Position Accuracy of Gold Nanoparticles on DNA Origami Structures Studied with Small-angle X-ray Scattering

Abstract

DNA origami objects allow for accurate positioning of guest molecules in three dimensions. Validation and understanding of design strategies for particle attachment as well as analysis of specific particle arrangements are desirable. Small-angle X-ray scattering (SAXS) is suited to probe distances of nano-objects with sub-nanometer resolution at physiologically relevant conditions including pH and salt, and at varying temperatures. Here we show that the pair density distribution function (PDDF) obtained from an indirect Fourier transform of SAXS intensities in a model-free way allows to investigate prototypical DNA origami-mediated gold nanoparticle (AuNP) assemblies. We analyze the structure of three AuNP-dimers on a DNA origami block, an AuNP trimer constituted by those dimers, and a helical arrangement of nine AuNPs on a DNA origami cylinder. For the dimers, we compare the model-free PDDF and explicit modeling of the SAXS intensity data by superposition of scattering intensities of the scattering objects. The PDDF of the trimer is verified to be a superposition of its dimeric contributions, i.e. here AuNP-DNA origami assemblies were used as test boards underlining the validity of the PDDF analysis beyond pairs of AuNPs. We obtain information about AuNP distances with an uncertainty margin of 1.2 nm. This readout accuracy in turn can be used for high precision placement of AuNP by careful design of the AuNP attachment sites on the DNA-structure and by fine-tuning of the connector types.

Bottom-up assembly enables the production of large numbers of identical structures at once. DNA based self-assembly is a versatile and powerful approach to nanoscale manufacturing in bulk.^1–3 In particular the design principle of DNA origami has proven to be easily controllable, versatile and robust.^{4, 5} It relies on folding of a long circular single stranded DNA scaffold into various 2D- and 3D shapes by short single stranded staple oligonucleotides via base pairing interactions. One of the most prominent features of DNA assemblies is the possibility to place and control guest molecules and particles with high precision.^6–22 Guest molecules can be attached and site-specifically arranged on the structures by selection and elongation of a certain set of oligonucleotides pointing outward from the structure. This allows for positioning of any guest molecule that can be attached to a complementary DNA-strand. DNA self-assembly has proven particularly useful for the spatial arrangement of metal nanoparticles into nanoantennae or more complex architectures for nanophotonic studies.^23–27 Up to date, however, the positioning accuracy of particles on DNA origami structures has not been studied systematically.

The success of DNA assemblies is often verified using imaging techniques such as AFM⁴ or TEM⁵. These techniques yield qualitative information about success of assembly and attachment, and first estimates on distances of the attached guest molecules. AFM is ideally suited to study relatively flat objects, however, particle attachments on origami structures are not rigid enough to allow for accurate localization under liquid conditions. Drying of the samples on the other hand results in significant distortion of the particle arrangements, both in AFM and TEM. Cryo-electron microscopy can even reveal atomic details of the nanostructures but requires freezing of the samples, which inhibits the observation of dynamic processes.²⁸ Fluorescence lifetime techniques have been used to analyze the influence of DNA–binding strategies on the attachment distance of large AuNPs to DNA origami.²⁹ For observing relative changes in distances, Förster resonance energy transfer (FRET) of attached dye pairs is highly sensitive in the range of 1-10 nm.^{18, 30, 31} To obtain absolute values, however, FRET can be cumbersome as it relies on fluorescent intensity yields, which are susceptible to solvent conditions and the chemical surrounding of the dyes.

