There have been some notable suc-cesses recently in constructing indi-vidual molecular components andmanipulating molecules with prob-

ing devices, but there are few methods for con-structing complex devices out of large numbersof these molecular components. We need meth-ods to help hold, shape, and assemble molecularcomponents into complex machines and sys-tems. Success will require new theoretical un-derstanding of nanoscale processes and new soft-ware infrastructure for simulating and designingmolecular nanostructures.

This article outlines the recent development—both theoretical and experimental—of self-as-sembled DNA nanostructures, which is the mostadvanced and versatile system known for pro-grammable construction on the nanoscale. Re-cent developments in this field provide methodsfor bottom-up construction of highly patternedsystems at the molecular scale. The methodol-ogy of DNA self-assembly begins with the arti-ficial synthesis of single-strand DNA moleculesthat self-assemble into macromolecular building

blocks called DNA tiles. These tiles have stickyends that match the sticky ends of other DNAtiles, facilitating further assembly into largestructures known as DNA tiling lattices. You canmake the DNA tiling assemblies form any com-putable two- or three-dimensional pattern, how-ever complex, with the appropriate choice of thetile’s component DNA.

Recent experimental results indicate that thistechnique is scalable. Molecular imaging de-vices—such as atomic force microscopes andtransmission electron microscopes—have demon-strated and visualized self-assembled two-dimen-sional DNA tiling lattices composed of hundredsof thousands of tiles. For the first time, our recentexperiments have demonstrated the execution ofcomputations through DNA tiling assemblies.These assemblies have several important poten-tial applications because they let us build scaf-folding on which to position molecular electron-ics and robotics components with precision andspecificity. The programmability will let this scaf-folding have the patterning required for fabricat-ing complex devices made of these components.

Nanotechnology potential

Several potentially revolutionary technologieswill likely result from the emerging field of mol-ecular nanotechnology. These applications will

32 COMPUTING IN SCIENCE & ENGINEERING

DNA LATTICES: A METHOD FORMOLECULAR-SCALE PATTERNINGAND COMPUTATION

DNA lattice research can provide unprecedented capabilities for molecular-scalecomputation and programmable pattern formation. The field has applications to manyother emerging technologies in molecular nanotechnology. This article outlines some of thesteps being taken to develop these applications.

JOHN H. REIF

Duke University

1521-9615/02/$17.00 © 2002 IEEE

B I O C O M P U T A T I O N

JANUARY/FEBRUARY 2002 33

span the medical, biological, computer, and ma-terial sciences. For example, prior breakthroughsin molecular nanotechnology have included thediscovery of the family of carbon moleculesknown as the fullerenes, which include carbon nan-otubes that have unprecedented strength in addi-tion to electrical and switching properties. Thesebreakthroughs also include the discovery of or-ganic molecules (with electrical transport andswitching properties) that will become the mole-cular components built into more complex mole-cular nanostructures, such as molecular machines.

The most critical technical barrier currentlyconfronting molecular nanotechnology is thedevelopment of assembly methods for con-structing complex devices out of molecular com-ponents. In the macroscopic world, we use awide variety of manufacturing technologies andinfrastructures for assembling and patterningvarious components into complex structures andmachines. Unfortunately, none of the essentialtechnology exists yet on the molecular scale. Partof the difficulty is that there is not yet a completetheoretical understanding of processes at themolecular scale. The most crucial problem toovercome is the lack of an established repertoireof experimentally demonstrated assembly meth-ods for effectively and reliably constructing com-plex devices out of molecular components.

Nevertheless, the task does not seem to be im-possible. In the process of cell evolution, naturedeveloped patterned assembly techniques at themolecular scale hundreds of millions of yearsago. Cell growth is an example of unmediatedbiochemical processes in biology that providestrong evidence of how biochemical processescan create nanostructures of surprising com-plexity. However, these nanostructures need tobe programmable and easily modifiable to be ofuse to us.

Known patterning methods

You can categorize the known patterningmethods used for manufacture at the microscaleas either top-down or bottom-up. Top-downmethods for patterning use a macroscopic deviceto pattern at some smaller scale, such as the mi-croscale or nanoscale. Top-down methods forpatterning objects date to at least the early 19thcentury. For example, Joseph Marie Jacquard inFrance used Holorith cards to control the me-chanical weaving of tapestry patterns.

Lithographic methods, which also date back tothe 19th century, use optically active chemical

etching to form patterns. This top-down methodbecame crucial for developing other manufactur-ing technologies in the 20th century. Starting inthe mid 20th century, for example, manufactur-ers used lithography for fabricating circuits andmicrocircuits. Lithography was the most success-ful microminiaturization technique developed bythis point. However, because of wavelength reso-lution limits, it is unlikely that lithography willever scale much below a few nanometers.

