BNL-112667-2016-JA

Lattice engineering through nanoparticle–DNA frameworks

Ye Tian, Yugang Zhang, Tong Wang, Huolin L. Xin, Huilin Li and Oleg Gang

Submitted to Nature Materials

February 2016

Center for Functional Nanomaterials

Brookhaven National Laboratory

U.S. Department of Energy USDOE Office of Science (SC), Basic Energy Sciences (SC-22)

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This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or any third party’s use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof or its contractors or subcontractors. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. Lattice engineering through nanoparticle–DNA frameworks

Ye Tian1,Yugang Zhang1,Tong Wang2, Huolin L. Xin1, Huilin Li2,3 and Oleg Gang1*

Advances in self-assembly over the past decade have demonstrated that nano- and microscale particles can be organized into a large diversity of ordered three-dimensional (3D) lattices. However, the ability to generate dierent desired lattice types from the same set of particles remains challenging. Here, we show that nanoparticles can be assembled into crystalline and open 3D frameworks by connecting them through designed DNA-based polyhedral frames. The geometrical shapes of the frames, combined with the DNA-assisted binding properties of their vertices, facilitate the well-defined topological connections between particles in accordance with frame geometry. With this strategy, dierent crystallographic lattices using the same particles can be assembled by introduction of the corresponding DNA polyhedral frames. This approach should facilitate the rational assembly of nanoscale lattices through the design of the unit cell.

he progress in nanomaterial fabrication methods was for a powerful approach for 3D crystallization14,15,38, where phases can a long time motivated by the idea that self-assembly will be controlled by means of particle sizes, shapes, tailoring of DNA endow us with the ability to organize nanoparticles (NPs) shells23,33, and even in a dynamic manner by selective interaction T 39 in designed arrays. In reality, the particle characteristics have a triggering . Despite these significant advances, assembled phases profound effect on the assembled structure thus, a little room remain determined by particle details. Here, we propose a remains for structural design. Yet, it would be far more powerful conceptually different approach, in which we shift the problem of to have the ability to generate the different desired types of 3D lattice design from tailoring nanoscale particles, into forcing the lattice from the same particles. Such freedom of lattice engineering connection between isotropic particles by precisely engineered will permit the fabrication of targeted materials, with properties anisotropic linkages. Specifically, polyhedral 3D DNA origami40,41 that can be enhanced and manipulated by precise organization of frames, whose vertices connect DNA-encoded NPs (refs 42,43), functional components1–5. facilitate the establishment of local particle coordination that Colloids, often presented as a model of atomic systems, results in the formation of 3D ordered NP–DNA frameworks have revealed great insight into the fundamentals of crystal (Fig. 1). We demonstrate that the same kind of NPs can be formation6–9 and the role of particle nature10–12. Although an assembled into different types of lattice by employing appropriately extremely rich variety of lattices have been demonstrated12–15, the designed polyhedral frames. Moreover, the crystallographic type particular particle characteristics—such as sizes13,16,17, interactions, of the assembled lattice (framework) is correlated with the frame entropic and many-body effects18–21, and shape22–24—dominate geometry. Thus, our strategy potentially permits the deliberate lattice formation. These dependences are both natural and useful; engineering of the unit cell by controlling the shape of the particle- numerous investigations have detailed how particle characteristics connecting frames and does not require particle modifications. drive structure formation12,24–28. Whereas these studies uncovered This approach addresses the challenge articulated by Ned Seaman a great depth of physical insight, the goal of lattice ‘engineering’ in his visionary work, more than three decades ago, that led to the remains elusive, owing to the complex dependences between the rise of the field of DNA nanotechnology44: how to create 3D lattices structural and energetic parameters of particles and lattices, and the that position guest species in a predetermined, regular manner. In necessity to tailor particles for each target lattice. this work, we designed45 five different DNA origami polyhedral Anisotropic interparticle interactions, induced by precise frames, including octahedron, cube, elongated square bipyramid arrangement of binding patches or by particle shaping, were (ESB), prism and triangular bipyramid (TBP) geometries, built considered as a means to simplify the lattice design. These using six-helix-bundle edges with lengths (depending on the particles have been extensively investigated for regulating phase frame shape) from 30 to 45 nm, as shown in Fig. 1 and detailed formation11,29,30, and diverse phases were predicted29. Several in Supplementary Methods. Every bundle has one single-stranded recent studies exploited directional interactions to create particle DNA chain extending from each of its ends. This chain can further clusters and arrays13,31–34. However, such approaches require hybridize with complementary DNA, which coats NPs uniformly. ample efforts in fabrication of building blocks with sophisticated Thus, for all our designs, the number of strands linking a frame anisotropic interactions. High-fidelity and high-yield fabrication of vertex to an individual NP is equal to the number of edges at these elaborate particles remains challenging, particularly on the the given vertex. The designed DNA frames thus connect NPs at nanoscale32,35–37. Besides, the resultant lattices are still determined by their vertices, establishing the overall lattice topology based on the specific particle design. DNA-based methods have emerged as frame geometry.

1

* ARTICLES

Frames Nanoparticle−DNA framework

Nanoparticle Particle−frame Framework assembly formation +

Figure 1 | Lattice assembly through NP–DNA frameworks. NPs (yellow ball) capped with oligonucleotides (blue curves) are mixed with polyhedral DNA frames (from top to bottom): cube, octahedron, elongated square bipyramid (ESB), prism, triangular bipyramid (TBP). The frames are designed to have complementary strands at the vertices for NP binding. An aggregation (framework formation) is expected when NPs and the correspondingly encoded polyhedral frames are allowed to mix and to hybridize. NP–DNA frameworks might exhibit an ordered lattice for optimized NP sizes, linking motif and annealing process. The crystallographic symmetry of the assembled lattice is controlled by the shape of the interparticle linking frames, but not by the NPs themselves. This strategy thus enables ‘engineering’ the lattice and its unit cell.

