DNA Lattices: A Programmable Method for Molecular Scale Patterning and Computation

John H Reif1

Department of Computer Science, Duke University

Abstract:The field of molecular nanostructures is at a critical stage of development. There have been some notable successes in the construction of individual molecular components (e.g., carbon nanotubes, and various molecular electronic devices), and the individual manipulation of molecules by probing devices. However, a key deficiency is the lack of methods for constructing complex devices out of large numbers of these molecular components. We need methods to help us hold, shape, and assemble various molecular components into complex machines and systems. The construction of such molecular scale structures is one of the key challenges facing science and technology in the twenty-first century. This motivates the development of programmable methods for construction of complex structured objects on the molecular scale. Success will require new theoretical understand of processes at the nanoscale, new software infrastructure for simulating and designing molecular nanostructures, and new experimental techniques for assembly of molecular structures.

This paper overviews the recent development, both theoretical and experimental, of self-assembled DNA nanostructures, which is most advanced and versatile system known for programmable construction on the nanoscale. It provides a methodology for bottom-up construction of highly patterned systems at the molecular scale. The methodology of DNA self-assembly begins with the artificial synthesis of single stranded DNA molecules, which self-assemble into macromolecular building blocks ("DNA tiles"). These DNA tiles have sticky ends that preferentially match the sticky ends of particular other DNA tiles, facilitating the further assembly into large structures known as DNA tiling lattices. These DNA tiling lattices may be periodic or aperiodic and have molecular-scale features. This methodology is programmable in the sense that in principle, by the appropriate choice of the set of DNA tiles, the DNA tiling assemblies can be made to form any computable 2D or 3D pattern, however complex, by the appropriate choice of the component DNA of the tiles.

There are some recent experimental results that indicate that the method is scalable. Self-assembled 2D DNA tiling lattices composed of hundreds of thousands of tiles have been demonstrated and visualized by molecular imaging devices such as atomic force microscopes and transmission electron microscopes. Our recent experiments have demonstrated for the first time computation (logical XOR) via DNA tiling assemblies.

DNA tile assemblies have many important potential applications. They allow us to build scaffolding on which molecular electronics and robotics components can be positioned with precision and specificity. The programmability will allow for this scaffolding to have patterning as required for fabrication of complex devices composed of these components.

1. Introduction: Motivation and Historical Perspectives

1.1 The Potential of NanotechnologyWe will use the term "molecular nanostructure" (or nanostructure for short) to denote a molecular object at the supramolecular or 10-100 nanometer scale, and we will use the term "molecular nanotechnology" to denote the corresponding research field.

There are many potentially advantageous and revolutionary technologies that may result from the emerging field of molecular nanotechnology. Potential applications span medicine, biology, computer and material

1 Address: D223 LSRC Building, Department of Computer Science, Research Drive, Duke University, Box 90129, Durham, NC 27708-0129. E-mail: reif@cs.duke.edu . Phone: 919-660-6568. fax: 919-660-6519

science disciplines. Prior breakthroughs in molecular nanotechnology include the discovery of the family of carbon molecules known as the fullerenes, which include carbon nanotubes and shown to have unprecedented strength and electrical and switching properties, as well as organic molecules that also have electrical transport and switching properties, for example the Read-Tour molecular wire and molecular diode. Such molecules are presumably the molecular components to be incorporated into more complex molecular nanostructures such as molecular machines and other molecular devices. However, how is that to be done?

1.2 The Need for Patterned Assembly Techniques at the Molecular ScaleThe most critical technical barrier currently confronting molecular nanotechnology is the development of assembly methods for constructing complex devices out of molecular components.

In the macroscopic world, we have a wide variety of manufacturing technologies and infrastructures for assembling and patterning various components into complex structures and machines. However, none of this essential technology exists yet on the molecular scale. Part of the difficulty is there is not yet a complete theoretical understanding of processes at the molecular scale. However, the most crucial difficulty is the lack of an established repertoire of experimentally demonstrated assembly methods for effectively and reliably constructing complex devices out of molecular components.

Nevertheless, this task does not seem to be impossible, and in fact in the process of the evolution of cells, nature developed patterned assembly techniques at the molecular scale hundreds of millions of years ago. Cell growth is one of numerous examples of unmediated biochemical processes in biology that provide strong evidence that biochemical processes can create nanostructures of surprising complexity. However, these need to be programmable and easily modified to be of use to us.