Another top-down approach to assemblingnanoscale objects uses a macroscale instrumentthat can move and probe at molecular-size scales,such as a scanning probe microscope. Major obsta-cles to using such instruments to construct com-plex devices at the molecular scale include thesequential nature of the technology and its con-trollability and scalability. Although scanningprobe microscopes can make use of a small num-ber of simultaneous probes, that number isdwarfed by the vast number of molecules thatneed to be manipulated.

Bottom-up approaches rely on patterning byself-assembly, which is the spontaneous self-or-dering of substructures into superstructures dri-ven by the selective affinity of the substructures.Bottom-up methods all use some form of self-assembly for patterning. Although self-assemblymethods are well known and have long beenused by chemists (for the self-assembly of lipidor polymer layers, for example), they typicallyresult in structures that have limited complexityand are not readily programmable.

Protein engineering is a bottom-up approachthat offers great promise for molecular devices,but it is developing slowly, and we do not yet fullyunderstand the folding rules for protein assem-bly. When you attempt to engineer proteins, youare limited by the degree of predictability of theresulting protein conformations. Another bot-tom-up approach is to reprogram biological cellsthat operate on the nanoscale. However, the ma-chinery available in biological cells is exceptionallydifficult to predict and control, and we are onlynow beginning to understand the complexity ofits control systems. Finally, the DNA self-assem-bly approach entails the spontaneous self-assem-bly of DNA strands into nanostructures driven byselective hybridization among DNA strands.

DNA tiles and tiling lattices

Single-strand DNA is a polymer that consistsof a sequence of four types of bases grouped intotwo disjoint pairs—known as Watson-Crick com-

34 COMPUTING IN SCIENCE & ENGINEERING

plementary pairs—that can bind together throughhydrogen bonding in an operation known as hy-bridization. DNA enjoys a unique advantage for ananostructure construction material because twosingle strands of DNA can be designed and con-structed by the experimental scientist to be se-lectively sticky and bind together to form dou-bly stranded DNA (see Figure 1). Hybridizationis much more likely to occur if the DNA basesequences are complementary—that is, if thecomponent bases are Watson-Crick pairs—andthe temperature and salinity are set appropri-ately. The resulting doubly stranded DNA is rel-atively rigid and forms the well-known double-helix geometry.

Nadrian Seeman first pioneered DNA struc-ture nanofabrication in the 1980s by assembling amultitude of DNA nanostructures (such as rings,cubes, and octahedrons) using DNA branchedjunctions.1 However, these early DNA nanos-tructures weren’t very rigid. To increase the rigid-ity of DNA nanostructures, Seeman used a DNAnanostructure found in nature and known as a

DNA crossover (also called a branched Holidayjunction). A DNA crossover consists of two dou-bly stranded DNA, each having a single strandthat crosses over to the other (see Figure 2). Pairsof crossovers, known as double crossovers, provide asignificant increase in the rigidity of a DNAnanostructure. Certain crossovers (also known asantiparallel crossovers) cause a reversal in the di-rection of strand propagation following the ex-change of the strand to a new helix.

DNA tiles are quite rigid and stable DNAnanostructures that are formed from multipleDNA antiparallel crossovers. DNA tiles typicallyhave a roughly rectangular geometry. These tilescome in multiple varieties that differ from one an-other in the geometry of strand exchange and thetopology of the strand paths through the tile. Thefirst DNA tiles developed2,3 are known as double-crossover tiles and composed of two DNA doublehelices with two crossovers. Recently, researchershave developed some novel DNA tiles known astriple-crossover tiles3 that are composed of threeDNA double helices with four crossovers. Thesetriple-crossover tiles have properties that can fa-cilitate one- and two-dimensional tiling assem-blies and computations.

Each DNA tile can be designed and con-structed by the experimenter to match the endsof certain other DNA tiles, a process that can fa-cilitate the assembly into tiling lattices. In partic-ular, each tile contains several short sections ofunpaired, single-strand DNA that extends fromthe ends of the tile. Both double- and triple-crossover tiles are useful for doing tiling assem-blies. The double-crossover tiles provide up tofour pads for encoding associations with neigh-boring tiles, whereas the triple-crossover tilesprovide up to six pads that are designed to func-tion as binding domains with other DNA tiles.

In particular, the tile pads complement—or“stick” to—the pads of other chosen DNA tiles,as Figure 3 shows. Individual tiles interact bybinding with other specific tiles through hy-bridization of their pads to self-assemble into de-

Figure 1. Hybridization of sticky single-strand DNAsegments. If the sticky single-strand segments thathybridize abut doubly stranded segments of DNA,you can use an enzymic reaction known as ligationto concatenate these segments.