Polyhedral frames as topological linkers NP–DNA framework assembly Assembly of polyhedral origami frames was carried out using We first discuss the assembly of a 3D lattice using an octahedral M13mp18 DNA and staple strands (1:10 ratio) in 1×TAE frame46. To prepare the assembled system, DNA octahedra and buffer with 12.5 mM Mg2+, annealed slowly from 90 ◦C to room NPs (10 nm core) were mixed at a ratio of 1:2. To explore the temperature (see Supplementary Information). Proper assembly role of particle–vertex linkages on the phase formation, we studied was confirmed using gel electrophoresis45 (Supplementary the assembly behaviour as a function of the length, d, of the Fig. 1), and negative-staining transmission electron microscopy DNA motifs connecting the frame vertices to the NP. Partially (Supplementary Fig. 3). Cryo-electron microscopy (EM) with complementary single-stranded (ss) DNA strands extend from 3D reconstruction, as described previously46, was also applied to the octahedra vertices and particles respectively—so-called ‘sticky visualize the assembled DNA frames (Supplementary Figs 4–7). ends’—providing attachment of NPs to frames. We regulate the We probed the ability of the frame to coordinate NPs, by creating linking motif (denoted as l-m-n, see Table 1) by changing the frame-defined NP clusters. Gold NPs were coated with synthetic number of oligonucleotides in both the non-complementary regions oligonucleotides, which are complementary to the strands on the (l for frame vertex strand, n for NP) and the complementary vertices of the frames (see Supplementary Information for the overlap (m) of the complementary parts. The mixed solution of details of strand sequences). The NPs and DNA frames were mixed NPs and frames was annealed from 50 to 20 ◦C at 0.3 ◦C h−1 to in a ratio of 2.5N:1 (where N is the number of vertices for the ensure the formation of thermodynamically equilibrium phases. frame) to form clusters31,32,46. EM imaging, following purification Dark aggregates were observed at the bottom of the tube after the with 1% agarose gel, demonstrated effective assembly of different annealing process, indicating the appearance of a NP–octahedra cluster architectures (Supplementary Figs 8–11), in which NPs condensed phase. are properly coordinated to the vertices of the corresponding We first probed the internal structures of these aggregates polyhedral frames. (systems I–V) by in situ small-angle X-ray scattering (SAXS). The Next, we investigated the formation of extended 3D NP–DNA 2D scattering patterns and the corresponding structure factors, S(q), frameworks, in which the same kind of NP can be arranged into where q is the scattering vector, are shown in Fig. 2a. Remarkably, different types of lattice by providing differently shaped connecting system II (motif 2-6-10) revealed about 30 orders of resolution- frames. We stress that the assembled NP–DNA framework might be limited Bragg peaks (Fig. 2a, S(q) green curve), which signifies or might not be crystalline. The formation of 3D ordered lattices a high degree of long-range order. The use of either shorter of NPs (Fig. 1) is non-trivial: if the particle size is significantly or longer NP linking motifs results in a significantly reduced larger than the frame dimensions, then a large number of frames correlation length for the order, as evidenced by the broadening of can be attached to a particle, disrupting lattice topology; if the NP the scattering peaks, and the greatly reduced intensity of the higher- size is too small, steric repulsion between frame edges will hinder order reflections. The peak positions (higher-order peaks relative to hybridization of multiple frames to each particle; the length and the first peak)√ for√ system√ II (green curve, Fig. 2) exhibit the ratios rigidity of strands connecting vertices to NPs will influence the q/q1 = 1: 4/3: 8/3: 11/3: 2..., which is expected for the face- particle displacement and thus lattice order. centred-cubic (FCC) phase. Given the nominal 1:2 stoichiometry of the lattices are the experimental basis for proposing suitable frame Table 1 | Summary of designed and experimentally observed arrangements for all systems shown in this work, and future studies lattices based on NP–DNA frameworks. might further refine those arrangements. For the assembled lattice of octahedral frames and NPs our experiment shows that the ratio Frame Linker Lattice Lattice parameters, of frames to NPs is about 1:2; moreover, the lattice structure does shape motif, type experimental and (designed) not depend on the nominal mixing ratio (Supplementary Fig. 26). l-m-n values Thus, for this lattice we propose a frame arrangement (Fig. 3a4 Octahedron 0-6-10 Amorphous - and Supplementary Fig. 14 for enlarged view) that is symmetric = = = 2-6-10 FCC a b c 67.7(64.6) nm and mechanically stable, and it satisfies the determined 1:2 ratio = = = ◦ α β γ 90 of frames to NPs and the observed FCC lattice of NPs. In the FCC = = = 9-6-10 FCC a b c 69.0(69.4) nm lattice, as shown for the unit cell in Fig. 2b (left panel) and the large- = = = ◦ α β γ 90 scale view in Fig. 3a4, the octahedron vertices have two different 6-9-21 Amorphous - binding modes with NPs: one is in the plane of equatorial vertices 0-15-15 Amorphous - (four octahedra per particle), and the second mode is along axial Cube 9-6-10 Amorphous - vertices (two octahedra per particle). Notably, if the linker motif = = = 6-9-21 Simple a b c 48.3(49.9) nm is too short (system I), the lattice formation is hindered because = = = ◦ cubic α β γ 90 particles might be mis-centred within the vertex cavity; in addition, 0-15-15 Amorphous - the edges of neighbouring octahedra might be in unfavourable = = = ESB 2-6-10 BCT a b 50.0(45.7) nm; c 86.6 proximity. On other hand, if motifs are too long (systems III–V) the = = = ◦ (77.7) nm; α β γ 90 excessive flexibility of the connections deteriorates the order. Both = = = 9-6-10 BCT a b 52.5(49.1) nm; c 91.0 scenarios were observed experimentally (Fig. 2a and Table 1). (85.0) nm; α =β =γ =90◦ 6-9-21 Amorphous - Enabling lattice types by shaping polyhedral frames Prism 2-8-22 Amorphous - = = = We applied the demonstrated strategy towards the creation of 2-8-32 Simple a b 71.1(74.9) nm; c 61.9 other lattice symmetries, based on other frame geometries: cube, α =β = ◦ γ = ◦ hexagonal (65.2) nm; 90 ; 120 prism, elongated square bipyramid (ESB), and triangular pyramid TBP Various Amorphous - ∗ (TBP). Following the successful construction of the FCC lattice designs for octahedron frames, we explored the assembly of ‘stretched’ For each lattice type and disordered structure, the table shows the corresponding polyhedral DNA frame (schematics shown in Fig. 5), linking motifs and lattice parameters octahedral (ESB) frames with 10 nm NPs (ESB/NP ratio of about from SAXS measurements and from estimates (in round brackets). See main text and 1:2, same linker motifs and annealing protocol as