2 Known Patterning Methods: Historical Perspectives and Limitations.

We now review the known patterning methods used for manufacture at the microscale. These methods for patterning can be categorized as being either top-down or bottom-up.

2.1 Top down methods for patterning:Top down methods for patterning use a macroscopic device to pattern at some smaller scale, e.g., the microscale, or nanoscale. Top down methods for patterning objects date to at least the early nineteenth century. (For example, Jacquard in France made use of Holorith cards to control the mechanical weaving of patterns in tapestries.)

(a) Lithographic methods, which use optically active chemical etching or deposition to form patterns, date to the late nineteenth century. This top down method for patterning was crucial to the development of many other manufacturing technologies in the twentieth century. Starting in the mid twentieth century, lithography was used for the fabrication of circuits and microcircuits and was the most successful micro-miniaturization technique developed so far. However, due to wavelength resolution limits, it is unlikely that lithography will scale down to the molecular scale, at below 10 nanometers.

(b) Scanning Probe Microscope-Aided Construction: One approach to assembling nanoscale objects is to use a macroscale instrument that can move at molecular size scales, such as a Scanning Probe Microscope (SPM). Major obstacles to using SPM to construct complex devices include the sequential nature of the technology and its controllability and scalability; although some parallelism exists, it is dwarfed by molecular parallelism.

2.1 Bottom Up Self-assembly Methods for Patterning Nanoscale Constructs: We now focus our discussion on another approach: patterning by self-assembly. Self-assembly is the spontaneous self-ordering of substructures into superstructures driven by the selective affinity of the substructures. Bottom up methods use some form of self-assembly for patterning.

(a) Chemical Self-assembly Methods. While self-assembly methods are well known and have been long used by chemists (for example, for the self-assembly of lipid or polymer layers), they conventionally result

in structures with limited complexity, and are not readily programmable.

(b) Protein Engineering. This holds great promise for molecular devices, but it is moving slowly and does not share the programmable nature of biochemistry, such as DNA. Also, this approach when applied to proteins is at this time limited by the degree of predictability of the resulting protein conformations.

(c) “Reprogramming" Biological Cells: Biological cells do operate on the nanoscale, but the machinery available in biological cells is exceptionally difficult to predict and control, and we are only beginning to fully understand the complexity of its control systems.

(d) DNA Self-assembly is the spontaneous self-assembly of DNA strands into nanostructures driven by selective DNA annealing among DNA strands. The advantages of this technique are described in the next section.

3. DNA Tiles and Tiling Lattices

We now focus our discussion on DNA self-assembly. We will first provide a brief overview of the relevant chemical and structural properties of DNA, and the assemblies that have been achieved.

3.1 DNA as a Construction Material. Single stranded DNA is a polymer that consists of a sequence of four types of bases. These four bases are grouped into two disjoint pairs, known as Watson-Crick complementary pairs, which can bind together via hydrogen bonding. DNA enjoys a unique advantage for a nanostructure construction material due the property that two single strands of DNA can be designed to be selectively “sticky” and anneal together to form doubly stranded DNA. This annealing is much more likely to occur if the DNA base sequences are complementary (that is, the component bases are Watson-Crick pairs) and the temperature and salinity are set appropriately. The resulting doubly stranded DNA is relatively rigid and forms the well-known double-helix geometry.

Figure 1. Annealing of sticky single stranded segments of DNA. If the sticky single stranded segments that anneal abut doubly stranded segments of DNA, then an enzymic reaction known as ligation can be used to concatenate these segments.

3.1 DNA Self-assembly. This entails the building up of superstructures from starting units consisting of single strands of DNA. The binding is via Watson-Crick base-pairing DNA sequences and is highly selective and specific. This insures that with the appropriate choice of these multiple component strands of DNA, in many cases predictable nanostructures self-assemble.

3.2 DNA Nanostructures. Nano-fabrication of structures in DNA was pioneered in the 1980s by Seeman [Seeman, 1999], who assembled a multitude of DNA nanostructures (e.g., rings, cubes, and octahedrons) using DNA branched junctions. However, these early DNA nanostructures were not rigid.To increase the rigidity of DNA nanostructures, one can use a DNA nanostructure found in nature, known as a DNA crossover (also known as a branched Holiday junction). It consists of two doubly stranded DNA, were each doubly stranded DNA has a single strand that crosses over to the other. Crossovers of interest

here (known as anti-parallel crossovers) cause a reversal in direction of strand propagation following exchange of strand to a new helix.

