Modular Self-assembly of Molecular Shapes
Bryan Wei Mingjie Dai Peng Yin January 30, 2012

A key challenge for molecular self-assembly is to develop a general method by which small monomer units mediated via local interactions can be programmed to self-organize into a prescribed global shape. Self-assembly of informational polymers such as nucleic acids provides an effective approach to synthesizing shapecontrolled structures.1–23 In “DNA origami,” a 7-kilobase DNA scaffold (M13 bacteriophage genome in common practice) was folded by hundreds of synthetic auxiliary strands into a desired shape.9,12–14,16,18,19,23 Modular self-assembly with DNA2–5,8,10,11,21 or RNA tiles7,20 also produced finite shapes,7,8,10 but with limited complexity (containing up to 16 distinct tiles7,8). Building on the robustness of folding and the modularity of tiling, we demonstrate here modular self-assembly of complex shapes using short synthetic DNA strands called single-stranded tiles.11 Each strand has 42 bases and is designed to bind to four designated neighbours. In one-pot annealing reactions, pools of unpurified strands self-assembled into two-dimensional structures with prescribed shapes, each containing hundreds of distinct tiles (some more than 1000). An assembled rectangle structure is analogous to a “bitmapped molecular canvas,” where each constituent strand folds into a 3 nm by 7 nm “molecular pixel.” Designing a shape amounts to choosing pixels on the canvas: a desired shape can be programmed simply by annealing a mixture including strands that map to “on” pixels and excluding those that map to “off” pixels. Through repipetting various subsets of a master strand collection that corresponds to a 310-pixel canvas, we constructed 107 distinct shapes, including those resembling polygons, emoticons, astrological symbols, Chinese characters, 10 Arabic numerals, and 26 English letters. Our work provides a simple, modular, robust and scalable framework for constructing nano-structures with prescribed shapes from de novo-designed, short synthetic DNA strands. More generally, it illustrates how modular molecular components can be programmed to self-assemble into complex shapes.
A canonical 42-base single-stranded tile (SST) motif11 consists of four domains (Fig. 1a), where domains 1 and 2 together measure 21 nucleotides (nt), and domains 3 and 4 together measure 21 nt. By designing the intermolecular binding interactions between these domains, a collection of distinct SST tiles can be arranged into a “brickwall” pattern, forming a DNA lattice composed of parallel helices connected by single-stranded linkages (Fig. 1b, left). The linkages between two adjacent helices are spaced at every two helical turns (i.e. 21 base pairs) and are all located in the same tangent plane between the two helices. In the diagram, a linkage point is artificially stretched for visual clarity – in physical reality, the linkage is expected to be the phosphate that connects domains 2 and 3 of an SST. The structure is also depicted with a different color scheme (Fig. 1b, middle) to differentiate distinct strand species (rather than domains within the same strand), and as a simplified “brick-wall” pattern (Fig. 1b, right).
The rectangular lattice in Fig. 1b contains 6 parallel helices, each measuring about 8 helical turns, and hence is termed a 6 helix × 8 helical turn rectangle and denoted as 6H×8T. Following the same strategy, a rectangle with different dimensions can be readily designed. Furthermore, an arbitrary shape can be designed by approximating it with an SST brick-wall pattern (see Fig. 1c for examples). Additionally, by concatenating two half-tiles on its top and bottom boundaries into one

