Energy landscapes of rotary DNA origami devices determined by fluorescence particle tracking

Abstract

Biomolecular nanomechanical devices are of great interest as tools for the processing and manipulation of molecules, thereby mimicking the function of nature’s enzymes. DNA nanotechnology provides the capability to build molecular analogs of mechanical machine elements such as joints and hinges via sequence-programmable self-assembly, which are otherwise known from traditional mechanical engineering. Relative to their size, these molecular machine elements typically do not reach the same relative precision and reproducibility that we know from their macroscopic counterparts; however, as they are scaled down to molecular sizes, physical effects typically not considered by mechanical engineers such as Brownian motion, intramolecular forces, and the molecular roughness of the devices begin to dominate their behavior. In order to investigate the effect of different design choices on the roughness of the mechanical energy landscapes of DNA nanodevices in greater detail, we here study an exemplary DNA origami-based structure, a modularly designed rotor-stator arrangement, which resembles a rotatable nanorobotic arm. Using fluorescence tracking microscopy, we follow the motion of individual rotors and record their corresponding energy landscapes. We then utilize the modular construction of the device to exchange its constituent parts individually and systematically test the effect of different design variants on the movement patterns. This allows us to identify the design parameters that most strongly affect the shape of the energy landscapes of the systems. Taking into account these insights, we are able to create devices with significantly flatter energy landscapes, which translates to mechanical nanodevices with improved performance and behaviors more closely resembling those of their macroscopic counterparts.

Significance

DNA self-assembly techniques allow the design and fabrication of mechanically active, supramolecular mechanisms. However, researchers still lack detailed knowledge of the effects that dominate the dynamics of such devices. Here, we demonstrate an in-depth study of the motion behavior of rotary devices, consisting of a rotor and a stator element. We prototyped different components of the modular rotor to systematically identify how different design features affect the rotation behavior and engineer devices with more homogeneous motion patterns. We use fluorescence tracking to determine the corresponding energy landscapes of about 5,000 individual nanodevices, allowing us to analyze the differences in the movement characteristics for different design variants as well as the variability within individual device variants.

Introduction

Mechanical apparatuses shaped our industrialized world by enabling us to move, manipulate, and manufacture objects faster, more easily, and more reproducibly. Nanotechnologists aim to create mechanical nanoscale devices with a similar level of control as their macroscopic counterparts. Such devices make it feasible to scale mechanical manipulation of objects down to individual (bio)molecules, thereby blurring the boundaries between mechanical and (bio)chemical processing (1,2,3).

In the macroscopic world, mechanical mechanisms rely mainly on rigid components connected by standardized bearings and joints to control the motion of their constituent parts. Traditional mechanical fabrication is based on machine elements that are themselves assembled either by hand or by automated manufacturing machinery. Nanoscale devices, however, cannot be assembled efficiently by placing machine elements together one by one using top-down methods but typically rely on self-assembly strategies.

Almost two decades ago, Nadrian Seeman, the founder of structural DNA nanotechnology, had already realized the great potential of DNA self-assembly for the development of molecular nanorobotics. In his 2006 paper “Operation of a DNA Robot Arm Inserted into a 2D DNA Crystalline Substrate” (4), he probably was the first to use the term “robot arm” in the context of DNA nanotechnology. This was followed by the impressive realization of the first proximity-based programmable DNA nanoscale assembly line in 2010 (1), for whose development he was awarded the Kavli Prize in Nanoscience 2010 and the Benjamin Franklin Medal in Chemistry in 2016.

With the development of the DNA origami technique (5), it has recently become possible to realize ever more complex nanomechanical elements for nanorobotics such as nanoscale hinges (6,7,8,9,10), sliders (6,11), and rotary devices (12,13,14,15,16,17,18,19,20). Such devices either rely on Brownian motion to drive the transition between their available conformations or can be actuated and controlled externally using changes in buffer conditions (10,21,22), chemical signaling like DNA strand displacement reactions (23,24,25), hydrodynamic flow (15), electric (11,13), or magnetic fields (16). Within these machines, rigid components are either connected via flexible DNA tethers or use complex stepwise assembly approaches to create mechanically interlocked supramolecular constructs held together only by steric hindrance—so-called suitanes and rotaxanes (12,26,27). Another strategy is the manufacturing of compliant mechanisms (28,29,30) to implement movable DNA nanodevices from a single monolithic part without any classical bearing. While these mechanisms can be more easily implemented from DNA using a single-step assembly approach, such devices typically exhibit only a constrained range of motion.

To make use of the biochemical versatility of supramolecular structures, e.g., for the manipulation of individual biomolecules, nanomachines require addressable positions that interact with the manipulated molecules. Within different machine states, these interaction sites can change their relative orientation to each other and thereby affect the interacting biomolecules. In contrast to solid-state-based nanomechnical devices, DNA as a construction material is particularly suited to be used as a molecular breadboard to place such addressable positions with various chemical functions at designed locations (31,32).

