Four different cuboid shapes with various dimensions were designed and tested experimentally. The number of folded layers of the DNA helical planes ranges from 2 to 8, as illustrated in Figure 2a–d. The dimensions of the cuboids, m
, where m
is the number of layers, n
is the number of helices per layer, and d
is the number of base-paired helical turns, are 2 × 21 × 15.75, 3 × 14 × 15.75, 6 × 12 × 7.5, and 8 × 8 × 9.0, respectively, which are translated into the length scale marked in the figures (assuming 3.5 nm per helical turn and 2.0 nm per helical diameter with no gap between helices). The scaffold used is the single-stranded M13mp18 (purchased from New England Biolabs, cat # N4040S), which is 7249 nt long, or else a variant with a site-directed insertion in the multiple cloning site that results in a final construct that is 8064 nt long.9
Target structures were designed so that 90–97% of the scaffold strand should be paired with staple strands. The remaining scaffold material was designed as unpaired loops at the ends of the helices. The 8 × 8 × 9.0 designs were implemented with a custom computer program. The 2 × 21 × 15.75, 3 × 14 × 15.75, and 6 × 12 × 7.5 designs were aided by the computer software caDNAno,14
which we modified to support this square-lattice design (the original version only supported the honeycomb-lattice pattern of antiparallel helices).
For the formation of each designed DNA cuboid, the 174 to 221 staple strands (desalted oligodeoxyribonucleotides, custom ordered on 96-well plates from Bioneer for the 2 × 21 and 3 × 14 designs and from Integrated DNA Technology for the 6 × 12 and 8 × 8 designs) were mixed with the scaffold strand in 5-fold or 10-fold molar excess. A one-pot reaction (see below for details of thermal ramp) allowed hybridization of the scaffold strand with the hundreds of staple strands that direct its folding into the target shape. The annealed mixtures were subjected to agarose-gel electrophoresis. Next, rapidly migrating bands corresponding to monomeric, well-folded species were excised from the gel and recovered by physical extraction using a Freeze-N-Squeeze column (see experimental details in the Supporting Information
). The purified structures were imaged by transmission electron microscopy (TEM) after negative staining by uranyl formate or directly imaged by cryo-EM where the native conformations of the structures might be better preserved in vitreous ice during the quick freezing. Successful folding for the 6 × 12 and 8 × 8 designs was observed at the following conditions: 1 × TAE•Mg buffer (pH 8.0) that contains 20 mM Tris•acetate, 1 mM EDTA, and 12.5 mM Mg2+
, and thermal annealing by rapid heating to 90 °C followed by slow cooling to 4 °C over 48 h (6 × 12 design) or 24 h (8 × 8 design). Successful folding for the 2 × 21 and 3 × 14 designs was observed at the following conditions: 5 mM Tris + 1 mM EDTA (pH 8.0), 16 mM MgCl2
, and a thermal annealing ramp from 80 to 60 °C over the course of 80 min, followed by a ramp from 60 to 24 °C over the course of 172 h.
The four objects displayed in demonstrate the generality of this square-lattice origami approach in constructing the multilayered 3D DNA nanostructures, with increasing number of DNA layers (2, 3, 6, or 8 layers). TEM images of negatively stained samples show both the side view and top views of the assembled products corresponding to the designed structures. High-resolution zoom-in images clearly reveal the number of helices per layer and number of layers in each structure. The images also show increased contrast with increasing number of layers, consistent with the expected constructive reinforcement. The top-view images of the two-layer structure have the lowest contrast due to the thinness of the particles. The estimated yields of each structure were 56%, 89%, 27%, and 59% for two-, three-, six-, and eight-layer structures, respectively (see Supporting Information
for methods of estimating yield used here in comparison to methods for estimating yield for previously analyzed honeycomb structures14
Figure 2 3D DNA origami solid blocks. (a) Two-layer structure. (b) Three-layer structure. (c) Six-layer structure. (d) Eight-layer structure. The 3D perspective cylinder view and the projections of the top view and the side view are shown. Each cylinder represents (more ...)
The side views of the two-layer and three-layer structures display significant global twisting, while the six-layer and eight-layer structures do not. This behavior can be understood on the basis of a global relaxation in response to local underwinding of double helices.13
In the square-lattice structures, the initially imposed double-helical twist density is set as 10.67 bp/turn (i.e., 8 bp per 0.75 turns). If the preferred double-helical twist density for B-DNA is 10.5 bp/turn, then the double helices in the square lattice are underwound. The bundle of double helices will adopt a global right-handed twist in order to relieve the strain of the local underwinding. The magnitude of the global twist should vary inversely with the torsional stiffness of the structure and vary directly with the amount of torque. The torsion constant J
for a cuboid as a function of cross-sectional dimensions can be approximated with the following formula:15
is the long width of the cross section and b
is the short width of the cross section. The torsional stiffness of each object should vary inversely with the length. We can estimate the normalized torsional stiffness of the 2 × 21 × 15.75, 3 × 14 × 15.75, 6 × 12 × 7.5, and 8 × 8 × 9.0 blocks as 1.0, 2.1, 24, and 19, respectively. Thus the 6 × 12 × 7.5 and 8 × 8 × 9.0 designs should be about 10 times more stiff than the 3 × 14 × 15.75 design. Furthermore, the total internal torque experienced by the 3 × 14 × 15.75 design would be expected to be significantly greater than for the 6 × 12 × 7.5 or 8 × 8 × 9.0 designs, since the underwound helices on the extremities of the block will contribute, by virtue of a larger mechanical advantage, a larger torque than the ones near the middle, and the average distance from the center is greater for the extended designs. Taken together, the combination of less internal torque and much greater torsional resistance would be expected to manifest as very little noticeable global compensatory twisting for the 6 × 12 × 7.5 and 8 × 8 × 9.0 designs.