described above). Supplementary Information for further details. ∗The designs for TBP are shown in the Figure 3b2 and Supplementary Fig. 5 show the reconstructed 3D Supplementary Information. model from cryo-EM images, which confirm the correct assembly of the ESB DNA frame and, consequently, the coordination of NPs in octahedra to NPs, we indeed expect an FCC arrangement, as shown the ESB-frame defined cluster (Supplementary Fig. 9). The length of in Fig. 2b. In this arrangement, the in-plane (equatorial) vertices the eight edges above and below the mid-plane is 1.25 times longer (four corners) bind four NPs, while each NP within this layer also than the other four in-plane ones. This simple modification of the binds four octahedra. Thus, a square NP pattern is established in frame shape acts as a stringent test of our ability to manipulate the plane formed by the octahedron equatorial vertices (top view; the lattice structure through rational frame design. Moreover, it see Fig. 2b, central panel). Consequently, these octahedra layers are allows the generation of lower-symmetry unit cells, in which bases connected by the out-of-plane (axial) vertices through another NP are not equal; that is, the lattice parameter c in the cubic Bravais that binds only two octahedra from the lower and higher layers (side lattice will be different from a and b. This type of structure has not view, Fig. 2b, right panel). been reported for DNA–NP systems; moreover, such special low- To verify the formation of an FCC lattice (Fig. 3a1), we symmetry arrangements are quite rare for spherical particles. quantitatively modelled47,48 S(q). Figure 3a2 shows a 3D model of an ESB–NP systems with appropriate motifs (Table 1) exhibit well- individual octahedral frame, reconstructed using cryo-EM (ref. 46). defined scattering peaks in S(q), as shown in Fig. 3b3. The peak It reveals that the edge length is around 29 nm, which agrees with the positions and relative intensities for this ESB–NP framework differ designed parameters of the octahedral frame (28.6 nm for 84 base markedly from the S(q) of the octahedra–NP FCC lattice (Fig. 3a3). pairs edge). The experimental S(q) for system II (Fig. 3a3, blue line) Peak indexing and detailed modelling reveal the structure to be matches well the calculated scattering profile for an FCC lattice a body-centred-tetragonal (BCT) lattice, shown in Fig. 3b4. The (Fig. 3a3, red line, see Supplementary Information for the details modelled S(q) (Fig. 3b3, red line, and see Table 1) is in good of scattering analysis). Importantly, not only do the calculated peak agreement with the experimental data (Fig. 3b3, blue line). Indeed, positions exactly match, but also the heights of the S(q) peaks for this unit cell a = b 6= c (Table 1 and Fig. 5), which is consistent are in excellent agreement between data and model, supporting with our lattice ‘engineering’ expectation. Interestingly, a lattice with the proposed lattice and demonstrating the precise positioning non-equal bases might have implications for distortion of a particle of NPs in the self-assembled lattice. The SAXS-determined FCC DNA shell, as we discuss below. lattice constant is 67.7 nm at room temperature, which is also in We next designed a cubic DNA frame, with edge lengths accordance with the design, 64.6 nm, considering the length of the similar to the octahedron (Fig. 3c1). Intriguingly, most of the octahedron edge and estimated sizes of NPs and DNA shells. individual non-linked cubes are significantly skewed, as revealed by Although the positions of NPs in the lattices can be determined cryo-EM images and representative 2D class projection (Fig. 3c2 from SAXS data, the exact placement of DNA frames cannot be and Supplementary Fig. 5). As this effect is observed only for extracted in these measurements owing to their low electron density cube frames, it might be attributed to the intrinsic flexibility in comparison with gold NPs, which dominates the scattering signal. associated with a cubic truss. Therefore, it is quite remarkable that, Therefore, we performed a stoichiometric study to find the ratio of when assembled with 10 nm NPs, these flexible frames form an frames to NPs in the assembled lattice (see details in Supplementary exceptionally ordered lattice (Fig. 3c3). The SAXS structure√ √ factor Information). We stress that the obtained frame-to-NP ratios for the exhibits nearly 30 peaks at the position of q/q1 =1: 2: 3: 2..., assembled lattices and the SAXS-determined placement of NPs in which is in excellent agreement with the calculated S(q) profile for a tahdt h etcso h uefaesoslwdistortion low shows frame cube the of particles by directions vertices formed all the cluster in NP to edges the attached cubic Indeed, all network. each of to the ‘pull’ linked stabilizes uniform particles eight the and NP, frame; four the single cubic a in binds to of skew linked effect ‘correcting’ NP cubes synergistic of eight certain each a absence is there and the that suggests Interestingly, lattice NPs, frames. neighbouring cubic different two proximity the close of in is edges Moreover,between repulsion frame of pair edge-to-edge a 27). other only minimizes frames: neighbouring with organization Fig. proposed comparison (Supplementary the in higher organizations exhibits stability and satisfies considered mechanical 16 ratio, organization Fig. and frame-to-NP Supplementary Such the symmetric (see illustration). on in 3c4 requirements model Fig. frames the Supplementary enlarged in cubic (see shown an of superlattice as for arrangement the lattice, SC in the the NPs propose order to we extreme frames Information), of the 1:2 towards ratio measured of points the Considering repeats. experimental lattice again many over preserved between curves estimation. designed simulated correspondence the and excellent with agreement the interparticle in the Moreover, with nm, 48.3 3c3) Fig. of in centre line distance the (red on shown lattice are (SC) framework cubic NP–DNA simple structured FCC the of views top and side corresponding The respectively. panel. panels, left right the and on red in shown are structure FCC lines). (black shown is lattice FCC S(q/ factors structure corresponding 2 Figure ssesIt ,fo otmt o)b hnigteDAlnigmtf o epciesses(nprnhss,mtf are motifs parentheses), (in systems respective For motif. linking DNA the changing by top) 9-6-10 to bottom from V, to I (systems (III), h omto faN–N Dltiewt caerlfae n h c fN–etxlne length. linker NP–vertex of eect the and frames octahedral with lattice 3D NP–DNA a of formation The | 6-9-21 I)and (IV) b a 0-15-15 rpsdasmldspratc fNsadothda h atce ihnasnl ntcl mre yrdlns of lines) red by (marked cell unit single a within particles The octahedra. and NPs of superlattice assembled Proposed b, V;seas al n upeetr nomto.Tecnrlpnlsos2 ASdt o ahsse.The system. each for data SAXS 2D shows panel central The Information. Supplementary and 1 Table also see (V);