Hybridization

Ligation

Figure 2. (a) A triple-crossover tile and (b) a triple-crossover tile that has two extra stem-loops that project into (black) and out of (green) the plane of the page.

(a) (b)

JANUARY/FEBRUARY 2002 35

sired superstructures. Using pads with comple-mentary base sequences lets you control theneighbor relations of tiles in the final assembly.

Recent research by Eric Winfree and NadrianSeeman has demonstrated the self-assembly oftwo-dimensional periodic lattices consisting ofhundreds of thousands of double-crossover tiles,4

which is strong evidence of this approach’s scala-bility. In addition, Thom LaBean and I, in col-laboration with Nadrian Seeman, have con-structed DNA triple-crossover molecules fromwhich we have also produced tiling lattices.3,5 Weobserved both classes of lattices through atomicforce microscopy (a mechanical scanning processthat provides images of molecular structures on atwo-dimensional plate) as well as through trans-mission electron microscopy (see Figure 4).

Distinguishing surface features can be de-signed into individual tiles by slightly modifyingthe DNA strands composing the tiles. Thesemodified DNA strands form short loops thatprotrude above the tile. To enhance definition,you can also affix metallic balls to these DNA

loops using known methods for affixing goldballs to DNA. You can program surface fea-tures—such as two-dimensional banding pat-terns—into these DNA lattices by using DNAtiles that assemble into regular repetitive pat-terns. You can observe these topographical fea-tures on the DNA tiling lattices with atomicforce and transmission electron microscopyimaging devices. Other literature provides amore detailed survey of current work in self-assembled DNA nanostructures.6

Constructing DNA lattices

You can use the assembly process describedearlier to perform computations by building upsuperstructures from the starting units so thatthe assembly process itself performs the actualcomputation. The most general method for two-dimensional molecular pattern formation is touse a small set of DNA tiles that self-assemblepredictably. We call this unmediated algorithmicself-assembly.

Figure 3. Thebinding ofDNA tile pad pairs. The two tilesinteract by hybridizationat their adjacent padsto form a two-tileassembly.

Figure 4. (a) and (b) Atomic force microscopy images of DNA lattices with triple-crossover tiles that measure 3 to 4microns on a side. (c) A transmission electron microscopy image of a platinum rotary-shadowed triple-crossover lattice.

(a) (b) (c)

5

6

36 COMPUTING IN SCIENCE & ENGINEERING

A body of theoretical work that dates back tothe 1960s indicates the power of this tiling ap-proach for patterning. Wang tilings, for example,are a class of tiling problems where you are givena finite set of unit-size square tiles, each of whosesides are labeled with symbols over a finite alpha-bet (the pads). Additional restrictions might in-clude the initial placement of a subset of these tilesand the dimensions of the region where tiles mustbe placed. The problem is to place the tiles—cho-sen with replacement—to completely fill thegiven region so that each pair of abutting tiles hasidentical symbols on their contacting sides.

The class of patterns generated by Wang tilingsincludes all computations. Berger7 gave the de-tails of a construction where tiles result in tilinglattices that can simulate any given Turing ma-chine computation. Eric Winfree2,8 proved thisresult in the context of DNA tiling lattices. Us-ing only a few component tiles, Winfree showedthat unmediated algorithmic self-assembly ofDNA tiling lattices is theoretically capable of cre-ating arbitrarily complex structures. This methodhas the advantage of being very general: It re-quires no input DNA strand encoding a pattern.Instead, the choice of the DNA tile set generatesthe two-dimensional pattern.

An interesting example being considered byWinfree for a possible unmediated algorithmicself-assembly in two dimensions is a tiling pat-tern that counts in binary. Winfree recently ob-served that the resulting two-dimensional pat-tern is nearly identical to the pattern for ademultiplexing RAM circuit. This pattern couldpotentially serve as a template for arrangingmolecular electronics components such as mol-ecular wires9 and molecular diodes10 into a de-sired demultiplexing circuit.

ComputationIn addition to forming complex patterns, you

can also use DNA tilings to perform massivelyparallel computations with inputs and outputsencoded by DNA strands. In this methodologyfor computation, you provide input by sets ofsingle-strand DNA (known as input strands) thatserve as nucleation sites for tiling assemblies. Youcreate output by concatenating to each inputstrand an additional output strand of DNA. Thisconcatenation is accomplished through an en-zymic reaction known as ligation. These outputstrands are formed and colocalized within thetiling assembly and wind through all the tiles ofa tiling assembly. After formation, the outputstrands can then be released by raising the tem-

perature so that the strands composing the tilesdisassociate into single strands of DNA. Inputand output can occur in parallel for multiple dis-tinct tiling assemblies.