full tile, the rectangle in Fig. 1b can be transformed into a tube with prescribed circumference11 and prescribed length (Fig. 1d).
A pre-designed rectangular SST lattice (Fig. 1e, top right) can be viewed as a “molecular canvas,” where each SST serves as a 3 nm × 7 nm “molecular pixel.” Designing a shape amounts to selecting its constituent pixels on the canvas. Two examples are shown: an eagle head and a triangle (Fig. 1e, bottom). These shapes, and more than 100 others, were designed and experimentally constructed here, demonstrating the self-assembly of complex molecular shapes from modular components (Supplementary Fig. S1).
Following the design in Fig. 1b, we assembled a 24H×28T rectangle. A simplified and a detailed schematic can be found in Fig. 2a and in Supplementary Fig. S2. Additionally, Supplementary Information S6 contains strand diagrams for this and all the other SST rectangles and tubes, and Supplementary Information S7 and S8 contain sequences for all the structures constructed in this paper. The rectangle contains 362 distinct SST species (310 internal standard full SST, 24 full SST on vertical boundaries, and 28 half-length SST on horizontal boundaries). It has 14,616 nucleotides and a molecular weight comparable to a typical DNA origami structure with an M13 phage scaffold.9 DNA sequences were designed to minimize sequence symmetry24 (see Methods for details). Unpurified DNA strands were mixed without careful adjustment of the stoichiometry. After one-pot annealing from 90 ◦C to 25 ◦C over 17 hours in 25 mM Mg2+ buffer (see Supplementary Information S2.3 for the effect of buffer ion strength and annealing time on the assembly yield), the solution was subjected to 2% native agarose gel electrophoresis. A single dominant band (Fig. 2b, Lane U) was observed. This band was extracted from the gel and purified via centrifugation. The purified product again produced a single band on an agarose gel (Fig. 2b, Lane P). Imaging of the purified product via atomic force microscopy (AFM) revealed expected rectangular morphology (Fig. 2c), with approximately expected dimensions (64 ± 2 nm × 103 ± 2 nm, N = 30). The formation of the full rectangle was further verified by the successful attachment of streptavidin at selected internal and boundary positions that display biotin modified strands (Supplementary Information S2.4).
The assembly yield was first estimated by native gel electrophoresis, in which the samples were stained with SYBR safe. The yield (referred to as “gel yield”) was calculated as the ratio between the fluorescent intensity of the desired product band and that of the entire lane (after background correction). A ratio of 17% was observed (Fig. 2b). However, due to the apparent structure and sequence-dependent variation in the staining efficiency of SYBR safe (Supplementary Fig. S3), this 17% ratio is likely a bounded (<50%) overestimate of the actual yield (see Supplementary Information S2.2.1 for detailed discussion). Thus, the actual yield is likely 12-17%. In the remainder of the paper, the unadjusted yield measurement is reported but should be considered as an approximate (within 50% accuracy) estimate.
It is instructive to compare the above yield to that of a DNA origami rectangle of similar size. When a large excess of staple strands (5×10× in common practice, and sometimes9 100×) are used, the incorporation ratio of the scaffold strand in the assembled origami rectangle is observed to be greater than 90% (see ref9 for AFM-based single molecule measurement; see Supplementary Fig. S5 for gel-based bulk measurement). However, if the yield is measured as the mass ratio between the assembled product and the starting materials (scaffold plus

a Single-stranded b Design of a rectangular shape

tile motif

Strand diagram

L1.1 L1.2 L1.3 L1.4

L1.1 L1.2 L1.3 L1.4

e Design of arbitrary shapes from a “molecular-canvas”

“Brick-wall” diagram

“Molecular canvas”

Domain 4 Domain 3 U2.1 U2.2 U2.3 U2.4 U2.5

U2.1 U2.2 U2.3 U2.4 U2.5

U3.1 U3.2 U3.3 U3.4

U3.1 U3.2 U3.3 U3.4

Domain 1

Domain 2

≡U4.1 U4.2 U4.3 U4.4 U4.5 U5.1 U5.2 U5.3 U5.4

U4.1 U4.2 U4.3 U4.4 U4.5 U5.1 U5.2 U5.3 U5.4

≡

U6.1 U6.2 U6.3 U6.4 U6.5

U6.1 U6.2 U6.3 U6.4 U6.5

L6.1 L6.2
c Design of an arbitrary shape

L6.3 L6.4

L6.1 L6.2 L6.3 L6.4
d Design of a tube

Eagle head

Triangle

Figure 1. Self-assembly of programmable molecular shapes using single-stranded tiles. (a) The canonical SST motif, adapted from ref.11 (b) Design of an SST rectangle structure. Left and middle, two different views of the same secondary structure diagram. Each standard (full) tile has 42 bases (labeled with U), and each top and bottom boundary (half) tile has 21 bases (labeled with L). Right, a simplified “brick wall” diagram depiction. A standard full tile is depicted as a thick rectangle, a boundary half tile as a thin rectangle, and the unstructured single-stranded portion of the boundary tiles are depicted as rounded corners. Each strand has a unique sequence. Colors distinguish domains in the left panel, and distinguish strands in the middle and right panels. (c) Selecting an appropriate subset of SST species from the common pool in b gives the design of a desired target shape, e.g. a triangle (left) or a rectangle ring (right). (d) Design of a tube with prescribed width and length. (e) Design of arbitrary shapes by selecting an appropriate set of monomers from a pre-synthesized pool that corresponds to a “molecular canvas” (top right). To make a shape, the SST strands corresponding to its constituent pixels (dark blue) will be included in the strand mixture, and the light blue ones will be excluded.

