Yuwen Zhang and Nadrian C. Seeman- Construction of a DNA-Truncated Octahedron

8/3/2019 Yuwen Zhang and Nadrian C. Seeman- Construction of a DNA-Truncated Octahedron

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J . Am. Chem. SOC. 994,116, 1661-1669 1661

Construction of a DNA-Truncated OctahedronYuwen Zhang and Nadrian C. Seeman'Contribution from the Department of Chemistry, New York University,New York, ew York 10003Received November 1 , 1993"

Abstract: A covalently closed molecular complex whose double-helical edges have the connectivity of a truncatedoctahed ron has been assembled from DN A on a solid support. This three-con nected Archimede an solid contains sixsquares and eight hexagons, formed from 36 edges arranged abo ut 24 vertices. The vertices ar e the branch points offour-arm DNA junctions, so each vertex has an ex tra exocyclic arm associated with it. The con struct contains sixsingle-stranded cyclic DNA molecules that form the squares and th e extra arms; in addition, there are eight cyclicstrands that correspond to the eight hexagons. The molecule contains 1440 nucleotides in the edges and 1110 in theextra arms; the estimated molecular weight for the 2550 nucleotides in the c onstruct is 79 0 kDa. Each edge containstwo turns of double-helical DNA , so that the 14 stran ds form a catenated str uctu re in which each strand is linked twiceto its neighb ors along each edge. Synthe sis is proved by demonstratin g the presence of each squ are in the object andthen by confirming that the squares are flanked by tetracaten ane substructures, corresponding to the hexagons. Thesuccess of this synth esis indicates that this technology has reache d the stag e where the con trol of topology is in hand ,in the sense of both helix axis connec tivity and s trand link age.

IntroductionOne of the major goals of both biotechnology and nanotech-nology1*2s the assembly of novel biom aterials that can be usedfor analytical, industrial, and therapeutic purposes. In particular,one would like a ratio nal approach to the con structionof individualobjects, devices, and periodic matter on the nanometerutilizing the inform ational macromo lecules of biological systems.For the past several years, our laboratory has been engaged inthe nano scale construc tion of stick figures, using branch ed D NAmolecules as building blocks. The edges of these figures consistof double-helicalDNA , and the vertices correspond o the branchpoints of stable DNA branched jun ction s.6~ ~ e have reportedthe assem bly in solution of molecules whose helix axe s have theconne ctivities of a quad rilateral8 and of a Platonic polyhedron,

the cube.gDifficulties encou ntered in the solu tion synthesis of the c ubehave stimulated hedevelopmen t of a solid-support-based syntheticprocedure that provides control over the formation of a singleedge at a time.10 This is accomplished by protecting witha hairpinloop each double-helical arm designated to participate in edgeformation; the loop is removed by a restriction endonuclease,thereby exposing a ligatable sticky end. Each intermediateprodu ct is a topologically closed molecule, which can be separa tedfrom ligation-failure products by denaturation on the support.Furthermore, intermolecular addition reactions and intramo-lecular cyclization reactions can be performed separately, inconditionsoptimized for each type of reaction; cy clizations usingsymmetric sticky ends would yield a mixture of intra- andintermo lecular products in solution, but th e isolation of moleculeson the supp ort makes them feasible.We have demonstrated previously that one can use the solid-support-based procedure to assemble polygons from individual

* Address correspondence to this author.e Abstract published in Advance ACS Abstracts, February 1, 1994.(1) Feynman, R. P. n Miniaturization; Gilbert, H. D., Ed.; Reinhold(2) Drexler, K.E. Proc. Natl. Acad. Sci. U.S.A . 1981, 78 , 5275-5278.(3) Robinson, B.H.; Seeman, N. C. Protein Eng. 1987, 1, 295-300.(4) Seeman, N. C . DNA Cell Biol. 1991, 10, 475-486.(5) Seeman, N. C. Nanotechnology 1991, 2, 149-159.(6) Seeman, N. C. J. Theor. Biol. 1982.99, 237-247.(7) Seeman, N. C. J . Biomol. Struct. Dyn. 1985, 3, 11-34.(8) Chen, J.-H.; Kallenbach, N. R.; Seeman, N. C. J . Am. Chem. Soc.(9) Chen, J.; Seeman, N. C. Nature (London) 1991, 350, 631-633.(10) Zhang, Y. ; eeman, N. C. J.Am. Chem.SOC. 992,114,2656-2663.

Publishing Corp.: New York, 1961; pp 282-296.

1989,111,6402-6407.

0002-7863194115 6- 66 $04.50/

branch ed junctions.10 It is ultimately d esirable to be able toconstruc t objects of much greater complexity than polygons. Herewe demo nstrate th at solid-su pport-b ased assembly can be usedto combine individual polygons and polygonal clusters into acomplex polyhe dral object, whose helix ax es have the connectivityofa truncated octahedron (Figure la). Th e truncatedoctahedronis an A rchimedean semiregular polyhedron, containing 14 faces(six squares and eight hexagons), 24 vertices, and 36 edges. Itis a three- connec ted object,11J2 meanin g tha t eac h vertex isconnected to three other vertices by an edge of the figure; inprinciple, it could be built from three-arm branched junctions.6Neverth eless, we have built this object from four-arm b ranchedjunctions; the extra arm s contain the potential for connectionsthat could produce periodic matter in one, two, or three dimensions,althoug h formin g such connectio ns is beyond th e scope of thework reported here.Th e edges of t he polyhedron contain seven specific sites forcleavage by restriction endon ucleases; in addition, each e xtraarm c ontains a restriction site. These sites facilitate analysis ofthe ligation reactions, because one can digest both intermediateand final structu res to generate well-defined breakdown produc ts.Each e dge of the polyhedron is designed to contain 20 nucleotidepairs, corresponding to two full double-helical turns of DN A.Consequently, each of the 14 faces correspo nds to a sin gle cyclicDNA molecule,'3 and the entire polyhedron is a complex 14-catenane. The cyclic molecules corresponding to the hexagonsare each exactly 120nucleotides ong, and each hexagon is linkedtwice to three 'square' molecules and to three othe r 'hexagons'.The cyclic molecules corresponding to the squares contain 80nucleotides linked twice to four differen t hexagons, plus the D NAin the 24 extra arm s, which varies from 40 to 50nucleotides. Th eentire molecule contains 1440 nucleotides in the edges and 11 10in the extra arms for a total of 2550 nucleotides; the total estim atedmolecular weight is about 79 0 kDa.Schematic views of the truncated octahedron are shown inFigure 1. Figure la s a drawing of the Archimed ean polyhedron.Figure l b is a modified Schlegel diagram of th e truncatedoctahedron. In this representation, the square in the center(labeled 5) is closest to th e viewer, those flankin g it, 2, 3,4, an d(1 1) Wells, A. F. Three-dimensional Nets and Pol yhed rrJo hn W wSons: New York. 1977.(12) Williams,' R. The Geometrical Foundation of Natural Structure;(13) Seeman, N. C. J. Mol . Graphics 1985, 3, 34-39.Dover: New York, 1979.

