The Proceedings of the 1989 NanoCon Northwest regional nanotechnology conference, with K. Eric Drexler as Guest of Honor.

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Appendix D: Branched DNA and Nanotechnology by Dr. Ned Seeman

Nanoscale Assembly and Manipulation of Branched DNA:
A Biological Starting Point for Nanotechnology

Nadrian C. Seeman

Department of Chemistry
New York University
New York, NY 10003


Molecular biotechnology is a promising point from which nanotechnology can evolve, because living systems can be thought of as a successful example of atomic and molecular manipulation on the nano-scale. Although enzymes manipulate atoms and molecular fragments on the Angstrom scale, biological systems make their structural components on the nanometer scale, where weak intermolecular energies direct the self-assembly process. This latter approach is likely to be the simplest motif for building the first nano-scale devices. The biological components that we are exploring for purposes of nano-scale assembly are branched nucleic acid junctions, whose synthesis and assembly are readily controlled with the current level of technology. It appears possible to use these junctions to make stick-figures and crystalline networks. These objects can be used for scaffolding to orient and juxtapose other molecules to form biochips, nanomanipulators and multienzyme complexes. Strategies for the synthesis of involve elimination of structural alternatives. Potential cloning strategies for DNA structures are based on single-stranded vectors.

Nanotechnology as an outgrowth of biotechnology

Nanotechnology may be approached from two directions, either top-down or bottom-up. The top-down approach was originally delineated by Feynman (1961), who suggested that machines could be constructed that could build successively smaller machines until the nano-scale was reached. Miniaturization of the sort Feynman suggested is actively pursued by numerous investigators (e.g., Angell, et al., 1983; A. Robinson, 1985). The bottom-up approach entails making objects and devices on the nano-scale from molecular and macromolecular components. There is good reason to believe that this approach is practical to some extent, since living systems already exemplify its success: cells manipulate chemical structure on the Angstrom scale via their enzymatic proteins; in addition, they contain self-assembling structural components, also usually proteins, although these are on the nanometer scale. Drexler (1981) has recognized the relationship between the tasks performed by the cell and the mechanical tasks fulfilled by our macroscopic technology.

It is important to differentiate the manipulation of intact molecules from the manipulation of individual atoms or molecular fragments to form new covalent molecules. Intact molecules bind to each other non-covalently by means of weak forces: One of the best-known tight-binding interactions involves two macromolecules in a complex, Lac repressor protein and its DNA operator sequence. Under cellular conditions the dissociation constant of the complex is 10-13 M (e.g., Stryer, 1988), corresponding to 18.2 Kcal/mole. Such intermolecular binding results from a combination of numerous weak interactions, such as hydrogen bonds, complementary van der Waals contacts and electrostatic interactions. The total number of covalent bonds in the molecules involved in a protein-DNA complex is over 1000. Breaking any of these covalent bonds would cost far more energy than pulling the molecules away from each other: Energies associated with single bonds found in biological systems are, H-O, 110, H-N, 84, H-C, 99, C-C, 80, C-N, 62, and C-O, 81 Kcal/mole (e.g., Moore, 1963). The making and breaking of covalent bonds in biological systems is almost always catalyzed by their protein-based catalysts, the enzymes. On the other hand, self-assembly is spontaneous. Manipulation that involves the breaking or formation of covalent bonds requires the control of processes in which large amounts of energy can be liberated or consumed (depending on reference states). Although protein engineering is a burgeoning field today, the efforts of workers in that area are largely directed at changing the stabilities and specificities of existing enzymes, rather than catalyzing new reactions. For example, work is in progress to change the features and substrates of molecules such as restriction enzymes, tRNA synthetases, proteases and reductases (e.g., Oxender and Fox, 1987), and much is hoped from abzymes (Pollack, et al., 1986; Tramantano, et al., 1986), but the goal of making new ceramics with protein-based enzymes is more remote.

Specific intermolecular self-assembly is much easier to control. However, because a large number of weak interactions are typically involved in this process, the scale of assembly must increase from the Angstrom scale to the nanometer scale. The following discussion is predicated on the premise that the low energies required for assembly and manipulation in an intermolecular context are easier to treat than the higher energies necessary to make and break chemical bonds. Thus, it is likely that we will move enzymes around and orient them to make new multi-functional complexes in the near future, but a much larger time-frame will be necessary to develop catalytic activities that do not deal with molecules of biological origin.

