Computational complexity and pragmatic solutions for flexible tile based DNA self-assembly (original) (raw)

Self-Assembly of Irregular Graphs Whose Edges Are DNA Helix Axes

Journal of The American Chemical Society, 2004

A variety of computational models have been introduced recently that are based on the properties of DNA. In particular, branched junction molecules and graphlike DNA structures have been proposed as computational devices, although such models have yet to be confirmed experimentally. DNA branched junction molecules have been used previously to form graph-like three-dimensional DNA structures, such as a cube and a truncated octahedron, but these DNA constructs represent regular graphs, where the connectivities of all of the vertexes are the same. Here, we demonstrate the construction of an irregular DNA graph structure by a single step of self-assembly. A graph made of five vertexes and eight edges was chosen for this experiment. DNA branched junction molecules represent the vertexes, and duplex molecules represent the edges; in contrast to previous work, specific edge molecules are included as components. We demonstrate that the product is a closed cyclic single-stranded molecule that corresponds to a double cover of the graph and that the DNA double helix axes represent the designed graph. The correct assembly of the target molecule has been demonstrated unambiguously by restriction analysis.

Design Optimization for DNA Nanostructures

American Journal of Undergraduate Research, 2011

This paper is concerned with minimizing the cost of self-assembling DNA nanostructures. We first demonstrate that the octet truss provides an accurate geometric framework for current branched junction molecule assembly. We then develop a method of differentiating among junction molecules, the basic building blocks of the nanostructures themselves, within this structure. We use this approach to find the minimum number of junction molecules necessary to construct all of the platonic and archimedean solids naturally occurring within the octet truss.

Computation by Self-assembly of DNA Graphs

Genetic Programming and Evolvable Machines, 2003

Using three dimensional graph structure and DNA self-assembly we show that theoretically 3-SAT and 3-colorability can be solved in a constant number of laboratory steps. In this assembly, junction molecules and duplex DNA molecules are the basic building blocks. The graphs involved are not necessarily regular, so experimental results of self-assembling non regular graphs using junction molecules as vertices and duplex DNA molecules as edge connections are presented.

Programmable assembly at the molecular scale: self-assembly of DNA lattices

Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164), 2001

DNA self-assembly is a methodology for the construction of molecular scale structures. In this method, arti cially synthesized single stranded DNA self-assemble into DNA crossover molecules tiles. These DNA tiles have sticky ends that preferentially match the sticky ends of certain other DNA tiles, facilitating the further assembly into tiling lattices. DNA self-assembly can, using only a small number of component tiles, provide arbitrarily complex assemblies. The self-assembly of large 2D lattices consisting of up to thousands of tiles have been recently demonstrated, and 3D DNA lattices may soon be feasible to construct. We describe various novel DNA tiles with properties that facilitate self-assembly and their visualization by imaging devices such as atomic force microscope. We discuss key theoretical and practical challenges of DNA self-assembly, a s w ell as numerous potential applications. We brie y discuss the ongoing development o f attachment c hemistry from DNA lattices to various types of molecules, and consider application of DNA lattices assuming the development of such appropriate attachment chemistry from DNA lattices to these objects as a substrate for: a molecular robotics; for manipulation of molecules using molecular motor devices, b layout of molecular electronic circuit components, c surface chemistry, for example ultra compact annealing arrays, We also discuss bounds on the speed and error rates of the various types of self-assembly reactions, as well as methods that may minimize errors in self-assembly.

Synthesizing Minimal Tile Sets for Patterned DNA Self-assembly

Lecture Notes in Computer Science, 2011

The Pattern self-Assembly Tile set Synthesis (PATS) problem is to determine a set of coloured tiles that self-assemble to implement a given rectangular colour pattern. We give an exhaustive branch-and-bound algorithm to find tile sets of minimum cardinality for the PATS problem. Our algorithm makes use of a search tree in the lattice of partitions of the ambient rectangular grid, and an efficient bounding function to prune this search tree. Empirical data on the performance of the algorithm shows that it compares favourably to previously presented heuristic solutions to the problem.