1994 American Chemical Society


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1662 J . Am. Chem.Soc., Vol. 116.No. , 1994 Zhanj -

Ictahedron. This drawing r e p m b he solid that has k e n uilt here. Shawnigure 1. Representationsaft he truncated octahedron. (a. top left) Solid truncateis the front half of an idealized molecule, which has bsm rotated sliihUy offa symmetrical view. Each q u a i abuts four hexagons, and each hexagon aham anedgewith three squaresand hreeother hexagons. The object has the same 432 symmetryasa cube. This is a threbmnnccted object, bceauae each vertex isconnectedby edges to three other vertices. (b, tap right) Modified schlc gd diagram of the truncated octahedron. In this mprcssntation. the squareat the mter is closcsito the vicwcr. and polygons further from the center arc further from he viewer. The square an the outside is at then ar of the objcct. Each edge is reprcscntedby two helical strandr, all of whme twisting is confined to the center of the edge, for clarity.9 The quares arc nu m be d with Arabic numerals, and the hexagonsarc numbered with Roman numerals. Each hexagon is drawn distorted fmm ideality. Thc inner hexagons (V-VIII) are drawn as hexagons with two right angle,and the outer hexagons (I-IV) are drawn as rap oi ds . with their inner edge reprcssnting three edges of th e polygon. Note that thc 14 polygons each anrcspondto a particular strand(Id r I-VIII), bccausc there s an integral number of full turns between vmi ccs: ncverthel*rs, eachedg is actuallymped of two strandsthat form a double helix. The =lid support is indicated at the upper left comer, so this dia- rsprrsents the construct just before release and annealing. Thecapital etten (A-G) indicate the w e n edges tha t are formed by ligation ofsticky ends S I S 7 , respectively)aped by sy ctri call y cleaving restriction enzymepairs; each edgemntains a restriction site. Note that the tetracatenme flankingNW squareexcept square6 an be released from a squarelamolecule by cleavageat two ol hesc sites. (c, bottom left)Double-helical representation of an ideal truncated octahedron. Each edge is colored, with the squares and atcmal hairpina r m d nd the hexagonal str ands blue. magenta, yellow, and green. The bases an hown BS white. Thc external hairpins have k e n shortened from th-conslrvcted for purpoacsofclarity: they ~ 1 5hown parallel to the fourfold axes of the molecule. Each pair ofvertice is separated by an edge containing two fullt m f double-helical DNA. This isa view down B fourfold axis of the molecule. The strands com pand ing to the quares are drawn in red. and the four strandscorresponding tovisible huagon sared rawn (connteffilochuiscfmmthcupperrigbt)ingrem,yellow,~gcnta,andh;; h u a g o n s o ~ t c t h c s s t h m n g h t h e o c n t e rof the molecule have the anme colors. Base pails are shown in white. (d, bottom right) OEtacatenane formed by the strands that correspond to the hexagons. Thevim is down one ofthe threefold axes of the molecule. The strand s corresponding to the squaresand extra arms have k e n removed. The hexagon is flanked bythreehexagonsandthreesquares. Natethateachsquarcisflmkedbystrandsoffourdiffcrcnteolors.Thebasesofthcsquanslrandshavebeenmainedfarclarity.


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DN A- Truncated OctahedronTable 1. Seauences of the Square Components of the Truncated Octahedron'

J . Am. Chem. Soc., Vol. 116, No. 5, 1994 1663

1.1.1:

1.1.2:

1.2.1:

1.2.2:

1.3.1:

1.3.2:

1.4.1:

1.4.2:

2.1.1:

2 . 1 . 2

2 . 2 . 1

2 .2 .2

2 . 3 . 1

2.3.2

2 . 4 . 1

2 . 4 . 2

3 . 1 . 1

3 . 1 . 2

3 . 2 . 1

3 . 2 . 2

3 . 3 . 1

3 . 3 . 2

3 . 4 . 1

3 .4 .24 . 1 . 1

SV-TAAGTGTGCTATTTACATCTGGAACTTTTGTTCCAGATCTAAATACCTGAACCT-3'S' .ACACCAAGGTTCACCGACCAGCGCCTGCTCATTTTTATGAGCAGGCGCTGGTCGGACACTTAGGCTAC-3'5'-TGGTGTAGGTCGTCCCACCTGGTACCGCACGTTTTCCTCCCGTACCAGGTCCCTGAGCCAAGCCGT-3'5'-TCCCTCACCATCACTCGGCGTGTCTTCCAATCCTTTTGGATTCGAAGACACGCCGAGTGATGGACGACCT-3'S'GTATAGTGGTTACTCCATGGCAATCTTTTGATTGCCATGCAGTAACCTGTTACC-3'5'-CGTCACCGTAACACCTCACAGCTCCTGCACGCTTTTGCGTGCAGCAGCTCTCACGACTATACACGGCT.3'5'-GTCACGGAAAGCTGCTCTATCCAGCAGAGACATTGTTTTTTAACAATCTCTCTGCTGGATAGACCTCTCACCCTACCC-3'5 ' -GGTGACACCAACCAGCCACTGTCCTATTTTTAGGACAGTGCCTCCTTGGACCTTTC-3'5'-TCGTAGTGGCAACATTGCGAGAAGAGAGTTCCTTTTGCAACTCTCTTCTCCCAATGTTGCCTGATACT-3'5'-ACACCAAGTATCACCTAAGCCTCTGCGGCATCATTTTTATCATCCCGCAGAGGCTTAGCACTACCACGCTAC-3'5'-TCCTGTAGGAAGTGCACCTACGCTGTGAGACTCCAACTTTTGTTGGAGTCTCACAGCGTAGGTCCTGAACGAAGCCGT-3'5'-TCGTTCACCAGCCCCTCCTCGGCTCATCTTTTCATGACCCGAGGAGGCCCTGGACTTCCT-3'5'4XTCTG TCG TG CAACCG ACAAG TCTTCATCCG CTTTTGCGGATGAAGACTTGTCGGTTGCACCTGTCACC-3n5'4XTGACGGTGACACCTCAGCCACGTCGGCACTGATTTTTCAGTGCCGACGTCCCTGAGGACAGACCACGGCT-3 '5'-GTCACGGTCGTGTGCCCTGCTCGTCAATCGCAGGTCGCCTATTTACGCGACCTGCGATTGACGAGCACGCCTGCCTTAGTAGCC5'-TAAGCCACCATCGCCTACCTGGCTTGTTTTTTAACAAGCCAGGTAGCCGATGGACACGAC-3 'S'.GAGATGTGGCTCAACCCGGGATGCCTTTTGGCATCCCCGGTTGAGCCTGATTCT-3'5'-ACACCAAGAATCACCAGTCACCTCGTGGTCATTTTTATGACCACGAGGTGACTGGACATCTCGGCTAC-3'5'-TCCTCTATCGACTGGTTCAAGGATCCACAACTTTTGTTGTCGATCCTTGAACCTGAACTCAGCCGT-3'5'4AGTTCACCGCTCACCCAGTGTCCTCTTT T GA GGA C A C T GC GT GA C C C GA C T C C A T -3 '5 ' -GCAAAGTCGCACTACCGCCGAAGAGCTTCGCTTTTGCCAAGCTCTTCCGCCCTAGTGCCTGCCGTC-3'5 ' -CCTGACGACGGCACCTAACACTCGGTGGCCGTTTTTACCGCCACCCAGTGTTAGGACTTTGCACGGCT-3'5 ' - C T C A C G C A A C A G T G G A C C T T G C T A T TTTTAATGGCTAGCAAGCTCCTCTCATCCTACCC-3'5 ' .CATG ACACCAACCACCG TG TG CTG AATTTTTTCAGCACACGGTGGTTGGACTGTTC-3'5'4XACTGTGGCACCTCGTCGCAGTCTTCTACAACTTTTCTTCTAGAAGACTGCGACGAGGTGCCTGATGCT-3'