Prior workLeonard Adleman’s seminal paper11 describes

the first experiment demonstrating the use of re-combinant DNA techniques for solving a smallcombinatorial search problem (known as theHamiltonian path problem). Adleman used asimple form of self-assembly computation. Hisalgorithm does not blindly generate all possiblesequences of vertices. Instead, the DNA se-quences and the use of DNA complementarybinding guides the self-assembly processes sothat the algorithm only generates valid paths.This work spawned further work in DNA com-putation,12 but much of the subsequent work inDNA computation required many tedious lab-oratory operations.

The use of DNA tiling lattices for doing com-putation avoids having to do these tedious lab op-erations. You only need to design DNA tiles withthe appropriate pads to specify individual stepsof the computation. Using pads with comple-mentary base sequences lets you control theneighbor relations of tiles in the final assembly.Thus the only large-scale superstructures formedduring assembly are those that encode valid map-pings of input to output. Rather than imple-menting a DNA computing algorithm using a se-quence of multiple laboratory procedures, theapproach essentially uses only four: mixing theinput DNA strands to form the DNA tiles, al-lowing the tiles to self-assemble into superstruc-tures, doing ligation of the strands that have beencolocalized, and then performing a single sepa-ration to identify the correct output.

Massive parallel computationThe massive parallelism inherent in DNA-

based computers has driven thinking in the field.Because DNA molecules are compact, the de-gree of parallelism can be up to 1016 or possibly1018. In computation by self-assembly, paral-lelism reveals itself in many ways. DNA self-as-sembly can be executed in massively parallelfashion with concurrent assemblies that mightexecute computations independently. As Figure5 shows, in global parallelism, each superstructurecan contain information representing a differentcalculation. In local parallelism, growth on eachindividual superstructure can occur at many lo-cations simultaneously.

JANUARY/FEBRUARY 2002 37

A tiling assembly’s depth is the maximumnumber of self-assembly reactions experiencedby any substructure—that is, the depth of thegraph of pad binding events—and a superstruc-ture’s is the number of tiles it contains. The ad-vantage of tiling assemblies of small depth andsize is that, because of local parallelism, their for-mation is more likely to be error-free. I devel-oped DNA self-assembly methods of linear sizeand small depth to solve several fundamentalproblems (such as arithmetic on n-bit numbersand sorting) that form the basis for the design ofmany parallel algorithms.13 Some of these de-signs (for integer addition, for example) requiredonly a single layer of tiles to be assembled withina nanostructure known as an assembly frame,which requires only the simplest form of linearself-assembly.

Eric Winfree and his collaborators proposed aspecial class of DNA tiles known as string tiles thatalso result in one-dimensional computationaltiling lattices.14 By allowing contiguous stringsof DNA to trace through individual tiles and theentire assembly multiple times, you can performsurprisingly sophisticated calculations with theseone-layer linear tiling assemblies. The triple-crossover tiles recently developed are particularlyuseful as string tiles.

Arithmetic and Boolean computationRecent research describes string tile systems

that compute binary number addition (wherethe binary numbers are encoded by strands ofDNA) by using the selective composition of ad-jacent tiles in the assembly to communicate thecarry-bits.5,15 Tile systems can also be used forcomputation of bit-wise logical operations onBoolean vectors encoded by strands of DNA.For computations on specific input, these pro-cedures use the scaffold strands mentioned ear-lier. Otherwise, the input tiles will randomly as-semble and generate a molecular look-up tablein which each reporter strand encodes the inputand output of a random calculation. A sufficientnumber of DNA tile molecules provides fullcoverage of all possible n-bit input strings. Suchlook-up tables can be useful as input for furthercomputations. They represent a unique libraryof sequences storing useful prior computations.

Some recent experiments have, for the firsttime, demonstrated computation through mole-cular assembly of triple-crossover DNA tiles.15

The computation is similar to that described forinteger addition but actually solves a simplercomputational task (known as cumulative XOR)

related to computing the carry sequence in in-teger arithmetic.6

Future research

You can view that cumulative XOR computa-tion15 as the first demonstration of unmediatedalgorithmic self-assembly in one dimension.However, research has not yet demonstrated un-mediated algorithmic self-assembly in two di-mensions for complex patterns beyond thebanded patterns described earlier. Nevertheless,numerous examples of unmediated biochemicalprocesses in biology (cell growth, for example)provide strong evidence that unmediated bio-chemical processes could create nanostructuresof surprising complexity.