Because the predominant examples of nanotechnology in nature derive from living systems, it is reasonable to look to those systems for the components of the first nanotechnological objects and devices. Thus, nanotechnology, which can come from many routes, is likely to evolve in part from molecular biotechnology. Because most of the functions performed within the cell are executed by proteins, most of the thinking has been directed towards those molecules. Although some progress has been made in this direction (e.g., Regan and DeGrado, 1988; Degrado, et al., 1989), the design and manipulation of protein structure is not straightforward: the largest gap in our understanding of the Central Dogma of Molecular Biology is the way in which the 3-D structure of proteins is directed by their sequence.

Nucleic acids as components of nanotechnological systems

For some years, we have been working on an alternative self-assembling biological system, the nucleic acids DNA and RNA. As known to all, these polymeric molecules can form double helical structures from two anti-parallel strands whose sequences are complementary: an adenine (A) on one strand pairs with a thymine (T) on the opposite strand, while the same relationship exists between guanine (G) and cytosine (C). The inherent difficulty of imagining DNA as an appropriate material for nano-scale construction is that the pre-eminent feature of nucleic acid molecules is that they are organized about linear helix axes; although the double helix may supercoil or writhe over a long distance, the helix axis remains unbranched. From a structural point of view, this means that nucleic acids correspond to line segments, which can only form longer lines or circles; the nucleic acid vertex is absent from most considerations of double helical DNA or RNA.

While attempting to model intermediates in genetic recombination that are naturally unstable, we devised minimal-symmetry sequence-specifying algorithms (Seeman, 1981, 1982; Seeman and Kallenbach, 1983) for making specific stable, self-assembling, branched nucleic acid complexes from synthetic oligonucleotides. An example of such a 'junction' structure with four arms is shown in Figure 1. This junction is termed 'immobile', because it contains no homologous twofold sequence symmetry about its center; junctions with small amounts of such sequence symmetry are called semi-mobile or partially mobile. As a practical matter, we have concentrated on DNA, rather than RNA or RNA-DNA hybrids, primarily because its synthesis is conveniently accomplished by solid-state automated techniques (Caruthers, 1982) and because it is less sensitive to hydrolysis. We and others have characterized and modeled these molecules and their interactions extensively (Kallenbach, et al., 1983a, 1983b; Seeman, et al., 1985; Wemmer, et al., 1985; Kallenbach and Seeman, 1986; Marky, et al., 1987; Cooper and Hagerman, 1987; Churchill, et al., 1988; Chen, et al., 1988; Duckett et al., 1988; Mueller, et al., 1988; Petrillo, et al., 1988; Seeman, 1988; Seeman and Kallenbach, 1988; Seeman, et al., 1989). For purposes of this discussion, the most important fact that has been established about junctions is that strands designed by these algorithms can self-assemble to form branched complexes, even though linear duplex nucleic acids are intrinsically more stable than branched ones (Courey and Wang, 1983). We have explored junctions with 3-6 arms in a preliminary study, and find that those with five and six arms are less stable than those with three and four arms (Mueller, et al., 1987).

Figure 1. A Stable DNA Branched Junction. The junction shown, called J1, is composed of four strands of DNA, labeled with Arabic numerals. The 3' end of each strand is indicated by the half-arrows. Each strand is paired with two other strands to form a double helical arm; the arms are numbered with Roman numerals. The hydrogen bonded base paring that forms the double helices is indicated by the dots between the bases. The sequence of this junction has been optimized (Seeman and Kallenbach, 1983) to minimize symmetry and non-Watson-Crick base pairing. Because there is no homologous twofold sequence symmetry flanking the central branch point, this junction cannot undergo the isomerization reaction known as branch point migration. This junction is stable, and has been extensively characterized (see text).
(Figure has been somewhat re-arranged from Dr. Seeman's manuscript.)

Construction with nucleic acid branched junctions

Genetic engineering with unbranched DNA molecules uses cohesive 'sticky' ends on different fragments to direct their assembly in a particular order (Cohen, et al, 1973): these single-stranded regions will pair with complementary single-stranded regions on other molecules to form complexes that are then annealed to covalency by DNA ligase (e.g., Maniatis, et al., 1982). Nucleic acid branched junctions can be treated in the same way. Attachment of particular sticky-ends to a branched nucleic acid structure converts it, in principle, to a highly specific valence cluster with addressable ends (Seeman, 1981, 1982, 1985a, 1985b). These branched molecules are building blocks that can, in principle, be assembled into stick-figures and N-connected networks, in which the edges are made from double helical DNA, and the vertices correspond to the branch points. Assembly of a 4-arm junction into a quadrilateral, with the potential of forming a 2-D lattice is illustrated in Figure 2. It is worth noting that this system is inherently a three-dimensional system, since the edges are helices, rather than parallel ladders, as they are drawn in Figure 2.