Similar to macroscale machine elements, nanomechanisms with highly defined motion patterns require small gap dimensions and tolerances. Therefore, the surfaces of components moving relative to each other need to be placed in close vicinity to each other to ensure that the moving parts are confined to the desired directions of movement. Strong confinement and small gap dimensions, however, make the assembly particularly vulnerable to inaccuracies in the design and assembly process. Thereby, interactions between closely confined surfaces can strongly affect the movement characteristics of the devices and their preferred (minimum energy) conformations.

For this reason, the movements of mechanical DNA devices are frequently observed to deviate from those of their corresponding ideal mechanical bearings (6,11,13). In an ideal mechanical bearing, all orientations of a rotary device are equally likely populated for diffusive motion. For typical experimental realizations, however, a multitude of interactions can cause a bumpy energy landscape, which biases the apparatus toward certain conformations and thereby influences its motion patterns. The difficulty to create devices with a flat (or otherwise well-defined and smooth) energy landscape over their entire range of motion and the resulting bias in the movements of the devices need to be accounted for when striving for more ambitious applications such as ultrasensitive biosensing or mechanochemical synthesis. The recent development of a DNA origami-based ratchet motor (33) capable of performing unidirectional rotational motion demonstrated the importance of controlling the shape of the energy landscapes. Here, obstacles added to the stator element of a rotary device shape the energy landscape. Externally applied electric alternating current (AC) fields provide energy required to drive the directional motion and periodically bias the combined energy landscape of the electric field and the intrinsic energy landscape of the device.

Previously, researchers investigated the dynamics of artificial nanodevices with coarse-grained molecular dynamics simulations (34). However, determining the underlying energy landscapes with these simulations is challenging, as the time it takes the nanodevice to fully explore its conformational space is, in most cases, drastically larger than the timescale accessible by simulation. Therefore, sampling strategies like umbrella sampling (35,36) and metadynamics (37) are required to access higher energy states. Despite coarse-graining and advanced sampling methods, simulations of mechanical DNA devices are computationally demanding and require experimental verification.

Experimental studies of the movements of nanodevices and their reaction in response to external stimuli are frequently performed using Förster resonance energy transfer (FRET) measurements (38). Bulk experiments (23,39) with devices fluorescently labeled at strategically chosen positions allow us to monitor transitions between sufficiently distinct mechanical states of such devices, but particle heterogeneity and molecular subpopulations remain hidden in ensemble data. Single-molecule FRET experiments (40,41,42,43,44) can distinguish between such subpopulations, but still the details of the movement between the FRET signal-producing states remain hidden.

As a label-free alternative, the conformation of the movable parts relative to each other can be extracted for individual nanodevices from transmission electron microscopy (TEM) snapshots (6,30,44,45). The corresponding energy landscape can then be determined from the ensemble distribution of the observed conformations. The use of cryo-TEM thereby allows us to reconstruct extremely detailed three-dimensional models of the different conformations assumed by the devices (18,46,47). As this approach averages over an ensemble of devices, however, it also hides the potential heterogeneity in the particle movements.

A more detailed view can be obtained by direct fluorescence tracking, which allows us to observe the movements of individual devices over an extended timespan. This strategy has been previously used for in-depth studies of the working principles of natural motor proteins (48,49) and has recently been applied to observe the diffusive motion and deduce the energy landscape of an artificial DNA-based linear transport system (11). In the present work, we explore the energy landscapes of rotor-stator assemblies. We observe the diffusive motion of the rotor relative to the stator unit by fluorescence tracking. Single-molecule total internal fluorescence microscopy is used for rotor tracking as well as super-resolution DNA-PAINT (50,51) to determine the relative stator orientation. Further, we prototype different design features of the device to systematically test for the impact of each device component on the rotor movement characteristics and the preferred orientations between rotor and stator. For the studied devices, an uneven surface topography of the contacting surfaces within the rotary device was identified as the major influence on the energy landscape. Stronger confinement of the rotor to the stator, analogous to the use of smaller gap dimensions, enhanced this effect. By creating rotationally symmetric stator elements, we were able to fabricate devices with a flatter contact surface topography, resulting in flat energy landscapes.

Materials and methods

DNA origami preparation

Individual DNA origami structure components, rotor extensions, and stator elements were folded in separate one-pot assembly reactions, containing 50 nM scaffold solution, a four times excess of staple strands relative to the molar scaffold concentration and the folding buffer (typically 1× TE + 20 mM MgCl₂ + 5 mM NaCl). Origami scaffold strands were kindly provided by the group of Prof. Dietz (52). Staple strands were synthesized by Integrated DNA Technologies (Coralville, IA, USA). The folding reactions were carried out with different thermal annealing ramps, specific to the folded structure variant, using a thermal cycler (peqSTAR 2X, Peqlab Biotechnologie, Erlangen, Germany) (cf. Note S1 for device-specific folding conditions).

