Introduction

Rapid advances in structural DNA nanotechnology for precise programming of shape and properties of structural DNA assemblies1,2,3 have presented broad applications with harnessing DNA-binding ligands in delivery systems4,5,6,7, property control8,9,10, and structural morphing11,12,13,14,15. To enhance mechanical or electronic properties, it has also been reported to bind inorganic materials to structured DNA assemblies, such as metalization16,17 and silicification18. Specifically, various ligands, including groove binders and intercalators, have been employed to generate chemo-mechanical responses of structured DNA assemblies, such as shape change in bending15 and twisting11,12, control of rigidity15 and chirality14,19, stability enhancement20, and supercoiling13. These structural functions originate from the modification of local geometry and mechanical properties of DNA by chemical interactions with base-pairs when a ligand noncovalently binds to DNA. Therefore, local effects of ligands on transforming DNA structures have been characterized by simulations21,22,23,24 and experiments25,26,27,28,29 at the strand level. For example, a common intercalator, ethidium bromide (EtBr), can both reduce the helical twist of DNA and elongate it23,25,27,30.

However, on the scale of structured DNA assemblies, developing a computational approach to systematically investigate effects of binding ligands remains a challenge, although several studies have been reported to qualitatively analyze structural morphing by introducing system-specific parameters of ligands11,15. Difficulty in developing a model is rooted in characterization and coarse-graining of structural properties of ligand-binding DNA as well as regular ones in DNA assemblies since computational cost inherent in all-atomic calculations severely limits simulation times and scales. In addition, validation of computational predictions is limited by the lack of models that match experimental concentrations to the number of ligands binding to DNA.

In this study, we present a computational framework that simulates the chemo-mechanical response of structural DNA assemblies (Fig. 1). We characterized geometry and mechanical properties of DNA base-pairs when EtBr molecules bound to them through molecular dynamics (MD) simulations and then integrated the features into the finite-element-based model, SNUPI31,32. In addition, a quantitative comparison with experiments was performed with a model of the binding density of EtBr to DNA structures. The proposed model successfully predicted EtBr-driven shape changes, flexibility modulation, and supercoiling instability of various DNA origami structures, in agreement with experiments.

Fig. 1: Computational framework to analyzing the chemo-mechanical response of structured DNA assemblies.
figure 1

Schematic representation of a computational framework to analyzing the chemo-mechanical response of structural DNA assemblies. The geometry and mechanical properties of EtBr-binding base-pair steps were characterized through molecular dynamics simulations and integrated into the structural model, SNUPI31,32. An EtBr-binding model was developed to connect the number of EtBr bound to DNA assemblies with its concentration in experiments. The proposed framework predicted the effect of EtBr-binding on the increase in persistence length, the variation of structural bending, twisting, and chirality, and the supercoiling of ring structures.

Full size image

Results

Chemo-mechanical analysis framework

To investigate the local mechanical effects of EtBr on DNA structures, we characterized the geometry and mechanical properties of a base-pair step when a single EtBr molecule was intercalated between two successive base-pairs. We assumed negligible binding effect of EtBr on single-stranded DNA33 because EtBr could hardly affect the configuration due to high flexibility and freely rotating nucleotides in single-stranded DNA. We employed dynamic trajectories of the previous MD simulations of 6HB (6-helix-bundle) structure15 (Fig. 2a and Supplementary Fig. 1). We then analyzed 43 base-pair steps of which each showed a stable RMSD (root-mean-square deviation) curve below 5 Å (Supplementary Fig. 2). Configurations of base-pair steps in the MD trajectories were converted into two triads, which were characterized using three translational (Dx: shift, Dy: slide, and Dz: rise) and three rotational (Rx: tilt, Ry: roll, and Rz: twist) parameters defined in 3DNA34 (Fig. 2b). Therefore, the trajectories of EtBr-binding base-pair steps were reduced to a set of the local six variables. Assuming quasi-harmonic energy in each of the six motions between two base-pairs, equilibrated geometry, mechanical rigidities, and coupling coefficients were obtained and compared with the reported values for regular base-pair steps35 (Fig. 2c). We did not consider sequence-dependent properties of EtBr-binding base-pairs.