0 d increase r hw clue ie/ice)o h ih.Teidxn fsatrn ekpstosaditniisfrthe for intensities and positions peak scattering of indexing The right. the on lines/circles) (coloured shown are ) | d | I II III IV V hs eurmns nti atc seSplmnayFg 7for 17 Fig. Supplementary (see satisfied that lattice 3d4) this (Fig. In model the requirements. suggest We these NPs. observed of and lattice NPs SH to an frames of (1:2) (SH) the ratio examined considering estimated We hexagonal arrangement experimentally S(q). simple frame experimental prism a for the possibilities that with different agrees found 3d4) we (Fig. and superlattice, prisms lattice for of the models ratio possible in the the considering NPs examining and framework By assembled line). the S(q) blue recognizable 3d3, the 20 (Fig. about revealed with peaks the above) lattice well-ordered (following described a NPs of procedures formation and annealing frames which and for prism faces, measurements mixing of SAXS structure square factor assembled the complicating three Nevertheless, the the orientations. to 3d1). and frame owing (Fig. triangular of formation prism crystal two a hinder for has might as triangle such prism frames, (equilateral The lower-symmetry approach our equivalent include extended We to cube). faces for squares ESB; all and octahedron with symmetry, greater provide arrangements lattice stability mechanical work non-floppy theoretical recent that that note predicted also We 10). Fig. (Supplementary S(q/q )