4 .1 .2

4 . 2 . 1

4 . 2 . 2

4 . 3 . 1

4 . 3 . 2

4 . 4 . 1

4 . 4 . 2

4 .1 .2

5 . 1 . 1

5 . 1 . 2

5 . 2 . 1

5 . 2 . 2

5 . 3 . 1

5 . 3 . 2

TT 5 . 4 . 1:.3'

5 . 4 . 2

6 . 1 . 1

6 . 1 . 2

6 . 2 . 1

6 . 2 . 2

6 . 3 . 1

6 . 3 . 2

6 . 4 . 1

6 .4 .2

5' -ACACCAAGCATCACCATACCATCCGCTGGAATCCTTTTCGATTCCAGCGGATCGTATGGACAGTGCGGCTAC-3'5~-TCGTCTAGCTGCTCCTCAACTCATGAACCTCTTTTGACGTTCATGAGTTGACCTGGACTCAGCCGT-3'S'.CAGTCCACCTATCCACTCCTTGGAACGCTTT T GC C T T C C A A GC A GT GGA T A GGA C C A GC T -3 '5,-GTGTCGTGCAGCTTCTCCAGTCATTTTTTAATCACTCGAGAAGCTCCTGTCACC-3'S 'XG TG ACG G TG ACACCTTACCAACCAATG G TTCG TTT T T A C GA A C C A T T C C T T GC T A A GGA C GA C A C A C GGC T -3 '5'-CTCACCGACAAGTGGCGTATGCGCGCCTCTATTTTTAG ACG CCCCCATACG CCTG G CTCCG TAG CC- 3*5'-CGAGCCACCATTCCACCGTCTGGTTTGATTT T T C A A A C C A GA C C GT GGA A T GGA C T T GT C - 3'Si -A C A C C A A CC A T C A C C A T A C C A TC C GC T GGA A T C C T TTTCGATTCCACCGGATGGTATGG ACAGTGCGGCTAC-3'5'-GCAGAGTGGTTCTCACTAGTCTACCTTT T GGT A GA C T A GT GA C A A C C T GA T GC T -3 'S ' . A C A C C A A GC A T C A C C A T T GGC C T GT C T GGC C GC C GT TT T T A C GGC GC C C A C A C A GC C C A A T GGA C T C T GC GGC T A C -3 'S* . T GGT GT A GGTGGT C GA GC A C T GA C GA C T C GCA GGT A T C C T C T TTTGAGCATACCTGCCAGTCCTCAGTGCTCCTGACTCCAGCCGT-3'S'.GCAGTCACCTTAGGCCGTrcTGCCCCGACTTTTTTAAGTCGGCCACG ACCGCCTAAGGACCACCT-3'5'-CGAACGTGCTGTTCACGCGTTTCACTTTTGTCAAACGCGTGAACACCTGGCTCC-3'5'-CGTGACCCAGCCACCAACGGCCTCAGCGGCCTTCATTTTTATGAAGGCCGCTGAGGCCGTTGGACGTTCCACGGCT-3'5'-CTCACCGTGCGGTCCACATCCAACCTCGTCTTCAACTGCTTTTGCAGTTGAAGACGAGGTTGGATGTCCTGTGTCCGTAGCC-3'5'-GCACACACCTCTCCCCATCTCGGCCACCTATTTTTACGTGGCCGAGATGGCCAGAGGACCGCAC-3 '5'-TGTCGCTGCCACTATCCGGAGTTCCTTT T GGA A C T C C GC A T A GT GC C T GC T C GT -3 '5 ' -ACACCAACGAGCACCTCTCCATCGTCCTGGTCATTTTTTAATGACCAGG ACGATCGAGAGGACCGACAGGCTAC-3'5'-TGCTGTAGGTGGTGGAGCATCGGTTCTGTCTTCATAGTCTTTTG ACTATCAACACAGAACCG ATG CTCCTGAACCG ACCCCT- 3'5'-CCCTTCACCATACCATTCCACTGGTTCGTTTTTACG AACCAG TGG AATG G TATG CACCACCT- 3'5'-GTGCTCTGCATTACGTCGACCTCACTTTTCTCAGGTCGACCTAATCCTGCATCC-3'5'-CGTCACGGATGCACCAGTCCATTGCCTTGGCTCTATTTTTAGACCCAAGGCAATCCACTCGACAGCACACGGCT-3 'S'.CTCACGGACAACTCGCGTATCGTACGCTCGCTTTTCCGAGCGTACGATACGCCTGCGACCGTAGCC-3'5'-CGTCGCACCGAACCAATCCGCTGGCTTGATTTTTCAAGCCAGCGGATTCGTTCGGACTTGTC-3'

The sequences of th e individual squares are given as squaresidestrand.6, are on he sides, and square 1, shown on the outside, is at th erear. One extra ar m of square 1 is illustrated attached to thesupport; hence, this diagram represents the truncated octahedronjust before cleavage from the support. Th e hexagons that flanksquare 5 (V , VI , VII, an d VIII) are shown as distorted hexagons.Those that abut square 1 (I , 11, 111, an d IV ) are shown astrapezoids, whose inner edges actually represent three edges ofthe hexagons. Th e double-helical twisting of the object is shown

for clarity899 only in th e cent ral portion of each edge, even tho ughit extends to the vertices. Figure I C s a diagram th at attem ptsto illustrate the stru ctur e the molecule would assume if it adoptedthe geometry of an ideal truncated octahedron, whose faces ar eall regular polygons. Such an object has 432 symmetry. Th eview in Fig ure IC s down one of the fourfold axes of the molecule.Figure Id shows the molecule a s it would app ear if stripped ofthe strands that correspond to the squares and the extra arms.