Fig. 2: Characterization and modeling of EtBr-binding base-pair properties.
figure 2

a Molecular dynamics (MD) simulation of the EtBr-intercalated 6HB structure. The MD simulations of the 6HB structure were performed until 400 ns using the atomic structure in the previous simulation15. b Geometric parameters of intercalated base-pair steps. Three translational (Dx: shift, Dy: slide, and Dz: rise) and three rotational parameters (Rx: tilt, Ry: roll, and Rz: twist) were calculated using the 3DNA definition34. c Local geometry and mechanical properties. The box plots of geometry, mechanical rigidities, and coupling coefficients of the regular35 and EtBr-binding base-pair steps were illustrated (Sample size for each plot: 143). Each box plot summarized measured data using five points (minimum, maximum, median, and the first and third quartiles).

Full size image

Results first revealed a noticeable increase in axial length (Dz) from 0.34 ± 0.01 nm to 0.82 ± 0.04 nm (mean ± std) when EtBr was bound (Supplementary Table 1). This could be attributed to the steric effect of EtBr, which physically increases the distance between base-pairs, consistent with previous reports on the increase in contour length of DNA helix23,36,37. Local bending angle toward backbone (Rx) was maintained on average since two backbone chains could limit rotation. It was also observed that local bending angle toward groove (Ry) increased because EtBr was intercalated in major groove38, and straight extension was hindered by geometric constraints imposed by crossovers in DNA structures (Supplementary Fig. 3). Axial twist (Rz) showed a decrease from 34.5° ± 2.7° to 28.8° ± 4.5° (mean ± std), in line with the reported literature24,30, which is the primary cause of left-handed torsion observed in various EtBr-binding DNA structures11,12,13,14. On the other hand, overall mechanical rigidities of the EtBr-binding base-pair step were decreased compared to the regular one, parallel to the decrease in the persistence length of DNA23,30. Rotational rigidities were less reduced than translational ones because backbones could constrain the fluctuation. This indicates that EtBr globally reduced stiffness, even with increasing axial length, as observed by the increase of deviation in the geometric parameters. It is therefore inferred that EtBr intercalation could lower configurational stability that was maintained by base-stacking. In addition, a representative coefficient of translational and rotational coupling (Rz-Dz) exhibited a considerable decrease from −277 ± 60 pNnm to −20 ± 63 pNnm (mean ± std), indicating that EtBr could weaken the negative twist-stretch coupling. This may be because EtBr-binding lowered helical diameter beyond mechanically interacting region between backbone and connected base-pairs, lowering twist-diameter coupling relevant to the twist-stretch coupling39,40.

Next, we predicted conformations and features of EtBr-binding DNA structures using SNUPI31,32, a multiscale modeling approach that enables the integration of molecular-level properties into a finite element model without any modifications. Local configurations of EtBr-binding base-pair steps were assumed to be similar. Once the number of EtBr binding to a DNA structure was determined, the same number of regular base-pair steps in random positions was converted into EtBr-binding base-pair steps, whose local stiffness matrices describing the characterized EtBr properties were assembled into a global stiffness matrix. The chemo-mechanical change of EtBr-binding DNA structures was predicted by minimizing total mechanical and electrostatic energies through nonlinear static procedures or dynamic simulations.

Flexibility modulation and binding model

To examine the chemo-mechanical response of EtBr to DNA structure, we first employed the straight 6HB structure previously designed on a honeycomb lattice15 (Fig. 3a). We systematically predicted EtBr-binding 6HB structures where the EtBr number varied from 0 to 700 at 50 intervals in random binding positions. For each case, static analysis was performed 20 times to obtain the deviation of shape and properties. The predicted structures were aligned to their one end, and high fluctuations were observed in shape due to increased flexibility as the number of EtBr binding to the structure increased (Fig. 3b).