We sought to diminish the global twisting observed for the 3 × 14 × 15.75 design by introducing targeted deletions to reduce the initially imposed double-helical twist density to 10.5 bp/turn. This was implemented by removing a single bp from all helices in a cross section of the structure every 64 bp. TEM imaging revealed that global twisting was reduced; however a significant amount of global twisting still was evident. This was surprising, as 10.5 bp/turn was previously found to result in no global twist for honeycomb-lattice designs.13
Next we sought to overwind the double helices past 10.5 bp/turn to eliminate the residual global twisting. We constructed two more versions of the 3 × 14 × 15.75 design, with initially imposed double-helical twist densities of 10.44 and 10.39 bp/turn, respectively. The former was achieved by removing four bp evenly spaced along the 192-bp length ((192 − 4)/(24 × 0.75) = 10.44), while the latter was achieved by removing five bp evenly spaced along the 192-bp length ((192 − 5)/(24 × 0.75) = 10.39).
To make visualization of global twisting more obvious, we programmed the structures to form ribbons consisting of head-to-tail multimers (Figure S2
). We folded the structures, gel-purified monomeric particles, and then added staple strands that bridge the front and back ends such that homomultimers should form. We verified that the 10.5 bp/turn design retains a right-handed global twist by imaging ribbons with the TEM goniometer turned to +40° and then again with the TEM goniometer turned to −40° (i.e., counterclockwise rotation) and observing the nodes of the ribbons moving upward.13
No systematic global twist could be discerned with the 10.44 bp/turn and 10.39 bp/turn designs. Why the local double-helical twist density has to be slightly overwound to eliminate global twist in square-lattice designs is unclear. One speculative possibility is that global twisting stiffness may have two components, perhaps related to the presence of crossover junctions: a soft mode for small-amplitude twists and a hard mode for larger-amplitude twists. In this model, when the average double-helical twist density is 10.5 bp/turn, the sum of right-handed global twisting over the slightly underwound segments, mainly absorbed by the soft mode, is not fully compensated by the left-handed global twisting of the highly overwound segments, which saturate the soft mode and enter the hard mode. An analogous model has been discussed for two-component stretching of dsDNA.16
To further reveal the 3D conformation of a square-lattice-based design, we investigated the eight-layer DNA-origami structure using cryo-EM imaging in which the structure might be better preserved in native conformation during quick freezing. We observed interesting internal structure that we can account for as described below. In our default design strategy, some staple breaks must be implemented between crossovers 8 bp apart. For the two-layer and three-layer structures, very few such breaks need to be incorporated. However, for the six-layer design, many such breaks must be used. We observed significantly lower yield for these structures. Introducing these breaks may be destabilizing for the structure. Alternatively, simply having a large number of layers with our default crossover pattern may be destabilizing, irrespective of the position of the breaks.
For the 8 × 8 design, we avoided the implementation of such staple breaks by omitting many crossovers in the core of the block (). For this design, we observed a high yield of well-folded structures. These results suggest that omitting crossovers produces more relaxed structures that are easier to realize or else that the omission of staple breaks positioned between crossovers 8 bp apart could improve folding quality as well. Future systematic studies will be required to determine the relative importance of these staple breaks toward affecting folding efficiency.
Figure 3 Cryo-EM images of the 8 × 8 square lattice. (a) Three-dimensional cylinder model of a hypothetical 8 × 8 square lattice with all default staple crossovers intact. Cross-sectional slices i to iv (parallel to the xy-plane, spaced at 8-bp (more ...)
The omission of crossovers we implemented leaves behind an uneven distribution of the remaining crossovers in the 8 × 8 square lattice (). We define the z
-axis as the helical axis, and the other two axes as x
, respectively. In our design, many helices that are adjacent in the x
-direction do not share any crossovers; thus electrostatic repulsion will cause them to bow away from each other. Consistent with our design, the cryo-EM images reveal that there are three distinguishable populations of particle views: (1) Particle views corresponding to the xz
-projection of the 8 × 8 square lattice (). In the averaged cryo-EM image, we can clearly see some larger spaces between two neighboring slices of DNA helices at the positions with a low number of crossovers summed along the y
-axis (low numbers indicated by red numerals). (2) Particles corresponding to the yz
-projection of the 8 × 8 square lattice (). Due to the even distribution of crossovers between helices that are adjacent in the y
-direction, the spaces between two neighboring slices of helices appear uniform at every position. (3) Particle views corresponding to the xy
-projection of the 8 × 8 square lattice (). This image clearly shows a 90° angle between the rows of helices arrayed along the x
- and y
-axes. However, only a small number of 8 × 8 structures could be found in this orientation; thus we could not generate accurate averaged images for this class of particle views. On the basis of these cryo-EM images, we estimated the effective diameter of the double helix in the structures as the width of the cuboids divided by the number of helix layers, which gives a result of 2.6 nm (±0.1 nm SD) per helix. Assuming an unhydrated helical diameter of 2.0 nm (although the hydrodynamic helical diameter17
has been estimated as 2.2 to 2.6 nm), this observation suggests the presence of interhelical gaps produced by electrostatic repulsion on the order of 0.6 nm, smaller than the 1.0 nm gap size estimated for Rothemund’s flat 2D origami and larger than the one observed in the 3D origami packed on the honeycomb lattice. This is possibly due to the longer distances between the crossover points along a pair of adjacent helices, i.e., three turns in the square-lattice design and two turns in the honeycomb-lattice design. Apparent differences in effective helix diameter between architectures may originate in part from staining artifacts (e.g., cavities where large amounts of positively charged stain accumulate, or flattening).13
Here the cryo-EM imaging should better resemble the native parameters.