Optimizing assembly techniquesFurther progress will require an improved un-

derstanding and control of the physical phe-nomena that determine lattice growth. Experi-ments must be conducted to evaluate the speedand error rates of the various types of self-as-sembly reactions. We must develop improvedmethods to minimize errors in self-assembly.Defect errors can occur in DNA lattice forma-tion and in solutions containing many distinctDNA tile types that compete during the latticeformation process.

Temperature optimization (including temper-ature cycling) and salinity should provide for de-creased defect rates in lattice formation. NovelDNA tiles must be developed with propertiesthat facilitate minimizing errors in their self-as-sembly and improve their being visualized withimaging devices such as the atomic force micro-scope. Initiating the process using a small num-ber of tiles to form a nucleation basis for the sub-sequent larger assembly might enhance theformation of defect-free DNA lattices.

Computer simulation and designTo develop a more fundamental understand-

ing of the self-assembly process, we need im-

Figure 5. Global and local parallelism in theformation of DNA tiling assemblies.

Global and local parallelism by linear assembly

38 COMPUTING IN SCIENCE & ENGINEERING

proved software simulation tools to model thekinetics of self-assembly. We can define tiling as-semblies so that, theoretically, we produce only aunique, correct tiling pattern with no errors,which means that all pads of each tile matchtheir neighbors perfectly. However, self-assem-bly is intrinsically a probabilistic process.

Winfree developed a stochastic software sim-ulation of DNA lattice formation. His computersimulations show that you can achieve low errorrates in certain computational DNA lattices inthe special case of very low tile concentrationsand near the melting temperature (where theDNA structures tend to disassociate). Becauseof his assumption about low tile concentrations,his simulation used a simplification of the chem-ical rate equations, which allowed only the in-sertion of single DNA tiles into a growing DNAassembly. We can enhance this software by in-corporating more sophisticated models of DNAlattice formation. For example, we can allow theassembly of groups of multiple DNA tiles thatare partially assembled.

There is also an acute need for more sophis-ticated modeling of DNA lattices’ kinodynamicproperties. Simulating large DNA lattices con-taining hundreds of DNA tile nanostructures iscomputationally challenging if we use conven-tional molecular dynamics simulation software.Developing DNA molecular dynamic simulationsoftware that employs semiempirical models forDNA dynamic simulation at the base-pair levelcan help avoid this difficulty.

DNA chains bend, twist, and stretch in re-sponse to base sequence and to specific interac-

tions with the chemical environment. It is possi-ble to extract a DNA model with local energycomponents, where the coefficients in the modelcome from empirical results of known DNA X-ray crystallographic literature. We can refinethese models to incorporate base-sequence-de-pendant variations in these parameters as well asin crossover junctions. The resulting simulationsoftware might be reliable enough to providehelpful insight on the dynamics of large DNAlattices and efficient enough so simulations ofvery large DNA lattices would be feasible.

We need improved software for designingnovel DNA tiles and tiling assemblies. Currentsoftware uses algorithms that provide for the de-sired binding of DNA strands that form duplexDNA in the DNA tiles and minimize undesiredbinding interactions between DNA strands.This software can be improved by incorporatingalgorithms that also provide for the DNA tilegeometry’s design, perhaps using the semi-em-pirical models for DNA dynamic simulationmentioned earlier.

Sequential step-wise assembly Unmediated algorithmic self-assembly of

complex patterns requires delicate control ofphysical phenomena to minimize assembly er-rors. An alternative approach is the step-wise as-sembly of a smaller number of DNA tiles underexternal control through sequential applicationof different reagents and tiles.13 This approachresults in a serial sequencing of tile assemblyevents (that might occur in parallel to form dis-tinct layers of tiles) and might provide increasedreliability and reusability during fabrication ofDNA nanotechnology structures.

Directed nucleation assemblyWe recently developed another method for as-

sembling complex patterns. In this method, wesynthesize an input DNA strand that encodes therequired pattern and then the specified tiles as-semble around blocks of this input DNA strand,forming the required one- or two-dimensionalpattern of tiles. This method uses artificially syn-thesized DNA strands that specify the pattern andaround which two-dimensional DNA tiles assem-ble into the specified pattern. As Figure 6 shows,this method generates the permanent features ofthe two-dimensional pattern for each case.

Shape-change-induced assemblyA vast body of practical engineering developed

to construct microelectro-mechanical systems

Figure 6. A directed nucleation assemblytechnique. The red area indicates an inputpattern strand of DNA. It encodes a two-dimensional pattern in modified row major order(each odd row traversing alternately left to rightand each even row traversing right to left). Specific DNA tiles self-assemble around each segment of this DNA input pattern strand, thenthe tiles self-assemble into a two-dimensionaltiling lattice with a pattern determined by thepattern strand. We executed a small instance ofthis method where up to 10 triple-crossover tilesassembled around a preformed scaffold DNAstrand.