Synthesizing Small and Reliable Tile Sets for Patterned DNA Self-assembly

Lecture Notes in Computer Science, 2011

We consider the problem of finding, for a given 2D pattern of coloured tiles, a minimal set of tile types self-assembling to this pattern in the abstract Tile Assembly Model of . This Patterned self-Assembly Tile set Synthesis (PATS) problem was first introduced by Ma and Lombardi (2008), and subsequently studied by Göös and Orponen (2011), who presented an exhaustive partition-search branch-and-bound algorithm (briefly PS-BB) for it. However, finding the true minimal tile sets is very time consuming, and the algorithm PS-BB is not well-suited for finding small but not necessarily minimal solutions. In this paper, we modify the basic partitionsearch framework by using a heuristic to optimize the order in which the algorithm traverses its search space. We find that by running several parallel executions of the modified algorithm PS-H, the search time for small tile sets can be shortened considerably. Additionally, we suggest a new approach, answer set programmin (ASP), to solving the PATS problem. We also introduce a method for computing the reliability of a given tile set, i.e. the probability of its error-free self-assembly to the desired target tiling, based on Winfree's analysis of the kinetic Tile Assembly Model (1998). We present empirical data on the reliability of tile sets found by the PS-BB and PS-H algorithms and find that also here the PS-H algorithm constitutes a significant improvement over the earlier PS-BB algorithm.

Programmable DNA tile self-assembly using a hierarchical sub-tile strategy

Nanotechnology, 2014

DNA tile based self-assembly provides a bottom-up approach to construct desired nanostructures. DNA tiles have been directly constructed from ssDNA and readily self-assembled into 2D lattices and 3D superstructures. However, for more complex lattice designs including algorithmic assemblies requiring larger tile sets, a more modular approach could prove useful. This paper reports a new DNA 'sub-tile' strategy to easily create whole families of programmable tiles. Here, we demonstrate the stability and flexibility of our sub-tile structures by constructing 3-, 4-and 6-arm DNA tiles that are subsequently assembled into 2D lattices and 3D nanotubes according to a hierarchical design. Assembly of sub-tiles, tiles, and superstructures was analyzed using polyacrylamide gel electrophoresis and atomic force microscopy. DNA tile self-assembly methods provide a bottom-up approach to create desired nanostructures; the sub-tile strategy adds a useful new layer to this technique. Complex units can be made from simple parts. The sub-tile approach enables the rapid redesign and prototyping of complex DNA tile sets and tiles with asymmetric designs.

Self-assembly of DNA into nanoscale three-dimensional shapes

Molecular self-assembly offers a 'bottom-up' route to fabrication with subnanometre precision of complex structures from simple components 1 . DNA has proved to be a versatile building block 2-5 for programmable construction of such objects, including twodimensional crystals 6 , nanotubes 7-11 , and three-dimensional wireframe nanopolyhedra . Templated self-assembly of DNA 18 into custom two-dimensional shapes on the megadalton scale has been demonstrated previously with a multiple-kilobase 'scaffold strand' that is folded into a flat array of antiparallel helices by interactions with hundreds of oligonucleotide 'staple strands' 19,20 .

Challenges and applications for self-assembled DNA nanostructures?

Lecture Notes in Computer Science, 2001

DNA self-assembly is a methodology for the construction of molecular scale structures. In this method, arti cially synthesized single stranded DNA self-assemble into DNA crossover molecules tiles. These DNA tiles have sticky ends that preferentially match the sticky ends of certain other DNA tiles, facilitating the further assembly into tiling lattices. We discuss key theoretical and practical challenges of DNA selfassembly, a s w ell as numerous potential applications. The self-assembly of large 2D lattices consisting of up to thousands of tiles have been recently demonstrated, and 3D DNA lattices may s o o n b e feasible to construct. We describe various novel DNA tiles with properties that facilitate self-assembly and their visualization by imaging devices such as atomic force microscope. We discuss bounds on the speed and error rates of the various types of self-assembly reactions, as well as methods that may minimize errors in self-assembly. W e brie y discuss the ongoing development of attachment chemistry from DNA lattices to various types of molecules, and consider application of DNA lattices assuming the development of such appropriate attachment chemistry from DNA lattices to these objects as a substrate for: a layout of molecular electronic circuit components, b surface chemistry, for example ultra compact annealing arrays, c molecular robotics; for manipulation of molecules using molecular motor devices. DNA self-assembly can, using only a small number of component tiles, provide arbitrarily complex assemblies. It can be used to execute computation, using tiles that specify individual steps of the computation. In this emerging new methodology for computation:-input is provided by sets of single stranded DNA that serve a s n ucleation sites for assemblies, and