SAXS is a complementary method for structure analysis of nano-objects and in particular for measurements of pair distances of AuNP arrangements in solution.³² It is widely used for structure determination of biomolecules such as proteins.³³ Furthermore, it can be used to verify the assembly of pure DNA-nanostructures.^{34, 35} We previously have performed SAXS measurements on undecorated single origami nanostructures to reveal their inner structure and behavior with changing concentrations of ions.³⁶ SAXS has also been used to characterize DNA-connected AuNP dimers for investigation of the connector.^{32, 37–39} The pair density distribution function (PDDF) is obtained by indirect Fourier transform of the scattering data and serves as a tool for investigation of these structures.^{34, 37, 38, 40, 41} In the context of DNA-AuNP assemblies, SAXS has been successfully used to characterize DNA-mediated gold nanoparticle DNA-assemblies⁴² and lattices^{43, 44} or more specifically DNA origami mediated lattice assemblies^45–48 and for verification of assembly of their components⁴⁹.

Here, we apply SAXS for structure determination of three prototypical gold decorated DNA origami nanostructures with increasing complexity: a dimer, a trimer, and a helix. AuNP pair distances of dimers and trimers in solution extracted with pair density distribution function (PDDF) analysis are in good agreement with the design estimates. The distances obtained from the PDDF agree with the values extracted from direct modeling of AuNP arrangements within 1.2 nm. We then use the PDDF to analyze design details of positioning of nanoparticles on DNA origami. We find that the attachment point position on the origami, the choice of the orientation of the DNA connector and the DNA length all influence the positioning. We see indications of repulsion between AuNP placed laterally next to each other, presumably due to their large DNA shell and their flexible connectors to the origami. Furthermore, the radius of a helical arrangement of nine nanoparticles can be obtained from the AuNP pair distances.

The synchrotron SAXS intensities of the components used in the assembly, namely the origami block and the AuNPs, and their assemblies are shown in Figure 1. They are plotted as functions of the magnitude of the scattering vector q = 4π/λ sin(θ) with wavelength λ and scattering angle 2θ. The scattering intensities from the bare DNA origami structures, a block and a cylinder shape, are well known from previous measurements³⁶ (i&ii). The AuNPs show the characteristic oscillations of spherical particles (iii), which allow us to measure their radius from model-based analysis of the scattering curve. At first glance, the scattering intensities from the AuNP dimers largely resemble the scattering of the single unbound AuNPs, since they are the dominating scattering objects in these assemblies due to their high electron density. A closer look, however, reveals characteristic interference effects at small q (iv), i.e. in the q range which probes the AuNP nearest pair distances d_NB via $q=\frac{2\pi }{d_{NB}}.$ Similarly, the helical AuNP arrangement mediated by the origami cylinder modulates the intensities at small q (v) (data shifted for clarity).

Figure 1.

Sketches (a) and measured SAXS pattern (b) of the components: i) a three-layered origami block, ii) an origami cylinder of 24 helices, iii) gold nanoparticles of approximately 10 nm diameter, iv) a gold nanoparticle dimer mediated by the DNA origami block, v) and a helical arrangement of nanoparticles mediated by the origami cylinder. Fits are shown for a dimer model considering only the scattering of the gold nanoparticles (solid line) and of a model taking into account the origami block and DNA shells around the particles (iv dashed line) in a zoom-in (c).

Before we analyze the SAXS data quantitatively we describe the design scheme in detail in order to define the estimated distance values for the AuNPs in the different constructs. To assemble the dimer, we attached DNA-functionalized gold nanoparticles of nominally 10 nm diameter to three different binding sites on block-shaped, three-layered DNA origami nanostructures¹⁸ (Figure 2a). The defined binding sites consist each of three single-stranded DNA extensions, which are protruding from the upper or lower surface of the block (marked red) in a triangular geometry. All protrusions have a length of 15 A-bases while the gold nanoparticles are functionalized with thiol-modified-oligonuleotides of 19 T-bases, which gives a single-stranded spacer of 4 nucleotides (nt), adding a certain degree of flexibility. Two binding sites are located on one side of the block, one at the center (A) and one at the edge (B), and one binding site at the middle of the other side of the block (C), enabling the formation of three different dimer pairs (AB, AC, BC). Attachment sites A and B are laterally displaced by a small and a large shift compared to C, respectively. For clarity, we call these arrangements lateral (AB), vertical (AC), and diagonal (BC).