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1664 J . A m . Chem. Soc., Vol. 116, No . 5, 1994 Zhang and Seeman

-l

S 2 4P

- -3 s4s 1 s2SS S6S7 DS

- c d- -- a

SQUARE ASSEMBLY

D2

Dl+1

TETRASQUARE ASSEMBLY

14 B- LIGATE

Figure 2. Synthetic schemes used to synthesize the truncated octahedron. (a, top) Solid-support construction of the polyhedron. The boxed diagramin the upper left corner indicates the numbering of the individual squares. Each squ are in the rest of the dia gram is show n with its restriction sitesindicated. Symm etrically cleaving restriction sites (decoded in Table 2) are named S, ndicated in pairs, with one member of the pair being primed;restriction sites that a re cut distally are named D; restriction sites on he exocyclic arm s are not indicated. The arm s that will eventually be combinedto form edges of the object are d rawn on he outside of each square, and th e exocyclic arm s are drawn on he inside of the square. A reaction is indicatedby a line above a restriction site name: This means th at the restriction enzyme (or enzyme pair for those labeled S) s added, protecting hairpins areremoved, and then the two sticky ends are ligated together. In the first step, square 1 is ligated to the support. In the second step, the tetrasquarecomplex is added to squ are 1. In he final intermolecular step, square 6 is ligated to the restricted p entasquare complex. The next seven intramolecularclosure steps entail seven individual pairs of restrictions, as indicated: S3 an d S3,S4 and S4, S1 and Sl, 2 nd S2, S5 and S5, S6 an d S6, ndS7 and S7. The S1 an d S2 reaction sets have also been done preceding the S3 and S4 reaction sets. The product is shown in two forms. On he left,th e S 1 S 6 closures are shown as triple edges, to emphasize their origins; the two strands of the edge formed by the S7 closure are separated to m aintainthe symmetry of the picture. On he right, a slightly rotated front view of a polyhedral representation of a trun cated octehedron is shown without theexocyclic arms; the 432 cubic symmetry of the ideal object is evident from this view. (b, bottom) Solution syntheses of the individual components.The assemblies of squares 1 and 6 are shown on the top part of this figure. Every outside strand of square 6 is radioactively labeled. The lower partof the figure illustrates the construction of the tetrasquare com plex. The outermost three quart ers of each of squares 3,4, and 5 are annealed in pairsand ligated together. The fo ur-strand complexes that constitute the linkers and closest sections of square 2 are then added to them. The three squares,attached to fragments of square 2 are then combined, along with the m issing portion of square 2, to make the final intermediate product. The labelsar e on the outer strand portions of both left edges of square 2 and both left edges of square 5; hence, combined with the labels on all outer strandson the edges of square 6, every hexagonal strand is labeled.


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D N A- Truncated Octahedron J . Am. Chem. SOC.,Vol. 116, No. 5, 1994 1665an d EarI to cleave D N A attached to the solid support has forcedus to condense the five-ligation intermolecular synthesis to thetwo-ligation process shown in Figure 2a: squares 2-5 ar e combinedwith preformed connecting edges in solution and added to squa re1; square 6 is then added to this intermediate. The assemblyschemes of individual squares and of the tetrasquare complex( 2 - 3 4 5 ) are shown in Figure 2b. Following construction ofthe six-square intermediate, the seven intramolecular closuresare d one sequentially, followed by removal from the support andthe addition of an ann ealing hairpinlo o mak e a covalently closedmolecule (Figure 2a). Thus, except for square 1, the attachmentsite, the cyclic strands corresponding to he squares of the truncate doctahedron ( the inner strands), is already intact when particularfragments are ligated to the support. Th e hexagons ar e derivedby restriction and ligation of the long outer strand of theheptacatenane visible in the lower left corner of Figure 2a.Materials and Methods

Synthesis and Purification of DNA. All DNA molecules used in thisstudy are synthesized on an Applied Biosystems 380B automatic DNAsynthesizer, removed from the support, and deprotected using routinephosphoramidite procedures.16 All strands greater than 30 nucleotidesin length are purified by polyacrylamide gel electrophoresis. Shorterstrands a re purified by preparative HPLC on aDuPont Zorbax Bio Seriesoligonucleotide column at room temperature, using a gradient of NaClin a solvent system containing 20% acetonitrile and 80% 0.02 M sodiumphosphate. Fractions from the m ajor peak are collected, desalted, andevaporated to dryness.Solution Syntheses of Individual Squares 1 and 6. Each strand isphosphorylatedasdescribedpreviouslylofor 2-3 ha t 37 C. One hundredeighty picomolesof each of th e eight strands of the squares are combinedin partially complementary pairs, heated to 90 OC for 10 min, slowlycooled down, and ligated with 20 units of T4 DNA ligase (USB) at 16OC or at room temperature. The square is purified on a 7% denaturingpolyacrylamidegel, electroeluted for 2 h at 200 V, and ethanol precipitated.The final yield is about 10%.Solution Synthesisof the Tetrasquare Complex. The outermost threequarters of each of squares 3,4 , and 5 are annealed in pairs and ligatedtogether. The four-strandcomplexes hat constitute he linkers andclosestsectionsof square2 are then added to them. The three squares, attachedto fragments of square 2, are then combined, along with the missingportion of sq uare 2, to make the final intermediate product. Thetetrasquare s purified on a 4S%denaturinggel, electroeluted,and ethanolprecipitated . The synthesis is conducted on the 350 pmol scale andproceeds with a final yield of 1%, about 3.5 pmol.Interm olecular Addition of Components to the Support. In the firststep, 20 pmol of square 1 is ligated in 30% yield to 10 nM of support,prepared as described previously,1 containing about 50 pmol of linker.The linker on the support consists of a psoralen-crosslinked 26-mer ligatedon one end to a 30-mer deoxythymidine strand synthesizedon he supportan d on the other end to an 18-mer linker containing a Hind111 site anda BbuI site. All restriction enzymes are purchased from New EnglandBiolabs. The square is added by incubating it in 1000 pL of buffer 1(New England Biolabs) with 50 units of restriction enzyme D1 (BbsI)overnight at 37 OC, adding a complement to the restricted hairpin,incubating 15 min at 37 OC, and ligating to the support with 30-40 unitsof T4 DNA ligase (USB) overnight at room temperature.In th e second step, 3.5 pmol of the tetrasquare complex is added tothe supportby incubating n the presence of 50units of restriction enzymeD2 (BsmAI) overnight at 50 OC. The tetrasquare is incubated with anexcess of the complement to the restricted hairpin for 15 min at 37 OC,added to the support, and then ligated overnight at room temperature;the yield is about 1-2 pmol, 30-50% efficiency. The complement to thehairpin restricted from the support need not be added, because it can bewashed off the support readily. All restrictions on the support are donein 200-pL volumes with 100 units of restriction enzyme an d proceedovernight.In the final intermolecular step, square 6 is restric ted with enzyme D1(BbsI), incubated with a complement to the ha irpin, an d then ligated torestricted pentasquare complex overnight a t room temperature. About2 pmol of the six-square heptacatenane is formed.Intramolecular Closure Reactions, Release from Support, andA ~ e a l i n g .The closure ligations are carried out sequentiallyovernight at 37 OC. All

(16) Caruthers, M. H. Science 1985, 230, 281-285.