Subsequently, we removed excess staple strands from the obtained origami sample by polyethylene glycol (PEG) precipitation using a protocol identical to the procedure used in previous studies (13). Samples were resuspended in the folding buffer, and fluorescent marker strands were added to the rotor extension samples using a twofold excess over the number of complementary binding sites on the structures. For attachment to the substrate, NeutrAvidin was added to the stator constructs with a 50-fold molar excess compared with the number of biotin-modified staple strands present in the device (typically six biotin anchors).

If not stated otherwise, stator elements with their attached short rotor segments and rotor extensions were separately purified by agarose gel electrophoresis as further described in Note S1. The final constructs were assembled by mixing purified rotor extension structures with a 1.5-fold excess over stator elements for 1 h at 37°C while shaking at 600 Rpm.

For the two rotation devices in this work, we used only the rotor extension as a movable component without extending an existing (short) rotor segment. In these cases, the rotor extension was directly attached to the substrate via a biotinylated staple strand. In these realizations, we employed a design with similar dimensions and modified staple and scaffold routing, which was inspired by a design from Wintersinger et al. (53).

Single-particle microscopy

Sample chambers were assembled from a reusable ceramic top part, a connecting double-sided tape layer forming the actual microscopy channel, and a coverslip (cf. Note S2 for chamber details). Coverslips were functionalized with a PEG-biotin layer according to an established protocol (13) to provide surface passivation and allow specific attachment of nanodevices. The assembled microscopy chambers were flushed with 150 μL of ddH₂O and imaging buffer (1× TE 1 M NaCl) before adding samples containing about 0.8 nM nanodevices and flushing with buffer to remove unbound devices. Microscopy videos for rotor tracking containing 5,000 frames (except for experiments Figs. 2 a and 4 b and c, where 4,000 frames were recorded, and Fig. 4 e, where 2,000 frames were recorded before release and 3,000 after release) were recorded with a frame rate of 100 frames per second. Subsequently, dye labels of the rotors within the observed field of view were bleached using 150 mW for at least 30 min to enable DNA-PAINT imaging using the same fluorescent channel. DNA-PAINT buffer (1 $\times$ PBS and 500 mM NaCl) containing 1 nM DNA-PAINT imager strands was added, and videos for DNA-PAINT super-resolution measurements were recorded (100 ms exposure, 10,000 frames). The detailed description of the analysis of the rotor tracking data and DNA-PAINT super-resolution reconstruction procedure can be found in Note S3.

Figure 2.

Motion analysis of different joint variations for the rotary device based on fluorescence tracking data. Description of the figure elements from left to right: (i) Symbolic depiction of the device configuration and 3D rendering of oxDNA relaxations of the investigated component (stator element was simulated separately and is shown for better visualization). (ii) Representative localization data of a single rotor (blue points). A circle is fitted to determine the angular rotor position (orange). DNA-PAINT localizations of labeled positions on the stator to determine its orientation (green). (iii) Angular energy landscapes. The averaged energy landscape is depicted as a thick line, and energy landscapes of all individual particles are overlayed in gray. (iv) Swarm- and boxplots of the $D_{KL}$ values of the angle histograms. In all boxplots, the black lines indicate the median value, boxes indicate 25–75 percentiles, and whiskers are set at 1.5 interquartile range. (v) Swarm plot of the energy minima orientations for all observed devices, visualizing the orientation of the rotors’ bias. (a–c) Variation of the joint position confine the rotor motion to smaller elevation angles, leading to more distinct energy landscape structures. Short and medium back length versions feature a 3-nt joint and the default version a 4-nt joint. (d) Variant with one of the two single-strand joint domains cut. The similar motion characteristics to the default variant excludes contribution of the joint design. (e) Variant with extended joint domains containing 14 nt instead of 4 nt. Longer joint domains did not result in decreased bias. To see this figure in color, go online.

Figure 4.