Figure 2.

a) Sketch of the trimer ABC with nanoparticles at different attachment sites A, B and C of the origami block. b) PDDF obtained from the scattering of the dimers AB, AC and BC and trimer ABC (blue solid line, dashed line, dash-dot line and black solid line respectively) with nanoparticles at different attachment sites. TEM images of all 3 dimers and the trimer are shown. Positions of the second peak indicate the center-to- center distances of the gold nanoparticles. c) Scheme of the tested connector types: (i) A₁₅ to T₁₉ (blue), (ii) A₉ to T₈ (orange) and (iii) A₁₅ to 3´ T₁₉ (green, zipper configuration). d) & e) PDDF for each of the three different connector types for dimers AC (d) and AB (e) are shown together with corresponding TEM images.

The distance between the A and B attachment points of the lateral arrangement corresponds to 63 basepairs (bp), i.e. we expect a AuNP distance of 21.4 nm for the AB dimer, accounting for 0.34 nm per bp⁵⁰. In dimer AC and BC, the attachment sites are on opposing sides of the origami block, and laterally displaced by 4.8 nm and 16.7 nm for AC and BC, respectively. The thickness of the three layer DNA origami block is 7.7 nm ³⁶, while the radius of the AuNPs has been determined from the SAXS data to be 4.2 nm. As a simple estimate we here calculate the connector length of the oligonucleotides binding the AuNP as 5.1 nm accounting for a distance equivalent to 0.34 nm per basepair for 15 bp. With this, we estimate AuNP distances of 27 nm and 31 nm for the vertical (AC) and diagonal (BC) dimer, respectively. Note that these distances are well beyond the standard range of FRET experiments. After we fabricate all three dimers (AB, AC, BC) and the trimer conformation (ABC) we employ TEM imaging (Figure 2b) confirming assembly of all four structures (Supplementary Note S1 and Supplementary Table S1). For distance measurements the TEM images are prescreened for top views and side views of the lateral AB and vertical AC and BC configurations, respectively. The average center-to-center distance for the lateral (AB) configuration is 21 with a standard deviation of 4 nm, which is in good agreement with the designed value of 21.4 nm. For the vertical and diagonal configuration AC and BC we find values of 25 ± 1 nm and 27 ± 2 which are slightly off the design-estimated values of 27 nm and 31 nm. The TEM analysis confirms the successful assembly and gives first estimates on the distances of the AuNPs, but the orientation of the objects when landing and drying effects can have a large influence on the particle configuration on the grids. These drawbacks can be overcome by SAXS measurements in solution. We will see below that center-to-center distances obtained by TEM are systematically smaller than the SAXS values for full hydration conditions (Supplementary Note S2).

We first analyze the SAXS data of the dimers as they exhibit the simplest geometry. First we used direct modeling to reproduce the scattering data (Supplementary Information S2). The most basic fit model (solid line in Figure 1c (iv)) considered only the superposition of the scattering amplitudes of two gold spheres, displaced by distance d, which was already sufficient to extract dimer distance values which lie in the expected range (Supplementary Table S1), however some fits did not converge. In order to refine the model, the origami block and the DNA shell of the functionalized AuNPs were included in the explicit modeling (dashed line). Now, AuNP distances could be extracted for all dimers. In the cases where both models converged, the agreement was better than 1 nm, while the full model yielded systematically slightly lower distances (Supplementary Table S1).