JANUARY/FEBRUARY 2002 39

(MEMS) from silicon substrates might bebrought to bear and leveraged to develop tech-niques for the multistep assembly of three-di-mensional DNA nanostructures from two-di-mensional DNA lattices. These devices areinitially fabricated within a two-dimensional do-main using optical lithography. Subsequentphases of fabrication use additional electron beamlithography (which uses a directed stream of elec-trons to form a pattern), chemical releaseprocesses, or simple environmentally dependentshape changes (electrostatic- or temperature-based) to assemble the resulting MEMS devicesin three dimensions. For example, you can as-semble a box-shaped device with an open top byfabricating the bottom square and also the foursides adjoining the bottom square and then forcethe sides upward, locking these sides togetherwith simple mechanical latches. These process-ing steps are of course not feasible for DNA lat-tice assembly, but related techniques might apply.

Similarly, some research has suggested that itmight be possible to assemble three-dimensionalDNA lattices from portions of two-dimensionalDNA lattices.1 In this method, complex assembliesof three-dimensional DNA nanostructures con-structed from two-dimensional DNA latticesmight be created using a multistep approach. Athree-dimensional assembly might begin with theassembly of two-dimensional DNA lattices fol-lowed by folding these two-dimensional assembliesinto a three-dimensional DNA nanostructure.

In this process, we would proceed in a man-ner similar to assembly processes used in con-structing MEMS. Using restriction enzymes(which can cut the lattices at specified locations)is analogous in DNA lattices to using electronbeam lithography and chemical release processesto construct MEMS. Environmental changes caninduce shape changes. Also, some researchershave developed nanomechanical transductiondevices constructed of DNA based on selectiveuse of DNA hybridization.16,17 You can selec-tively control these devices by adding or releas-ing controller strands of DNA. We can adapt ei-ther of these techniques to manipulate the shapeof DNA lattices and control their flexibility. Wecan use various DNA reactions such as hy-bridization and ligation in place of the mechan-ical latches used in the MEMS field to secure theMEMS devices.

Stateful DNA latticesDNA lattices with shape-change programma-

bility of the sort described earlier also might offer

a mechanism to do DNA computation on latticeswhose elements—the tiles—hold state. That is,the DNA assemblies might be able to simulate aparallel computing model known as cellular au-tomata, which consists of arrays of finite-state au-tomata, each of which holds state. The transitionsof these automata and communication of valuesto their neighbors might be done by conformalgeometry changes, again using programmability.There are numerous examples of one-dimen-sional cellular automata that can do computationsfor which tiling assemblies would have required afurther dimension (for example, integer multi-plication in one dimension instead of two).

Applications

Ultimately, the significance of patterned DNAnanostructures lies not in their existence but intheir application as scaffolds for positioningother materials. We know that a large variety ofother molecules (including RNA, proteins, andother organic and metallic molecules) can selec-tively bind directly to short strands of DNA orindirectly to DNA with appropriately designedattachment chemistry.

It is feasible to bind such molecules to specificsites on DNA tiles within the DNA lattices.These sites might be short stem loops that wecan design to protrude above a DNA tile. Thistechnique provides for a highly flexible nanos-tructure construction methodology. By selec-tively attaching various other types of moleculesto the lattices’ tiles, we can use these lattices assuperstructures for placing nanocomponentscomposed of a wide variety of other materials.DNA lattices can potentially also juxtapose dis-tinct molecules and they might be capable of ori-enting these molecules.

The ability to form programmable patternednanostructured DNA lattices will likely createmany opportunities for applied research innanoscale science and engineering. These in-clude their application as scaffolds and super-structures for molecular electronics, molecularoptical transduction and memory components,protein alignment for crystallography studies,receptor protein alignment, carbon nanotubearrangement, and nanorobotics.

Templating with DNA latticesAs Figure 7 shows, it might be possible to use

gold-sulfur affinity chemistry for binding goldnanospheres to a DNA lattice. A segment ofDNA containing sulfur can be incorporated into

40 COMPUTING IN SCIENCE & ENGINEERING

the end of the stem loop protruding from aDNA lattice at fixed sites. Alternatively, you canmake thiolated segments of DNA react directlywith gold nanospheres to yield single-strandDNA-labeled gold that can hybridize to its com-plementary strand displayed on the lattice onprotruding stem loops. As Figure 7 shows, thefinal step in the production of long continuouswires involves fusing the immobilized goldnanospheres in the presence of the appropriatechemistry.