Motion analysis of different stator variants, analogous to Fig. 2, including (i) 3D renderings. (ii) Transmission electron microscopy micrographs of the assemblies. (iii) Exemplary localization data for a single device including rotors (blue) and orientation markers on the stator (green). (iv) Averaged (bold) and single particle (gray overlay) energy landscapes. (v) Swarm- and boxplots of the $D_{KL}$ values. (vi) Swarm plots of the angular positions of energy minima. (a) The default rotary device, featuring a square shaped plate as stator. (b) Rotor extension directly attached to the substrate without addressable stator via NeutrAvidin (depicted as avidin (60)). No orientation bias is observed. (c) Variant with a plate designed in the honeycomb lattice leads to flatter but asymmetric features of the energy landscape compared with the default stator element. (d) Stator plate with its DNA helix orientation perpendicular to the rotation plane leads to strongly reduced but randomly oriented energy landscape features. (e) Ring-shaped stator variant. A large variety of motion patterns and energy landscapes is observed. Motion patterns range from strongly biased twofold symmetric patterns to comparably homogeneous distributions where a sixfold symmetry becomes apparent, as shown in detail within single-particle plots (cf. Note S12). To see this figure in color, go online.

We record microscopy videos with a custom-built, three-color total internal fluorescence microscopy setup (642, 532, and 488 nm) based on an Olympus IX71 (Olympus, Tokyo, Japan) microscope body. In this project, only the 642 nm laser (Toptica iBeam smart, diode laser, 150 mW, Gräfelfing, Germany) was used. A 100× oil immersion objective (UAPON 100× TIRF objective, NA 1.49 oil, Olympus) was employed. Samples were positioned using a U-780.DOS XY stage and a P-611.Z piezo z-stage (both Physik Instrumente PI, Karlsruhe, Germany). Imaging was performed with a filter set consisting of a ZT532/640RPC dichroic mirror and a ZET532/640 (Chroma Technology, Olching, Germany) emission filter. Images were captured with an ORCA-Fusion digital CMOS camera (Hamamatsu Photonics, Shizuoka, Japan).

TEM imaging

Negative-stain TEM micrographs were recorded using a Philips CM100 100 kV TEM and an AMT 4 × 4 megapixel CCD camera as described previously (13). Therefore, origami samples were deposited on glow-discharged formvar-coated carbon Cu400 TEM grids from Science Services (München, Germany) and stained with a 2% uranyl formate solution.

oxDNA simulations

Coarse-grained molecular dynamics simulations were performed using the nucleic acid simulation framework oxDNA (54,55). caDNAno design files were converted to oxDNA format using tacoxDNA (56), and sequences were mapped onto the structures using custom scripts. We used the oxDNA2 model (57) with a salt concentration set to 1.0 M and the “john” thermostat (parameters: T = 20C, dt = 0.005, verlet_skin = 0.5, diff_coeff = 2.5, newtonian_steps = 103). The structures were relaxed for at least 5 × 10⁸ simulation steps or a 7.6 μs simulation time. Subsequently, we performed 5 × 10⁸ additional steps (1,000 configurations) to determine mean structures using the compute_mean function of the oxDNA analysis toolset (58).

Results and discussion

Modular DNA nanomachine design

The rotary device used in this work consists of three functional components—stator, joint, and rotor—each of which can be modularly exchanged. The stator takes the shape of an addressable, surface-immobilized DNA origami plate. The joint is comprised of two single-stranded DNA (ssDNA) domains and connects the stator to a short (ca. 50 nm) rotor segment. For efficient fluorescence tracking, the short rotor segment is extended by a much longer (ca. 400 nm) rotor extension segment, labeled with an array of up to 39 fluorophores at its tip (cf. Fig. 1 a).

Figure 1.

(a) Modular rotary DNA device system consisting of an addressable stator element (light gray) fixed to the substrate via biotin-NeutrAvidin bonds, a flexible joint (red) to connect stator and rotor (blue and dark gray). The short (blue) rotor segment is extended by another rotor segment (rotor extension, gray) to facilitate fluorescent tracking microscopy. (b) Three-dimensional (3D) rendering of the default rotary device based on oxDNA relaxations. Rotor and stator were simulated independently and combined for better visualization. The rotor extension is omitted for clarity. (c) Transmission electron microscopy micrograph of an assembled nanodevice. (d) Example snapshot of a total internal fluorescence microscopy video. (e) Reconstructed localization heatmap of tracked rotor positions of the same video (red) superimposed with DNA-PAINT image (cyan) of stator. Right side: two typical particles shown in larger magnification (scale bar: 200 nm). (f) Individual localizations for a single particle (blue) and DNA-PAINT localization (green) to determine the stator orientation. (g) Extracted angular histogram of the observed single particle (orange) and derived energy landscape (blue). To see this figure in color, go online.

The default stator unit, which is used as a reference for our design variations, consists of two sheets of parallel helices stacked on top of each other, forming a 55 × 55 nm square-shaped plate. The helix direction of the top layer is oriented orthogonal to the helix direction of the bottom layer. The default short rotor segment is realized as a rod with a 12 DNA helix cross section as shown in Fig. 1 b and c. Cadnano design maps of all design variants are provided in Note S10.