Fig. 3: Persistence length and binding model.
figure 3

a Straight 6HB structure. The EtBr-binding 6HB structures15 were predicted for different binding numbers ranging from 0 to 700 at intervals of 50 in random binding positions. b Conformations of predicted structures. High fluctuations were observed in shape due to increased flexibility as the intercalated number of EtBr increased. c Persistence length. The persistence length of the 6HB structures was calculated through normal mode analysis. The results were compared with the previous experiments15 in box plots (Sample size for each plot: 20). Each box plot summarized measured data using five points (minimum, maximum, median, and the first and third quartiles). d Binding model. A simple binding model was developed to connect the number of EtBr binding to the structure with the EtBr concentration by fitting the predicted persistence length to the experimental measurements.

Full size image

To quantitatively assess the change in persistence length of the 6HB structures, we performed normal mode analysis to obtain eigenmodes. Considering the slender 6HB structure as the Euler-Bernoulli beam, persistence length was calculated using eigenvalues corresponding to bending eigenmodes, observed in the lowest mode for all cases. Results demonstrated a gradual decrease of up to 68% in the persistence length of the 6HB structures with increasing EtBr number (Fig. 3c and Supplementary Table 2). In addition, we theoretically investigated that the EtBr-binding could reduce the persistence length of the 6HB structures using the characterized bending rigidity of EtBr-binding base-pair steps (Supplementary Note 1).

Moreover, we connected the number of EtBr binding to structure with the EtBr concentration to compare computational prediction with experimental measurements. Assuming independent binding, no cooperative effect, and equilibrium of EtBr-binding, the EtBr fraction was simply modeled as \({C}_{{EtBr}}/\left({K}_{d}+{C}_{{EtBr}}\right)\varXi\), where \(C_{EtBr}\) is the observed EtBr concentration in the solution, \({K}_{d}\) is the dissociation constant, and \(\varXi\) is the saturated binding density as the number of base-pairs per one EtBr molecule, respectively. The two constants were determined to be Kd = 3.2 ± 0.6 μM and \(\varXi=7.3\pm 0.2\) base-pair/EtBr, in agreement with reported values11,20,29,41,42 (Supplementary Table 3) through a nonlinear fitting procedure using the predicted persistence length and previous experimental measurements15 (Fig. 3c). This binding model described the relation between EtBr fraction and concentration (Fig. 3d). Therefore, the number of EtBr binding to a structure (\({N}_{{EtBr}}\)) was calculated by multiplying the EtBr fraction with the total number of base-pairs (BPs) consisting of the structure (\({N}_{{BP}}\)) as \({N}_{{EtBr}}={N}_{{BP}}\left[{C}_{{EtBr}}/\left({K}_{d}+{C}_{{EtBr}}\right)\varXi \right]\) (Supplementary Table 4).

Shape variation

We validated the proposed model by predicting the shape of various EtBr-binding DNA structures. Typically, the unwinding of local helices by EtBr has been employed to induce global left-handed twist of DNA structures11,12,14. We first investigated the twist of straight 12HB structures consisting of two parallel 6HB structures12 (Fig. 4a). The twisted shapes were predicted for different EtBr numbers ranging from 0 to 1600 at intervals of 200. Their twist angles were then calculated as the sum of local twist angles between successive 84-base-pair-long crossover planes (Supplementary Table 5). We compared the predicted and measured12 twist angles of the 12HB structures for the EtBr concentrations that were converted from the simulated EtBr numbers using the proposed binding model. The results confirmed a negative correlation between the global twist angle and the EtBr number (Fig. 4b). It is noted that our model used a helicity value of 10.43 ( = 360°/34.51°) for regular helices, which is slightly smaller than the intended helicity of 10.5 for the DNA structures designed on the honeycomb lattice. This could induce a right-handed intrinsic twist of about 0.5 turns. Still, both our model and experiments showed an analogous decrease in twist angle of approximately −0.14 and −0.17 turns per 100 EtBr molecules, respectively.