Figure 2. Formation of a two-dimensional lattice from an immobile junction with sticky ends. A is a sticky end and A' is its complement. The same relationship exists between B and B'. Four of the monomeric junctions on the left are complexed in parallel orientation to yield the structure on the right. Note that A and B are different from each other, as indicated by the pairing in the complex. DNA ligase can close the gaps left in the complex. Note that the complex has maintained open valences, so that it can be extended by the addition of more monomers.
(Figure has been somewhat re-arranged from Dr. Seeman's manuscript.)

We have demonstrated that individual three-arm junctions can be ligated together to form 2-connected linear and macrocyclic oligomers, using a variety of junction-flanking sequences (Ma, et al., 1986). The same experiment has been performed with all six pairs of arms of a particular 4-arm junction (Petrillo, et al., 1988). In all these cases, the first macrocycle formed is the trimer, while the final products are at least as high as linear and cyclic decamers and hexamers, respectively. The ability to form all these different closed macrocycles indicates that junctions are flexible, both a problem and an advantage in using them as structural components.

The ligation experiments described so far have all been performed with junctions separated by two turns of DNA in the final product. When the same experiment is done with one and a half turns of DNA between junctions, the ladder of macrocyclic products begins with the tetramer, although a trace of the highly strained trimer can be detected (Petrillo, et al., 1988). This result demonstrates the importance of taking twist into account when engineering with nucleic acids. Parallel line representations of DNA, such as Figure 2, are only valid if the junctions are separated by an integral number of turns of DNA. The geometrical aspects of construction with helical components have been analyzed (Seeman, 1985a), and an interactive computer-graphics program has been written to facilitate design in this context (Seeman, 1985b).

The ligation experiments described above involve repetitive linkage of a single type of junction molecule. In addition, we have demonstrated that assembly of a particular structure can be directed by utilizing a set of junctions with individually addressable sticky ends (Chen, et al., 1989). In this case, a particular quadrilateral was designed to yield two hextuply linked circles when its four component junctions are ligated (Figure 3). A pentameric restriction site is incorporated into one exocyclic arm of each circle. These are particular loci where DNA is recognized and cleaved by endonucleases called restriction enzymes. When the DNA has been cleaved here after the synthesis, its sequence can be determined (Maxam and Gilbert, 1977) to establish the proper assembly of components. We have performed this analysis to demonstrate formation of the desired product. Thus, it appears that the addressability of the sticky ends is indeed a reliable property of this self-assembling system (Chen, et al., 1989).

Figure 3. The Scheme of Synthesis of a DNA Quadrilateral. The individual reactant junctions are shown on the left of the figure and the product is shown on the right. For clarity, the double helicity of the DNA has been represented merely as parallel lines in the vicinity of the branch sites, and is confined to regions distal to the branch sites; nevertheless, all the twisting expected on the main cycle is shown on both sides of the figure. On the left, thick strands and the thin strands are associated in pairs to form 3-arm junctions, in which one 'exocyclic' arm is closed in a hairpin loop. Arrowheads represent the 3' ends of individual strands. Strand numbering is indicated on the left by the numbers from 1 to 8. The 5' and 3' symbols indicate the sense of the single-stranded overhangs. The overhangs are all on the short strands. The filled region in the exocyclic stem formed by strand 6 represents a restriction site, while the filled region in the stem of strand 4 corresponds to a different restriction site. When the ligation is complete, the four junctions are expected to form two intersecting DNA circles that are linked 6 times.
(Figure has been somewhat re-arranged from Dr. Seeman's manuscript.)