Motion analysis of rotary devices

A typical motion analysis of a rotary device is based on the angular distribution of the rotor localizations obtained from microscopy videos for individual devices (Fig. 1 d–f). In order to determine the rotor direction with respect to the underlying stator plate, the orientation of the plate is determined with super-resolution DNA-PAINT (59) imaging of a characteristic point pattern placed on the stator element. We reconstruct energy landscapes of individual nanorobotic devices from histograms of the angular distributions as shown in Fig. 1 f. Corresponding ensemble-averaged histograms for all structure variants are presented in Note S11. As a statistical measure of the total strength of the orientation bias as well as to determine the variability within one species of rotors, we calculate the Kullback-Leibler-divergence ($D_{KL}$) or relative entropy for each observed nanodevice, for which we compare the angular distribution histograms with a uniform angular distribution. Lower $D_{KL}$ values represent a more ideal rotational bearing that is not influenced by distinctive features of its energy landscape. We determine the minima of the energy landscapes of individual devices to identify the direction of preferred rotor orientations relative to the stator.

Influence of motion confinement and joint design

Irrespective of the physical nature of potential rotor-stator interactions, we hypothesize that stronger confinement of the rotor to movements close to the stator leads to increased interactions. The mean rotor-stator distance can be varied by the position of the joint as well as by the design of the joint itself. For instance, shifting the position of the joint from the back end of the rotor to an interior position reduces the range of accessible elevation angles and thus enforces a rotation approximately parallel to the stator plane.

For joint positions further from the back end of the rotor, fluorescence tracking localizations lie more consistently on a circle with its radius matching the dimensions of the rotor (cf. Fig. 2 a–c). This indicates that for longer back ends, the elevation angles are more limited in the Z-direction, and thus a stronger confinement to in-plane rotation is achieved. The rotational energy landscapes show a more pronounced structure when confined to small elevation angles. Increasing $D_{KL}$ values confirm this trend of the orientation bias. Interestingly, the energy landscape patterns show two opposing minima. This feature also becomes more apparent with increasing length of the rotor’s back end. We assume that this twofold symmetry in the rotational energy landscape is caused by similar interactions for the back and front part of the rotor with the underlying stator plate.

For all further design iterations that we investigated in this work, we placed the joint at a similar distance from the rotor’s back end. The resulting tight confinement of the rotor motion ensures that our tested design features cause a measurable change of the energy landscape. Of note, we consistently found that the directions of favored rotor orientations align approximately orthogonal to the helix direction of the top DNA layer of the underlying square-shaped plate.

Our standard joint consists of two ssDNA domains with a length of four nucleotides (nt) each that connect the stator plate and rotor (legacy designs were used for short and intermediate back length rotors with similar 3-nt joints). Upon rotation, this joint design may wind up and could thereby create additional torque, which might also influence the energy landscape. To test a potential impact of this feature, we cut one of the joint domains with a restriction enzyme prior to folding of the structure, thus allowing the joint to rotate freely (cf. Fig. 2 d and Note S1). We do not observe a significant effect on the $D_{KL}$ values or a strong influence on the shape of the deduced energy landscape, which lets us exclude a major effect of the two-stranded joint design (cf. Note S5 for a statistical analysis of the differences in $D_{KL}$ for different design variants). Further, we tested if a longer joint variant, featuring 14 instead of 4 nt within each joint domain could lead to a flatter energy landscape by reducing the confinement of the rotor, similar to the effect of shorter rotor back ends (cf. Fig. 2 e). In our experiments, we actually observed higher $D_{KL}$ values, corresponding to a more structured energy landscape for the longer 14-nt joint variant. This increase is consistent with a slightly longer back end of 23.8 nm (vs. 16.7 nm) for the long joint variant and a negligible influence of the increased joint length. We assume that entropic coiling of the joint domains merely results in a minor increase of the effective joint length and thus only a minimal decrease in rotor confinement. Analysis of the joint sequences (cf. Note S9) does not suggest a pronounced secondary structure of either joint domain.

Influence of rotor cross section

Next, we tested the impact of the rotor shape on the energy landscape of the rotary device. For this reason, we varied the cross section of the short rotor segment that interacts with the stator. As shown in Fig. 3, the $D_{KL}$ values for different rotor cross sections vary only slightly, indicating that the tested variants only have a small effect on the magnitude of the energy landscape features. However, we observe a slight trend toward a reduced orientation bias for designs that result in a larger contact area with the underlying plate. The orientation of the energy landscape minima remained orthogonal to the helix direction of the top layer of the underlying plate for all variants of the short rotor segment.

Figure 3.

