Programming Dimensional Transitions in DNA Brick Crystals via Interfacial Connectivity

ABSTRACT

The precise control of assembly dimensionality and macroscopic structural parameters remains a fundamental challenge in molecular self‐assembly. Here, we introduce a programmable strategy to govern the 1D‐to‐2D dimensional transition and structural width of DNA brick crystals by engineering their connecting interfaces. Using the number of interface connecting strands (N _x) as a quantitative design parameter, we discover a sharp dimensional threshold that is preserved across both honeycomb and square lattices. At N _x ≤ 8, the assembly is strictly confined to one‐dimensional nanoribbons; whereas at N _x ≥ 12, lateral coupling activates extended two‐dimensional arrays whose structural width increases monotonically with N _x. Thermal and thermodynamic analyses reveal that this sharp threshold behavior is lattice‐independent and originates from the size‐dependent thermal stability of the laterally connected domains. Our work establishes interfacial connectivity as a predictive handle for the on‐demand engineering of self‐assembled nanostructures with programmable dimensionality and prescribed widths.

By tuning interfacial connectivity (N_x ), this study establishes a quantitative thermodynamic framework to control the 1D‐to‐2D dimensional transition in DNA brick crystals. A sharp, lattice‐independent threshold governs this transition, driven by the size‐dependent thermal stability of laterally connected domains. This approach provides a predictive and sequence‐independent design rule for programming the assembly dimensionality and structural width of nanoscale arrays.

1. Introduction

The programmatic arrangement of low‐dimensional nanomaterials into long‐range ordered arrays is fundamental to exploiting unique physical properties that arise from size confinement and directional boundaries [1, 2, 3]. Achieving such architectural precision requires not only nanoscale resolution but also precise control over the spatial dimensions and monodispersity of the assemblies. While conventional top‐down lithography [4, 5] and template‐free bottom‐up synthesis [6] face persistent challenges in balancing scaling limits with orientation uniformity and architectural complexity, biomolecular self‐assembly offers a highly predictable route to program complex, discrete architectures. However, translating this molecular‐level programmability into the quantitative control of macroscopic crystal dimensions, specifically, guiding and bounding growth from individual tracks into continuous periodic arrays, remains a poorly understood frontier.

The programmability of DNA interactions has enabled the construction of a wide variety of periodic 2D lattices and crystals since the early demonstrations of designed DNA tile arrays [7, 8, 9]. Sub‑10 nm features have been routinely achieved in these systems, as exemplified by the two‐dimensional periodic array [10] and more recent DNA brick crystals [11, 12, 13]. The programmability of DNA bricks has enabled not only the construction of periodic crystals with prescribed depths and three‑dimensional features but also their functionalization into device‑relevant platforms [14, 15]. For example, DNA brick crystals have served as templates for the precise arrangement of gold nanoparticles into close‑packed arrays with sub‑2 nm spacing, essential for strong plasmonic coupling [16]. They have also been used to align carbon nanotubes into highly ordered, evenly spaced arrays with pitch as small as 10.4 nm [17]. Moreover, extended DNA tile arrays have been directly assembled on silicon wafers and used as etching masks to produce ∼8.6 nm features, offering a scalable and low‑cost alternative to serial electron‑beam lithography [18].

Despite this remarkable capability for precise construction, most existing designs have focused on whether a target structure can be formed rather than systematically exploring the dimensional transition that governs the growth from one‑dimensional (1D) to two‑dimensional (2D) growth. Such dimensional transitions have been extensively considered in colloidal and molecular systems with directional interactions, where the effective valence between building blocks has been identified as a key parameter governing the transition from discrete aggregates to extended networks [19, 20]. Related concepts have also begun to emerge in DNA self‐assembly. For example, Minev et al. showed in DNA slat assemblies that joint‐neighbor capture and higher coordination numbers can sustain kinetic barriers to spontaneous nucleation while enabling rapid seeded growth into micrometer‐scale ribbons [21]. However, these studies were primarily concerned with nucleation control and seeded polymerization, rather than with the quantitative control of assembly dimensionality in periodic DNA brick crystals. In DNA brick systems, despite their programmability, a similar quantitative descriptor for dimensional control has remained elusive.