Table 2. Restriction Enzvmes Used for Synthesis and Analysiscode mate mate unionname name code name union codeD1D2D5s1s2s3s4s5S6s7

BbsIBsmAIBbvIBglII S1 BamHI DpnII ANcoI S2 BspHI nlaIII BNheI S3 SpeI RmaI CMluI S4 BssHII BstUI DXmaI S5 BspEI MspI EXhoI S6 Sal1 Tag1 FAcc65I S7 BsiWI RsaI G

a Restriction enzymes Si and Si have different six-base recognitionsites that both expose the same four-base symmetric sticky end. Theunion is the restriction enzyme tha t cleaves the four-base symmetric siteformed by ligation of the sites.This is an octacatenane, viewed down a threefold axis; itscomponents are the strands that correspond to th e hexagons.Synthetic Scheme

Th e sequence of the trun cated octahedron h as been designedusing the program SEQUIN.14 The squares are th e basic unitsused in the assembly, and the hexagons are derived by ligatingthe squares together. Each square consists of two cyclic strands,an inner strand corresponding to a square of the truncatedoctahedron and four extra arms and an outer strand that willbe used for ligation to oth er squares; the nucleotides of the outerstrand will ultimately be pa rt of th e hexagons in the final product.The sequence of each of the square units has been designedseparately and, insofar as possible, in accord with the basicprinciples of sequen ce symm etry minimization,6 using sequenceelements of length 6. Th e program has been modified from itsreported versionI4 to enable absolute exclusion of specifiedsequences, so th at restriction sites cannot occur adventitiously a tunwanted positions. Th e sequence of the squares is shown inTable 1. Each branch point is flanked by the same sequence thatsurrounds the branch point of the well-characterized junctionJ 1.Is Each edge of each square is formed by ligating six-nucleotidesticky ends, two of which ar e 5 overhangs an d two of which are3 overhangs, a s done previously;8 the sam e set of sticky end s isused for each square. The exocyclic arm s of each square containthe same interrupted restriction site (square 1, AlwNI; 2, BglI;3, DraIII; 4, PflMI; 5, SfiI; 6, BsrXI), except for square 1 . Oneof its exocyclic arm s contains a BbsI site, used to a ttach it to thesuppo rt. Eac h of the five interm olecular ligation sites is designedto be deprotected by a restriction enzyme that cleaves distallyfrom its recognition site on the hairpin loop. Two of theserestriction enzymes (BspMI an d EarI) have been found to beineffective when used todig est D N A attached to the solid support,forcing us to modify the planned syn thetic scheme. Th e sevenintramolecular ligation sites are composed of pairs of six-basesymmetric sites th at expose four-base sticky ends. Ligation resultsin the destruction of these sites10 but p roduces four-b ase sym metricsites that can be used for product analysis.

Whe reas the solid-support procedure permits on e to performligations in a stepwise fashion, we initially p lanned to ligate th esquares together one at a time. The squ are numbering is shownin Figure 2a. Th e positions of distal-cuttin g restriction enzymes( D l , D2, and D5) used in intermole cular linkages are shown, aswell as those of symmetrically cleaving restriction enzym es (Sl,Sl, ...,S7 ,S7),used to form edge sfrom intramolecular ligations.Th e correspondence between our notation and restriction enzymenames is shown in Table 2. Th e planned synthesis entailed theattachmen t of square 1 to the support and of square 2 to square1, and then the attachm ent of squares 3-5 to square 2, and finallythe attachment of square 6 to square 5 . Th e failure of BspMI(14) Seeman, N. C. J . Biomol. Struct. Dun.1990, 8, 573-581.(15) Kallenbach, N . R.; a, R.-I.; Seeman, N. C.Nature (London) 983,305, 29-831.


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1666 J. Am. Chem. Soc.. Vol. 116. No. . 1994 Zhang and Seeman1 2 3 4 5 6 7 1 2 3 4 5 e 7 8 e t o i i i z-2 3 4 5 6 7 8

Fm 3. Synthesis of the components of the polyhedron. (a, left) Square 1. This is an autoradiogram of a 7% (191 arrylamide/bisacrylamide)denaturing gel. Both strands of square I are labeled for this demonstration. although neither is labeled in the synthesis of the final product. LaneI contains the intact molecule. and lanes 2-5 contain the digestion producta of the outer circle with restriction enzymes S I (BgllI) . S2 (Ned),S7(Ace651). and D2 (BsmAI). Lane 6 contains the cleavage producta of DI (Bbsl) ,and lane 7 contains the AlwNI digestion products from three siteson the inner circle . Lane 8 contains a series of linear length markers. (b. center) Squ are 6. This is an autoradiogram of a 7% ( 1 9 1 acrylamide/bisacrylamide) denaturing gel. Only the outside strand is labeled on square 6. As in part a, lane I contains th e intact square, and the last lane, lane7, wntainsaserie sof linear lengthmarkers. LanesZ-Scontain theresultsofdigestingtheoutercirclerespcctively it h reslrictionen=ymesSS(BspEI).S6(Soll). S7(BsiWl),and DI (BbsI). Linear strands of the expected lengths, 236,236,236, and 220 nucleotides. are produced. Lane 6 containsthe visible digestion product of treating the square with BsrXI, the labeled outside circle. (c, right) Tetrasquare. This is an autoradiogram of a 4 5 %(401 acrylamide/bisacrylamide) denaturing gel. la n e 1 contains the intact tetrasquare. and lanes 2-9 contain respcctively the digestion products ofsymmetric enzymes SI (BamHI), S5 (Xmal ) .S3 (NhrI) ,S3(SpeI).4 (BssHII),S4 (MluI) .S6 (X h o l ) ,and SZ (BspHI). Lane IO contains theD2 BsmAI) digest. an d lane 1 I contains the DI (BbsI)digest. Lane 12 contains a series of linear length markers . The strands corresponding to thesquares are not visible in these gels, because they are unlabeledligations are carried out in 200-3W r L of the ligation b uffer dw ribc dpreviously.o Theseven intramolecularclosuresle~entailscvcnindi~d~lpairs of restrictions: S3 and S3.S4 and S4. SI and SI, S2 and S2.SS and SS, S6 and S6. and S7 and S7. The SI and S2 reaction setshave also been done preceding the S3 and S4 reaction sets. The sevenintramolecular reactions p r d ith about 50% yield each, for a finalyield of about IS fmol. The final step entails releasing the polyhedronfrom the support by means of enzyme D5 (Bbul) an d ligating on anannealing hairpin to close the central strand of square I .Results

Synthesis of th e Squares and the Tetrasquare. Figure 3ademonstrates the successful assembly of sq uare I , and Figure 3bsimilarly illustrates the syn thesis of squar e 6. These areautoradiograms of denaturing gels, showing that the cleavage ofexocyclic arms by restriction enzy mes yields specific predictedlinear and cyclic molecules. Lane 1 of Figure 3a contains theintact square, the lanes 2.3.4, and 5 contain respectively the SI(Bgll l) , S2 (Ncol). S7 (AcE65I. and D2 (BsmAI) digestionproducts,corresponding ocleavageof theouter strand in Figure2a. Each of these cleavages leaves the inn er circle (262nucleotides) intact and resultsin a 232-nucleotidelinear ragment,except for D2, which leaves a 220-nucleotide fragment. Lane 6contain s the cleavage produ cts of DI (BbsI),on he inner circle,which leavesth e 252-nucleotideoutercircle and a 226-nucleotidelinear fragment. Lane 7 contains h ecleavage productsofAlwN1,which bas three sites on the inner circle and which also leaves a252-nucleotideouter circle. Figure 3b illustrates thesam e analysisfor square 6. It is clear that the products expected from therestriction of properly formed squares are obtained.Figure 3c contains a denaturing gel that demonstrates theasgemblyofthetetrasquaremolecule,y showing that the digestio nprod ucts of each of its ten ou tside arms leave a linear moleculeof the expected length. Lane 1 shows the intact tetrasquare,labeledonlyon theoutsidestran d. Cleav ageo fthis trand by thesymmetrically cleaving enzymes (SI, SS, S3,S3. S4. S4, S6,S2) generates a molecule containing 848 nucleotides, whereascleavage by DZ produces a molecule with 836 nucleotides and