Motion analysis of rotor variants with different cross sections (rotor regions in close contact with the stator are marked in red), analogous to Fig. 2, including (i) schematic cross section and 3D renderings. (ii) Exemplary localization data for a single device including rotors (blue) and orientation markers on the stator (green). (iii) Averaged (bold) and single particle (gray overlay) energy landscapes. (iv) Swarm- and boxplots of the $D_{KL}$ values. (v) Swarm plots of the angular positions of energy minima. (a) Default rotor segment with 12-helix cross section. (b) 6-helix cross section with additional skids on both sides of the 6-helix tube to increase the contacting surface. (c and d) Rotor segment variants with even more increased contact area. With increasing contact area, $D_{KL}$ values decrease slightly, and increased energy landscape asymmetry occurs. For the 3D renderings of variants (b) and (c), no mean structure could be obtained due to high structural flexibility. Here, individual simulation snapshots after relaxation are shown instead. To see this figure in color, go online.

In a model conception, we assume that the interactions leading to distortions of the energy landscapes (i.e., deviations from a flat landscape) are mainly influenced by the topography of the contacting surfaces. Similar to a deformed macroscopic bearing with a noncircular axle, two uneven or nonplanar surfaces like a twisted sheet and a rod that rotate relative to each other would display preferred orientations with reduced sterical hindrance. Thereby, a perfectly flat and rotationally symmetric stator would eliminate orientation preferences. In the case of an uneven stator, making the rotor component more planar also results in a flatter energy landscape.

This picture suggests steric hindrance as the main interaction between contacting DNA surfaces, but these might be complemented by other interactions such as electrostatic forces, as of course the charge distribution is similarly modulated by the geometry of the DNA objects. However, $D_{KL}$ measurements with different salt species and ionic strengths (Note S6) do not show a strong effect of the buffer composition, indicating that the strength of electrostatic interactions does not have a mayor influence on the shape and amplitude of the rotational energy landscapes.

Strikingly, designs with the largest contact areas with the underlying rotor plate show asymmetric barriers within their energy landscapes. A potential explanation for this asymmetry could be torsional deformations of the rotor, created by residual twist of the honeycomb lattice geometry of the rotor constructs. For the default variant (Fig. 3 a), only a single helix of the rotor is exposed to the stator element, and the contacting skids in the design shown in Fig. 3 b are potentially quite flexible. Both designs show more symmetric energy landscape features. Further, the default rotor construct resembles a rod shape with a rather round cross section. Such an object changes its overall shape only slightly when twisted around its axis. The rotor segments shown in Fig. 3 c and d can present a clearly twisted surface to the stator, as visualized with oxDNA relaxations. These rotors resemble sheet- or cuboid-like objects with a rather rectangular cross section. When twisted, such an object changes its overall shape drastically. In the experiments, both show asymmetric landscape features and no significant difference in their $D_{KL}$ value.

Influence of the stator geometry

We further determined the effect of the design of the stator on the rotational energy landscape. First, we tested the effect of removing the plate entirely and placed the rotor extension directly onto the PEG-biotin-coated glass substrate without addressable stators. The rotor extension was attached to the substrate with a single biotinylated staple strand (cf. Fig. 4 b). These rotors actually showed a very uniform angle distribution (and a $D_{KL}$ close to zero), which confirms that orientation bias is not caused by interactions of the rotor with the substrate far from the stator plate but rather originates from interactions between the rotor and stator units. This finding is in agreement with previous studies on other nanorobotic rotary devices (13,18,33), which have shown that their preferred orientations tend to reflect the symmetry of the connected stator element. Next, we tested a stator plate design similar in size to the square-shaped plate, designed, however, in the honeycomb lattice geometry, which features a corrugated double sheet cross section (cf. Fig. 4 c). Due to scaffold length restrictions, we employed a rotor variant similar to the default short rotor segment. This rotor maintained the identical geometry close to the contacting surface and the identical length of the back end compared with the default variant. For the honeycomb-based rotary device, we observe a reduced orientation bias compared with the square-shaped stator plate (cf. Fig. 4 a). Additionally, we observe a strong asymmetry of the energy landscape, which now displays minima at angles corresponding to a rotor alignment almost parallel to the helix direction of the plate. Presumably, as for the default square-shaped plate, any deviation from a perfectly planar geometry leads to a distortion of the energy landscape. For any sheet-like object, bending preferentially occurs along a single axis, as bending along two axes requires stretching of the material. In most experiments in this study, we observe twofold symmetry of the preferred orientations, further indicating that such deformations are the source of the orientation bias. We surmise that residual twist within the honeycomb lattice might lead to more asymmetric energy landscapes for this design even if the energy landscapes are overall flatter for the honeycomb design. This stands in contrast to the square-shaped structure, which appears to display more global bending of the upper layer into trough-like conformations. These deformations are actually visible in oxDNA simulations; however, these model calculations must be treated with caution, especially as they neglect the impact of substrate attachment. The shape of the stator elements when attached to the PEG-biotin substrate with multiple anchors may deviate from the conformations adopted in solution.