staples in the case of origami), the SST rectangle and a typical origami rectangle give roughly comparable yields.
For the purified structure, we measured the fraction of the “wellformed” shapes as a percentage of all identifiable shapes in an AFM field. The SST rectangle is considered to be “well-formed” if it has no defects in its expected outline greater than 15 nm in diameter (a criterion adapted from ref9) and no defects in its interior greater than 10 nm in diameter. Following the above criteria, we obtained a “wellformation” ratio, or an “AFM yield,” of 55% (N = 163, see Supplementary Fig. S6 for details). This number, however, is likely an underestimate for the actual ratio of the “well-formed” structures within the purified product, reflecting the relative fragility of the SST rectangle and the significant post-purification damage that likely occurred during sample deposition or imaging (see Supplementary Information S2.2.2 for detailed discussion). Such fragility may be mitigated by introducing more covalent bonds into the assembled structures, e.g. via ligation25 of two ends of an SST or crosslinking26 of neighboring SSTs.
We next tested the design (Fig. 1d) to form a DNA barrel. By concatenating its top and bottom boundary (half-length) SST strands, we expected to transform the 24H×28T rectangle into a 24H×28T barrel (Fig. 2d). Following similar experimental procedures as described above, one-pot annealing of unpurified DNA strands produced the expected barrel product: native gel electrophoresis produced a dominant product band (Fig. 2e, gel yield, 14%). Furthermore, direct imaging of the purified product using transmission electronic microscope (TEM) revealed expected barrel-like morphology (Fig. 2f) with approximately expected dimensions (98±2 nm in length, 24±1 nm in diameter; TEM yield, 82%, N = 89). Here the TEM yield was defined as the percentage of identifiable tubes that measure within 5 nm deviation from the expected full barrel length of 98 nm = 28 × 3.5 nm, based on a 3.5 nm (see below) per helical turn estimation.
The modular nature of SST assembly permits straightforward generalization of the above rectangle and tube designs to construct structures with prescribed dimensions and molecular weights across scales. We experimentally constructed 7 rectangles (Fig. 2g) and 5 tubes (Fig. 2i). AFM imaging of the SST rectangles (Fig. 2g) and TEM imaging of the SST tubes (Fig. 2i) revealed expected molecular morphology and dimensions. In addition to length measurements, the formation of full-length 8H×84T tubes and full-length 12H×177T tubes were also confirmed by streptavidin labeling of the tube ends (Supplementary Information S3.4.4). See Supplementary Information S3 for the details of the rectangle and tube designs, gel results, AFM and

TEM images, gel and imaging yields and analyses, and length and width measurements; see the caption to Fig. 2g-i for a summary.
The measured lengths and widths of these structures were plotted against the designed number of constituent helices and against the number of designed helical turns within a helix in each structure. A linear relationship (R2 > 0.99 for both cases) was observed, revealing an average helix width of 2.6 nm and an average helical turn length of 3.5 nm (Supplementary Information S3.5). Direct measurement of the helical width from a high resolution AFM image of a triangle shape (construction details to be described later) gave a consistent measurement for the helical width (Supplementary Fig. S38).
It is worth noting that the 12H×177T tube had 44,856 nucleotides, roughly 3 times more than a typical DNA origami structure. Furthermore, it contained greater than 1000 distinct molecular components, roughly 4 times more than previous one-pot annealing based structures with prescribed finite shapes. Compared with previous finite shape structures assembled from modular components,7,8 this tube contained over 60 times more distinct tile species.
We next sought to construct arbitrary shapes following the “molecular canvas” design (Fig. 1e). The 24H×28T rectangle was used as the “canvas.” It had 310 internal SSTs, which correspond to 310 “molecular pixels” (Fig. 1e, top right). We first attempted to assemble a triangle (Fig. 1e, bottom right) by annealing the SST species that correspond to its pixels. However, severe aggregation was observed on the agarose gel and no clear product band could be detected (data not shown). The aggregation was attributed to the non-specific interactions between exposed single-stranded regions of the SST on the hypotenuse boundary of the triangles. Two designs were tested to prevent such aggregations (see Supplementary Information S4.1 for details). In the first design, we replaced each exposed domain in a boundary SST strand by a poly-T segment of the same length. In the second design, each exposed domain was covered by an “edge protector” that binds to it. Each “edge protector” consisted of a segment complementary to the exposed domain, followed by a 10 or 11 nt poly-T segment. Both designs eliminated the aggregation and produced the desired triangles with comparable gel yields (20% and 16%) and AFM yields (35% and 37%). See Supplementary Information S4.2 for details.
In principle, both designs can be used to construct a pre-synthesized common pool of SST strands and auxiliary strands that represent the full molecular canvas. By selecting appropriate tile strands and the auxiliary strands that correspond to its boundary, an arbitrary prescribed shape can be constructed from this pool – no new sequence