cleavage by D1 generates a molecule with 832 nucleotides. Th eproducts expected from the complete outer strand are clearlypresent. We dem onstrate the presence of each inner strand below.Intenno lecuhr Ligation on the Solid Support. Th e product ofintermolecular ligation on the solid support is the six-squareheptacatenane intermediate seen at the lower left of Figure 2a.There ar e two parts to the demo nstration that this molecule has

been formed: ( I ) We con firm that restriction with any of the 14symm etric restriction sites on the outer circle produces the samepredicted linear molecule; (2) we show that the intact objectincreases in mobility as we succ ssive ly restrict and remove eachof the inner squares. Parts a and b of Figure 4 demonstrate thefirst point, and pa rt c illustrates the second point. Th e circle ispredic ted to contain 1220 nucleotides, when restricted by an y ofth e 14 enzymes. It is clear from parts a and b that the samefragment, m igrating as expected relative to standards, resultsfrom cleavage with each of the 14 enzymes.Figure4 c con tains the results of removing stepwiseeach of thesquares from the heptacatenane. Lane 1 contains intact h e ptacatenane corresponding to the six-square intermediate. Lane2 contains the products of cleaving square 1 with AlwNI. toproducea hexacatenane. Lane 3 contains hep roductsofcleavingthe hexacatenane in square 6 with BsfXI to produce a penta-catenane. Lane 4 contains the products of cleaving the penta-catenane in square 5 with SjiI o produce a tetracatenane. Lane

5 contains the produ cts of cleaving th e tetracatena ne in square4 with PflMl to produce a triple catenane. Lane 6 contains theproducts of cleaving the triple catenane in square 3 with Ora111to produce a double catenane. Lane 7 contains the products ofcleaving the double catenane in square 2 with Bgn to producetheoutercircle. LaneBcontains theresultsofcleaving theoutercircle with Bglll to produce the 1220-nucleotide inear molecule.This gel clearly demonstrates that each of the inner squares isindeed a component of the intermediate.Intramo lecuhr Ligation on the Solid Support. It is necessaryto demonstrate that each of the strands corresponding to the

hexagons is contained within the structure. In the absence of


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DNA- Truncated Octahedron 1.Am . Chem. Soc.. Vol. 116. No. 5. 1994 16611 2 3 4 5 6 7 8 92 3 4 5 6 7 8 9 1 2 3 1 1 6 7 f i O

- 1 7 1 - -*o s

F k w4 Restriction analpis of he ria-squarehcptacatenane. (a. left, and b, ccnln) Restrictionof the outer circle. Thc omstrun WM cleaved fmmthe sup+ with H i n d l l l . The label in the molecule is only in the OUM circle, which i s destined 10 form all of the hexagons. These two ~ c l s reautoradiogramsdAB(a1crylamidc/bisaarrylamide)dcnaturinggels. Eachshowsthesamelinearbendthat resultsuponcleavagewitha ymmetrieallycleaving restriction endonuclcase. Both gels have the same formal, in which lane I contains uncleaved sixaquare product and lane 9 contains linearlength markers. In pan a, lanes 2-8 contain respectively the results of digestion with S5' (BspEl).S6 (Xhol) .S6' (Sofl).S3'(Sprl), S2' (BspHI),Sl (Acr651). andS7' ( B s l w I ) . In part b. lanes 2 - 8 conlain respectively the results of digestion with SI ( B g f l l ) .SI' (BomHI),S2 (Ncol ) .S3 N hc l ) ,S4 (Mful).S4'(BssHII). and S5 (Xmol) . In a11 cases. the band corresponds to the 1220-nuclcolidc predicted produn. (c. right) Restrictionof thesquares. The sia-square construct was cleaved from the support with Bbul. and the missing hairpin was llgatedto square I to complete the structureofthcinlermediate. Tbis panel shmsanautoradiogramora 3% (4O:l acrylamlde/bisacrylamide) denatunnggcl showingthedigestionofthc constructby sucassively greater numbers of restriction enzymes that cleave the exocyclic arms of the cyclic molecules that correspond to the squares of thetruncated octahedron. Lane 9 containsa seriesof linear lengthmarkers. Lane I contam the mtact sia-square ntermediate product. Lane 2 containsthe results of digesting that material with A f w N I . the enzyme that cleaves square 1. Lane 3 contains the results of digesting the material in lane 2with BsrXI. the enzyme that cleaves square 6. Lane 4 contains the resultsofdigesting he material in ane I with SJI, the enzyme that cleaves square5. Lane 5 contains the resultsof digesting he mater ia l in lane4 with Pf7MI. the enzyme that cleaves square4. Lane6contains the results ofdigestingthe material in lane 5 with Dmll l , the enzyme that cleaves square 3 . Lane1 ontains the results of digesting the material in lane 6 with Bgll. theenzyme that cleaves square 2. Lane 8 contains the results of cleaving the molwulc with Bgfll. which cleaves the outer strand. A certain amountofmaterial corresponding o breakdowno f the outer strand S visible in cach lane. It is clear from this gel that each square i s contained in the sir.squarcprodunstandards or of standard analyses for this type of molecule, wefeelthatthcfollowingdcmonstrateslhatthc 4-catmanemoleculehas indccd bcen made. I n analogy to proof of the synthesis ofthe cube-like molecule? we believe that the degradation of thefinal product to a characterizable oligocatcnanc standard wil lsufficetodcmonstratcthcsynthesis:Wedegradethe 14-catenancl o the cyclic arrangement of four-hexagon tctracatenanes thatflank each square. Three of these tctracatcnancs are visible inpan in Figure Id. For example. the square on the upper rightisflanked byred,bluc,green,and yellow strands;thctop hexagonhasanedgcthatleadstothered-bluecomcrofthesquare,showingthecatenalionof thosestrands; the front (green) hexagon showsthe catenation of the blue and green strands and the catenationof the green and yellow strands; and the hexagon on the lowerright shows the catenalion of the yellow and red strands. It ispossible 10 prepare a standard four-hexagon cyclictetracatcnanewith thissystem, byomittingtheadditionofsquarc6,closingtheedges corresponding o sites SI. S2. S3. nd S4. releasing fromthesupportwilhoutannealing,andthendigestingatthcrestricfionsites in squares 2-5 (data not shown). The presence of two ofthesctetracatenanes lankingoppositesquaresconstitutes minimalproofofthe simullaneousprcscnceofallcight hexagonal strands.We show here that five of the si x possible tetracatenancs areproducedbythcappropriatcrestrictions;theinadvertent missionof restriction sites on the edges between hexagons I and I I andbetwcen hexagons V and V I (Figure Ib) prevents us fromdemonstrating the prcscnfeof the tetracatenane lanking square6.