Here we introduce a programmable design strategy that uses the number of interface connecting strands (N _x) as a control parameter to regulate assembly dimensionality in DNA brick crystals. By systematically varying N _x in two distinct lattice geometries (honeycomb, HC, and square, SQ), we uncover a sharp threshold that switches the system from 1D nanoribbons to extended 2D arrays. Moreover, beyond this threshold, the structural width of the 2D arrays can be tuned in a predictable manner.

2. Results and Discussion

2.1. Design and Parameterization of Interfacial Connectivity

To quantitatively investigate the effect of interfacial connectivity on assembly dimensionality, we first designed L‐shaped repeating units in a HC lattice. It is important to note that the L‑shaped unit is a conceptual design used to program the sequence specificity of DNA bricks. The actual assembly occurs via non‑hierarchical addition of individual bricks (design details and corresponding sequences are presented in Figures S1–S19 and Tables S1–S4). As shown in Figure 1a, each brick is a 48‐nt single‐stranded DNA containing four 12‐nt binding domains. Adjacent bricks hybridize through 12 base pairs, forming an angle of approximately 120° (Figure 1b). By precisely programming the interface sequences, two binding domains of each brick are locked into the interior of the unit, while the other two face adjacent units, thereby mediating growth along the X‐ and Z‐directions.

FIGURE 1.

Programming the structural width of DNA brick crystals via the number of connecting strands. (a) Schematic of the 48‐nt single‐stranded DNA brick motif. (b) Model of two DNA bricks interacting via 12 base pairs to form an angle of approximately 120°. The left shows a strand model, and the right shows a geometric line model. (c) Structural diagram of the HC‐74B unit. The left side shows a cylinder model with an oblique view, indicating the connecting interfaces in both the X‑ and Z‑directions. The right part displays an enlarged view of the X‑direction connecting interface, while the lower part shows an enlarged view of the Z‑direction connecting interface. For clarity, strands mediating extension in both directions are shown in orange (“connecting strands”), and strands for internal assembly are shown in gray. In this design, the number of interface connecting strands is N _x = 8. (d) Top‑view cylinder model of the unit (top) and its simplified geometric representation (bottom), illustrating the assembly from individual units into an array. (e) Schematic illustrating the threshold behavior of the number of connecting strands N _x. A threshold value N _T is observed. When N _x is equal to or below this threshold, the assembly forms one‐dimensional nanoribbons. When N _x exceeds this value, two‐dimensional arrays are formed, and the structural width W _x increases with increasing N _x.

Figure 1c shows the design details of a representative structure, HC‐74B. The cylinder model indicates that the L‐shaped repeating unit consists of a Z‐direction module (3H × 8H × 294B) and an X‐direction module (5H × 8H × 74B), with module lengths defined as L _z and L _x, respectively. The unit is named “HC‐74B” based on the lattice type and the number of base pairs in L _x. The overall size of the assembly in the X‐direction is defined as the structural width W _x (Figure 1d). Here we introduce the number of interface connecting strands (N _x) as the core variable describing interfacial connectivity. In our design, the right side of each unit carries connecting strands (shown in orange in Figure 1c), while the left side contains no connecting strands but presents sequences that are complementary to the connecting strands on the right. This complementarity allows identical units to extend along the X‑direction by hybridization between the right‑side connecting strands of one unit and the left‑side sequences of the next. The Z‑direction interface is designed similarly. This study focuses on the X‑direction connectivity, and N _x is defined as the number of single‐stranded DNA directly involved in X‐direction interactions between adjacent units (in this example, N _x = 8). In our experimental design, N _x is tuned by varying the length of the lateral module L _x.

By design, the interfacial connectivity N _x governs the physical strength of lateral coupling between units. We propose that a critical threshold N _T exists in DNA brick crystal growth. When N _x is below this threshold, lateral connections are insufficient to stabilize higher‐dimensional structures, and the assembly remains one‐dimensional. When Nx exceeds this threshold, lateral coupling becomes effective, enabling the formation of extended two‐dimensional arrays. In this regime, the structural width W _x increases with increasing N _x (Figure 1e).