Fig. 4: Shape variation.
figure 4

a Straight 12HB structure. The twist of the 12HB structures12 was revealed by the crossing sites of two parallel 6HB structures. b Twist angle. The twist angle of 12HB structures was predicted for different EtBr numbers ranging from 0 to 1600 at intervals of 200 and compared with the previous experiments12 in box plots (Sample size for each plot: 10). Each box plot summarized measured data using five points (minimum, maximum, median, and the first and third quartiles). The fitted linear lines showed gradients of −0.14 and −0.17 per 100 EtBr for simulations and experiments, respectively. c, d Conformational change. The overall twist of the 12HB structure was changed by 282 EtBr corresponding to 4 μM. The predicted shapes were converted to S-type ratios and compared with previous experiments14. e, f Chirality and diameter change. The chirality and diameter of the 24HB structure were changed as the EtBr number increased. The decrease in diameter by increasing the EtBr number from 0 to 800 at intervals of 200 was compared with the previous report19 (Sample size for each plot: 10). Each box plot in the diameter results summarized measured data using five points (minimum, maximum, median, and the first and third quartiles).

Full size image

Next, we investigated the shape change induced by EtBr-binding for initially twisted 12HB DNA structures in the right- and left-handed directions (Fig. 4c). Two conformational types (S-type or C-type) of these structures were observed in the previous experiments14 (Supplementary Fig. 4), and their ratio was used to indirectly deduce the EtBr-driven change in global shape. To compare results, we first predicted the structures with and without EtBr and then theoretically converted their shape into an S-type ratio (Supplementary Note 2), which is a function of the structural twist angle, contour length, and torsional persistence length. For the structure with a right-handed twist when no EtBr is bound, we observed a twist angle of approximately 106°, which corresponded to the S-type ratio of 0.59 (C-type ratio of 0.41). These values were in line with an experimental S-type ratio of 0.61 (C-type ratio of 0.39)14 (Fig. 4d and Supplementary Table 6). As the EtBr concentration increased to 4 μM, our binding model suggested that 282 EtBr molecules would bind to the structure. This binding induced a more left-handed twist, resulting in structural morphing toward a C-type conformation. Consequently, the S-type ratio decreased to 0.19 (C-type ratio of 0.81), which agreed with the experimental values of 0.11 (C-type ratio of 0.89)14. On the other hand, the structure with an initially left-handed twist exhibited a conformation with a twist angle of 70°, corresponding to an S-type ratio of 0.39 (C-type ratio of 0.61). However, when EtBr was bound, the generated left-handed twist increased the S-type ratio to 0.80 (C-type ratio of 0.20) at the EtBr concentration of 4 μM. The change in the S-type ratio from 0.30 to 0.84 observed in the experiment14 was consistent with our prediction, supporting the accuracy of the proposed model.

EtBr can also be exploited to control the chirality of DNA structures as well (Fig. 4e). We considered the 24HB structure, which showed right-handed chirality without EtBr-binding from the previous report14,19 (Supplementary Fig. 5). By increasing the EtBr number from 0 to 800 at 200 intervals, we observed a gradual decrease in the right-handed chirality, which aligned with the experiment19. It is noteworthy that, as more EtBr was bound, the structural curvature increased, leading to a decrease in diameter, as observed in the experiment19 (Fig. 4f). This suggests a coupled phenomenon of structural twisting and bending by EtBr. Therefore, to investigate the mechanical effect of EtBr on a DNA structure (Supplementary Note 3), we analytically derived a relation of the structural geometry (θ: bending, ω: out-of-plane bending, and ϕ: twisting) with the characterized properties of EtBr-binding base-pair steps. The result revealed that the number of EtBr binding to a DNA structure is positively correlated with its bending (θ > 0), chirality (ω < 0), and left-handed twisting (ϕ < 0). Our comprehensive analysis can explain all observed shape changes of DNA structures induced by EtBr, providing a potential for further applications to other ligands.

Furthermore, we investigated how EtBr-binding affects the structural morphology of wireframe structures designed as planar and 3D polygons43,44,45,46 (Supplementary Figs. 6–9). For the same number of EtBr binding, wireframes with DX (2HB) edges showed higher distortion than structures with 6HB edges due to the lower mechanical rigidity of 2HB than 6HB. We also observed out-of-plane distortion for planar structures and degradation of shape integrity for 3D wireframes. These results supported the applicability of the proposed approach to explore the chemo-mechanical responses of various DNA structures. In addition, a sensitivity analysis of the twist for different sizes and cross-sections of 4HB, 6HB, 10HB, and 14HB structures showed that the structural twist was larger for the smaller number of cross-sectional helices or the longer axial length (Supplementary Fig. 10 and Supplementary Table 7).