I have described a self-assembling system for making stick-figures, in which the ends are highly addressable. In addition, the individual edges are relatively stiff: The persistence length of DNA is usually taken to be about 600 Å (Allison and Schurr, 1979; Barkeley and Zimm, 1979), although it can vary from 450 Å to 1000 Å, depending on conditions (Hagerman, 1988); most of the applications envisioned here entail specific links every 70-100 Å (2-3 turns of DNA). The least favorable feature of this system is that the 'valence angle' between any pair of arms is not fixed, but may vary extensively from junction to junction, or even within the same junction, over time. This flexibility of the junction cluster may be partly advantageous for junctions with four or more arms: When four or more different objects are attached to a central object to form a rigid 3-dimensional cluster, the cluster forms in both right-handed and left-handed mirror images of each other. The presence of both mirror images in a reaction mixture can yield a multitude of products, but flexible junctions are not frozen into left-handed and right-handed configurations of sticky ends before ligation occurs.

Flexibility is not necessarily a problem in directing assembly for an isolated device, because sticky-ended associations can be used to specify connectivity; since no symmetry is necessary among the various sticky ends employed, flexibility need not lead to ambiguity in the connectivity of the object. Nevertheless, the geometry of an object is not fixed by connectivity in a flexible system. For example, closure of a belt-like object to form a prism can yield, in principle, two isomers, with one side of the belt or the other on the outside of the prism. Furthermore, for an infinite device, such as a crystal (Seeman, 1981, 1982) or a crystal-based biochip (Robinson and Seeman, 1987) the two complementary ends of adjacent unit cells are inherently identical throughout the lattice. Therefore, flexible connections can lead to cyclization and hetereogeneous structures, because different angles may be formed between different repeating units. In macroscopic terms, one might think of this system as being like Tinker Toys, in which the linear connectors are made from moist, but not fully hydrated pasta, such as double helical rotini, while the junction pieces that they impale are made out of marshmallows.

In general, in order to minimize these 'valence angle flexibility' assembly problems, one must utilize synthetic protocols and structural motifs that minimize sensitivity to flexibility. Consider, for concreteness, the 5-connected network shown in Figure 4. This drawing shows the lattice of interstitial octahedra formed by a periodic array of truncated cubes. In principle, this array could be constructed from repeat units of individual rigid octahedra having external arms that contain the appropriate sticky ends. However, since each individual junction is so flexible, connections between octahedral corners on different octahedra cannot be guaranteed to form squares; triangles or pentagons, for example could form with an octahedron at each vertex. With this flexible system, one would need to construct a specific square array of these octahedra, and perhaps the entire cube-like array in Figure 4, because of the flexibility of the joints flanking the vertices. Thus, connecting nucleic acid polyhedra by corners or edges does not appear to guarantee the extent of control necessary to construct pre-specified periodic lattices of these objects.

Face-connected motifs appear to be a means around this sort of problem. For example, the assembly of the truncated octahedra of Figure 5 ought to be immune to junction flexibility, because orientation is controlled by multiple contacts in each direction. This type of inter-object contact ought to be fostered under stringent hybridization conditions to avoid mispairing, which can produce improper linkages. Note that an extra aspect of specificity can be incorporated into the truncated octahedra of Figure 5 by using different lengths (shown) and different polarities (not shown), as well as different sequences for the four contacts/face connection illustrated. Nevertheless, a sequential association protocol is advisable, in order to avoid association of the hexagonal faces instead of the square ones.

Figure 4. A 5-Connected Array of Octahedra Flanking a Truncated Cube. Each of the edges in this figure consists of double helical DNA, and each of the vertices corresponds to a 5-arm junction. In principle, this network can be extended infinitely. The unique portion of this array is the individual octahedron. By synthesizing the entire object shown from symmetry-minimized DNA, a face-connected cohesive pattern could be used to extend this structure infinitely.
(Figure has been somewhat re-arranged from Dr. Seeman's manuscript.)

Figure 5. A Square Group of Face-Connected Truncated Octahedra. Shown are 4 face-connected truncated octahedra, linked at their square faces. The polyhedron formed by the connections is a cube, drawn slightly elongated here. Only two directions of cohesion are illustrated, but the squares on the front and back faces are available as well to form a 3-D lattice from this basic building block. The individual lines connecting the truncated octahedra are made from double helical DNA. The arrowheads indicate the longer double helices in each pair that are to be ligated. The set of these on each square face is the lock-and-key feature on which specificity relies in this illustration. Note that the arrangement of long and short connecting pieces is used in the horizontal direction is different from that in vertical direction. No use is made of polarity (3' or 5' overhangs) in this figure to increase specificity, but this feature can also be employed, as noted in Figure 3. Extension of this array in the direction out of the page will create a central cavity shaped like a great rhombicuboctahedron (Williams, 1979).
(Figure has been somewhat re-arranged from Dr. Seeman's manuscript.)