3.3 DNA Tiles. These are quite rigid and stable DNA nanostructures that are formed from multiple DNA anti-parallel crossovers. DNA tiles typically have a geometry that is roughly rectangular. These tiles come in multiple varieties that differ from one another in the geometry of strand exchange and the topology of the strand paths through the tile. The first DNA tiles developed [Winfree,et al 1996] and [Winfree, et al 1998] are known as double crossover (DX) tiles; they are composed of two DNA double-helices with two crossovers. Recently some novel DNA tiles known as triple cossover (TX) tiles have been developed [LaBean, et al, 2000b]; they are composed of three DNA double-helices with four crossovers and have properties that facilitate certain tiling assemblies and computations.

3.4 The Pads of DNA Tiles. Each DNA tile is designed so that they preferentially match the ends of certain other DNA tiles, facilitating the further assembly into tiling lattices. In particular, each tile contain several short sections of unpaired, single-strand DNA extending from the ends of the tile. (Both DX and TX tiles are useful for doing tiling assemblies; the DX tiles provide up to four pads for encoding associations with neighboring tiles, and the TX tiles provide up to 6 pads.) These pads are designed so as to function as binding domains with other DNA tiles; in particular, the tile pads are “sticky” (complementary) to the pads of other chosen DNA tiles. Individual tiles interact by annealing with other specific tiles via their pads to self-assemble into desired superstructures. The use of pads with complementary base sequences allows the neighbor relations of tiles in the final assembly to be intimately controlled; thus the intended superstructures are formed during assembly.

Figure 3: The binding of pairs of pads of two DNA tiles.

3.5 Regular Patterned DNA Lattices. Recently there have been demonstrated the self assembly of 2 D periodic lattices consisting of hundreds of thousands of DX tiles [Winfree, et al 98]. This is strong evidence of the scalability of this approach. In addition, we have constructed DNA triple crossover molecules (TX) from which we have also produced tiling lattices [LaBean, et al, 2000a and 2000b]. Both classes of lattices were observed by atomic force microscopy (an atomic force microscope is a mechanical scanning device

Figure 2a A TX Tile Figure 2b A TX tile with two extra stem-loops which project into (black) and out of (green) the plane of the page.

that provides images of molecular structures laying on a flat 2D plate) as well as by transmission electron microscopy (TEM).

Figure 4a. Figure 4bFigures 4a and 4b give AFM images of DNA lattices with TX tiles 3-4 microns on a side.

Distinguishing surface features were designed into individual tiles by adding to the DNA strands composing the tile additional segments of DNA forming short loops that protrude above the tile (to enhance definition, one may also affix metallic balls to these DNA loops, using known methods for affixing gold balls to DNA). Surface features such as 2D banding patterns have then been readily programmed into these DNA lattices by using such DNA tiles that assembled into regular repetitive patterns, and these topographical features on the DNA tiling lattices were observable by AFM and TEM imaging devices.

For a more detailed survey of current work in self-assembled DNA nanostructures, see paper: [Reif, et al, 2001].

4 Constructing DNA Lattices with Complex Patterning

4.1 Unmediated Algorithmic Self-assembly of Patterned DNA LatticesThe assembly process described above can be used to perform computations. This entails the building up of superstructures from the starting units such that the assembly process itself performs the actual computation. The most general method we know of for 2D molecular pattern formation is the use of a small set of DNA tiles that self-assemble in a predictable manner. We shall call this unmediated algorithmic self-assembly.

There is a body of theoretical work that dates to the 1960s that indicates the power of this tiling approach for patterning. Wang tilings are a class of tiling problems defined by Wang [Wang, 1963]. One is given a finite set of unit size square tiles, each of whose sides are labeled with symbols over a finite alphabet (the pads). Additional restrictions may include the initial placement of a subset of these tiles, and the dimensions of the region where tiles must be placed. The problem is to place the tiles, chosen with replacement, to completely fill the given region so that each pair of abutting tiles have identical symbols on their contacting sides.

The class of patterns generated by Wang tilings has been shown to include all computations. Berger [Berger, 1966] gave a construction where tiles are defined that result in tiling lattices that can simulate any given Turing Machine computation. Winfree [Winfree, 1995] and [Winfree,et al 1996] proved this result in the context of DNA tiling lattices. Hence, using only a small number of component tiles, unmediated algorithmic self-assembly of DNA tiling lattices is theoretically capable of creating arbitrarily complex structures. This method has the advantage of being very general; it requires no input DNA strand encoding a pattern, and instead the 2D pattern is essentially generated by the choice of the DNA tile set.