h oyerlfae icse bv aerltvl high relatively have above discussed frames polyhedral The 0 12345 49 . q /q 0 h egho h ikr sincreased is linkers the of length The a, 0-6-10 (I), 2-6-10 (II), a3 a2 b2 b3 10 8 8 6 6 S( q ) S( q ) 4 4 10 nm 2 2 10 nm a1 0 0 0.00 0.02 0.04 0.06 0.08 b1 0.00 0.02 0.04 0.06 0.08 q (Å−1) q (Å−1) a4 b4

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c3 c2 d3 d2 1.5 6 30 nm c4 30 nm 4 1.2 d4 S( q ) S( q )

2

0 0.9 0.00 0.02 0.04 0.06 0.08 0.00 0.02 0.04 0.06 q (Å−1) q (Å−1)

Figure 3 | Diversity of NP superlattices assembled through DNA frames. a–d, DNA-coated NPs (10 nm gold core) bound to four dierent types of frame using complementary DNA strands at their respective vertices. The four polyhedral frames are: octahedron (a1), ESB (b1), cube (c1) and prism (d1). For each, we show EM image (2; see the Supplementary Information for the details of 3D reconstruction from cryo-TEM measurements), X-ray scattering structure factor, S(q), extracted from the 2D SAXS pattern (3) and the proposed superlattice structures (4), as discussed in the text. See Supplementary Figs 14–17 for the enlarged views of lattice models and the idealized arrangements of DNA frames. For each lattice structure, the experimental scattering profile is in blue and the model fitting is in red. The black peaks mark the standard peak positions of the proposed lattice: FCC by the octahedra (a3), BCT by ESB (b3), simple cubic by the cubes (c3) and hexagonal by the prisms (d3). an enlarged view), every particle binds three prisms, one on one yield quasi-crystals over a wide range of TBP vertex truncations50. side of the particle hemisphere and two prisms on the other side. Thus, it is quite possible that the observed amorphous organization Thus, a layer of hexagonally arranged NPs is formed owing to the of the NP–TBP system is related to this aspect of TBP geometry. triangular linking geometry of each prism base, and those layers are stacked on top of each other because of the rectangular shape Direct imaging of NP lattices of the lateral faces of the prism. To reduce the repulsion between Next, we complemented the ensemble-averaged representation DNA bundles for the given SH lattice and measured frame/NP ratio, of lattices, as obtained from scattering studies, with a local the prisms’ arrangement in different layers is suggested to follow probing of NP arrangements in the assemblies by applying cryo- A–B–A stacking of prisms (A) and voids (B). For this framework, electron microscopy. The assembled structures were frozen with we found that a=b6=c (a=b=71.1 nm and c =61.9), α =β =90◦, their native solution by plunging the sample into nitrogen- and γ = 120◦. We note that lattices with unequal bases, such as cooled liquid ethane, following by imaging with an annular those built with ESB and prism frames, show a larger deviation dark-field scanning transmission electron microscope (STEM; see from the calculated frame dimensions than those with equal bases, Supplementary Information). In this imaging mode, gold particles such as those built with octahedron and cube frames. This effect appear higher in intensity than the surrounding ice. We show is probably caused by the differences in binding modes between a in Fig. 4 the representative cryo-STEM images for two types of frame and NP. For example, the number and location of particle- STEM-studied lattice, assembled with cubic and BCT frames (see bound frames might depend on the node location within the also Supplementary Figs 23–25). Due to the random orientation framework. Consequently, that can result in some deformation of of crystallites in ice, different lattice projections can be observed. the DNA shells of particles, and the frames themselves. Figure 4a1 illustrates the observed projection of the (111) plane We investigated the assembly of NPs using triangular bipyramid for the simple cubic lattice, which agrees well with the shown (TBP) frames. These systems did not exhibit crystalline superlattices lattice model (top left), and particle arrangements (top right). for any of the investigated linking motifs (see Supplementary Table 2 The nearest-neighbour interparticle distance obtained from STEM for details and Supplementary Fig. 18). The crystallization in this is 40.2 nm, matching well the SAXS result (39.4 nm). The tilted (100) case may be problematic owing to the kinetic trapping and complex projection for this lattice (shown in Fig. 4a2) also demonstrates ground state. Additionally, TBP was computationally predicted to a good agreement between interparticle distances (from untitled ARTICLES

