Results 1  10
of
25
Two computational primitives for algorithmic selfassembly: Copying and counting
 Nano Letters
, 2005
"... Copying and counting are useful primitive operations for computation and construction. We have made DNA crystals that copy and crystals that count as they grow. For counting, 16 oligonucleotides assemble into four DNA Wang tiles that subsequently crystallize on a polymeric nucleating scaffold strand ..."
Abstract

Cited by 55 (5 self)
 Add to MetaCart
Copying and counting are useful primitive operations for computation and construction. We have made DNA crystals that copy and crystals that count as they grow. For counting, 16 oligonucleotides assemble into four DNA Wang tiles that subsequently crystallize on a polymeric nucleating scaffold strand, arranging themselves in a binary counting pattern that could serve as a template for a molecular electronic demultiplexing circuit. Although the yield of counting crystals is low, and pertile error rates in such crystals is roughly 10%, this work demonstrates the potential of algorithmic selfassembly to create complex nanoscale patterns of technological interest. A subset of the tiles for counting form informationbearing DNA tubes that copy bit strings from layer to layer along their length. The challenge of engineering complex devices at the nanometer scale has been approached from two radically different directions. In topdown synthesis, information about the desired structure is imposed by an external apparatus, as in photolithography. In bottomup synthesis, structure arises spontaneously due to chemical and physical forces intrinsic to the molecular components themselves. A significant challenge for bottomup techniques is how to design
Compact ErrorResilient Computational DNA Tiling Assemblies
"... The selfassembly process for bottomup construction of nanostructures is of key importance to the emerging of the new scientific discipline of Nanoscience. For example, the selfassembly of DNA tile nanostructures into 2D and 3D lattices can be used to perform parallel universal computation and to ..."
Abstract

Cited by 46 (9 self)
 Add to MetaCart
The selfassembly process for bottomup construction of nanostructures is of key importance to the emerging of the new scientific discipline of Nanoscience. For example, the selfassembly of DNA tile nanostructures into 2D and 3D lattices can be used to perform parallel universal computation and to manufacture patterned nanostructures from smaller unit components known as DNA tiles. However, selfassemblies at the molecular scale are prone to a quite high rate of error, and the key barrier to largescale experimental implementation of DNA tiling is the high error rate in the selfassembly process. One major challenge to nanostructure selfassembly is to eliminate/limit these errors. The goals of this paper are to develop theoretical methods for compact errorresilient selfassembly, to analyze these by stochastic analysis and computer simulation (at a future date we also intend to demonstrate these errorresilient selfassembly methods by a series of laboratory experiments). Prior work by Winfree provided a innovative approach to decrease tiling selfassembly errors without decreasing the intrinsic error rate # of assembling a single tile, however, his technique resulted in a final structure that is four times the size of the original one. This paper describes various compact errorresilient tiling methods that do not increase the size of the tiling assembly. These methods apply to assembly of boolean arrays which perform input sensitive computations (among other computations). We first describe an errorresilient tiling using 2way overlay redundancy such that a single pad mismatch between a tile and its immediate neighbor forces at least one further pad mismatch between a pair of adjacent tiles in the neighborhood of this tile. This drops the error rate from # to appr...
Complexity of compact proofreading for selfassembled patterns
 In Proc. 11th International Meeting on DNA Computing
, 2005
"... Abstract. Faulttolerance is a critical issue for biochemical computation. Recent theoretical work on algorithmic selfassembly has shown that error correcting tile sets are possible, and that they can achieve exponential decrease in error rates with a small increase in the number of tile types and ..."
Abstract

Cited by 19 (4 self)
 Add to MetaCart
Abstract. Faulttolerance is a critical issue for biochemical computation. Recent theoretical work on algorithmic selfassembly has shown that error correcting tile sets are possible, and that they can achieve exponential decrease in error rates with a small increase in the number of tile types and the scale of the construction [24, 4]. Following [17], we consider the issue of applying similar schemes to achieve error correction without any increase in the scale of the assembled pattern. Using a new proofreading transformation, we show that compact proofreading can be performed for some patterns with a modest increase in the number of tile types. Other patterns appear to require an exponential number of tile types. A simple property of existing proofreading schemes – a strong kind of redundancy – is the culprit, suggesting that if general purpose compact proofreading schemes are to be found, this type of redundancy must be avoided. 1
Toward Reliable Algorithmic SelfAssembly of DNA Tiles: A FixedWidth Cellular Automaton Pattern NANO LETTERS
, 2007
"... Bottomup fabrication of nanoscale structures relies on chemical processes to direct selfassembly. The complexity, precision, and yield achievable by a onepot reaction are limited by our ability to encode assembly instructions into the molecules themselves. Nucleic acids provide a platform for inv ..."
Abstract