Therestriction sitsavailablc todemonstrate heintramolecularclosure of the object are those on the extra arms of the squares,as we l l as those sites shown as the capital lettersA 4 n FigureIb. These sites are located on the seven edge formed byintramolecular closure (Table 2). They correspond espectivelyto the four-base restriction sites that remain after ligating the

arms that had contained restriction sitesSI47 nd their primedcomplements. Figure Sa illustrates the presence of the tetra-catenanes that flank squares 1-3. and Figure 5b illustrates theprcsence of the tetracatcnanes that flank squares 4 and 5. I neach case, the completed. annealed polyhedron s digested in amixture of the restrict ion enzymes that digest a l l the exocyclicarmsofthesquares. Thismixtureisthcndividedintofivealiquotsand digested by the restriction enzymes corresponding to s i t sthat liberate tetracatcnanes: ( I ) C and D (Rmaland BsfUI) toliberatcthetetracatenanethatflankssquare ; @ ) Eand F(Msp1and Taql) to liberate thetetracatcnane that flankssquare 2; (3)B and D (Nlalll and BsfUl) lo liberate the tetracatenane thatflanks square 3; (4) A and C (Dpnll and Rmal) to liberate thetetracatenanc that flanks square 4; and (5) A and B (Dpnll andNlalll) to liberate the tetracatenanc that flanks square 5. Ineach case. the final digestion products comigratc with the cyclicteiracatcnancmarker onthcsamcgcl. When thctetracatcnancs(includingthcstandard)aretreated withcxonucleasc Ill.certainamount of material that comigrates with dicatcnanc appears,perhapsduetoatopoisomcrascI-likcstrandpassagcactivitythatfrequently contaminates preparationsof this enzyme; treatmentof DNA knots with commercial preparations of exonuclease 111produces circles ( S . M. Du and N.C.S.. unpublished). andtreatment of catenanes produces smaller catenanes (Y.Z . andN.C.S..unpublished). The integri ly of the multistrand bandona denaturing gel and the persistence of the tetracatenane bandwhile much longer amounts of linear material (at the bottom ofthe gel) ar e digested suggest that such disappearance of thetetracatcnaneas i s seen results rom this contaminating activityand that the material is covalently c l d .

Comtndom of the Twuted Octladrom. The truncatedoctahedron constructedhere is the most complex object bui lt to


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1668 J. Am . Chem. Soc.. Vol. 116,No. . 1994 Zhang and Seeman1 2 3 4 5 6 7 0 9 1 2 3 4 5 6 7

E ' -

0 0 -...FImre5. Retriction analysis to demonstrate the prescna of all the hexagonal strands. Theentire clarcd and annealed polyhedron is purified on a3.5%(4o:l arrylamide/bisacrylamide)denaturing gel and digested in 100 pL of New England Biolaba buffer 3 with a mixture containingBt l l (whichalso cleaves Sfil sites). DrolIl. AlwNI. PJIMI. and BsfXI. This produces a squareless octacatenanc that is then divided into five t u b a mntaining 20pL each for further digestion. Th e p i t i o n s of the tetracatenane and of the intact molaulc are indicated to the left of each gel. (a. left) Digestionto release the cyclic tetracatcnanes that flank squares I . 2. and 3. This is an autoradiogram of a 5%(4O:l acrylamide/bisacrylamidc)denaturing gel.Lane 1 contains a cyclic tetracatmane marker prepared byclcsing the edgescorresponding to SI.S2. S3. and S4 in th e five-square hcxacatenanc shownon theuppcr right portion of Figure 2a, followedby digestionofitsconstituentsquares; his tetracatenane hasbscn ch ar ac te rid by successive restriction(data not shown). Lane 2 contains undigested target truncated octahedron. Lane 3 contains the results of reating the squarelcss octacatenane withrestriction cnzymesC and D (Rmol an d BsrUI) to liberatethetetracatenane(I.II. 111, IV) hat flanksquare 1. Lane 4 containsthe resultsoltreatingthe material in lane 3 with exonuclease 111(US iochemical). Lane 5 contains the results of treating the squareless octacatenanc with restrictionenzymes E nd F (Mspl and TaqI) to liberate the tetracatenane (1. II. V, I) that flankssquare 2. Lane 6 contains the results of treating the materialin lane 5 with exonuclease Ill . Lane 7 contains the results of treating the squarelessoctacatenanewith restriction enzymes Band D (NloIIIand BslUI)to libcrate the tetracatenane (1. 111. V. VIII) that flanks square 3. Lane 8 contains the exonuclease 111digestion products of the material in lane 7.Lane 9 contains a series of linear length markers. (b, right) Digestion to release the cyclic tetracatcnanes that flank squares 4 and 5. This is anautoradiogram of a 5% (401 acrylamide/bisacrylamidc) denaturing gel. As in part a. lane I contains the tetracatenane marker, and lane 2 containsundigested material. Lane 3 contains theresults ofdigesting thesquareless octacatenanewith restriction enzymes A and C (Dpnl l and RmoI) tolibcratethe tctracatenane (11. IV.VI, VII) that flanks square 4. Lane 4 contains the results of digesting the material in lane 3 with exonuclease 111. Lane5 contains the results of igesting the squareless octacatenanc with restriction enzymes A and B (DpnlI an d N la l l l ) to liberate the tetracatenane (V.VI.VII. VIII) that f lanks square 5 . Lane 6 contains the results of digesting the material in lane 5 with exonuclease 111. Lane 7 contains a scries oflinear length markers. Note that. in both parts a and b, substantial quantitie s of linear DNA are digested by exonuclease Ill, but only small quantitiesof the target catcnanes are degraded by this enzyme. Whereas this is a denaturing gel. associations of linear molecules are unlikely to pcrsist on it.date from branched DN A components. Th e construction of thesqu are components in solution proceeds read ily with 10%yields,but synthesisof the tetrasquare com ponent in solution isonly I%efficient. This reflects the experienceof constructing a cube-likemolecule in solution, which also proceeds in 1%yield. Ligationsof components to the solid suppor t are fairly efficient. with 3 s50% yields. Surp risingly, the intramole cular closures on th esupport do not proceed well, ca.50% yield each, in contrast tonearly quantitative yields seen in intramolecular closures of aquadrilateral on the support.'o Neve rtheless, a molecule withthree times the number of edges contained in th e cube has becnconstructed in similar yield to the cube by means of the solid-support methodology.