a1 (111) a2 (100) with tilt b1 (111) b2 (100) Tilt

50 nm 50 nm

50 nm 25 nm

Figure 4 | Cryo-STEM images for simple cubic (SC) (a1, a2) and body-centred-tetragonal (BCT) (b1, b2) lattices of NPs assembled with cubic and ESB frames, respectively. a1, STEM image of the (111) plane projection for the SC lattice; the nearest interparticle distance is 40.2 nm. a2, STEM image of the (100) face projection for the SC lattice that is tilted in one direction; the nearest interparticle distance is 50.7 nm. b1, STEM image of the (111) face projection of the BCT lattice; the nearest interparticle distance is 46.5 nm. b2, STEM image of the (100) face projection of the BCT lattice; the nearest interparticle distance is 53.2 nm. The top left and right parts of each panel show the lattice model with the corresponding projection and the particle arrangements, respectively. The corresponding particles from the models and images are highlighted by red circles.

a Octahedron FCC b Cube Simple cubic

cdESB BCT PrismSimple hexagonal e TBP

Figure 5 | Frame shapes (left) and the corresponding unit cells (right) of the experimentally observed lattices. a, Octahedron and FCC unit cell. b, Cube and simple cubic unit cell. c, Elongated square bipyramid (ESB) and BCT unit cell. d, Prism and simple hexagonal unit cell. e, Triangular bipyramid (TBP) was not observed to induce ordered phases of NPs. See main text, Table 1 and Supplementary Information for the details of system designs. direction) obtained from STEM, 50.7 nm, and SAXS, 48.3 nm. For Supplementary Figs 23–25) indicate the lattice integrity within the the BCT lattice assembled with elongated octahedra, two different crystalline domains, with a very low number of vacancies. projections are shown in Fig. 4b1 (111), and Fig. 4b2, (100). The (111) projection indicates that each imaged NP is surrounded by Outlook six neighbours, and four of them are closer than the other two. Our results show that the proposed approach allows organization The STEM-measured nearest-neighbour interparticle distance is of the same particles into different crystallographic lattices, as 46.5 nm, in agreement with the SAXS-determined 47.0 nm. For the illustrated in Fig. 5, where the lattice types are determined by the (100) projection the observed interparticle distance, 53.2 nm, is shapes of the used interparticle connecting frames and the onset of also in close correspondence with the SAXS result, 52.5 nm. Thus, order also depends on the details of the frame–NP linking motifs our direct microscopic observations confirm the structure of the (Table 1). As the binding of frames to particles occurs at vertices, the assembled lattices and interparticle distances, and crystallites sizes geometry of the frames has a profound effect on the lattice type. This determined by the scattering method. Furthermore, the probing is because the assembly is driven by maximization of particle–frame using real-space imaging allows examination for the presence of attachments, and the ideal lattice formation should satisfy all bonds defects and vacancies in the lattice, which is difficult to reveal for vertices, which translates the frame geometry to the particular using scattering methods. The microscopic images (Fig. 4 and lattice type. We note that particles should not be significantly larger than frames. Otherwise the effect of frame geometry will 5. Xiong, H., Sfeir, M. Y. & Gang, O. Assembly, structure and optical response of be diminished. On the other side, topological connections between three-dimensional dynamically tunable multicomponent superlattices. Nano particles and frames should be realized in a way that minimizes Lett. 10, 4456–4462 (2010). the inter-frame repulsion. This can be achieved by separating frame 6. Alder, B. J. & Wainwright, T. E. Phase transition for a hard sphere system. J. Chem. Phys. 27, 1208–1209 (1957). attachment spots on particle surfaces via the choice of particle 7. Zhu, J. X. et al. Crystallization of hard-sphere colloids in microgravity. Nature sizes and/or linking motifs between the vertex and the particle 387, 883–885 (1997). surface. Moreover, as we demonstrated, the systems can also choose 8. Casey, M. T. et al. Driving diffusionless transformations in colloidal crystals the appropriate ratio of frames to minimize the repulsion, but using DNA handshaking. Nature Commun. 3, 1209 (2012). still maintain the lattice. That reflects the balance between lattice- 9. Travesset, A. Binary nanoparticle superlattices of soft-particle systems. Proc. stabilizing factors (NP–frame bonds), inter-frame repulsion and Natl Acad. Sci. USA 112, 9563–9567 (2015). 10. Kranendonk, W. G. T. & Frenkel, D. Simulation of the adhesive-hard-sphere entropic effects. model. Mol. Phys. 64, 403–424 (1988). We summarize in Table 1 the effect of the frame–NP linking 11. Damasceno, P. F., Engel, M. & Glotzer, S. C. Predictive self-assembly of motifs on the lattice formation. The crystallization favours the great- polyhedra into complex structures. Science 337, 453–457 (2012). est number of frame–NP bonds, and entropic gains associated with 12. Leunissen, M. E. et al. Ionic colloidal crystals of oppositely charged particles. arrangements of shaped frames. However, the repulsion between Nature 437, 235–240 (2005). frame edges and steric constraints can impose restrictions on the 13. Shevchenko, E. V., Talapin, D. V., Kotov, N. A., O’Brien, S. & Murray, C. B. Structural diversity in binary nanoparticle superlattices. Nature 439, topology of connections provided by frames, and that can hamper 55–59 (2006). the lattice formation. Indeed, we observed both effects by changing 14. Nykypanchuk, D., Maye, M. M., van der Lelie, D. & Gang, O. DNA-guided the length of the frame–NP binding motif. We first note that for crystallization of colloidal nanoparticles. Nature 451, 549–552 (2008). our systems, each particle can accommodate more than 10 frames, 15. Park, S. Y. et al. DNA-programmable nanoparticle crystallization. Nature 451, based on simple area estimation. However, in reality, a much smaller 553–556 (2008). 16. Auyeung, E. et al. Synthetically programmable nanoparticle superlattices using number of frames are attached to particles in lattices, which is due a hollow three-dimensional spacer approach. Nature Nanotech. 7, 24–28 (2012). to inter-frame repulsion, as discussed above. Furthermore, in this 17. Talapin, D. V. et al. Quasicrystalline order in self-assembled binary case, short frame–NP linking motifs will result in close proximity of nanoparticle superlattices. Nature 461, 964–967 (2009). edges of neighbouring frames (see Supplementary Figs 14–17) and 18. Rechtsman, M. C., Stillinger, F. H. & Torquato, S. Synthetic diamond and that can destabilize the structure. On the other side, the excessive wurtzite structures self-assemble with isotropic pair interactions. Phys. Rev. E flexibility of frame–NP bonds will mask the frame shape; that is, 75, 031403 (2007). 