2.2. Dimensional Switching in Honeycomb Lattices

To test the hypothesized threshold behavior, we designed and synthesized six HC series units with different numbers of interface connecting strands N _x, which are HC‐74B (N _x = 8), HC‐98B (N _x = 12), HC‐123B (N _x = 14), HC‐147B (N _x = 16), HC‐221B (N _x = 24), and HC‐294B (N _x = 32). Note that the step size of N _x is not unity because the length of the X‑direction module L _x is tuned by discrete brick layers. Intermediate values (e.g., 9, 10, 11) would not allow a uniform distribution of the connecting strands at the interface. For N _x < 8, the X‑direction module is expected to be non‑functional because the three‑directional connectivity cannot be properly established (Figure S1). The morphologies of the assembled products were systematically characterized by transmission electron microscopy (TEM) (Figure 2a–f).

FIGURE 2.

Design, synthesis, and statistical analysis of HC lattice DNA brick crystals with different N _x. (a–f) Assembly characterization of six HC series units with increasing N _x. For each design, the images include from top to bottom a cylinder model of the basic unit, representative TEM images, and a pseudo‐colored magnified TEM image. (a) HC‐74B (N _x = 8), (b) HC‐98B (N _x = 12), (c) HC‐123B (N _x = 14), (d) HC‐147B (N _x = 16), (e) HC‐221B (N _x = 24), (f) HC‐294B (N _x = 32). The TEM images reveal that when N _x exceeds the threshold N _T, the structural width of the assemblies increases significantly with N _x. Scale bars: 200 nm (TEM images) and 100 nm (pseudo‐colored images). (g) Statistics of W _x (left axis) and the ratio Median(W _x)/N _x (right axis) for the HC series units. Sample sizes (n) are 211, 184, 147, 128, 145, and 115, respectively. Box plots show the median (center line), interquartile range (box), and 1.5 × interquartile range (whiskers); individual measurements are shown as data points. The dashed line marks the critical threshold N _T. The ratio remains low when N _x ≤ 8 and increases sharply when N _x ≥ 12, indicating the dimensional transition. (h–j) Large‐field TEM images of (h) HC‐74B (N _x = 8), (i) HC‐147B (N _x = 16), and (j) HC‐294B (N _x = 32). Scale bars: 1 µm.

When N _x = 8 (HC‐74B), TEM images showed nanoribbons with lengths up to several micrometers and structural widths approximately equal to the width of a single nanoribbon; no obvious lateral expansion was observed (Figure 2a). This observation indicated that the interfacial coupling at this connectivity is not sufficient to support lateral growth. When N _x increased to 12 (HC‐98B), long‐range ordered 2D nanoribbon arrays began to appear, with structural widths significantly larger than those of the N _x = 8 design (Figure 2b). As N _x further increased to 14, 16, 24, and 32, the assemblies became more continuous and laterally extended as N _x increases (Figure 2c–f). Although the units were designed with base pair insertions and deletions to correct for twisting, some degree of curling is still observed in all assembled structures; however, this does not compromise the long‐range lattice order within the 2D arrays. To quantitatively describe the evolution of structural width with N _x, we measured the structural width W _x at the widest X‐direction position of the assemblies, ensuring a Z‐direction length of at least two repeating units (Figure S20). The statistical analysis revealed a clear transition in assembly dimensionality (Figure 2g). When N _x ≤ 8, W _x is close to the width of a single nanoribbon (∼9 nm); when N _x ≥ 12, W _x starts to increase significantly, showing a monotonic increase from ∼0.1 µm to ∼0.3 µm as N _x increases from 12 to 32. The dashed line in Figure 2g marks the critical threshold N _T. The right axis of Figure 2g shows the ratio Median(W _x)/N _x, which remains low when N _x ≤ 8 and increases sharply when N _x ≥ 12. The large‑field TEM images (Figure 2h–j) provided an overview of the assembled structures for HC‑74B (N _x = 8), HC‑147B (N _x = 16), and HC‑294B (N _x = 32), confirming that the structural width increase is representative of the entire ensemble, complementing the higher‑magnification views in Figure 2b–f (more representative images are shown in Figures S21–S26).