Since DNA based materials are composed of double-stranded DNA (dsDNA) helices, their structure is strongly anisotropic, comparable to wood, which always has a specific fiber direction. As for carpentry in the macroscopic world, the fiber direction influences the mechanical properties and potential mechanical warping and distortions of the created assemblies. Thus, the orientation of the helix direction is expected to influence the deformations displayed by the DNA constructs. Accordingly, the orientation of the bias perpendicular to the helix for the square-shaped platform or the more parallel orientation in the case of the honeycomb lattice design is not a direct result of specific features of individual DNA helices or orientation-specific DNA-DNA interactions. Rather, the anisotropy of the building material leads to certain characteristic deformations correlating with the helix direction. These deformations define the bias orientation. To obtain a topographically flatter stator element, we thus created a plate composed entirely of short helix elements oriented perpendicular to the plate’s surface (cf. Fig. 4 d). oxDNA relaxation of the structure predicts that the plate would be slightly curved into a concave arc above the surface, with the rotor mounted to its top (cf. Note S8 for detailed renderings of the different stator constructs). Most likely, the curvature is caused by repulsion between the asymmetrically connected helices within the structure. Simulations of other plate designs discussed above typically revealed a rather saddle-like topography with rotors positioned at the saddle point of the construct.

We speculate that the attachment of the rotor to an elevated point on the stator unit could reduce steric repulsion and thus lead to a flatter energy landscape. As a drawback of the unconventional plate design of Fig. 4 d, featuring many short parallel helices with limited connectivity, the stator plates turned out to be rather flexible and displayed considerable shape heterogeneity and deviation from the designed shape. This can be deduced, e.g., from the distances between DNA-PAINT positions on the structures, whose measured values differ from those designed (cf. Note S7). Nevertheless, for this stator design, we indeed observe a significantly reduced orientation bias, illustrated by a smaller $D_{KL}$ compared with the other stator plates. Further, the energy landscape does not display deep minima at any preferred orientation, but we rather find more shallow minima distributed over all angles. Note that due to the variability of the position of the minima averaging results in a flatter mean energy landscape compared with individual particle landscapes. Similar to the honeycomb lattice-based stator variant, we used a short rotor segment, which reproduces the default rotor geometry within the region close to the stator.

The particular design shown in Fig. 4 d thus indeed displays less orientation bias but might be less practical for nanorobotic applications due to its increased flexibility and structural heterogeneity. However, for this study, we deliberately created addressable plates of similar size for all stator elements to provide a comparable scenario for the determination of orientation bias. Devices based on the same design principle as in Fig. 4 d could be easily constructed with longer helix domains, which would allow more interhelix connections to reduce flexibility and simultaneously result in a smaller contact surface area and thus further reduced orientation bias.

Engineering of a circular stator unit

As an alternative strategy to realize a stator element with a rotation symmetric contact surface that does not exhibit a preferred angular direction, which could induce structure deformations, we created a ring-shaped stator unit (cf. Fig. 4 e). This ring-shaped stator element is constructed as a curved origami helix bundle, in which the constituent helices are bent to form a circle with a radius of about 41.4 nm. Such a ring-shaped device lacks an addressable DNA helix at the center for the positioning of a joint that connects to a nanorobotic rotor. We therefore directly attached the rotor to the substrate via a biotin-NeutrAvidin bond using a dsDNA linker. This strategy requires a temporary fixation of the rotor on the ring using a pair of displaceable staple extensions. Displacement of the rotor from the fixation leaves behind two ssDNA extensions on the ring’s top surface, which again would break the rotational symmetry. We therefore place four additional (dT)₁₉ extended “dummy” strands on the ring surface to create a uniform hexagonal pattern of ssDNA extensions. On the rotor element, two short dsDNA domains remain after the release.

Following the addition of the release strands that displace the temporary connection between rotor and ring, we observe a wide distribution of $D_{KL}$ values as shown in Fig. 4 e. Among the individual recorded localization patterns and energy landscapes, two different types occur. Most particles show energy landscapes with two distinct bias directions (cf. example particle in Fig. 4 e iii, left) and $D_{KL}$ values comparable to those of the honeycomb lattice-based stator design. However, some particles show a hexagonal pattern of the localization events, which aligns well with the gaps between single residual stranded segments on the ring (temporary attachment points and the positions of the dummy strands), as shown for an example particle (cf. Fig. 4 e iii, right). The hexagonal symmetry can best be identified within averaged orientation histograms of the devices as shown in Note S11 and Fig. S14. This particle species typically features flat energy landscapes (low $D_{KL}$ values), which frequently show six small minima and maxima. From the observed hexagonal patterns, we conclude that even smallest deviations form a flat stator shape, like the mere presence of short ssDNA segments positioned in a 40-nm distance from the rotation center, can give rise to dominant features in the energy landscape.