a bUPc
Unpurified strands One-pot annealing
d eUP f

g R1 R2 R3 R4 R5 R6 R7

h* 1 2 4 8 16 32 64 128 256 512 ×100 nt

T5

i T1

T2

T3

T4

Figure 2. Self-assembly of SST rectangles and tubes. (a to c), 24H×28T (24 parallel helices × 28 helical turns) SST rectangle. a, Schematic. b, 2% native agarose gel electrophoresis. U, unpurified; P, purified (by gel extraction from Lane U). c, AFM image. Inset shows magnified view of the structure indicated with the dashed box. See Supplementary Fig. S2 for a larger AFM image. (d to f), 24H×28T SST tube. d, Schematic. e, 2% native agarose gel electrophoresis. U, unpurified; P, purified. f, TEM image. Inset shows magnified view of the structure indicated with dashed box. See Supplementary Information S2.5 for a larger image. (g to i), Rectangles and tubes across scales. g, AFM images of SST rectangles. The designed dimensions are (R1, 4H×4T), (R2, 6H×7T), (R3, 10H×10T), (R4, 12H×14T), (R5, 18H×20T), (R6, 24H×28T) and (R7, 36H×41T). Scale bars, 100 nm. h, Logarithmic molecular weight axis. Pink star indicates the weight of a typical M13 DNA origami9 as a reference point. i, TEM images of SST tubes. The designed dimensions are (T1, 8H×28T), (T2, 8H×55T), (T3, 8H×84T), (T4, 24H×28T), and (T5, 12H×117T). Scale bars, 100 nm. See Supplementary Information S3.1 for the schematics of the rectangles and tubes, and for a depiction of the molecular weights of all the 118 distinct structures constructed in this paper. See Supplementary Information S3.2 for the number of constituent distinct SST species (ranging from 12 to 1,068), the number of nucleotides (420 to 44,856), the measured widths (11 to 91 nm) and lengths (16 to 621 nm), the measured gel yield (0.4% to 32%), and the measured AFM yield (25% to 61%) of the 12 rectangles and tubes. See Supplementary Information S3.3 (rectangles) and S3.4 (tubes) for gel results, larger AFM and TEM images, and gel and imaging based yield analysis.

design or strand synthesis is needed. In our experimental implementation, we chose the second design as it involves a smaller (4× instead of 15×) number of auxiliary species than the first design (Supplementary Fig. S43), and synthesized 1,344 edge protectors (each 21 nt) to supplement the existing 362 SST strands (see Supplementary Information S4.2 for details). By selecting from this common “molecular canvas” strand pool, three more shapes (chevron, heart, rectangular ring) were successfully constructed (Fig. 3a).
To thoroughly interrogate the generality and robustness of this molecular canvas method, we proceeded to design and construct a large set of diverse shapes (see Supplementary Information S4.3 for details). Together with the shapes described above, we designed 110 distinct and geometrically representative shapes. On the first assembly trial, 103 designs produced discernible product bands on the gel and expected target shapes under AFM, giving a 94% success rate. The 7 failed designs were shapes resembling 0, 3, ∼, @, a hollow H, and two Chinese characters (Supplementary Fig. S57). The first 4 of these (0, 3, ∼, @) were slightly redesigned (primarily by eliminating putative weak points, e.g. narrow connections) and were subsequently produced successfully. No redesign was attempted for the remaining three failed shapes due to their apparent geometrical complexity. With both trials combined, 114 designs were tested and 107 succeeded (94% success rate). See Supplementary Information S4.3 and S4.6 for schematics and AFM images and S4.5 for gel yields (6%∼40%). Fig. 3c gives AFM images for 100 distinct shapes, including 26 capital letters for the full English alphabet, 10 Arabic numerals, 23 punctuation marks and other standard key board symbols, 10 emoticons, 9 astrological symbols, 6 Chinese characters, and various miscellaneous symbols.
Fig. 3c shows the AFM image of “alphabet soup” of 26 English letters, which were assembled and purified separately and then mixed together for efficient imaging. Note that although the letters shared the same set of core SST strands, they co-existed stably without merging with or deforming each other. Also note that most of the designed shapes observed under AFM had the desired orientation (facing up towards the viewer, 96%, N = 49, details in Supplementary Information S4.8). This biased orientation likely reflects the asymmetric landing of the structures on the mica surface before AFM imaging. Such an asymmetric landing may be attributed to the putative curvature in SST structures.11 In principle, this curvature may be eliminated by using a