We note that the standard deviation of the assembly width, W _x, increases with N _x (Figure 2g), and the assembly rate analysis is shown in Figure S27. This trend likely originates from the reduced nucleation barrier at higher interfacial connectivity. When N _x exceeds the threshold, two‑dimensional nucleation becomes facile, which can lead to secondary nucleation events on existing arrays or in solution. Subsequent fusion of these secondary nuclei with the main array results in a broader width distribution. Additionally, the enhanced lateral affinity at high N _x promotes the coalescence of smaller 2D fragments, contributing further to the dispersion. While this effect does not compromise the conclusion that width increases with N _x, it may represent a limitation for applications requiring highly monodisperse arrays. We anticipate that the distribution can be tightened by optimizing the annealing protocol, for example by narrowing the annealing window or using isothermal assembly at a temperature just above transition temperature. Seed‑induced growth or further reducing the cooling rate may also suppress secondary nucleation and improve uniformity. Such strategies will be explored in future work.

All crystals showed a slight left‐handed twist, which also probably arose from the 10.29 bp/turn underwound design. As a result, we observed that the crystals sometimes appeared twisted and folded on top of themselves in TEM images (Figure 2b–f).

2.3. Validation in Square Lattices

To test whether the observed threshold behavior depends on the specific lattice geometry, we extended the same design principle to a SQ lattice system (Figure S3). As shown in Figure 3a, the SQ‐52B unit is built from 52‐nt DNA bricks, and its X‐direction interface also features a programmable number of interface connecting strands (N _x = 8 in this example).

FIGURE 3.

Design, synthesis, and size statistics of SQ lattice DNA brick crystals. (a) Structural diagram of the SQ‐52B unit. Left is an oblique view of the cylinder model. Center is an enlarged view of the connecting interface in the Z‑direction while right is an enlarged view of the connecting interface in the X‑direction. Strands mediating extension in both directions are shown in orange (“connecting strands”), and strands for internal assembly are shown in gray. The number of interface connecting strands N _x = 8. (b) Top‐view cylinder model (top), representative TEM image (bottom left), and pseudo‐colored magnified TEM image (bottom right) of SQ‐52B. (c–h) Assembly characterization of six SQ series units. For each design, the images include from top to bottom a cylinder model of the basic unit, representative TEM images, and a pseudo‐colored magnified TEM image. (c) SQ‐78B (N _x = 12), (d) SQ‐104B (N _x = 16), (e) SQ‐130B (N _x = 20), (f) SQ‐156B (N _x = 24), (g) SQ‐234B (N _x = 36), (h) SQ‐312B (N _x = 48). The observed morphologies follow the same trend as in the HC lattice, with a transition from one‐dimensional structures to extended two‐dimensional arrays as N _x increases. The scale bars are 200 nm for TEM images and 100 nm for pseudo‐colored images. (i) Statistics of W _x (left axis) and the ratio Median(W _x)/N _x (right axis) for the SQ series units. Sample sizes (n) are 120, 242, 95, 204, 81, 149, and 119, respectively. Box plots show the median (center line), interquartile range (box), and 1.5× interquartile range (whiskers); individual measurements are shown as data points. The dashed line marks the critical threshold N _T. The ratio remains low when N _x ≤ 8 and increases sharply when N _x ≥ 12, confirming the dimensional transition observed in the HC lattice.

In addition to SQ‐52B, we designed and synthesized six SQ series units, which are SQ‐78B (N _x = 12), SQ‐104B (N _x = 16), SQ‐130B (N _x = 20), SQ‐156B (N _x = 24), SQ‐234B (N _x = 36), and SQ‐312B (N _x = 48). TEM characterization (Figure 3b–h; more representative images are shown in Figures S28–S34) revealed that the SQ lattices exhibit dimensional transition behavior consistent with that of the HC lattices. When N _x = 8 (SQ‐52B), the assemblies remained locked in a 1D nanoribbon morphology and failed to form continuous lateral networks (Figure 3b). When N _x was increased to 12 or higher, extended two‐dimensional arrays were observed, accompanied by a progressive increase in structural width.