Alternatively, the Reed-Tour molecular elec-tronics components such as molecular wires9 andmolecular diodes10 have ends containing sulfurthat have an affinity to gold. This means theycan be self-assembled between the gold balls at-tached to the DNA lattices. We can also adaptother methods for our purposes of targeting andimmobilization molecules, such as proteins, met-als, and single-wall carbon. For example, we canadapt various surface chemistry methods usedfor labeling cells and cell sorting for attachmentchemistry to DNA lattices.

Aligning proteinsAligning proteins for crystallography stud-

ies has been a principal objective at New YorkUniversity.1 Determining protein structure iscrucial for many medical and biological appli-cations (such as drug design). You can deter-mine the structure of crystallizable proteins byknown computation methods using the dif-fraction patterns resulting from X-ray crystal-lography studies. However, a considerable per-centage of all proteins cannot be crystallized,which means we do not currently know theirstructure. Seeman’s idea for determining thestructure of otherwise noncrystalline proteinsis to create periodic three-dimensional DNAlattices that will capture protein molecules andalign them into regular lattices that are applic-able to X-ray crystallography. Another possi-ble application of Seeman’s idea is the scaf-folding of nanoelectronic systems in threedimensions.

The field of DNA lattices is an emerg-ing technology that can provide un-precedented capabilities in the areasof molecular-scale computation and

programmable pattern formation. There remainmany open research issues that we are currentlypursuing. For example, to what extent can we,in practice, scale the parallelism of DNA self-assembly computations? Potentially, DNA self-assembling assemblies and computations canscale up to 1016 or possibly 1018 molecules.However, there may be critical barriers that wemust overcome. Defect errors, self-assembly ki-netics, and other processes might limit this scale.We do not yet know what optimal parametersettings (such as time, solution concentrations,and so forth) provide the best avenue to scale thesize of assemblies to extremely large numbers ofmolecules.

Various error-resilient techniques might becrucial here. We are conducting experiments toevaluate the speed and error rates of the varioustypes of self-assembly reactions and are investi-gating and comparing error control by free ver-sus step-wise assembly. Self-assembly might berestricted so that certain assembly reactions canproceed only after others have been completed(serial self-assembly). Alternatively, self-assem-bly reactions might be limited by no such re-strictions (free self-assembly). It is not yet knownif free self-assembly is faster and more robustthan serial self-assembly or if it is less error-prone. We are making careful experimentalstudies of these two possible methods for self-assembly, in particular to determine whichmethod produce the fewest errors. Also, we areinvestigating various mechanisms for error re-pair in DNA tiling computations.

We are also asking to what degree we can, inpractice, scale the complexity of computationsusing DNA self-assembly. To date, the compu-tations we have demonstrated via DNA self-as-sembly have been Boolean operations executedin one dimension. Earlier in this article, I citedtheoretical results establishing the potential

Figure 7. Binding gold nanospheres to a DNA lattice and fusing these into a molecular wire by metal deposition.

DNA strands Annealed lattice Bound nanoparticles Metal deposition Fused wire

JANUARY/FEBRUARY 2002 41

power of tiling assembles to construct arbitrarilycomplex assemblies in two and three dimensions.Extending this work to two and three dimen-sions provides many further opportunities.Moreover, we can have multiple distinct DNAself-assembly computations occurring simulta-neously and asynchronously, and these may po-tentially interact with each other.

In addition to the scaling issues I discussedearlier, the field of DNA lattices applies to manyother emerging technologies in molecular nan-otechnology. It is essential that we aggressivelydevelop these applications by combining the ex-citing recent advances in DNA lattices with ad-vances in molecular electronics, peptide, protein,RNA, and carbon nanotube engineering. Doingso will require a collaborative interdisciplinaryresearch approach that spans many disciplines.We expect that in the next decade, researcherswill succeed in attaching various classes of mol-ecules (these may include organic, electronicallyactive molecules, peptides, proteins, RNA, andcarbon nanotubes) to DNA arrays, and a signif-icant portion of the application work I discussedabove will come to pass.

AcknowledgmentsThanks to Thom LaBean at Duke University for his usefulcomments on this article and the use of Figures 2, 5, and7. This article describes a vision of DNA technology sharedalso by my collaborators, Nadrian Seeman and Eric Winfree,who pioneered this emerging field. I acknowledge and thankthem for their impact to this article’s discussions of methodsand applications of DNA nanotechnology.

References1. N.C. Seeman, “DNA Engineering and Its Application to Nan-

otechnology,” Trends in Biotech, vol. 17, 1999, pp. 437–443.

2. E. Winfree, X. Yang, and N.C. Seeman, “Universal Computationvia Self-assembly of DNA: Some Theory and Experiments,” Proc.DNA Based Computers II: June 10-12, 1996, DIMACS Series in Dis-crete Mathematics and Theoretical Computer Science, AmericanMathematics Society, Providence, R.I., vol. 44, 1998, pp.191–213.