corrugated design.4,17
In his 1959 talk, “There is plenty of room at the bottom,” Richard Feymann posed the challenge of writing the Encyclopædia Britannica on the head of a pin. The above “DNA nano-letters” have suitable dimensions for this task. The remaining challenge is to arrange them into words, sentences, paragraphs, and perhaps eventually a book.
The molecular canvas approach makes the traditionally timeconsuming tasks of structure design, sequence selection, and strand synthesis no longer rate-limiting. With the pre-designed and synthesized molecular canvas SST strands, strand picking and mixing now becomes the new bottleneck to fast construction of diverse shapes. A computer program was written to automate this process (Fig. 3d). It provides the user with a graphical interface to draw (or load the picture of) a target shape, and then outputs instructions for a robotic liquid handler to pick and mix the suitable strands for subsequent annealing. Each robot batch produces 48 shapes in roughly 48 hours, effectively reducing several man-hours of labour to 1 machine-hour per shape, and avoids potential human mistakes. The robot was used to construct 44 of the shapes described above.
Unlike DNA origami, which is typically a hybrid structure composed of half biological components (the M13 scaffold) and half synthetic components (staple strands) with sequences derived from the biological parts, the SST structures are composed entirely of de novo designed and synthesized short DNA strands. This synthetic nature allows more freedom in sequence design and material choice, as demonstrated by the following two experiments. First, the 24H×28T rectangle was designed by populating the SST motifs with completely random sequences (i.e. no sequence symmetry requirement was imposed during the sequence design; see Methods for details), which successfully produced the target structure (gel yield,14%; AFM yield, 33%, N = 119; see Supplementary Information S5.1 for details). Second, a 4H×4T rectangle was synthesized using L-DNA (see Supplementary Information S5.2 for details). L-DNA is the mirror-image of D-DNA, which is commonly found in nature and used for DNA nanostructure construction. Unlike D-DNA, L-DNA-based nano-structures27 are resistant to degradation by DNA nucleases. The successful formation of the L-DNA SST rectangle was verified by gel electrophoresis and by AFM (Supplementary Fig. S87). After incubation with DNaseI or T5 exonuclease for 2 hours, no significant degradation was observed

ab

c
…

(1) Annealed and purified as separate letters (2) Mixed and
imaged as “alphabet soup”

d
(1) Design on molecular canvas

(2) Robot instruction set
5 µL → {A01 A03 A07} 5 µL → {C05 C07 D05} 5 µL → {G03 H01 H05} 5 µL → {A01 A07 B01} 5 µL → {D05 E01 E09} 5 µL → {H07 H11} 5 µL → {A01 A03 A05} 5 µL → {B09 B11 C05} 5 µL → {E01 E09 E11} 5 µL → {H05 H07 H11}

(3) Robot pipetting (4) One-pot annealing

(5) AFM imaging

Figure 3. Complex shapes designed using a “molecular canvas.” a, “Molecular canvas” design. Top, schematic. Bottom, 500 nm × 500 nm AFM images. The structures were constructed using the edge protector strategy, with respective gel yields of 16%, 19%, 22%, and 16% (details in Supplementary Information S4.5), and AFM yields of 37%, 37%, 51% and 36% (details in Supplementary Information S4.7). b, 100 distinct shapes. Image size, 150 nm × 150 nm. c, AFM image of “alphabet soup” that contains all 26 English letters. Each distinct letter was assembled and purified separately and then mixed together to produce the “soup.” Scale bar, 500 nm. d, Automated shape design and construction. See Supplementary Information S4.4 for details.

for the L-DNA rectangles, whereas D-DNA rectangles with identical sequences were degraded (Supplementary Fig. S87b).
Our SST experiments are inspired by the robustness of DNA origami folding.9,12–14,16,23 Like the origami work, our experiments use unpurified strands without careful adjustment of their stoichiometry, and the assembly works with sequences that are not optimally designed (e.g. completely random sequences as described above). Our design, however, differs by avoiding a central scaffold strand, and using only short SST strands. The use of a scaffold with half the weight of the assembled structure is commonly considered a central design feature that enables DNA origami’s robust success:9,23 it restricts the designed binding interactions only to those between the scaffold and a staple strand, and eliminates the need to manage binding interactions (and hence stoichiometry) among numerous staple strands. The robust self-assembly of complex SST shapes is thus surprising, and calls for systematic investigation of the kinetic mechanism that underlies its success; it is conceivable that sparse and slow nucleation followed by fast growth may enable successful, complete assembly.
Our SST design builds on the rich history of DNA/RNA tiling2–5,7,8,10,20 and inherits its characteristic programmable modularity. In the SST approach, however, a monomer unit, or the “tile,” is a floppy single-strand composed entirely of concatenated sticky ends.11 It has no well-defined structure as a stand-alone monomer and only folds into a tile-like shape due to its interaction with neighboring SSTs during the assembly. In contrast, in previous work,2–5,7,8,10,20 a tile