Restriction-growth cycles

A general synthetic strategy suggested by our experience with the quadrilateral (Chen, et al., 1989) involves successive cycles of purifying covalently closed intermediates by enzymatic digestion, followed by restriction. The major step in purifying the quadrilateral is treatment of the crude ligation product with exonuclease III, which removes impurities that contain free ends. In this synthesis, only one impurity resists exonuclease treatment, and that substance is readily purified away from the desired product by electrophoresis. Besides exonuclease resistance, covalently closed intermediates are stable under denaturing conditions, while species with free ends will denature. Thus, the formation of covalently closed intermediates is a convenience in synthesis.

Of course, covalently closed intermediates contain no ends. Fortunately, it is possible to create new cohesive ends by treating these intermediates with restriction endonucleases, once the exonuclease has been removed. This technique is shown in Figure 6, illustrating the 2-step synthesis of a cube. One must take precautions not to increase the symmetry of the cohesive ends unnecessarily by restriction; the sequence symmetry of most restriction sites is known to be twofold (e.g., Yuan, 1981). This problem may be overcome in at least two ways: (1) use of the few restriction enzymes that do not cut symmetrically, or (2) use of multiple attachment sites for a single contact, as illustrated above in Figure 5. The different lengths of the 4 arms connecting faces of the truncated octahedra provide the lock-and-key on a larger scale; so long as they are different, symmetry in the individual cohesive ends will not destroy control of associations in the entire contact region. This approach is analogous to the high specificity of base pairs that derives from the placement of hydrogen bonds in a double helical context: although A is complementary to G, for example, the backbone imposes a structure that causes A-G pairing to cost free energy, relative to pairing with pyrimidines. Similarly, forming one connection between polyhedra, rather than four, costs free energy at stringent temperatures, and will not be favored.

Figure 6. Ligation-Restriction-Ligation Cyclic Scheme for the Synthesis of a Cube in two steps.

Step 1 -- Combine "Squares"

to Form a "Ladder"

Step 2 -- Activate the Ends

ligate, and the cube is complete
Figure 6. Ligation-Restriction-Ligation Cyclic Scheme for the Synthesis of a Cube. Half-arrows indicate the 3' ends of strands. Bold letters are symbolic of cohesive ends; complements are indicated by primes. Note that A and B cohesive ends are masked by hairpins. The numbered thunderbolt arrows are sites of restriction endonuclease sites needed for analysis of product; each edge contains a unique restriction site. Every edge is designed to be two helical turns long, and thus the parallel-line representation of double helix between junctions is valid. The first step of synthesis involves hybridization of two unique 3-strand squares, whose corners are 3-arm junctions. All 5' ends are phosphorylated and available for ligation at this stage. The ligation reaction seals the central strands of the squares and joins C and C', as well as D and D'. When the ligation is complete, the 3-square, belt-like covalently-closed intermediate is formed in molecules we wish to use further. All contaminating species containing free ends are digested with exonuclease III at this stage. A and B sites are then exposed by restriction, thereby providing new sticky ends for further growth. The 5' ends in A, A', B and B' are then phosphorylated, and the second ligation joins A and A', B and B' to yield closure of the cube.
(Figure has been somewhat re-arranged from Dr. Seeman's manuscript.)

DNA networks as molecular scaffolding

It is clearly desirable to be able to orient a molecule relative to any other molecule. This capability could provide fundamental information about the structural and thermodynamic parameters that characterize the relationship between the molecules, as discussed below in the section on nanomanipulation. In addition, there are technological reasons for wishing to achieve such ends. DNA is particularly well-suited for use as a scaffolding medium, since it is a thick (2 nanometer diameter), stiff molecule over a range of a few nanometers, a molecule whose structure is unlikely to be perturbed markedly by attaching smaller non-interactive molecules to it. Neutral versions of DNA can be made (Froehler, 1986) which may prove more useful than the naturally-occurring polyanion.