2.4. Thermal Stability Correlates With Lateral Size

To probe the origin of the dimensional threshold, we measured thermal assembly and melting behavior using fluorescence measurements. For the HC series, all six structures exhibited similar annealing transition temperatures (T _trans) centered around 53.5°C (Figure 4a). The SQ series showed a similar grouping around 56.5°C (Figure 4b). All designs within each lattice family assembled within a similar temperature window. In contrast, the melting temperature T _m increased systematically with lateral design size (Figure 4c,d). For the HC series, T _m rose from 59.4°C at N _x = 8 to 63.2°C at N _x = 32; for the SQ series, from 60.2°C at N _x = 8 to 64.9°C at N _x = 48. Therefore, although all structures assemble within similar temperature windows, their final thermal stabilities differ markedly; larger lateral designs yield more stable crystals. This result indicates that lateral growth capability is limited by the stability of the laterally connected addressable bulk phase.

FIGURE 4.

Thermodynamic analysis. (a) Annealing curves of the six HC series structures. The transition temperature (T _trans, orange line) is approximately 53.5°C for the HC series, indicating that the overall onset of assembly occurs within a similar temperature window across different designs. Fluorescence signals were normalized to the values at 60°C and 50°C. (b) Annealing curves of the seven SQ series structures. The transition temperature (T _trans, orange line) is approximately 56.5°C for the SQ series, again indicating similar global assembly windows for different designs. Fluorescence signals were normalized to the values at 60°C and 50°C. (c, d) Quantitative correlation between the size of the addressable bulk phase and the melting temperature (T _m) of the corresponding crystal. In both lattice systems, larger addressable bulk phases exhibit higher T _m, indicating enhanced thermal stability. These results indicate that lateral growth is governed by the size‐dependent thermal stability of the laterally connected domains. (e) Schematic illustration of the proposed growth model.

3. Conclusion

Lateral growth requires the formation of a sufficiently large and stable interfacial domain. When N _x is small (≤ 8), lateral association generates only a small interfacial domain. When the domain is small, it is thermally unstable and dissociates before further growth can occur. Due to the discrete layering constraint of our design, intermediate values (N _x = 9, 10, 11) are not feasible; thus, the threshold is strictly defined as lying between 8 and 12. When N _x exceeds the threshold (≥ 12), the laterally connected domain becomes larger and more stable, allowing it to persist and serve as a platform for further lateral propagation. This interpretation is strongly supported by thermal characterization. Within each lattice family, all designs show similar annealing transition temperatures (≈53.5°C for HC, ≈56.5°C for SQ), indicating comparable assembly windows. In contrast, the melting temperature T_m increases monotonically with N _x (e.g., from 59.4°C to 63.2°C in HC, and from 60.2°C to 64.9°C in SQ). Thus, although the systems enter the assembly process at similar temperatures, the final crystals differ markedly in thermal stability, and larger lateral designs yield more stable assemblies.

The dimensional transition can also be understood in terms of nucleation‑limited anisotropic growth. In the initial stage of assembly, free single‑stranded bricks collide and form metastable clusters before nucleation. When N _x is below the threshold of 8, longitudinal (Z‑direction) growth proceeds readily, rapidly forming 1D nanoribbons. Lateral growth requires the formation of a stable 2D nucleus on the side surface of these ribbons [22, 23, 24, 25]. In the present system, the relevant cooperativity is not a strong increase in the intrinsic binding probability of each individual oligonucleotide, since DNA brick assembly proceeds through stepwise incorporation of single strands, but rather the collective stabilization of laterally associated intermediates. When N _x is small, the laterally connected block generated at the interface remains limited in size, so that the corresponding addressable bulk phase is too small to effectively retain bound strands. As a result, strand dissociation remains frequent, leading to a high effective barrier for sustained lateral nucleation and growth. As N _x increases, the laterally connected block becomes larger and the associated addressable bulk phase becomes more stable, reducing strand dissociation and thereby lowering the effective barrier for continued lateral incorporation. Under these conditions, lateral growth can initiate earlier and proceed in parallel with longitudinal extension. The competition between rapid longitudinal growth and delayed lateral nucleation therefore provides a physical basis for the observed dimensional transition.