monomer is a compact, well-folded, multi-stranded structure that contains a well-defined, structurally rigid (or semi-rigid10) body and several sticky ends. Previous work, when using purified, stoichiometrically controlled strands, produced finite shapes of limited complexity (with up to 16 distinct tiles7,8). On the other hand, the SST approach, when using un-purified strands without careful adjustment of stoichiometry, produced prescribed shapes of significantly higher complexity (with up to 1000 distinct tiles). The structural reconfiguration or the assembly-induced folding of SST may help raise the assembly nucleation barrier through increased configurational entropy penalty,11 producing sufficient rate separation between nucleation and growth to achieve robust and complete assembly. Additionally, the structural flexibility of SST may further help correct assembly errors dynamically, e.g. by permitting a correct SST to displace an SST that is either erroneously incorporated or that contains synthesis errors such as truncations. To generalize the design principles of SST to construct more diverse modular motifs suitable for robust assembly, detailed studies on how the structural difference between SST and other tiles may affect their assembly behaviors would be required.
We believe the SST approach can be adapted to create more complex, diverse and larger shape-controlled structures. Extension of the two-dimensional construction to ensions would generalize the “molecular pixels” concept to “molecular voxels.” The freedom to use designed sequences may permit encoding engineered nucleation control,28 logic and computation,29 and prescribed dynamic pathways30

in the assembly process, which will in turn help scale up SST assembly. Additionally, either a hierarchal8,9,12,14,17–19 or an algorithmic5 assembly strategy may be exploited to create even larger structures. As the structure grows larger, issues such as accumulated mechanical strain12 must be addressed. Besides L-DNA, it would be interesting to implement SST with other informational polymers, e.g. DNA with chemically modified backbones, DNA with artificial bases, and RNA. Shape-controlled nano-structures with custom (bio)chemical properties (e.g. nuclease resistance and non-immunogenicity rendered by L-DNA) may enable diverse application development, e.g. in drug delivery and therapeutics.
A more comprehensive and exciting picture for nucleic acid selfassembly is now emerging. DNA origami demonstrates that a long scaffold strand can be folded by many short staple strands into a prescribed shape without getting “tangled up;” the SST work, on the other hand, demonstrates that numerous small monomer units can selfassemble into a dominant desired structure without getting drowned by ill-formed or aggregated by-products. Both approaches produce complex shapes and work robustly with unpurified strands. These two complementary approaches likely represent two ends of an extraordinarily rich design spectrum for self-assembled DNA structures, where diverse components (e.g. a mixture of long and short strands) may be engineered to cooperatively self-assemble into complex prescribed shapes. Thus SST and DNA origami,9,12–14,16,18,19,23 together with multi-stranded DNA and RNA tiles,2–5,7,8,10,11,20,21 logic gates,29 kinetic hairpins,30 and many other structures,22 suggest the vastness of the practical design space for nucleic acid nano-structures, and more generally for information directed molecular self-assembly.

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METHODS SUMMARY
DNA sequences were generated by minimizing sequence symmetry24 (for most structures) or by populating the SST motifs with completely random sequences (for the structure in Supplementary Fig. S86). Without careful adjustment of stoichiometry, unpurified strands were mixed manually or using a liquid handling robot, and supplemented with 12.5 or 25 mM Mg2+. After one-pot annealing over x hours (17 ≤ x ≤ 58; for most structures, x = 17) from 90 ◦C to 25 ◦C, the solution was subjected to native agarose gel electrophoresis. The desired product band was extracted, purified via centrifugation, and imaged with atomic force microscopy or transmission electron microscopy.

Supplementary Information is linked to the online version of the paper at www.nature.com/nature.
Acknowledgements The authors thank Sarendran Chandarasekaran and Xenia Lim for technical assistance, Adam Marblestone, Robert Barish, William Shih, Yonggang Ke, Erik Winfree, Sungwook Woo, Paul Rothemund, and Damien Woods for discussions, and Jaclyn Aliperti for help with draft preparation. This work was funded by Office of Naval Research Young Investigator Program Award N000141110914, Office of Naval Research Grant N000141010827, NIH Director’s New Innovator Award 1DP2OD007292, NSF CAREER Award CCF1054898, and Wyss Institute for Biologically Inspired Engineering Faculty Startup Fund to P.Y.