We have recently discussed the use of DNA as a scaffold for the assembly of an information storage device or biochip, consisting of a network of organic conductors, molecular switches and an oxidation-reduction-based metallic bit (Robinson and Seeman, 1987): The forms of attachment suggested include both covalent links between the DNA and the conducting network, as well as non-covalent links that exploit the specificity with which both proteins and drugs recognize specific sites on DNA molecules. Of course, other nucleic acid molecules can also be used for attachment by forming non-covalent triple-stranded complexes (Moser and Dervan, 1987); cycles formed from combinations of 'third strands' and the assembled networks of conductors could result in topological bonding to the DNA network, although no covalent bonds are formed with it. It is critical that the network of other material being assembled by the DNA scaffolding be capable of being assembled in parts. In order to achieve this modular feature, we suggested making 'junctions' in the conducting material based on coordination complexes (Robinson and Seeman, 1987).

The biochip we proposed is predicated on the ability to self-assemble a 3-dimensional crystal of branched DNA networks, to which the conducting material and active components are appended. Addressability of individual unit cells within the crystal is based on the ability to address a given column within the crystal from each direction: When switches triggered in two perpendicular directions are both open, then information may be placed into or retrieved from a given unit cell via the third direction. Scanning-tunneling microscopes (e.g., Beebe, et al., 1989) and atomic force microscopes (Drake, et al., 1989) already have 2-dimensional addressing capabilities much finer than needed for forming the interfaces to macroscopic circuitry. The device is designed to work at electronic speeds, rather than phonon speeds, to which molecular mechanical devices are limited. The dimensions of each bit in the device are 280 by 280 by 374 Å; an array of these elements 1 millimeter on a side (smaller than typical diamonds in a ring) would contain 3.4 x 1013 bits, enough to naively encrypt each of the approximately 107 books ever written three times apiece. The reader is referred to Robinson and Seeman (1987) for a fuller explanation of this device.

In addition to the biochip, we have suggested that stick-figures fashioned from DNA branched junctions can function to orient and cage active biological macromolecules (Chen, et al., 1989); the goals in this application include the development of new multi-functional enzymes, as well as drug delivery of therapeutic macromolecules. The large size and expected imperturbability of DNA structure make it a good medium for the attachment of macromolecules. Linear duplex DNA has the disadvantage that many of the desirable distances between macromolecules are 'hidden' from one another by being on opposite sides of the double helix. By contrast, branched structures offer surfaces with many unoccluded loci in proximity to each other.

The original goal of linking junctions together involved the formation of crystals of DNA networks for use in diffraction methods (Seeman, 1981, 1982, 1985a). All spatially periodic arrays of matter (crystals) diffract x-rays and neutrons, and hence it is possible to determine their 3-dimensional structures in detail (e.g., Glusker and Trueblood, 1985). A common technique in the determination of structures involves having a large structure host a smaller structure that binds to it in a specific fashion (e.g., Blundell and Johnson, 1976). Crystals of DNA networks should be able to behave as macromolecular zeolites, in which guest macromolecules can be oriented and caged.


Mechanical control of objects on the nanometer scale is a major concomitant of many nanotechnological proposals. Although their motions are limited to phonon speeds, nano-mechanical objects are of potentially great utility, as Feynman (1961) and Drexler (1981) have both suggested. Mechanical systems involving DNA can be designed which use known conformational isomerizations of the molecule. The isomerizations most readily controlled are those that involve the unwinding of DNA. The most precipitous change in the winding of DNA is the B-->Z transition (e.g., Rich, et al., 1984). This isomerization involves a reversal of the handedness of the DNA double helix from right-handed to left-handed at particular sites (primarily at alternating pyrimidine-purine sequences). This alteration corresponds to a change in the average winding/residue of about -65° in the affected region, from from roughly +34.5° (Wang, 1979; Rhodes and Klug, 1980) to -30°. A markedly less precipitous unwinding of the DNA structure can be effected by binding particular protein molecules, such as Lac repressor (Wang, et al., 1974), which unwinds the DNA by roughly 45° over a stretch of about 17 nucleotide pairs, about -2.5°/residue.

A second mechanical manipulation of DNA involving unwinding takes place at the branch points of junctions with homologous twofold sequence symmetry; this phenomenon is known as branch migration (Thompson, et al., 1976). Cruciform structures in DNA are known to form in response to underwinding closed circular DNA (Gellert, et al, 1978; Lilley, 1980). The migratory position of a partially mobile junction (Seeman, 1981, 1982; Chen, et al., 1988) ought to be as readily controlled by torque exerted on opposite arms of the junction, since its extrusive movement will relax the torque.