As proposed in Figure 4e, after nucleation, longitudinal growth along the Z‑direction readily generates one‑dimensional primary nanoribbons. Lateral growth in the X‑direction requires the formation and retention of a laterally connected addressable bulk phase between neighboring ribbons. When the size of this addressable bulk phase is too small, the resulting laterally connected intermediate is thermally unstable and tends to dissociate before it can be further reinforced, thereby confining the assembly to a 1D morphology. As the lateral module increases (i.e., N _x increases), the size of the addressable bulk phase formed upon lateral association becomes larger, which enhances its thermal stability and allows the laterally connected intermediate to survive and propagate, ultimately leading to 2D nanoribbon arrays.

The observation of the same threshold behavior in both HC and SQ lattices demonstrates that the dimensional transition is lattice‑independent and arises from the size‑dependent thermal stability of laterally connected domains. Thermodynamic analysis combining perfect‑design and mismatch experiments (see Supporting Information, Tables S5–S7 and Figure S35) shows that the dimensional switching can be meaningfully described by the interfacial free energy. For the HC‐98B system, the critical total free energy for the 1D to 2D transition lies approximately between −298 and −263 kcal/mol. It should be emphasized that different values of N _x or binding lengths may shift the critical range. A higher number of connecting strands overcomes the lower total free energy by enhancing multivalent cooperativity. These insights provide a thermodynamic foundation for the geometric design rule based on N _x. Therefore, N _x should be regarded not merely as a connectivity count but as a practical design handle for programming the stability of the addressable bulk phase. To obtain stable 2D nanoribbon arrays, the lateral interface must be designed to exceed the stability threshold (here, N _x ≥ 12). Conversely, narrow 1D nanoribbons can be reliably obtained by keeping N _x ≤ 8. This quantitative framework provides a predictive route for on‑demand fabrication of sub‑10 nm nanostructures with programmable dimensionality and width.

The finding of a sharp threshold for dimensional switching in DNA brick crystals not only provides a quantitative design rule for controlling assembly dimensionality but also opens several avenues for future exploration. The resulting long‐range ordered nanoribbon arrays can serve as highly programmable templates for the precise anisotropic arrangement of metal nanoparticles [26, 27], semiconductor quantum dots [28], or single‐molecule devices [14, 29] at sub‐10 nm spacings through specific binding sites. In addition, these 2D nanoribbon arrays can be used as templates to fabricate sub‐10 nm metal ribbon arrays with tunable widths via metallization [30, 31] or etching [13, 18, 32], expanding their potential applications in plasmonics [33, 34] and quantum devices [35, 36]. Furthermore, if the N _x value is designed as a dynamically responsive module (e.g., via strand displacement [37] or photoregulation [38, 39]), reversible switching between 1D and 2D morphologies could be achieved, offering new avenues for smart responsive materials and reconfigurable nanodevices.

Author Contributions

Xin Huang: writing – original draft, writing – review and editing, investigation, validation, visualization, conceptualization, methodology, formal analysis, data curation, software. Yue Wang: conceptualization, methodology, writing – original draft, formal analysis. Wenhe Ma: conceptualization, methodology, formal analysis. Yunxiao Lin: conceptualization, methodology, visualization. Bochen Li: conceptualization, methodology. Jiang Li: supervision, funding acquisition, project administration, resources. Lihua Wang: funding acquisition, project administration, resources, supervision. Chunhai Fan: supervision, funding acquisition, project administration, resources, writing – review and editing. Sisi Jia: funding acquisition, project administration, resources, supervision, writing – review and editing. Xiaoguo Liu: writing – review and editing, supervision, resources, project administration, funding acquisition, visualization, methodology, conceptualization.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

The authors have cited additional references within the Supporting Information [40–44]. Supporting File: anie73273‐sup‐0001‐SuppMat.pdf

Data Availability Statement

The data that supports the findings of this study are available in the Supporting Information of this article.