Full Methods and any associated references are available in the online version of the paper at www.nature.com/nature.
Received 20 November 2011; accepted xx xx xxxx.

Author Contributions B.W. designed the system, conducted the experiments, analyzed the data, and wrote the paper. M.D. conducted the experiments, analyzed the data, and wrote the paper. P.Y. conceived and guided the study, analyzed the data, and wrote the paper.

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Author Information Reprints and permissions information is available at www.nature.com/reprints. The authors declare competing financial interests in the form of a pending provisional patent. Correspondence and requests for materials should be addressed to P.Y. (py@hms.harvard.edu).

METHODS
DNA sequence design. DNA sequences were designed with the Uniquimer software31 by minimizing the sequence symmetry24 (for most of the structures) or by populating the SST motifs with completely random sequences (for the random sequence set in Supplementary Fig. S86). For the sequence minimization based design, there are several criteria for sequence generation: 1) Nucleotides (i.e. A, C, G, T) are randomly generated one-by-one. 2) Complementary nucleotides to those generated are matched following the base pairing rule: A to T and vice versa, C to G and vice versa. 3) No repeating segment beyond a certain length (8 nt or 9 nt) is permitted. When such repeating segments emerge during design, the most recently generated nucleotides will be mutated until the repeating segment requirement is satisfied. 4) No four consecutive A, C, G or T bases are allowed. 5) Pre-specified nucleotides at the single-stranded linkage points (e.g. T and G for the 21st and 22nd nucleotides, respectively, for most of the strands) are used to avoid sliding bases around the linkage points. In the design using completely random sequences (Supplementary Fig. S86) however, restrictions in steps 3 to 5 were not applied.
Manual design and/or optimization was used for the handle segment sequence design (e.g. handle segment to accommodate 3 biotin strand for streptavidin labeling and concatenation of poly-T domains). Additionally, in some cases, segments from different SST structures were manually combined to transform an existing structure into a new structure. For example, additional rows of SSTs were introduced to convert a rectangle design into a tube design (e.g. converting the 24H×28T rectangle design to the 24H×28T barrel design, and converting the 24H×28T rectangle design to the 8H×84T tube design). Similarly, we also manually converted a tube design to a rectangle design (e.g. converting the 12H×177T tube to the 36H×41T rectangle).
Sample preparation. DNA strands were synthesized by Integrated DNA Technology, Inc. (www.idtdna.com) or Bioneer Corporation (us.bioneer.com). To assemble the structures, DNA strands were mixed to a roughly equal molar final concentration of 100 nM per strand species for most of the structures (except for different shapes based on a 24H×28T rectangle, which were prepared in 200 nM) in 0.5× TE buffer (5 mM Tris, pH 7.9, 1 mM EDTA) supplemented with 12.5 or 25 mM MgCl2. Note that the concentrations were based on the manufacturer spec sheet, and no additional in-house calibration was performed. Thus, the stoichiometry for the strands were not tightly controlled. The mixture was then annealed in a PCR thermo cycler by cooling from 90 ◦C to 25 ◦C over a period of 17-58 hours with different cooling programs. The annealed samples were then applied to a 1.5 or 2 percent agarose gel electrophoresis (gel prepared in 0.5× TBE buffer supplemented with 10 mM MgCl2 and pre-stained with SYBR safe) in an ice water bath. Then, the target gel bands were excised and put into a Freeze ’N Squeeze column (Bio-Rad Laboratories, Inc.). The gel pieces were crushed into fine pieces by a microtube pestle in the column and the column was then directly subjected to centrifugation at 438 g for 3 minutes. Samples centrifuged through the column were collected for concentration estimation by the measurement of ultraviolet absorption at 260 nm. Such estimation will be useful for estimating the dilution factor before AFM or TEM imaging.
Streptavidin labeling. Streptavidin labelings were done with two different approaches. 1) Labeling the top and bottom row or internal loci of the 24H×28T rectangle. Each tile of the top and bottom rows (or internal loci) of the 24H×28T rectangle was modified to have a 3 17 nt handle (TT as spacer and GGAAGGGATGGAGGA to be complementary to the 3 biotin modified strand whose sequence is TCCTCCATCCCTTCC-biotin). Special tiles of the top and bottom rows (or internal loci), and the rest of the component tiles of the rectangular lattice were mixed with 3 biotin modified strands of 1-2× concentration (when concentration of special and common component tiles was 100 nM and there were 14 different special tile species, 1× concentration of the 3 biotin modified strand was 100 × 14 = 1400 nM), which is complementary to the handle sequence of the special tiles, in 0.5× TE buffer (25 mM MgCl2). They were then annealed over 17 hours and purified after agarose gel electrophoresis. The purified sample was then subjected to AFM imaging. After the first round of imaging, streptavidin (1 µL of 10 mg/mL in 0.5× TE buffer (10 mM MgCl2)) was added to the imaging sample (∼40 µL) for an incubation of 2 minutes before re-imaging. 2) Labeling the poly-T ends of tube structures. After tube purification, 3 biotin modified poly-A strand (5-10× to the poly-T counterparts) was mixed with the sample at room temperature overnight. The sample was then subjected to AFM imaging. After the first round of imaging, streptavidin (1 µL of 10 mg/mL in 0.5 × TE buffer (10 mM MgCl2)) was added to the imaging sample on mica for an incubation of 2 minutes before re-imaging.
Robot automation for sample preparation. A custom MATLAB program