An interesting example being considered for a possible unmediated algorithmic self-assembly in 2D is a tiling pattern that counts in binary. Winfree has recently observed that the resulting 2D pattern is nearly

Figure4c. TEM image of platinum rotary shadowed TX lattice.

identical to the pattern for a demultiplexing RAM circuit and so this pattern could potentially serve as a template for arranging molecular electronics components such as molecular wires [Reed, et al 1997] and molecular diods [Chen, et al 1999] into a desired demultiplexing circuit.

4.2 Computation by DNA Tiling. Besides forming complex patterns, DNA tilings can also be used to perform massively parallel computations with inputs and outputs encoded by DNA stands.In this emerging new methodology for computation:

Input is provided by sets of single stranded DNA (known as input stands) that serve as nucleation sites for tiling assemblies, and

Output can be made by the concatenation (concatenation of stands is done by an enzymic reaction known as ligation) to the input stands additional output strands of DNA. These output stands are formed and co-localized within the tiling assembly. They wind through all the tiles of a tiling assembly. After formation, the output stands can be then released by for example raising the temperature so that the stands composing the tiles disassociate into single strands of DNA.

Note that input/output can occur in parallel for multiple distinct tiling assemblies.

4.3 Comparison with Prior Work in DNA Computation.In the seminal paper of Adleman [Adleman, 1994] describing the first experiment demonstrating the use of recombinant DNA techniques for solving a small combinatorial search problem (known as the Hamiltonian path problem), Adleman made use of a simple form of computation by self-assembly. His algorithm does not blindly generate all possible sequences of vertices; instead, the DNA sequences and the use of DNA complementary binding guides the self-assembly processes so that only valid paths are generated. This work spawned considerable further work in DNA computation (See the comprehensive survey of [Reif, 1998]). However, much of the subsequent work in DNA computation required many tedious laboratory operations to be performed.

The use of DNA tiling lattices for doing computation avoids these difficulties. One only needs to design DNA tiles with the appropriate pads so as to specify individual steps of the computation. The use of pads with complementary base sequences allows the neighbor relations of tiles in the final assembly to be intimately controlled; thus the only large-scale superstructures formed during assembly are those that encode valid mappings of input to output. Rather than implementing a DNA computing algorithm using a sequence of multiple laboratory procedures, the approach essentially uses only four:

mixing the input DNA strands to form the DNA tiles, allowing the tiles to self-assemble into superstructures, ligation of the strands that have been co-localized, and then performing a single separation to identify the correct output.

4.4 Massive Parallel Computation by DNA Tiling.The massive parallelism inherent in DNA-based computers has, since its inception, driven thinking in the field. Due to the very compact form of DNA molecules, the degree of parallelism (due to distinct tiling assemblies) may be up to 1016 or more. In computation by self-assembly, parallelism reveals itself in many ways. DNA self-assembly can be executed in massively parallel fashion, with concurrent assemblies that may execute computations independently. In global parallelism, each superstructure may contain information representing a different calculation. In local parallelism, growth on each individual superstructure may occur at many locations simultaneously.

Figure 5. Global and Local Parallelism in the Formation of DNA Tiling Assemblies

The depth of a tiling assembly is the maximum number of self-assembly reactions experienced by any substructure (i.e., the depth of the graph of pad binding events), and the size of a superstructure is the number of tiles it contains. The advantage of tiling assemblies of small depth and size is that, due to local parallelism, their formation is swift their formation is more likely to be error-free. Reif [Reif, 1999] developed DNA self-assembly methods of linear size and small depth to solve a number of fundamental problems (e.g., arithmetic on n bit numbers and sorting) that form the basis for the design of many parallel algorithms. Some of these designs (e.g., for integer addition) required only a single layer of tiles to be assembled within a nanostructure known as an assembly frame, requiring only the simplest form of linear self-assembly. Winfree and Rozenberg [Winfree and Rozenberg, 1998] proposed a special class of DNA tiles, known as string tiles that also result in 1D computational tiling lattices. By allowing contiguous strings of DNA to trace through individual tiles and the entire assembly multiple times, surprisingly sophisticated calculations can be performed with these 1-layer linear tiling assemblies. The TX tiles recently developed are particularly useful as string tiles.