Supercoiling instability

We further investigated the chemo-mechanical supercoiling instability of DNA origami ring structures. Langevin dynamic simulations32 were performed since finding supercoiled configurations in equilibrium by static analysis is numerically difficult due to their highly large geometric deformation. We selected ring structures with three different cross-sections (4HB, 6HB, and 10HB), each of which was designed to maintain a circular shape with diameters of approximately 180, 120, and 80 nm without EtBr-binding (Supplementary Fig. 11). The ring structures deformed into a positive supercoiled shape to compensate for the induced negative torsional strain as many EtBr were bound to them (Fig. 5a and Supplementary Figs. 12–14). The supercoiled conformation was quantified as Lk, Tw, and Wr, representing the linking number as the initial twist applied by EtBr, the twist, and the writhe of the ring structure, respectively, which have a relation of Lk = Tw + Wr (Supplementary Note 4). As a result, we observed a larger global deformation of the ring structure with lower rigidity, consistent with that the structural rigidity is positively related to the number of comprising helices31. For example, for the structurally weakest 4HB ring, the writhe increased to 5.0 with considerable distortion when 600 EtBr was bound, whereas the writhe of the 10HB ring reached 0.3 even with 700 EtBr bound. Accordingly, for the 4HB ring, a long simulation time of more than 2 μs was required for RMSD to converge (Supplementary Fig. 15 and Supplementary Table 8), and its decrease in the radius of gyration was the largest (Supplementary Fig. 16).

Fig. 5: Supercoiling instability of DNA origami rings.
figure 5

a Supercoiling of ring structures. DNA origami ring structures with 4HB, 6HB, and 10HB cross-sections were simulated and quantified as Lk (linking number), Tw (twist), and Wr (writhe). The structures deformed into a positive supercoiled shape to compensate for the negative torsional strain caused by EtBr-binding. b Experimental observation. AFM images of the 4HB ring structure were demonstrated for different EtBr concentration values along with images of the 6HB and 10HB ring structures in our prior literature13. c Analysis of ring structures. The dynamic trajectories of the writhe and twist of ring structures showed the supercoiling dependency on the EtBr number. d Critical twist angle. The ring structures showed a threshold response by increasing the EtBr number. The critical twist angle values of supercoiling in simulated and experimental conformations were compared with Mitchell’s approach, positively related to the number of comprising helices of DNA structures.

Full size image

Interestingly, the ring structures can store torsional strain energy by topological self-constraint for twist and then exhibit buckling, switching from ring to supercoil above a certain critical twist13. In the simulations, out-of-plane distortion rarely occurred when 200, 300, and 500 EtBr were bound to the 4HB, 6HB, and 10HB rings, respectively, but their supercoiling was observed when more EtBr was bound. Our results showed agreement with the experiments including the previous report for 6HB and 10HB13 (Fig. 5b and Supplementary Fig. 17). The simulation trajectories revealed that below a certain number of EtBr, the writhe and twist could remain zero and constant, respectively, as in the case without EtBr (Fig. 5c and Supplementary Fig. 18). On the other hand, arc structures could be gradually twisted rather than buckled along the helical axis as the EtBr number increases because torsional energy can be converted into a global twist without restriction (Supplementary Fig. 19).

This unique deformation mode of the ring structures can be explained by Mitchell’s instability13,47,48. We analyzed the critical number of EtBr binding to the structures where supercoiling occurs by comparing the results from simulations, experiments, and Mitchell’s approach (Fig. 5d). The critical twist was presented by Mitchell as \({\phi }_{c}=2\pi \sqrt{3}(B/C)\), which is only affected by the ratio of the bending (B) to torsional (C) rigidity of a structure. Accordingly, to obtain the theoretical critical twist and the corresponding critical number of EtBr, we employed the rigidity formulas of DNA bundle structures and the rigidity values derived from normal mode analysis (NMA)31 (Supplementary Table 9). The ring structures were regarded to be supercoiled conformations if the ratio of non-circular structures was greater than 0.5 in the experiments, and the writhe was greater than 0.5 in the simulations. We confirmed that the critical twist (or EtBr number) tends to increase linearly as a function of the number of comprising helices at the structural cross-section. However, the ring structure, which is a complex of sequences with non-uniform properties, intrinsic curvature, and a small initial distortion in an out-of-plane direction, differs from Mitchell’s assumptions of an isotropic and stress-free elastic rod in a straight shape. This could support our observation that the critical twist values in simulations and experiments were lower than those in theory since a realistic ring structure could buckle more easily than an ideal one.

