors, and signal transduction molecules, and edges represent signal transduction pathways and intercellular interactions, can provide deeper insights into intercellular signal transduction. Furthermore, by incorporating functional materials such as fluorescent molecules39, therapeutic nanoparticles40,41, or drug molecules42,43 onto DNA origami nanostructures, DR-AMCN holds substantial potential for various applications in the fields of bioimaging, disease diagnosis, and drug delivery.

Methods

Materials

All short DNA strands were purchased from Sangon (ULTRAPAGE purification, Shanghai, China). Biotin modified oligonucleotides were obtained from Sangon and purified by high-performance liquid chromatography (HPLC purification). All staple sequences used in this study are listed in Supplementary Data 1. All chemicals were supplied by Sigma (USA). M13mp18 DNA was purchased from BIORULER (Jiangsu, China) which was used as received. All solutions were prepared with Milli-Q water (resistivity = 18.2 MΩ cm).

Synthesis and purification of DNA origami nodes

The DNA origami nodes were prepared by a one-pot process. 2.5 nM of the M13mp18 DNA scaffold strand, was mixed with 25 nM of original staple strands, 25 nM of biotin-staple stands and 25 nM of connector strands in 1 × TAE/Mg2+ buffer (40 mM Tris, 20 mM acetic acid, 2 mM EDTA, and 12.5 mM magnesium acetate, pH 8.0), and then annealed in a thermal cycler from 95–25 °C in 2 h. Finally, the prepared DNA origami nodes were purified four times with 100 kDa (MWCO) centrifuge filters to remove excess DNA strands, and then redispersed in 1 × TAE/Mg2+ buffer.

Annealing for establishing communication between nodes

Design and fabricate individual DNA origami node unit according to the specified communication network. Then, all origami nodes species were mixed according at the molar concentration of which was consistent with the weight of the nodes in the network, and the mixed samples were annealed to assemble multimers. The PCR annealing process was performed over 12 h using a thermocycler (Thermo Fisher. Veriti Fast) with the following process: heating to 45 °C at 1 °C s–1, 45 to 37 °C in 4 h (0.1 °C per 3 min), 37 to 25 °C in 8 h (0.1 °C per 4 min) then cooling and holding at 4 °C.

Streptavidin labeling

The streptavidin powder was commercially purchased and then dissolved in 1× PBS Mg2+ buffer (10 mM sodium dihydrogen phosphate, 2 mM disodium hydrogen phosphate, 137 mM sodium chloride, 2.7 mM potassium chloride, and 12.5 mM magnesium acetate, pH 7.4) for storage. For the labeling process, streptavidin was added to DNA origami purified from excess biotinylated staples at a 5:1 molar ratio relative to each biotinylated site. The reaction was carried out at 37 °C for 2 hours for streptavidin-biotin interaction. The labeled DNA origami was then directly used for AFM characterization without additional purification of excess streptavidin.

UV irradiation

In order to correct the distortion of DNA nanostructured multimers, we utilized a handheld UV analyzer (Model: WFH-204B, Shanghai Chitong Industrial Co., Ltd.) with wattage of 6 W. The samples were exposed to the wavelength of 254 nm and irradiated for 8 minutes before AFM imaging.

AFM characterization

Samples were diluted with 1× TAE/Mg2+ (final concentration: ~1 nM), and then a drop ( ≈ 4 μL) of sample solution was deposited for 2 min on freshly cleaved mica at room temperature. These were then completely dried using an ear washing bulb after washing the substrate three times with ultrapure water, the sample was imaged by a MultiMode 8 AFM with NanoScope V Controller (Bruker, USA) at scananalyst mode in air.

Gel electrophoresis

Samples were electrophoresed on agarose gels (~0.8–1.2%) for 100 min at 70 V bias voltage (about 3.7 V cm–1) in an ice-filled water bath (Bio-Rad). The running buffer was 1× TAE/Mg2+. Staining was conducted with 0.5 μg ml–1 ethidium bromide (Sangon). Gel images were laser scanned using the GelDoc XR+ device and Image Lab v.5.1 program (Bio-Rad).

Preparation of glycerol gradient

Firstly, glycerol gradient with various volume ratios (50%–70%, v/v) were prepared in clean and dry tubes. The components were carefully added into a 5 mL ultracentrifugation tube. The volume of each layer was 667 μL with a 5% glycerol concentration decrement per layer. The tube containing five layers of glycerol gradient was incubated overnight at 4 °C to allow the formation of a quasi-continuous gradient.

Ultracentrifugation and recovery of samples

For ultracentrifugation, 300 μL of sample were carefully loaded on top of the glycerol gradient in 5 mL ultracentrifugation tubes. Then, the tubes were centrifuged using supercentrifuge (Beckman, Optima XPN-100) at 320,000 g for 1.5 h. After centrifugation, the sample fractions (100 μL per fraction) were collected from the top to bottom, each fraction was hold in tube separately. Then remove 20 μL from each tube for gel electrophoresis characterization. After that, the fractions containing desired DNA origami products were combined and recovered in 1×  TAE-Mg2+ buffer using Amicon Ultra 0.5 mL filters.