4.4 Arithmetic Computation by 1 D DNA Tiling.We now outline a procedure for using a string tiles described above to perform massively parallel arithmetic. [LaBean, et al, 2000a] and [Mao, et al, 2000] describes string tile systems that compute binary number addition (where the binary numbers of encoded by strands of DNA) by using the selective composition of adjacent tiles in the assembly to effectively communicate the carry-bits. (They can also be used for computation of bit-wise XOR of Boolean vectors encoded by strands of DNA). For computations on specific inputs, these procedures will make use of the scaffold strands mentioned above. Otherwise, the input tiles will randomly assemble and thereby generate a molecular look-up table in which each reporter strand encodes the inputs and outputs of a random calculation. A sufficient number of DNA tile molecules provide full coverage of all possible n-bit input strings. Such look-up tables may be useful as input for further computations as they represent a unique library of sequences with a complex structural theme.

Recent experiments have demonstrated for the first time computation via molecular assembly of TX DNA tiles [Mao, et al, 2000]. The computation is similar to that described for integer addition, but actually solves a simpler computational task (known as logical XOR) related to computing the carry sequence in integer arithmetic. For an overview of these computations, and a number of examples, see [Reif, et al, 2001].

5 Future Research on the Assembly of Patterned DNA Lattices.The above mentioned XOR computation [Mao, et al, 2000] can be viewed as the first demonstration of unmediated algorithmic self-assembly in 1D. However, unmediated algorithmic self-assembly in 2D has not yet been demonstrated for complex patterns beyond the banded patterns described above. Nevertheless, there are numerous examples of unmediated biochemical processes in biology (e.g., cell growth) that proved strong evidence that unmediated biochemical processes can create nanostructures of surprising complexity.

5.1 Optimizing Assembly Techniques. Further progress will require an improved understanding and control of the physical phenomena that determine the lattice growth. Experiments need to be conducted to evaluate the speed and error rates of the various types of self-assembly reactions. Also, improved methods need to be developed to minimize errors in self- assembly. Defect errors can occur in DNA lattice formation can occur in solutions containing many distinct DNA tile types that compete during the lattice formation process. Optimization of temperature (including temperature cycling) and salinity should provide for decreased defect rates in lattice formation. Novel DNA tiles need to be developed with properties that facilitate minimize errors in their the self-assembly and improve their visualization by imaging devices such as atomic force microscope. The formation of defect-free DNA lattices may be enhanced by initiating the process using a small number of tiles (seed tiles) forming a nucleation basis for the subsequent larger assembly.

5.2 Computer Simulation and Design of DNA Tiling Assemblies. Improved software simulation tools are needed for modeling the kinetics of self-assembly with the goal of developing a more fundamental understanding of self-assembly processes.

Tiling assemblies can be defined so that theoretically only a unique, correct tiling pattern is produced with no errors (all pads of each tile match perfectly with their neighbors) However, the self-assembly of DNA tiles is intrinsically a probabilistic process. A stochastic software simulation of DNA lattice formation was developed by Winfree [Winfree, 1998]. His computer simulations show that low error rates can be achieved in certain computational DNA lattices in the special case of very low tile concentrations and near the melting temperature (where the DNA structures tend to disassociate). Due to his assumption of low tile concentrations, his simulation used a simplification of the chemical rate equations, which allowed only the insertion of single DNA tiles into a growing DNA assembly. This software might be enhanced by incorporating more sophisticated models of DNA lattice formation with insertion of groups of multiple DNA tiles that are partially annealed. There is also an acute need more sophisticated modeling of the kinodynamic properties of DNA lattices. The software simulation of large DNA lattices containing hundreds of DNA tile nanostructures is an enormous computationally challenging task if we use conventional molecular dynamics simulation software. This computational difficulty may be circumvented by the development of DNA molecular dynamic simulation software that instead employ semi-empirical models for DNA dynamic simulation at the base-pair level. DNA chains bend, twist, and stretch in response to base sequence and to specific interactions with the chemical environment. It is possible to extract a DNA model with local energy components, where the coefficients in the model come from empirical results of known DNA X-ray crystallographic literature. These models may be refined to incorporate base sequence dependant variations in these parameters as well as crossover junctions. The resulting simulation software might be reliable enough to provide helpful insight on the dynamics of large DNA lattices, and yet efficient enough so simulations of very large DNA lattices would be feasible. Also, improved software is needed for the design of novel DNA tiles and tiling assemblies. Current software for design of the stands composing DNA tiles use algorithms that allow for the desired binding of DNA strands that form duplex DNA in the DNA tiles and minimize undesired binding interactions between DNA strands. This software would be improved by the incorporation of algorithms that also provided for the design of the geometry of the DNA tile, perhaps using the semi-empirical models for DNA dynamic simulation mentioned above.

