# Elucidating the Mechanical Energy for Cyclization of a DNA Origami Tile
## 2 Materials and Methods  
### Origami Tile Design  
Figure 1 shows the design of a single-layer DNA origami rectangle used as a model system in this computational study. There are 32 helices in height (i.e., 32 rows of ds  
DNA bundles) and 224 bases in width (in each row). The origami tile is sketched in caDNAno2 [48]. To avoid blunt-ended stacking, only 192 bases in width are used and the 16 nucleotides (nt) on either side are left unpaired. The sequence information is available in our previous report [27]. The designed width is calculated to be approximately 64 nm based on 0.332 nm/bp along the axis of regular, right-handed B-form DNA. The height is estimated using the diameter of a dsDNA bundle (\(\sim\)2.2 nm) and the distance between the center of neighboring bundles (\(\sim\)2.3 nm when closely packed) [20; 46]. However, the gap between adjacent bundles is noticeably wider than the bundle diameter based on our previous AFM results [27]. For a fair estimation, we assume the gap to be approximately \(2.3\times 1.2\) nm. Thus, the designed height is estimated as \(\sim\)88 nm. A set of linker staples, if introduced in an experiment, can hybridize with upper and lower boundaries (rows 1 and 32) simultaneously, thereby cycling the tile into a tube, as we demonstrated in a previous report [27]. Experimentally, the DNA tile experiences thermal fluctuation that deforms the structure randomly, and the linkers seal the upper and lower edges when they are in proximity. By design, the cyclized tube is approximately 64 nm in width and 28 nm in diameter. If collapsed to a flat surface, the origami will be about 64 nm in width, 44 nm in height, and 4 nm in thickness (double layer). The AFM results suggest that the synthesized tile measures about 90 \(\times\) 65 \(\times\) 2 nm and the flattened tube is around 45 \(\times\) 65 \(\times\) 4 nm [27].  
The DNA origami tile is designed in a square lattice, with a crossover every 16 nt. Typically a staple is 32 nt in length--the middle 16 nt binds with a dsDNA helix while the 8 nt parts at both 5' and 3' ends bind with neighboring two dsDNA bundles. This is equivalent to  
Figure 1: Folding path diagram of a DNA origami tile. Black line denotes the scaffold strand, which routes clockwise (5′ to 3′ end). Blue, gray, and red lines represent staples. The color marks different shape and directions. Blue and gray staples have the same shape but opposite directions: blue goes down while gray goes up from 5′ to 3′ end. The red staples secure the scaffold in the middle of the origami and thus have a different shape compared with blue and gray. A typical staple length is 32 nt. The dsDNA bundles are numbered 1 through 32, as noted on the left. Note that a total of 13 gray and blue staples were used to seal the upper and lower edges to form a cyclized tube in the experiment. The 13 pairs of the black dots indicate the cut sites of the linker staples. This design was used in the MD simulations.  
a helicity of 10.67 bp/turn. Therefore, the tile will have a slight, right-handed global twist if subjected under 10.5 bp/turn conditions. In the simulations, 13 linker staples designed to cyclize the DNA origami rectangle were cut into halves as illustrated in Figure 1. The cutting sites are marked with 13 pairs of black dots and labelled 1 through 13. The origami tile can then be cyclized by applied external forces.