19. Jain, A., Errington, J. R. & Truskett, T. M. Dimensionality and design of the frame geometry cannot be translated effectively to the particle isotropic interactions that stabilize honeycomb, square, simple cubic, and organization, and that leads again to the amorphous state. Besides, diamond lattices. Phys. Rev. X 4, 031049 (2014). our experiments (see Supplementary Figs 21 and 22) confirm that to 20. Tkachenko, A. V. Morphological diversity of DNA-colloidal self-assembly. Phys. maintain the topological connectivity required for a given symmetry Rev. Lett. 89, 148303 (2002). of unit cell, the particle diameter (including DNA shell) should 21. Angioletti-Uberti, S., Varilly, P., Mognetti, B. M. & Frenkel, D. Mobile linkers be smaller than the frame dimensions. To fully develop the ‘engi- on DNA-coated colloids: valency without patches. Phys. Rev. Lett. 113, 128308 (2014). neering’ methodology for the creation of desired lattices, detailed 22. Glotzer, S. C. & Solomon, M. J. Anisotropy of building blocks and their computational and theoretical investigations are required. The assembly into complex structures. Nature Mater. 6, 557–562 (2007). future studies will shed light on the mechanism of lattice formation, 23. Jones, M. R. et al. DNA-nanoparticle superlattices formed from anisotropic on the precise positions of frames in the lattices and they might building blocks. Nature Mater. 9, 913–917 (2010). establish a direct correspondence between the frame geometry and 24. Zhang, Y., Lu, F., Lelie, D. v. d. & Gang, O. Continuous phase transformation in the lattice symmetry. nanocube assemblies. Phys. Rev. Lett. 107, 135701 (2011). 25. Xiong, H. M., van der Lelie, D. & Gang, O. Phase behavior of nanoparticles We stress that engineering of lattices using the presented assembled by DNA linkers. Phys. Rev. Lett. 102, 015504 (2009). approach can be extended beyond the demonstrated examples 26. van Anders, G. et al. Entropically patchy particles: engineering valence through of using vertices of polyhedral frames to connect particles into shape entropy. ACS Nano 8, 931–940 (2014). frameworks. For example, we suggest several elaborations of our 27. Macfarlane, R. J. et al. Nanoparticle superlattice engineering with DNA. Science approach: the frame can be encoded to accommodate particles 334, 204–208 (2011). not only at vertices, but also at arbitrary positions within the 28. Paik, T. & Murray, C. B. Shape-directed binary assembly of anisotropic nanoplates: a nanocrystal puzzle with shape-complementary building blocks. frame; more than one type of particle can be incorporated, using Nano Lett. 13, 2952–2956 (2013). corresponding DNA encoding of particles and their anchoring 29. Romano, F., Sanz, E. & Sciortino, F. Phase diagram of a tetrahedral patchy points on a frame; and the combination different frame shapes will particle model for different interaction ranges. J. Chem. Phys. 132, permit the creation of more complicated designed unit cells. 184501 (2010). 30. Russo, J., Tartaglia, P. & Sciortino, F. Association of limited valence patchy particles in two dimensions. Soft Matter 6, 4229–4236 (2010). Methods 31. Chen, Q., Bae, S. C. & Granick, S. Directed self-assembly of a colloidal kagome Methods and any associated references are available in the online lattice. Nature 469, 381–384 (2012). version of the paper. 32. Wang, Y. et al. Colloids with valence and specific directional bonding. Nature 491, 51–56 (2012). Received 11 September 2015; accepted 18 January 2016; 33. Lu, F., Yager, K. G., Zhang, Y., Xin, H. & Gang, O. Superlattices assembled published online 22 February 2016 through shape-induced directional binding. Nature Commun. 6, 6912 (2015). 34. O’Brien, M. N., Jones, M. R., Lee, B. & Mirkin, C. A. Anisotropic nanoparticle complementarity in DNA-mediated co-crystallization. Nature Mater. 14, References 833–839 (2015). 1. Talapin, D. V., Lee, J.-S., Kovalenko, M. V. & Shevchenko, E. V. Prospects of 35. Edwardson, T. G. W., Carneiro, K. M. M., McLaughlin, C. K., Serpell, C. J. & colloidal nanocrystals for electronic and optoelectronic applications. Chem. Sleiman, H. F. Site-specific positioning of dendritic alkyl chains on DNA cages Rev. 110, 389–458 (2010). enables their geometry-dependent self-assembly. Nature Chem. 5, 2. Hu, T. et al. Self-organization of plasmonic and excitonic nanoparticles into 868–875 (2013). resonant chiral supraparticle assemblies. Nano Lett. 14, 6799–6810 (2014). 36. Suzuki, K., Hosokawa, K. & Maeda, M. Controlling the number and positions 3. Cargnello, M. et al. Substitutional doping in nanocrystal superlattices. Nature of oligonucleotides on gold nanoparticle surfaces. J. Am. Chem. Soc. 131, 524, 450–453 (2015). 7518–7519 (2009). 4. Kuzyk, A. et al. DNA-based self-assembly of chiral plasmonic nanostructures 37. Ye, X. et al. Shape alloys of nanorods and nanospheres from self-assembly. with tailored optical response. Nature 483, 311–314 (2012). Nano Lett. 13, 4980–4988 (2013). 38. Zheng, J. P. et al. From molecular to macroscopic via the rational design of a 50. Haji-Akbari, A., Chen, E. R., Engel, M. & Glotzer, S. C. Packing and self-assembled 3D DNA crystal. Nature 461, 74–77 (2009). self-assembly of truncated triangular bipyramids. Phys. Rev. B 88, 39. Rogers, W. B. & Manoharan, V. N. Programming colloidal phase transitions 012127 (2013). with DNA strand displacement. Science 347, 639–642 (2015). 40. Rothemund, P. W. K. Folding DNA to create nanoscale shapes and patterns. Nature 440, 297–302 (2006). Acknowledgements We thank W. Shih and Y. Ke for help with DNA octahedra design and useful discussions. 41. Douglas, S. M. et al. Self-assembly of DNA into nanoscale three-dimensional We thank L. Bai for help with the cryo-STEM sample preparations. We thank D. Chen for shapes. Nature 459, 414–418 (2009). assistance with schematic drawing. Research carried out at the Center for Functional 42. Zhao, Z., Jacovetty, E. L., Liu, Y. & Yan, H. Encapsulation of gold nanoparticles Nanomaterials, Brookhaven National Laboratory was supported by the US Department in a DNA origami cage. Angew. Chem. Int. Ed. 50, 2041–2044 (2011). of Energy, Office of Basic Energy Sciences, under Contract No. DE-SC0012704. H.L. and 43. Schreiber, R. et al. Hierarchical assembly of metal nanoparticles, quantum dots T.W. were supported by a National Institute of Health R01 grant (AG029979). and organic dyes using DNA origami scaffolds. Nature Nanotech. 9, 74–78 (2014). 44. Seeman, N. C. Nucleic-acid junctions and lattices. J. Theor. Biol. 99, Author contributions Y.T. and O.G. conceived and designed the experiments. Y.T. performed the experiments. 237–247 (1982). Y.Z. contributed to the model fitting of the SAXS data. Y.T., T.W. and H.L. contributed to 45. Douglas, S. M. et al. Rapid prototyping of 3D DNA-origami shapes with the cryo-EM imaging and reconstruction. Y.T. and H.L.X. contributed to the STEM caDNAno. Nucleic Acids Res. 37, 5001–5006 (2009). imaging of the superlattice. Y.T., Y.Z. and O.G. analysed the data. Y.T. and O.G. wrote the 46. Tian, Y. et al. Prescribed nanoparticle cluster architectures and paper. O.G. supervised the project. All authors discussed the results and commented on low-dimensional arrays built using octahedral DNA origami frames. Nature the manuscript. Nanotech. 10, 637–644 (2015). 47. Yager, K. G., Zhang, Y. G., Lu, F. & Gang, O. Periodic lattices of arbitrary nano-objects: modeling and applications for self-assembled systems. J. Appl. Additional information Crystallogr. 