Discussion

All-atomic simulations are accurate but computationally heavy, limiting their use in investigating ligand effects on large DNA systems. To address this, we proposed a framework that can infer the chemo-mechanical response of structured DNA assemblies by EtBr molecules with molecular-level accuracy. Through MD simulations, we systematically quantified the effects of EtBr on DNA, which could be weak but considerable when accumulated. To consider the EtBr-binding effects at the structure scale, we incorporated local properties into the finite element model. The proposed method successfully predicted shape variation, flexibility modulation, and supercoiling instability by EtBr-binding on the structural level. Moreover, combined with the binding formula, our predictions were quantitatively verified with experimental observations, confirming the accuracy of the model.

Our study paves the way to analyze various chemo-mechanical effects and design binding-induced structural morphing of DNA assemblies, enabling broader applications. For example, in programming reconfigurable structures with large deformations, chemical binders could be introduced as triggers rather than strand displacement that requires sequence designs. Our model also has the feasibility to include various chemo-mechanical effects by characterizing the effects of binders on DNA at the strand level or employing reported properties. We therefore expect a generalization of the proposed framework that predicts the structural effects of diverse groove binders or intercalators5,7,49.

One of future studies is an investigation of sequence-dependent effects of EtBr-binding24. Examining disparities in the mechanical properties and dissociation constants for various sequence combinations can provide valuable insights into not only the mechanical behavior but also the binding affinity and specificity of EtBr of DNA assemblies. It is also worthwhile to improve the binding model to consider the structural flexibility50, the spatial distribution of groove direction of base-pairs, or the mixture of multiple intercalators. These investigations could enhance our understanding of EtBr-DNA interactions and contribute to refining the predictive capabilities of the proposed framework.

Furthermore, combining the release kinetics of chemicals with the structural characteristics could offer a promising avenue for biomedical applications4,5,6,51. We envision a design pipeline of structured DNA assemblies for programming the delivery rate and amount of drug molecules depending on the type and surrounding environment.

Methods

Characterization of EtBr properties

We employed the previous 400-ns-long MD trajectories of the 6HB structure15. The atomic 6HB structure without EtBr molecules was designed and generated using caDNAno52 and SNUPI31. In the atomic structure, 60 EtBr molecules were manually intercalated in major-groove sites between two successive regular base-pairs (Supplementary Fig. 1). To prepare for a molecular system, the structure was explicitly solvated using the TIP3P water model53, and ionized as 20 mM MgCl2 in a cubic box. The MD simulation was performed under the isobaric-isothermal (NPT) ensemble using NAMD54 with the CHARMM36 force field55 and the CHARMM general force field56, periodic boundary conditions, short-range potentials with 12 Å cut-off, and long-range potentials using the smooth Particle-Mesh-Ewald method57 with 1 Å grid.