An example of a crystalline nanomanipulator is illustrated in Figure 7. A two-dimensional version of a single unit cell is illustrated. The purpose of this device is to derive structural and thermodynamic information for the same reaction. In Figure 7A, the two cubes, representing protein molecules, for example, are in contact. Note that the cube on the right is eccentrically attached to a piece of left-handed Z-DNA. This is the only sequence present readily capable of achieving the Z structure. In Figure 7b, the conditions favoring Z-formation have been relaxed, and the DNA supporting the cube on the right returns to the right-handed B conformation. This removes the cube on the right from contact with the cube on the left, and turns it around, as indicated by the shading. The thermodynamics of this reaction, with appropriate baseline controls, can be measured in the same way as any other reaction. However, given the crystalline context, structure can also be determined by the X-ray diffraction experiment, before and after the transition. Clearly the Z-->B driving force must be sufficient to overcome the binding between the 'cubes' or the reaction will not occur, and nothing will be visible crystallographically. The device shown in Figure 7 is a 2-state nanomanipulator; nanomanipulators involving more available states are easily imagined, based on a combination of the elements described above.

Figure 7 - A crystalline nanomanipulator:

Figure 7A

a Z to B transition gives:

Figure 7B
Figure 7. A Crystalline Nanomanipulator Based on the B-Z Transition. Both portions of this figure show the repeat unit of a two dimensional lattice of DNA. The two cubes represent globular macromolecules, such as proteins or tRNA. One side of each cube is shaded, to indicate polarity. All of the DNA in the figure is right-handed B-DNA, except for the part attached to the right cube in (A), which is left-handed Z-DNA. (A) The cube on the right is eccentrically attached to the piece of Z-DNA, and it will move away from the cube on the left if the DNA to which it is attached undergoes a Z-->B transition. This is shown in (B), in which the DNA attached to the right cube has undergone a Z-->B transition. The cube has rotated so that its opposite face is visible, and it is no longer in contact with the cube on the left. Note that the crystalline nature of this nanomanipulator permits both thermodynamics and structure to be measured for the same reaction.
(Figure has been somewhat re-arranged from Dr. Seeman's manuscript.)


One of the obvious questions that must be asked of any DNA-based material is, 'Can it can be cloned?' Cloning permits relatively inexpensive production of large quantities of a substance, by having micro-organisms do the synthesis. The answer to the question is not an unambiguous yes or no. From experience, it is clear that chemical synthesis of DNA primary structure is much easier than enzymatic synthesis of branched DNA secondary structure. It is obvious that any sequence of DNA can be inserted into a vector. However, it is also clear that if the opposite arms of a single junction, such as that shown in Figure 1, were inserted into a plasmid, a single round of replication would eliminate its branched character. On the other hand, cloning into a single-stranded vector, such as M13 (Maniatis, et al., 1982), affords opportunities not present in double-stranded vectors. The crucial assumption on which this strategy rests is that desired hybridization will occur, once the designed sequence is freed from the vector. To exploit this approach, it is necessary to construct a figure whose features can be fashioned from a continuous strand. While this may appear impossible, the goal becomes feasible if one allows restriction of hairpin loops and extra junction arms to create the ends of some double helical arms. Figure 8 illustrates a tetragonal pyramid whose features are formed from a single strand. Each of the edges formed from an odd number of half-turns of DNA are illustrated with only a single crossover, for clarity. Note that two central edges of the pyramid are a half-turn longer than the other two, a step necessary to maintain the continuity of the DNA.

Figure 8. A Tetragonal Pyramid Formed from a Single Long Strand and Cloned into a Single-Stranded Vector. The pyramid is viewed from the bottom and the apex of the pyramid is in the center of the square. The apex is a 5-arm junction, while the other four vertices are 4-arm junctions. The apex is shown attached to the cloning vector, single-stranded bacteriophage M13. Edges with an even number of half-turns between vertices are shown as parallel lines, while those with an odd number of half-turns are shown as having a single crossover. The filled regions are restriction sites that can be cut all at once or individually to yield the final structure. Note that any restriction site can be annealed by ligating a hairpin over it at some future time, as desired. The rules for constructing such an object are that strands must enter and leave a vertex on adjacent edges of the figure, and that polarity must be maintained. Adhering to these rules results in the edges that approach the apex of the pyramid being mixed, two with crossovers, and two without. Thus, the pyramid is somewhat distorted.
(Figure has been somewhat re-arranged from Dr. Seeman's manuscript.)