The ultimate synthetic schemes of both the cube and thetruncated octahedron have incorporated modifications ne ass i-tated byunanticipatedexperimentaldifficulties: t w asimpossibleto purify th e key intermediatesofthecubeundernativeconditions,so a denaturation-reconstitution step was included; the inabilityof Ear1 or BspMl to cleave DNA on the support required thelow-yield tetrasquare intermediate to be used, nstead of a seriesofindividualsquares. Thereasons forthefailureofthcscenzymeson hesupport areunclear but may berelated ton need for multiplesubstrates to be avai lable s imul taneo ~sly. '~ - '~t is possible toconnectupsixsquaresintherequiredorderusingonlytwodistallycutting enzymes, but wherea s a new sequen ce would have neededtobedesignedandsynthesized,we ried thetetrasquareapproachfirst. I t is clear that further developments in the synthetic

(17) Barter. B. K.;Topal. M. D. lorhm#rrry 1993.32.8291-8298.( 1 8 ) Y a w. C. C.:Topl, M. D. iorhrmisrry 199% 31.9657-9664.(19)OIlrr. A. R.: Vandcn Bract. W. . Conrad. M.: Tonal. M. D.

methodologies will be required before syntheses can be plannedand automated routinely.Structureof tbe M o l d e . Th e earlier construction of a c u blike molecule entailed th e closure of a belt-like intermediate.'Oneof theuncertaintiesasmciatedwith suc ha p rocedure involvesthe determination of the inside and outside of the polyhedron,because a belt can lose in twostru cturally inequivalent directions.I t is likely that thisuncertainty has b eenovercomein thesynthesisof the truncated octahedron, because one of the exocyclic armsisattachedtothesupportat thestartofthesynthesis. Webelievethat this feature has selected those molecules that have theirexocyclic arms facing outward rather than inward.As n the case of the cube-like molecule, we have establishedthe connectivity of the product catenane, rather th an th e 3-Dstructure of the molecule. We assume that each edge indeedconstitutes a double linking of two cyclic single strands. The

method of synthesis suggests that this type of linking structurewould bemo st probable; however, there is nodirectevidencethata link somewhere is not missing. In contrast to the techniquesused in the solution synth esis of the cube,9one of the strengthsofthesolid-support methodology isthat nosinglestrandis requiredto hybridize intermolecularly to thre e sep arate strands, possiblymissing a link to the central strand. Here, we have had to dotriple hybridizations only with the edge intermediates in th esynthesis of the tetrasqu are (Figure 2b); whereas the edges arethe dom inant portions of these objects and no strain appears tobe involved, we feel that missing links are unlikely in thesemolecules.Wed onotkn owthesh apethat themoleculeassumes. In da d,the high flexibility of th e four-arm junctionm makes it likely tha t

many differentconfo rmers of the molecule exist. If the molecule


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DNA- Truncated Octahedronwere to adopt the form of an ideal semiregular truncatedoctahedron, it would resemble the shape shown in Figure IC . Inthis idealized structur e, the vertices constitute a mac rom olecula r-scale version of the arrangement of Si(A1) atoms in sodalite;extending this structu re n three dimensions by joining the externalarm s of numerous cages in the directions in dicated would crea tean expanded version of a material similar to zeolite A (e.g. ref21). Given a 68-A edge, the distance between opposite square sof a polyhedron inscribed inside the DNA would be 192 A, an dthe distance between opposite hexagons would be 166 A. Thevolume of the inscribed polyhedron would be 3557 nm3.Suggestions for Improved Syntheses. Th e synthesis of an objectfrom DN A as complex as a truncated octahedron with approx-imately two worker years of labor demo nstrates that D N A is atract able medium for nanoscale construction. Th e successfulassembly of the truncated o ctahedron from DN A demonstratesthat the technology has attained control of DNA topology, interms of both stra nd linking and helix-axis connectivity. It seemsreasonable to suggest th at an y Platonic, Archimedean, or Catalansolid could probably be constructed from this system. Th e facttha t we have been able to constru ct a polyhedron from polygonsaugur s well for the chances of building 3-D ar rays from p olyhedra.Nevertheless, the methodology could benefit from severalimprovements: (1) Means mu st be found to rende r a complexsynthe ticdesign less sensitive to th e failu re of biologically derivedcomponents, such as the problems encountered here withres tr ic tion enzymes . Poss ib ly , chemical c l e a ~ a g e ~ ~ , ~ ~r moregeneral enzymatic24325or mixed chemical-enzymatic26 techniques

J . A m . Chem.SOC., ol. 116, No. 5, 1994 1669

(20) Petrillo, M. L.; Newton, C. J.; Cunningham, R. P.; Ma, R.-I.;(21) Meier, W.M.;O lson,D.H.nAdvancesinChemistrySeries;American(22) Horn, .; Downing, K.;Gee, Y.;Urdea, M . S.Nucleosides Nucleotides(23) Sigman, D. S. ;Chen,C. B.; Gorin, M. B. Nature (London)1993,363,(24) Kim, S. C.; Padhajska, A . J.; Szybalski,W . Science 1988,240, 504-(25) Lyamichev, V. ; Brow, M. A. D. ; Dahlberg, J. E. Science 1993, 260,

Kallenbach, N. R.; Seeman, N . C . Biopolymers 1988, 27, 1337-1352.Chemical Society: Washington, DC, 1971; Vol. 101, pp 155-170.1991, 10, 299-302.474-475.506.778-783.

can be developed as emergency m easures to use at specific stepsto produ ce asymmetric sticky ends when rou tine restriction fails.(2) Before incorporation into a synthetic scheme, all enzymesshould be tested for their activity on the suppo rt, preferrably inthe presence of branched D N A molecules. In addition, enzymesshould be free of stran d-passa ge activities, as well as of nonspecificendonuclease activities. (3) Th e use of more rigid components,such as those identified recently by Leontis a nd his colleague^,^^might pe rmit th e incorp oration of multiple steps in the synthesis.Mo re rigid com ponents are probably necessary for the assemblyof periodic matter. (4 ) If DN A is to be used as scaffolding todirect the associations of other m ac ro m ~l ec ul es ,~ -~he enzymaticcleavage process used here will need to be replaced w ith selectivechem ical procedures tha t will not be sensitive to the presence ofbulky molecules tethered to the DNA. (5) Likewise, chemicalligation28J9 might prove m ore effective than enzym atic ligation.However, one must be aware that DNA ligase is capable oftransducing the energy of its AT P cofactor to generate strainedtarget products th at ar e not seen when chemical ligation is used(S.M. D u and N.C.S., unpublished). (6) The synthesis of complexobjects and periodic matter w ould be simplified by th e automa tionof the process. It is to be hoped that the implem entation of theseimprovements will lead to even more effective chemistry on th enanometer scale.

Acknowledgment. We thank Francis Barany for invaluableadvice abo ut restriction enzymes. This research has beensupported by Gra nts N00014-89-5-3078 from theOfficeofN ava1Research andGM-29554 from th eN IH 0N.C.S. and bya DeansDissertation Fellowship from New York University to Y .Z. Th esuppo rt of Biomolecular Imaging on the NY U campus by the W.M. Keck Fo undation is gratefully acknowledged.(26) Kimball, A. S.; Lee, J. ; Jayaram, M.; Tullius, T. D . Biochemistry(27) Leontis, N. B.; Kwok, W.; Newm an, J . S. Nucleic Acids Res. 1991,(28) Ashley, G. W. ; Kushlan, D. M . Biochemisrry 1991,30, 2927-2933.(29) Zuber, G.;Sirlin, C.; Behr, J . P. J . A m . Chem. SOC. 993,115,4939-

1993, 32, 4698-4701.19, 759-766.

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Documents

Yuwen Zhang and Nadrian C. Seeman- Construction of a DNA-Truncated Octahedron