Final 300-ns-long trajectories of 43 base-pairs with well-bound EtBr were used to characterize the geometry and mechanical properties (Supplementary Fig. 2). From the MD trajectories of EtBr-binding base-pair steps, the relative geometry between the triads of the constituent two base-pairs was calculated in three translational and three rotational degrees of freedom by 3DNA definition34. The six relative motions were represented for three translations (Δ) and three rotations (Θ) as \({{{\bf{r}}}}=\left[{{{\mathbf{\Delta }}}},{{{\mathbf{\Theta }}}}\right]=\left[{{{\rm{Dx}}}},{{{\rm{Dy}}}},{{{\rm{Dz}}}},{{{\rm{Rx}}}},{{{\rm{Ry}}}},{{{\rm{Rz}}}}\right]\), denoting shift, slide, rise, tilt, roll, and twist, respectively. The covariance matrix was computed from the collected six motions under quasi-harmonic approximation58,59 as \({{{\bf{F}}}}=\left\langle \left({{{\bf{r}}}}-\left\langle {{{\bf{r}}}}\right\rangle \right)\bigotimes \left({{{\bf{r}}}}-\left\langle {{{\bf{r}}}}\right\rangle \right)\right\rangle\), where the bracket denotes the ensemble average. The six mechanical rigidities corresponding to the local directions as \({{GA}}_{y}\), \({{GA}}_{z}\), \({EA}\), \({{EI}}_{y}\), \({{EI}}_{z}\), and \({GJ}\) and fifteen mechanical coupling coefficients between two of them as \(g\left({{{\mathbf{\Delta }}}},{{{\mathbf{\Delta }}}}\right)\), \(g\left({{{\mathbf{\Theta }}}},{{{\mathbf{\Theta }}}}\right)\), and \(g\left({{{\mathbf{\Delta }}}},{{{\mathbf{\Theta }}}}\right)\) were obtained by multiplying the axial translation parameter (Dz) with the diagonal and off-diagonal terms of the stiffness matrix, which is the inverse covariance matrix as \({{{\bf{K}}}}={k}_{B}T{{{{\bf{F}}}}}^{-1}\), where \({k}_{B}T\) is the product of the Boltzmann constant and the absolute temperature of 300 K. We did not consider sequence-dependence of EtBr-binding base-pair steps.

Measurement of persistence length

The persistence length of a 6HB structure was estimated by assuming that the structure is an Euler-Bernoulli beam since its aspect ratio of the length to the thickness is more than ten. For the free end condition without external force, the bending rigidity was derived as \({EI}=M{\omega }^{2}{L}_{c}/{\left(\beta {L}_{c}\right)}^{4}\), where M is the total mass of the structure, ω is the natural frequency, Lc is the contour length, and \(\beta {L}_{c}\) is numerically determined to be 4.733 for the first bending mode. Through normal mode analysis, the natural frequency of the structure was obtained from the eigenvalue corresponding to the eigenmode of the bending shape as \(\omega=\sqrt{\lambda }\). Finally, the structural persistence length was obtained as \({L}_{P}={EI}/{k}_{B}T\).

Binding model

Assuming independent binding, no cooperative effect, and equilibrium in binding, the binding reaction is expressed as \(B+I\rightleftharpoons {BI}\), where B and I represent the free base-pairs and free intercalators (EtBr), and BI is EtBr-binding base-pairs. This relation provides the dissociation constant in equilibrium as \({K}_{d}=[B][I]/[{BI}]\). The EtBr per base-pair (v) is then expressed from the EtBr concentration divided into the total concentration of base-pairs, giving a relation of \(v={C}_{{EtBr}}/\left({K}_{d}+{C}_{{EtBr}}\right)\), where \({C}_{{EtBr}}\) is the observed EtBr concentration in the solution. The total number of intercalators bound to a DNA structure was derived by multiplying the EtBr per base pair with the maximum number of base-pairs that can be bound to the structure as \({N}_{{EtBr}}=v\left({N}_{{BP}}/\varXi \right)={N}_{{BP}}\left(v/\varXi \right)={N}_{{BP}}\left[{C}_{{EtBr}}/\left({K}_{d}+{C}_{{EtBr}}\right)\varXi \right]\), where \({N}_{{EtBr}}\) is the number of EtBr binding to the structure, and \({N}_{{BP}}\) is the total number of base-pairs, \(\varXi\) is the saturated binding density, and \(v/\varXi\) indicates the EtBr fraction of the DNA structure. Next, the experimentally measured persistence length of 6HB structures at different EtBr concentrations15 was used as reference data. A numerical procedure was employed to fit the dissociation constant and the binding density as Kd = 3.2 ± 0.6 μM and \(\varXi=7.3\pm 0.2\) base-pair/EtBr. In short, the number of EtBr binding to the structure for a given EtBr concentration was calculated as \({N}_{{EtBr}}={N}_{{BP}}\left[{C}_{{EtBr}}/\left({K}_{d}+{C}_{{EtBr}}\right)\varXi \right]\), and conversely, an EtBr concentration was computed for an EtBr number as \({C}_{{EtBr}}={N}_{{EtBr}}{K}_{d}/\left[{N}_{{BP}}/\varXi -{N}_{{EtBr}}\right]\).