Before we turn to the quantitative discussion of the distance values, we use the indirect Fourier transform of the scattering data obtained in a model-free way through the software package GIFT⁵¹. This software calculates the pair density distribution function (PDDF) p(r). The PDDF is a histogram of distances r which can be found inside the scattering object and p(r) = r²γ(r) with the averaged self-convolution of the density distribution $\gamma (r)=\langle \rho (\overrightarrow{r})*\rho (-\overrightarrow{r})\rangle .$ ^52–54 The PDDF distribution for a pair of spheres is supposed to show two maxima.⁵⁵ The first maximum is determined by the AuNP-sphere radius, the second maximum is determined by the center-to-center distance (Supplementary Note S2). We find that all PDDFs of dimers show a second maximum at a different characteristic position for lateral, vertical and diagonal configuration (Figure 2b, solid line, dashed line, dash-dot line, respectively). For the lateral, vertical, and diagonal configurations, the maxima indicate distances of 23.1 nm, 26.9 nm and 30.2 nm, respectively. These values are in good agreement with the design values. Furthermore, we find that distances obtained from the second maximum position of the PDDF agree within 1.2 nm with the analysis of SAXS intensities by simple geometric shape models and trends are the same. Thus, particle distances can be read off directly from the experimental PDDF (Supplementary Note S2).

With the goal of investigating the influence of DNA design details, we collected SAXS intensities of the lateral and vertical dimers (AB & AC) using different connectors (Figure 2c). Particle attachment was performed in three different ways. The AuNP were conjugated to (i) T₁₉ with thiol with a 6 carbon spacer at the 5´end, (ii) T₈ with thiol with a 6 carbon spacer at the 5´end, and (iii) to T₁₉ with thiol with a 3 carbon spacer at the 3’end (Figure 2c). The origami structures were prepared with protrusions of either A₁₅ or A₉ extending from 3´ends of 3 designated staple strands to capture the nanoparticles covered with T₁₉ or T₈ strands, respectively. We expect that attachment thus occurs via hybridization and the formation of 3 double strands of 15 and 8 bp in (i) and (ii). The third configuration (iii) is designed to form a 15 bp double strand in a so-called “zipper” configuration.²⁹ Assembly of the different constructs was first confirmed using TEM (Figure 2d& e) followed by detailed SAXS studies.

For the vertical dimers (AC) we find that the second maximum positions indicate the dimer distances, 26.9 nm, 21.8 nm and 23.1 nm for configuration i, ii, and iii, respectively (Figure 2d). This can be rationalized by the following geometrical arguments: The observation that the distance in configuration (i) is 5 nm larger than (ii) can be explained by the length difference of the connecting oligonucleotides. The zipper configuration (iii) might be expected to yield the smallest dimer distance by zipping the nanoparticles tightly to the DNA origami surface. One should consider, however, the effect of sterical hindrance by the single-stranded DNA shell, which is 11 nt larger for the zipper configuration (iii) than for configuration (ii). The sterical hindrance of long oligonucleotides and the T₄ single stranded spacer may cause the larger binding distance of the zipper configuration (iii) compared to the T₈ configuration (ii).

For the lateral dimer (AB), we find that the second maximum positions indicating the distances vary slightly for the three connector types: 23.1 nm, 21.0 nm, 21.6 nm for configuration i, ii, and iii, respectively (Figure 2e). The measured distances of the lateral AB dimer with the shorter connectors (ii and iii) are close to the calculated attachment point distance of 21.4 nm. The long linker configuration (i) yields a 2 nm larger value for the center-to-center distance. We here want to estimate if at this distance an influence of repulsion due to the DNA-shell on the AuNPs can be expected: Analysis of SAXS measurements of the AuNP functionalized with (i), (ii), and (iii) using a core-shell model as approximation indicate an equal Au core size of 4.2 nm and the largest shell for T₁₉ with the six carbon spacer and the smallest for T₈ as expected (Supplementary Note S2). If the single stranded oligonucleotides covering the surface of the AuNP behaved as ideal polymer random coils, the DNA shells would be of the order of the Flory radius⁵⁶ of 4 and 2 nm for T₁₉ and T₈, respectively. However, as the configuration of oligonucleotides attached with thiol via a carbon spacer on a curved and densely covered surface deviates from this picture, we expect a different behavior. In order to verify for dense particle functionalization with DNA, we performed UV/vis spectroscopy control measurements for selected samples. We find that the number of DNA oligonucleotides, e.g. of 10 nm AuNPs functionalized with T₁₉, is on the order of ~ 80 strands per particle, yielding surface densities of ~ 0.2 strands per nm² which is consistent with previously reported values⁵⁷. At high surface densities, DNA is expected to adopt a “brush” configuration with oligonucleotides being stretched away from the surface.^{58, 59} Due to the rigid core of the AuNP, the remaining space in between two AuNP sitting next to each other in the AB configuration is only 13 nm. This length corresponds to about 26 nt in a stretched configuration.⁵⁸ This implies that the 19 nt -long DNA strands covering the AuNPs would overlap and hence induce steric repulsion, while for AuNPs covered with 8 nt-long DNA no repulsion would be expected. Indeed, we find an enlarged distance for the longest T₁₉ connectors. For the shorter connectors (ii) and (iii) the particle separations are close to the nominal value. We assume that the shorter connector (iii) allows for less movement of the particles away from the attachment point. This explains a lower deviation of the AuNP distance from the attachment point distance due to repulsion in configuration (iii). The trend of larger AuNP distances for T₁₉ (i) compared to T₈ (ii) obtained here in full hydration is also observed for dried samples on TEM grids for the lateral AB as well as for the vertical AC configuration of the dimer.