Particles with higher $D_{KL}$ values and a twofold symmetric energy landscape pattern do not show a preferred orientation of these two favored orientations with respect to the initial attachment position. We therefore assume that the roughness of the energy landscape for particles displaying a twofold symmetric motion pattern is not caused by any specific feature of the ring design, as this would lead to a systematic deviation from the designed shape instead of statistical device-by-device variations. Such symmetry-breaking variations could be caused by an eccentric fixation of the rotor’s biotin anchor or by missing origami staple strands, which could result in buckling of the ring at random locations. In contrast, we consider the particles showing hexagonal patterns as correctly assembled.

Single-particle energy landscapes of presumably correctly assembled, ring-based rotary devices (cf. Fig. S26) demonstrate that it is, in principle, possible to achieve comparatively uniform and smooth energy landscapes. The energy landscape of these devices contains only small features at the scale of the thermal energy while still closely confining the motion of the rotor in the desired rotation plane. However, the comparatively elaborate assembly scheme that is required by these structures leads to a relatively low yield of devices with the desired, homogeneous motion behavior. Improved assembly and design strategies, such as adding alignment spacers to provide a reliable and precisely centered attachment point of the rotor, could eliminate the need for a multistep assembly procedure.

Conclusion

In this study, we determined the rotational energy landscapes of rotary nanodevices made from DNA by tracking the diffusive rotational motion of single nanoscale rotary devices. Such molecular devices usually do not provide completely flat energy landscapes, and therefore certain angular positions are favored over others. We tested the effect of various design features on the shape of this energy landscape and quantified the rotational anisotropy of the orientations of these molecular rotors.

As a general trend, more pronounced minima in the energy landscape were observed for devices, in which the movements of the rotors were more strongly confined to a rotation plane close to the stator unit. Control experiments with different joint variants and the comparably flat energy landscapes of the perpendicular helix design featuring the standard joint design indicate that the actual joint element has a small effect on the rotational energy landscape. We identified the roughness in the topography of contacting surfaces between moving components as a key parameter for the bias in rotor orientations. In particular, a flat stator plate led to a smoother energy landscape than corrugated or intrinsically bent stator plates. This indicates that steric hindrance is the dominating interaction between DNA surfaces in close contact, and thus geometric roughness turned out to be the decisive parameter for the design of devices with a flat energy landscape. For instance, we found that topographical irregularities even as small as short ssDNA extensions placed tens of nanometers from the center of rotation can have measurable effects on the energy landscape of individual nanodevices. We further found that rotary devices with twisted rotor or stator components led to asymmetric landscape features. Such asymmetric energy landscape features could be deliberately engineered by increasing the twist and used as one of the key components required to generate directional motion for many Brownian ratchet concepts (61). While we identified steric effects as the main contributor to the energy landscapes’ shape for our designs, energy landscapes could be also reshaped by introducing weak attractive interactions like short complementary DNA docking sites.

In an attempt to develop rotational devices that act more like ideal bearings, we achieved significantly flatter energy landscapes for structure variants with rotation symmetric stator elements. These designs lacked DNA double helices with a symmetry-breaking orientation within the plane beneath the rotor element. Hence, there is no distinct orientation in the sliding plane that would set the direction for geometric deformations like buckling or twisting, which are inherent features of most DNA assemblies. We achieved stator elements with higher orders of symmetry using two design strategies, the orthogonal orientation of DNA helices to the substrate surface and bending the constituent DNA helices into a ring shape. While these rotation symmetric devices are still difficult to assemble with high yield, understanding the effects that govern the motion behavior of such molecular machine elements will promote engineering of more efficient and “well-behaved” molecular machinery. The ability to precisely design DNA devices with energy landscapes of arbitrary shapes—ranging from flat landscapes to custom-designed energy barriers—will be critical for the further application of DNA-based nanomachines for controlled molecular manipulation, as the processes involved typically occur at an energy scale close to the thermal energy.

Author contributions

A.B., E.K., F.C.S., and J.L. planned the research; A.B. conducted the fluorescence microscopy measurements; A.B., M.V., E.K., and J.L. analyzed the data; A.B., E.K., and J.L. designed and fabricated the DNA nanoconstructs; and A.B., E.K., and M.L. generated the relaxed structure models using coarse grained simulations. All authors wrote the article.

Editor: Yi Qin Gao.

Data and code availability

Raw data, including TIRF microscopy videos, are available from the corresponding author upon reasonable request.

The source code of the data analysis routines and simulation files employed in this study are available from the corresponding author upon reasonable request.