5.3 Sequential Step-wise Assembly Techniques. Unmediated algorithmic self-assembly of complex patterns requires delicate control of physical phenomena to minimize errors of assembly. An alternative approach, first proposed by Reif [Reif, 1999], is the step-wise assembly of a smaller number of DNA tiles under external control via sequential application of different reagents and tiles. This approach results in a serial sequencing of tile assembly events (that may occur in parallel to form distinct layers of tiles) and may provide increased reliability and reusability during fabrication of DNA nanotechnology structures.

5.4 Directed Nucleation Assembly Techniques. We have recently developed another method for assembly of complex patterns, where an input DNA strand is synthesized that encodes the required pattern, and then specified tiles assemble around blocks of this input DNA strand, forming the required 1D or 2D pattern of tiles. This method makes the use of artificially synthesized DNA strands that specify the pattern and around which 2D DNA tiles assemble into the specified pattern; in this method, the permanent features of the 2D pattern are generated uniquely for each case (see Figure 6).

Figure 6. Our Directed Nucleation Assembly Technique. In red is an input “pattern” strand of DNA. It encodes a 2D pattern in modified row major order (each odd row traversing alternately left to right, and each even row traversing right to left). Specific DNA tiles self-assemble around each segment of this input “pattern” strand of DNA. Then the tiles self-assemble into a 2D tiling lattice with a pattern determined by the “pattern” strand. A small instance of this method has been successfully executed where up to 10 TX tiles assembled around a preformed scaffold DNA strand.

5.5 Shape-Change Induced Assembly of 3D DNA Nanostructures from 2D DNA lattices.

Leveraging Known MEMS Fabrication Techniques. There is now a vast body of practical engineering developed in the construction of microelectro-mechanical systems (MEMS) from silicon substrates that might be brought to bear and leveraged to develop techniques for the multi-step assembly of 3D DNA nanostructures from 2D DNA lattices. These devices are initially fabricated within a 2D domain using optical lithography. Subsequent phases of fabrication use additional E-beam lithography, chemical release processes, and/or simple environmentally dependent shape changes (electrostatic or temperature based) to fully assemble the resulting MEMS devices in 3D. For example, a box-shaped device (with an open top) can be assembled by fabricating the bottom square and also the four sides adjoining the bottom square, and then forcing (e.g., via environmentally dependent shape changes) the sides upward, and locking these sides together via simple mechanical latches. These processing steps are of course not feasible for DNA lattice assembly, but related techniques might be applied.Application to Multi-step Assembly of 3D DNA Nanostructures. Similarly, Seeman has suggested that it may be possible to assemble 3D DNA lattices, from portions of 2D DNA lattices. In his scheme, complex assemblies of 3D DNA nanostructures constructed from 2D DNA lattices might be created using a multi-step approach, where the assembly proceeds in a series of steps. A 3D assembly might begin with the assembly of 2D DNA lattices followed by the folding of these 2D assemblies into a 3D DNA nanostructure. In this process, we would proceed in a manner similar to the above described assembly process used in MEMS. The use of restriction enzymes (which can cut the lattices at specified locations) provide an analogue in DNA lattices to the use in MEMS of E-beam lithography and chemical release processes. It is feasible to achieve simple shape changes in DNA lattices by a variety of techniques. Environmental changes can induce shape changes. Also, both Seeman [Mao, et al, 1999] and Yurke at Bell Laboratories [Yurke, et al, 2000] have developed nano-mechanical transduction devices constructed of DNA based on selective use of DNA hybridization which can be selectively controlled by adding or releasing “controller” strands of DNA. Either of these might be adapted for manipulating the shape of DNA lattices and controlling their flexibility. Finally, various DNA reactions such as annealing and ligation might be used in place of the mechanical latches used in the MEMS field to secure the MEMS devices.