was designed to aid complex shapes design and automate strand mixing by a liquid handling robot (Bravo, Agilent). For each shape, 5 µL of 10 µM of each single strand tile in water solution was picked and mixed into a final volume of less than 2 mL (the exact volume was determined by the number of constituent strands for the target shape), and was then vacuum evaporated to a 200 µL of 250 nM solution. This mixture was then supplemented with 50 µL 62.5 mM Mg2+ buffer to reach a 250 µL final mixture ready for annealing. This preannealing solution had the following final concentrations: 200 nM DNA strand per SST species and 12.5 mM Mg2+. Each run accommodated 48 shapes and took around two days to finish.
AFM imaging. AFM images were obtained using an SPM Multimode with Digital Instruments Nanoscope V controller (Vecco). A 5 µL drop (2∼5 nM) of annealed sample with purification followed by a 40 µL drop of 0.5× TE (10 mM MgCl2) was applied onto the surface of a freshly cleaved mica and left for approximately 2 minutes. Sometimes, additional dilution of the sample was performed to achieve the desired sample density. On a few occasions, supplemental 10 mM NiCl2 was added to increase the strength of DNA-mica binding.32 Samples were imaged using the liquid tapping mode. The AFM tips used were the short and thin cantilevers in the SNL-10 silicon nitride cantilever chip (Vecco Probes).
TEM imaging. For imaging, 3.5 µL sample (1∼5 nM) were adsorbed onto glow discharged carbon-coated TEM grids for 4 minutes and then stained using a 2% aqueous uranyl formate solution containing 25 mM NaOH for 1 minute. Imaging was performed using a JEOL JEM-1400 operated at 80 kV.
Yield quantification with SYBR safe staining. Yield was first estimated by native agarose gel electrophoresis analysis. The ratio between the fluorescence intensity of the target band and that of the entire lane was adopted to present the gross yield of structural formation. For the 24H×28T rectangle, as an independent alternative quantification procedure, the intensity of the target band was compared with a standard sample (1500 bp DNA of 1 kb ladder mixture). The mass value of the target band was deducted from the intensity-mass curve based on the standard sample, and was used to calculate the yield of the desired structure. See Supplementary Information S2.2.1 for more details.
Measurement and statistics. AFM measurements were obtained using Nanoscope Analysis (version 1.20) provided by Veeco. The cross section function was applied for the distance measurement task (lengths and widths of the rectangles of different sizes). “Well-formed” structures were chosen for the measurements. TEM images of the tubes were analyzed using ImageJ (version 1.43u) by NIH. The “Straight Line” function was applied in order to measure the width of a tube. The “Segmented Line” function was applied to highlight and measure the contour length of a tube. Thirty sample points were collected for each distance measurement (e.g. width of a 24H×28T rectangle) and the statistics (e.g. average, standard deviation) were based on the 30 data points. See Supplementary Information S3.5 for measurement details.
31 . B. Wei, Z. Wang, and Y. Mi. Uniquimer: software of de novo DNA sequence generation for DNA self-assembly: an introduction and the related applications in DNA self-assembly. J. Comput. Theor. Nanosci. 4 , 133–141 (2007).
32 . Hansma, H. G. & Laney, D. E. DNA binding to mica correlates with cationic radius: assay by atomic force microscopy. Biophys. J. 70 , 1933–1939 (1996).