3. T.H. LaBean, “The Construction, Analysis, Ligation, and Self-As-sembly of DNA Triple Crossover Complexes,” J. American Chem-ical Society, vol. 122, no. 9, Mar. 2000, pp. 1848–1860;www.cs.duke.edu/~reif/paper/DNAtiling/tilings/JACS.pdf.

4. E. Winfree et al., “Design and Self-Assembly of Two DimensionalDNA Crystals,” Nature, vol. 394, Aug. 6, 1998, pp. 539–544.

5. T.H. LaBean, E. Winfree, and J.H. Reif, “Experimental Progress inComputation by Self-Assembly of DNA Tilings,” Proc. DNA BasedComputers V: June 14-16, 1999. DIMACS Series in Discrete Mathe-matics and Theoretical Computer Science, American Mathemati-cal Society, Providence, R.I., vol. 54, 2000, pp. 123-140;www.cs.duke.edu/~reif/paper/DNAtiling/tilings/labean.pdf.

6. J.H. Reif et al., “Challenges and Applications for Self-AssembledDNA Nanostructures,” Proc. Sixth International Workshop on DNA-Based Computers, June, 2000, DIMACS Series in Discrete Mathe-matics and Theoretical Computer Science, Springer-Verlag, Berlin,vol. 2054, 2001, pp. 173-198: www.cs.duke.edu/~reif/paper/SELFASSEMBLE/selfassemble.pdf.

7. R. Berger, “The Undecidability of the Domino Problem,” Memoirsof the American Mathematical Society, Providence, R.I., vol. 66,1966.

8. E. Winfree, “On the Computational Power of DNA Annealingand Ligation,” Proc. DNA-Based Computers: April 4, 1995, DIMACSSeries in Discrete Mathematics and Theoretical Computer Science,American Mathematical Society, Providence, R.I., vol. 27, 1996,pp. 199–211.

9. M.A. Reed et al., “Conductance of a Molecular Junction,” Sci-ence, vol. 278, Oct. 1997, pp. 252–254.

10. J. Chen et al., “Observation of a Large On-Off Ratio and NegativeDifferential Resistance in an Electronic Molecular Switch,” Sci-ence, vol. 286, no. 1550, Nov. 19, 1999, pp. 1550–1552.

11. L. Adleman, “Molecular Computation of Solution to Combina-torial Problems,” Science, vol. 266, no. 1021, Nov. 11, 1994, pp.1021–1023.

12. J.H. Reif, “Paradigms for Biomolecular Computation,” Uncon-ventional Models of Computation, C.S. Calude, J. Casti, and M.J.Dinneen, eds., Springer-Verlag, New York, 1998, pp. 72–93;www.cs.duke.edu/~reif/paper/paradigm.pdf.

13. J.H. Reif, “Local Parallel Biomolecular Computation,” Proc. DNA-Based Computers, III: DIMACS Series in Discrete Mathematics andTheoretical Computer Science, American Mathematical Society,Providence, R.I., vol. 48, 1999, pp. 217–254; www.cs.duke.edu/~reif/paper/Assembly.pdf.

14. E. Winfree, T. Eng, and G. Rozenberg, “String Tile Models forDNA Computing by Self-Assembly,” Proc. Sixth InternationalWorkshop on DNA-Based Computers, Leiden, The Netherlands, June,2000. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Springer-Verlag, Berlin, vol. 2054, 2001, pp.63–88.

15. C. Mao et al., “Logical Computation Using Algorithmic Self-As-sembly of DNA Triple-Crossover Molecules,” Nature, vol. 407,Sept. 2000, pp. 493–495; www.cs.duke.edu/~reif/paper/SELF-ASSEMBLE/AlgorithmsAssembly.pdf .

16. W. Mao et al., “A DNA Nanomechanical Device Based on the B-Z Transition,” Nature, vol. 397, Jan. 1999, pp. 144–146.

17. B. Yurke et al., “A DNA-Fuelled Molecular Machine Made ofDNA,” Nature, vol. 406, Aug. 2000, pp. 605–608.

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John H. Reif is a professor of computer science at DukeUniversity. His current research interests include mol-ecular-scale computing and DNA nanostructures. Hereceived a PhD in applied mathematics from HarvardUniversity and is the author of over 120 publications(see www.cs.duke.edu/~reif/vita/papertopics.html). Heis a fellow of the IEEE, the ACM, and the Institute ofCombinatorics. Contact him at D223 LSRC Building,Dept. of Computer Science, Research Dr., Duke Univ.,Box 90129, Durham, NC 27708-0129; reif@cs.duke.edu.