In choosing random binding positions in a DNA structure, we considered minor steric hindrance that binding probability has similar levels between inner and outer helices. This assumption could be supported by previous studies, that the measured EtBr number was similar to the expected number when uniformly bound in multilayer DNA structures20, and the difference in binding affinity to slender and bulky structures was not considerable for doxorubicin7 and methylene blue50.

SNUPI simulations

In static simulations, an initial configuration and finite elements were built for the design information of a DNA structure. The same number of regular base-pair steps in random positions was then converted into EtBr-binding base-pair steps as the number of EtBr binding to the DNA structure. For each finite element, the geometry and mechanical properties of base-pair or crossover steps were used to calculate local stiffness matrices, which were assembled into a global stiffness matrix. The relaxed configuration was finally predicted through the iterative numerical procedure31.

Through Langevin dynamic simulations32, the global nonlinear deformation driven by EtBr-binding was observed for the 4HB, 6HB, and 10HB ring structures (Supplementary Fig. 11). The initial circular shapes of the ring structures without EtBr-binding were statically predicted, and their dynamic simulations with different EtBr numbers began from the circular configuration. We employed a time step of 5 ps, a hydrodynamic bead radius of 1.1 nm, and the dynamic viscosity of water of 890 μΝ s/m2 at 300 K for all simulations. Dynamic trajectories were saved and analyzed every 10 ns.

Synthesis of DNA origami structures

The 4HB ring structures were designed on square lattice using the open source software, caDNAno52 and we utilized a M13mp18 scaffold strand (7249 nucleotides) provided by GUILD. Staple strands for the structure were obtained from the caDNAno design52 (Supplementary Table 10) and produced by Bioneer (www.bioneer.co.kr). The folding mixture was prepared by combining a concentration of 20 nM scaffold DNA, 100 nM of each staple strand, 1 × TAE buffer (40 mM Tris-acetate and 1 mM EDTA, Bioneer), and 20 mM of MgCl2 (Sigma-Aldrich, www.sigmaaldrich.com). The mixture was then annealed in a thermocycler (T100, Bio-Rad, www.bio-rad.com) by gradually reducing the temperature from 80 to 60 °C with a rate of −0.25 °C/min and from 60 to 25 °C at a rate of −1 °C/h. Excessive staple strands were removed by ultrafiltration using a five-buffer exchange procedure at 5 krcf for 8 min with a 5 mM MgCl2 solution. The concentration of the resulting structure was adjusted with the same buffer used for purification. The concentration of the folded ring structures was measured using a Nanodrop One UV spectrophotometer (Thermo Fisher Scientific).

AFM imaging

A purified sample was diluted with folding buffer (1 × TAE and 20 mM of MgCl2) and mixed with various amounts of EtBr molecules prior to deposition. To ensure that sufficient monomers could be detected for image analysis, the final concentration of each DNA structure was adjusted to 0.3 nM. A volume of 20 μl of the diluted sample with different EtBr concentrations was deposited and incubated on a freshly cleaved mica substrate (highest grade V1 AFM Mica, Ted-Pella Inc.) for 5 to 10 min. After incubation, the substrate was washed with DI water and gently dried using an N2 gun at less than 0.1 kgf/cm2 pressure. AFM images were acquired using an NX10 system (Park Systems, www.parksystems.co.kr) operating in a non-contact mode within the SmartScan software. A PPP-NCHR probe with a spring constant of 42 N/m (Nanosensors) was used for the measurements. Each image had a sample area of 5 μm × 5 μm with a resolution of 1024 × 1024 pixels. Images were flattened using the XEI 4.1.0 program (Park Systems) with linear and quadratic order adjustments.