47, 118–129 (2014). Supplementary information is available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints. 48. Zhang, Y. G. et al. Selective transformations between nanoparticle superlattices Correspondence and requests for materials should be addressed to O.G. via the reprogramming of DNA-mediated interactions. Nature Mater. 14, 840–847 (2015). 49. Mao, X., Souslov, A., Mendoza, C. I. & Lubensky, T. C. Mechanical instability at Competing financial interests finite temperature. Nature Commun. 6, 5968 (2015). The authors declare no competing financial interests. Methods then slowly cooled down from 50 ◦C to room temperature at a rate of 0.3 ◦C h−1. Design of polyhedral DNA origami frames. DNA origami polyhedral frames were Buffer conditions in the frameworks are the same as the conditions when folding designed using caDNAno software (http://cadnano.org). Each edge of the frames is the origami structures: 1×TAE, 12.5 mM Mg2+. Black–reddish aggregates were composed of a six-helix bundle (6HB). For octahedral and cubic frames, the length found at the bottom of the tubes, and the above solution was clear. Then the of each 6HB is 28.6 nm (84 base pairs); for prism and triangular bipyramid (TBP) aggregates were transferred to a quartz capillary with the same buffer. These frames, the length of the 6HB is 42.8 nm (126 base pairs); for elongated square aggregates were investigated by in situ SAXS to identify the internal structure, bipyramid (ESB) frames, the length for four edges in the mid-plane is 28.6 nm and lattice type and degree of order for all studied frame shapes and DNA the other eight edges have a length of 35.7 nm (105 base pairs). One single-stranded linking motifs. DNA chain (sticky end) at each end of the 6HB is designed to be complementary to the DNA attached to the gold NP. For octahedron and ESB frames, there are four Electron microscopy. The carbon-coated grids were glow-discharged in a sticky ends at each vertex; for cube and prism frames, there are three sticky ends at 0.39 mbar air atmosphere for 1 min by using PELCO easiGlow (Ted Pella). each vertex; while for TBP frames, there are four sticky ends at vertices of the Cryo-EM grids were prepared in an FEI Vitrobot IV at 20 ◦C with the relative mid-triangle plane and three sticky ends at the two vertices above and below humidity set to 90% and force set to 0. A 3.5 µl volume of the DNA specimen was the mid-plane. pipetted onto a freshly glow-discharged lacey carbon grid covered with an additional thin layer of continuous carbon film. The sample solution was incubated Folding of DNA origami. DNA origami frames were prepared by mixing 10 nm on an EM grid for 3 min, and blotted for 5 s before being plunged into liquid ethane scaffold DNA (M13mp18, Bayou Biolabs, LLC) and 100 nM of each staple that was pre-cooled by liquid nitrogen. The cryo-EM grids were then transferred to oligonucleotide in buffer solution that contains 1 mM EDTA, 12.5 mM MgCl2 and and stored in liquid nitrogen. The cryo-EM grids were transferred in liquid 5 mM Tris (pH = 7.9 at 20 ◦C). Then the mixture was rapidly heated from room nitrogen into a Gatan 626 cryo-specimen holder and then inserted into the temperature to 90 ◦C, maintained for 10 min, and then cooled from 80 to 60 ◦C at a microscope. The specimen temperature was maintained below −170 ◦C during rate of 1 ◦C min−1, and then 60 to 20 ◦C at a rate of 1 ◦C h−1 to fold the target data collection. Cryo-EM imaging was performed in a JEOL JEM-2010F TEM frames. Samples were then electrophoresed on 1% agarose gels (1×TBE, 10 mM operating at 200 kV. Cryo-EM images were recorded in the low-dose mode −1 − −2 MgCl2, 0.5 µg ml cyber gold) at 60 V for 2–3 h at room temperature, as shown in (15 e Å ) at ×30,000 or ×40,000 microscope magnification on a Supplementary Fig. 1. Gatan UltraScan 4000 CCD (charge-coupled device) camera (4,096×4,096 pixel), corresponding to 3.52 or 2.64 Å pixel−1 sampling at the specimen level. Preparation of DNA-capped gold NPs. Gold NPs (10 nm, 20 nm, 30 nm) functionalized with citric acid were purchased from Ted Pella. NPs were modified Dynamic light scattering. We conducted the dynamic light scattering with alkanethiol oligonucleotides by adding oligonucleotides to the aqueous NP measurements using a Malvern Zetasizer ZS instrument at the backscattering solution at the mole ratio of 300:1 (DNA/NP, 1,000:1 for 20 nm NPs and 2,000:1 for geometry (173◦). It was equipped with a laser source (633 nm) and a backscattering 30 nm NPs) between DNA and NPs. After mixing for 2 h, the solution was buffered detector. For measuring the melting temperatures of each NP/frame assembly, we at pH 7.4 (10 mM phosphate buffer). Salt (NaCl) was added gradually to the cooled the samples (1×TAE buffer with 12.5 mM Mg2+) slowly in the chamber of mixture until reaching the final concentration of 0.3 M. Twelve hours later, the machine from 50 ◦C to room temperature. The dependence of measured excessive reagents were removed by centrifugation for 60 min at 15,700 r.c.f. and aggregate size versus temperature was obtained. washed four times with 0.1 M PBS buffer (0.1 M NaCl, 10 mM phosphate). Cryo-scanning transmission electron microscopy (STEM). Sample vitrification Preparation of DNA frame/NP nanoclusters. To fabricate nanoclusters, 10 nm was carried out in an FEI Vitrobot plunge-freezing device set to an operating (or 20 nm, or 30 nm) gold NPs functionalized with the corresponding DNA temperature of 10 ◦C with 90% relative humidity and 0 force for the blotting pad. sequences were added into the solution of DNA frames discussed above. The final Three microlitres of the sample was applied to the freshly glow-discharged EM grid ratio between the concentration of the NPs and frames depends on the number of (company&size); after 180 s, the grid was blotted for 0.5 s and plunged into the vertices of each frame; we used for assembly a ratio (Ncorner ×2.5):1, where Ncorner is liquid-nitrogen-cooled liquid ethane to prepare the cryo-sample. It was the number of vertices in the frame. The mixed solution was then annealed from subsequently cryo-transferred to a cryogenic holder cooled down to 50 ◦C to room temperature at a rate of 3 ◦C h−1, incubated overnight and liquid-nitrogen temperature. The sample was then imaged in a field-emission concentrated by a 100K column (Millipore Cooperation). The obtained samples transmission electron microscope (JEOL 2100F) operated at 200 keV in annular with red colour were then electrophoresed on 1% agarose gels (1×TBE, 10 mM dark-field scanning transmission electron microscopy mode (ADF-STEM). −1 MgCl2, 0.5 µg ml cyber gold) at 60 V for 3 h, as shown in Supplementary Fig. 12. In this imaging mode, the spatial resolution is not reduced by the inelastic The target bands on the gel were cut, purified by a cellulose acetate spin column scattering events that have occurred in the sample. In contrast, these (Bio-rad Cooperation) and ready for use. inelastically scattered electrons would render significant resolution loss due to the chromatic aberration of the conventional TEM imaging mode. Therefore, Preparation of NP–DNA frameworks. For the preparation of the NP–DNA ADF-STEM is superior to conventional TEM when imaging through frameworks, the DNA frames of corresponding shapes and NPs were mixed, and micrometre-thick ices.