5.6 DNA lattices that Store StateA DNA lattices with shape change programmability of the sort just described also may offer a mechanism to do DNA computation on lattices whose elements, the tiles, hold state. That is, the DNA assemblies may be able to simulate a parallel computing model known as cellular automata, which consist of arrays of finite state automata, each which holds state. The transitions of these automata and communication of values to their neighbors might be done by conformal (geometry) changes, again using this programmability. There are numerous examples of 1 D (2 D, respectively) cellular automata that can do computations that tiling assemblies would have required a further dimension (for example, integer multiplication in one dimension instead of two).

6 Applications of Patterned DNA Lattices

Ultimately, the significance of patterned DNA nanostructures lies not in their existence, but in their application as scaffolds for positioning other materials.

6.1 Attachment Technology. A large variety of other molecules (including RNA, proteins, and many other organic and metallic molecules) are known to be capable of selectively binding directly to short stands of DNA, or indirectly bind to DNA via appropriately designed attachment chemistry. It is feasible to bind such molecules to specific sites on DNA tiles within the DNA lattices (these sites might be short stem loops that that can be designed to protrude above a DNA tile). This provides for a highly flexible nanostructure construction methodology: by selectively attaching various other types of molecules to the tiles of the lattices, these lattices can be used as superstructures for placement of nanocomponents composed of a wide variety of other materials. DNA lattices can potentially also juxtaposing distinct molecules. Furthermore, they may be capable of orienting these molecules

6.2 Potential Applications. The ability to form programmable patterned nanostructured DNA lattices will open many opportunities for applied research in nanoscale science and engineering. These include their application as scaffolds and superstructures for:

molecular electronics (e.g., patterning and quantum dots, molecular circuit layout and interconnection),

molecular optical transduction and memory components, aligning proteins for crystallography studies, aligning receptor proteins, arranging carbon nanotubes, and nanorobotics.

We now give a brief description of two applications of DNA lattices.

6.3 Targeting of gold nanospheres into desired patterns by templating with DNA lattices. For example, as illustrated in the figure 7 below, it may be possible to use gold-sulfur affinity chemistry for binding of gold nanospheres to a DNA lattice. A segment of DNA containing sulfur can be incorporated into the DNA lattice so it at the end of the stem loop protruding from the lattice at fixed sites. Gold nanoparticles have been added to the annealed lattice and bind the immobile sulfur. Alternatively, thiolated segments of DNA can be made to react directly with gold nanospheres to yield single-strand DNA labeled gold which can be subsequently annealed to its complementary strand displayed on the lattice on protruding stem loops. As shown in the figure above, the final step in the production of long continuous wires would involve fusion of the immobilized gold nanospheres in the presence of the appropriate chemistry.

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

Alternatively, the Reed-Tour molecular electronics components such as molecular wires [Reed, et al 1997] and molecular diods [Chen, et al 1999] have ends containing sulfur that have an affinity to gold. Hence they can be self-assembled between the gold balls attached to the DNA lattices.

Other methods for targeting and immobilization of other molecules, such as proteins, metals and single-wall carbon nanotubes might be adapted to our purpose. For example, various surface chemistry methods used for labeling cells and cell sorting might be adapted for attachment chemistry to DNA lattices.

6.4 Aligning proteins in regular 3D DNA lattices. The problem of aligning proteins for crystallography studies is one that has been a principal objective of Seeman at NYU. The determination of the structure of proteins is crucial for many medical and biological applications (e.g., drug design). The structure of crystallizable proteins can be determined by known computation methods using the diffraction patterns resulting form X-ray crystallography studies. However, a considerable percentage of all proteins cannot be crystallized and hence their structure is not currently known. His idea for determining the structure of otherwise non-crystalline proteins is to create periodic 3D DNA lattices which will capture the protein molecules, thus aligning them into regular lattices which are applicable to X-ray crystallography. Another possible application of Seeman’s idea is the scaffolding of nanoelectronic systems in 3D.

7 ConclusionsDNA lattices is an emerging technology providing unprecedented capabilities in the areas of molecular scale computation and programmable pattern formation. It has applications to many other emerging technologies in molecular nanotechnology. It is essential that these applications be aggressively developed, by combining the exciting recent advances in DNA lattices with advances in molecular electronics, peptide, protein, RNA, and carbon nanotube engineering. This will require a collaborative interdisciplinary research approach spanning many disciplines.

WIRE

DNA strands. Annealed Lattice. Bound Nanoparticles. Metal Deposition. Fused Wire.

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