NATUREIVol 440/16 March 2006 ARTICLES scaffold and create the periodic crossovers. Staples reverse direction Wherever two staples meet there is a nick in the backbone. Nicks at these crossovers; thus crossovers are antiparallel, a stable config occur on the top and bottom faces of the helices, as depicted in ration well characterized in DNA nanostructures. Note that the Fig. Id In the final step, to give the staples larger binding domains crossovers in Fig. Ic are drawn somewhat misleadingly, in that single- with the scaffold (in order to achieve higher binding specificity and stranded regions appear to span the inter-helix gap even though the higher binding energy which results in higher melting temperatures design leaves no bases unpaired. In the assembled structures, helices pairs of adjacent staples are merged across nicks to yield fewer, longer, are likely to bend gently to meet at crossovers so that only a single staples(Fig. le). To strengthen a seam, an additional pattern of phosphate from each backbone occurs in the gap(as ref. 16 suggests breaks and merges may be imposed to yield staples that cross the for similar structures). Such small-angle bending is not expected to seam; a seam spanned by staples is termed"bridged. The pattern of greatly affect the width of DNA origami(see also Supplementary merges is not unique; different choices yield different final patterns of nicks and staples. All merge patterns create the same shape but, as The minimization and balancing of twist strain between crossovers shown later, the merge pattern dictates the type of grid underlying is complicated by the non-integer number of base pairs per half-turn any pixel pattern later applied to the shape (5.25 in standard B-DNA)and the asymmetric nature of the helix(it has major and minor grooves). Therefore, to balance the strain Folding M13mp18 genomic DNA into shapes caused by representing 1.5 turns with 16 bp, periodic crossovers are To test the method, circular genomic DNA from the virus M13mplt arranged with a glide symmetry, namely that the minor groove faces was chosen as the scaffold. Its naturally single-stranded 7,249-nt alternating directions in alternating columns of periodic crossovers sequence was examined for secondary structure, and a hairpin with a (see Fig. ld, especially cross-sections 1 and 2) Scaffold crossovers are 20-bp stem was found. Whether staples could bind at this hairpin not balanced in this way. Thus in the fourth step, the twist of scaffold unknown, so a 73-nt region containing it was avoided. When a linear crossovers is calculated and their position is changed (typically by a scaffold was required, M13mp18 was cut(in the 73-nt region)by ngle bp)to minimize strain; staple sequences are recomputed digestion with Bsr BI restriction enzyme. While 7, 176 nt remained accordingly. Along seams and some edges the minor groove angle available for folding, most designs did not fold all 7, 176nt; short (150%) places scaffold crossovers in tension with adjacent periodic ($25 nt)remainder strands' were added to complement unused crossovers(Fig. ld, cross-section 2); such situations are left sequence. In general, a 100-fold excess of 200-250 staple and unchanged remainder strands were mixed with scaffold and annealed from A △v Figure 2 I DNA origami shapes. Top row, folding paths. a, square; is the lst base, purple the 7,000th. Bottom two rows, AFM images. White gle; c, star; d, disk with three holes; e, triangle with rectangular lines and arrows indicate blunt-end stacking. White brackets in a mark the domains; f, sharp triangle with trapezoidal domains and brid height of an unstretched square and that of a square stretched vertically(by a them(red lines in inset). Dangling curves factor >1.5)into an hourglass. White features in f are hairpins; the triangle equence. Second row from top, diagrams showing the bend is labelled as in Fig. 3k but lies face down. All images and panels without scale crossovers(where helices touch) and away from crossovers bars are the same size, 165 nm x 165 nm Scale bars for lower AFM images: bend apart). Colour indicates the base-pair index along the folding path; red b, 1 um; c-f, 100 2006 Nature Publishing Group© 2006 Nature Publishing Group scaffold and create the periodic crossovers. Staples reverse direction at these crossovers; thus crossovers are antiparallel, a stable configu￾ration well characterized in DNA nanostructures16. Note that the crossovers in Fig. 1c are drawn somewhat misleadingly, in that single￾stranded regions appear to span the inter-helix gap even though the design leaves no bases unpaired. In the assembled structures, helices are likely to bend gently to meet at crossovers so that only a single phosphate from each backbone occurs in the gap (as ref. 16 suggests for similar structures). Such small-angle bending is not expected to greatly affect the width of DNA origami (see also Supplementary Note S2). The minimization and balancing of twist strain between crossovers is complicated by the non-integer number of base pairs per half-turn (5.25 in standard B-DNA) and the asymmetric nature of the helix (it has major and minor grooves). Therefore, to balance the strain15 caused by representing 1.5 turns with 16 bp, periodic crossovers are arranged with a glide symmetry, namely that the minor groove faces alternating directions in alternating columns of periodic crossovers (see Fig. 1d, especially cross-sections 1 and 2). Scaffold crossovers are not balanced in this way. Thus in the fourth step, the twist of scaffold crossovers is calculated and their position is changed (typically by a single bp) to minimize strain; staple sequences are recomputed accordingly. Along seams and some edges the minor groove angle (1508) places scaffold crossovers in tension with adjacent periodic crossovers (Fig. 1d, cross-section 2); such situations are left unchanged. Wherever two staples meet there is a nick in the backbone. Nicks occur on the top and bottom faces of the helices, as depicted in Fig. 1d. In the final step, to give the staples larger binding domains with the scaffold (in order to achieve higher binding specificity and higher binding energy which results in higher melting temperatures), pairs of adjacent staples are merged across nicks to yield fewer, longer, staples (Fig. 1e). To strengthen a seam, an additional pattern of breaks and merges may be imposed to yield staples that cross the seam; a seam spanned by staples is termed ‘bridged’. The pattern of merges is not unique; different choices yield different final patterns of nicks and staples. All merge patterns create the same shape but, as shown later, the merge pattern dictates the type of grid underlying any pixel pattern later applied to the shape. Folding M13mp18 genomic DNA into shapes To test the method, circular genomic DNA from the virus M13mp18 was chosen as the scaffold. Its naturally single-stranded 7,249-nt sequence was examined for secondary structure, and a hairpin with a 20-bp stem was found. Whether staples could bind at this hairpin was unknown, so a 73-nt region containing it was avoided. When a linear scaffold was required, M13mp18 was cut (in the 73-nt region) by digestion with BsrBI restriction enzyme. While 7,176 nt remained available for folding, most designs did not fold all 7,176 nt; short (#25 nt) ‘remainder strands’ were added to complement unused sequence. In general, a 100-fold excess of 200–250 staple and remainder strands were mixed with scaffold and annealed from Figure 2 | DNA origami shapes. Top row, folding paths. a, square; b, rectangle; c, star; d, disk with three holes; e, triangle with rectangular domains; f, sharp triangle with trapezoidal domains and bridges between them (red lines in inset). Dangling curves and loops represent unfolded sequence. Second row from top, diagrams showing the bend of helices at crossovers (where helices touch) and away from crossovers (where helices bend apart). Colour indicates the base-pair index along the folding path; red is the 1st base, purple the 7,000th. Bottom two rows, AFM images. White lines and arrows indicate blunt-end stacking. White brackets in a mark the height of an unstretched square and that of a square stretched vertically (by a factor .1.5) into an hourglass. White features in f are hairpins; the triangle is labelled as in Fig. 3k but lies face down. All images and panels without scale bars are the same size, 165 nm £ 165 nm. Scale bars for lower AFM images: b, 1 mm; c–f, 100 nm. NATURE|Vol 440|16 March 2006 ARTICLES 299