Finally, we turn to the question whether also assemblies with more than two AuNP yield meaningful PDDFs. This question is highly relevant in order to confirm that analysis of AuNP-DNA assemblies with the model-free PDDF is possible by standard data processing based on the indirect Fourier transform. We find that the PDDF of the trimer arrangement is indeed a superposition of the three PDDFs obtained separately for the dimers (see Figure 2b). A disentanglement of the respective dimer distances is, however, difficult, since all dimer distances (AB, AC, BC) agree within a few nm, i.e. the trimer is similar to an equilateral triangle. We therefore turn to a construct that has more characteristic pair distances; a helical arrangement of nine AuNP attached to a cylinder-like 24 helix bundle origami²¹. The measured PDDF of the helical AuNP arrangement is shown in Figure 3a (black solid line). The experimental PDDF shows side maxima at various pair distances in a discrete helix (Figure 3b). The first and second side peak at 21.2 nm and 36.4 nm agree with the nearest and next nearest neighbor distances of AuNPs in the discrete helix design, shown in the schematic (Figure 3b) as purple and blue lines. With these neighbor distances, it is possible to estimate the radius of the helix to approximately R=18.4 nm assuming a pitch of 57 nm. This value is in good agreement with the design (Supplementary Note S3). At larger distances multiple peaks overlap in the PDDF. Here it is only possible to analyze the PDDF via comparison of the whole function with a simulated PDDF based on our structure model using a Monte Carlo approach (Figure 3a, dash-dot line, details can be found in Supplementary Information S2).^60–62 The agreement of the experimental PDDF with the simulation is remarkably good considering the complexity of this assembly.

Figure 3.

a) PDDF of the helical arrangement (solid line) and by Monte Carlo simulation (dash-dot line)(see also Supplementary Note S2). b) The distances (colored arrows in the scheme) occurring in the PDDF (colored squares) confirm a helical arrangement with an overall helical radius of approximately 18.4 nm.

Our data shows how SAXS can be used to investigate the placement precision capabilities of DNA origami. While DNA origami itself has fairly predictable spacing properties along the axis of DNA, the attachment of relatively large structures such as the AuNPs of 10 nm diameter used in this study requires multiple attachment strands, which adds further complexity. Here, SAXS measurements can provide distance information within an uncertainty range of 1.2 nm for fine tuning of object positioning by choosing, measuring and adjusting the connectors of the AuNPs to tailor the structures to fit the needs of the experiments. The presented measurements have been performed at a synchrotron facility but initial experiments performed on an in-house setup yielded almost the same resolution. The PDDF analysis is applicable to simple particle systems, which is confirmed by comparison to direct modeling. For many component AuNP-origami objects such as AuNP helices it is possible to extract key design parameters such as the helix radius from characteristic next neighbor distances.