If one is willing to have an external arm associated with every polygon of a polyhedron, then the entire structure can be cloned. This is quite general for polyhedra whose vertices are separated by an integral number of turns of DNA, since each polygon is formed from a DNA cycle, and they can in theory be hooked together in an arbitrary fashion. Figure 9 illustrates the Schlegel diagram of a dodecahedron to be constructed in this fashion. The Schlegel diagram of a polyhedron is a way of representing it in a plane: The central polygon is closest to the viewer and the polygon on the outside of the figure is at the rear of the figure; the connectivity of vertices is shown properly, but relative edge lengths and angles are distorted. Twelve vertices of the dodecahedron (selected by excluding a set of eight that lie on the body diagonals of a cube) have been used to allow entry and exit from each of the twelve polyhedra. The connections between polygons are indicated in Figure 9 by the dotted lines. Once formed, the external arms can be restricted to form the polyhedron cleanly. Additional hairpin arms can be added to this dodecahedron, as shown in Figure 10, so that each vertex has an external attachment point after restriction. Note that for polyhedra with more faces than vertices, such as the icosahedron or octahedron, some junctions must provide two extracyclic restrictable arms, rather than one or none, as seen here with the dodecahedron.

Figure 9. A Single-Stranded Representation of a Pentagonal Dodecahedron Cloned into a Single-Stranded Vector. A Schlegel diagram of a dodecahedron is shown in the thickest lines. Flanking these lines are short anti-parallel arrows, drawn less heavily; these represent the double helical DNA corresponding to each edge of the dodecahedron, with an arrowhead indicating the 5'-->3' polarity of the strand. Each edge is an integral number of turns long, so that the parallel line model of DNA is valid here. Each of the twelve pentagons contains an exocyclic double helical arm. The sites of these exocyclic segments have been selected by eliminating the eight vertices that lie on the body diagonals of a cube. Each exocyclic double helical segment contains a restriction site, so that it can be severed from the connecting DNA. The dotted lines represent connecting DNA that links the pentagons to each other and to the M13 cloning vector. This is the DNA that will be cut away upon formation of the structure. No attempt at topological representation is made here: all connecting DNA (dotted lines) lies behind the polygonal DNA for purposes of clarity.
(Figure has been somewhat re-arranged from Dr. Seeman's manuscript.)

Figure 10. A Single-Stranded Cloned Pentagonal Dodecahedron with Exocyclic Arms on All Vertices. The same conventions apply as in Figure 9. Here the eight vertices that do not contain exocyclic arms in Figure 9 have been provided with them in the form of hairpin loops that contain restriction sites.
(Figure has been somewhat re-arranged from Dr. Seeman's manuscript.)


The most prominent example of a successful nanotechnological system is living matter. As we understand living systems in more detail, and as molecular biotechnology grows, it is likely that many of the earliest strands in the fabric of nanotechnology will derive from biotechnology. Biological systems are very facile at self-assembly on the nanometer scale, utilizing large numbers of non-covalent interactions. It is much easier to control the low energies necessary to direct weak intermolecular interactions, rather than the large energies involved in making and breaking covalent bonds. Thus, nanometer-scale construction, emulating self-assembling biological systems, appears to be the easiest link to form between molecular biotechnology and nanotechnology.
I have exploited this approach here in presenting a self-assembling structural system based on nucleic acids that can be used for engineering on the nanometer scale. The pre-eminent feature of nucleic acids that makes them so useful for these purposes is the control one can exercise over their intermolecular associations: the entire biotechnology industry is based on it. The introduction of stable, branched DNA (Seeman, 1981, 1982; Kallenbach, et al., 1983a) makes nucleic acids a system in which this structural control may be used to make specific individual stick-figures and N-connected networks in 3 dimensions. These materials may in turn be useful as nanomanipulators, as well as scaffolding for other molecules in both biochips, multienzyme complexes, diffraction studies and biological applications.

ACKNOWLEDGEMENTS: This research has been supported by grant GM-29554 from the National Institutes of Health. Many of the ideas mentioned here have grown out of discussions with Neville Kallenbach, whose criticisms have vastly improved this manuscript, and with Bruce Robinson.


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In addition to this paper, Dr. Seeman has also presented a talk to this conference.

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