Cited by 15 (1 self)
 Add to MetaCart
Bottomup fabrication of nanoscale structures relies on chemical processes to direct selfassembly. The complexity, precision, and yield achievable by a onepot reaction are limited by our ability to encode assembly instructions into the molecules themselves. Nucleic acids provide a platform for investigating these issues, as molecular structure and intramolecular interactions can encode growth rules. Here, we use DNA tiles and DNA origami to grow crystals containing a cellular automaton pattern. In a onepot annealing reaction, 250 DNA strands first assemble into a set of 10 free tile types and a seed structure, then the free tiles grow algorithmically from the seed according to the automaton rules. In our experiments, crystals grew to ∼300 nm long, containing ∼300 tiles with an initial assembly error rate of ∼1.4 % per tile. This work provides evidence that programmable molecular selfassembly may be sufficient to create a wide range of complex objects in onepot reactions. The WatsonsCrick complementarity of DNA molecules allows one to design not only simple doublestranded helices but also complicated woven structures consisting of many DNA strands. 1 Welldesigned structures will selfassemble during annealing from a high initial temperature at which point all molecules are singlestranded to a lower final
Complexity of graph selfassembly in accretive systems and selfdestructible systems
 In Proc. 11th International Meeting on DNA Computing
, 2005
"... Abstract. Selfassembly is a process in which small objects autonomously associate with each other to form larger complexes. It is ubiquitous in biological constructions at the cellular and molecular scale and has also been identified by nanoscientists as a fundamental method for building nanoscale ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
Abstract. Selfassembly is a process in which small objects autonomously associate with each other to form larger complexes. It is ubiquitous in biological constructions at the cellular and molecular scale and has also been identified by nanoscientists as a fundamental method for building nanoscale structures. Recent years see convergent interest and efforts in studying selfassembly from mathematicians, computer scientists, physicists, chemists, and biologists. However most complexity theoretic studies of selfassembly utilize mathematical models with two limitations: 1) only attraction, while no repulsion, is studied; 2) only assembled structures of two dimensional square grids are studied. In this paper, we study the complexity of the assemblies resulting from the cooperative effect of repulsion and attraction in a more general setting of graphs. This allows for the study of a more general class of selfassembled structures than the previous tiling model. We define two novel assembly models, namely the accretive graph assembly model and the selfdestructible graph assembly model, and identify one fundamental problem in them: the sequential construction of a given graph, referred to as Accretive Graph Assembly Problem (AGAP) and SelfDestructible Graph Assembly Problem (DGAP), respectively. Our main results are: (i) AGAP is ¤¦ ¥complete even if the maximum degree of the graph is restricted to 4 or the graph is restricted to be planar with maximum degree 5; (ii) counting the number of sequential assembly orderings that result in a target graph (#AGAP) is §¨ ¥complete; and (iii) DGAP is ¥�©�¥����� �complete even if the maximum degree of the graph is restricted to 6 (this is the first ¥�©�¥����¨ �complete result in selfassembly). We also extend the accretive graph assembly model to a stochastic model, and prove that determining the probability of a given assembly in this model is §� ¥complete. 1
Selfhealing tile sets
 Foundations of Nanoscience: SelfAssembled Architectures and Devices, 2005
, 2005
"... Summary. Molecular selfassembly appears to be a promising route to bottomup fabrication of complex objects. Two major obstacles are how to create structures with more interesting organization than periodic or finite arrays, and how to reduce the fraction of side products and erroneous assemblies. ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
Summary. Molecular selfassembly appears to be a promising route to bottomup fabrication of complex objects. Two major obstacles are how to create structures with more interesting organization than periodic or finite arrays, and how to reduce the fraction of side products and erroneous assemblies. Algorithmic selfassembly provides a theoretical model for investigating these questions: the growth of arbitrarily complex objects can be programmed into a set of Wang tiles, and their robustness to a variety of possible errors can be studied. The ability to program the tiles presents an alternative to directly physical or chemical means for reducing error rates, since redundant information can be stored so that errors can be detected, corrected, and/or prevented during the selfassembly process. Here we study the ability of algorithmic selfassembly to heal damage to a selfassembled object. We present block transforms that convert an original errorprone tile set into a new tile set that performs the same construction task (at a slightly larger scale) and also is able to heal damaged areas where many tiles have been removed from the assembly. 1 Algorithmic Crystal Growth
COMBINING SELFHEALING AND PROOFREADING IN SELFASSEMBLY
"... Abstract. Molecular selfassembly is a promising approach to bottomup fabrication of complex structures. A major impediment to the practical use of selfassembly to create complex structures is the high rate of error under existing experimental conditions. Recent theoretical work on algorithmic sel ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Abstract. Molecular selfassembly is a promising approach to bottomup fabrication of complex structures. A major impediment to the practical use of selfassembly to create complex structures is the high rate of error under existing experimental conditions. Recent theoretical work on algorithmic selfassembly has shown that under a realistic model of tile addition and detachment, error correcting tile sets are possible that can recover from the attachment of incorrect tiles during the assembly process. An orthogonal type of error correction was recently considered as well: whether damage to a completed structure can be repaired. It was shown that such selfhealing tile sets are possible. However, these tile sets are not robust to the incorporation of incorrect tiles. It remained an open question whether it is possible to create tile sets that can simultaneously resist wholesale removal of tiles and the incorporation of incorrect ones. Here we present a method for converting a tile set producing a pattern on the quarter plane into a tile set that makes the same pattern (at a larger scale) but is able to withstand both of these types of errors.
Selfassembling tile systems that heal from small fragments
 in Preliminary Proceedings of DNA Computing 13
"... Tile systems have proved to be a useful model for understanding selfassembly at the nano scale. Selfhealing tile systems, introduced by Winfree, have the property that the selfassembled shape can recover from the loss of arbitrarily many tiles, provided the seed tile of the assembly remains intac ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Tile systems have proved to be a useful model for understanding selfassembly at the nano scale. Selfhealing tile systems, introduced by Winfree, have the property that the selfassembled shape can recover from the loss of arbitrarily many tiles, provided the seed tile of the assembly remains intact and the assembly remains connected. In this paper, we present improved selfhealing tile systems for the selfassembly of several interesting classes of shapes, including counters, squares, and Turingcomputable shapes. Our tile systems can recover from the loss of arbitrary many tiles, including the seed, provided that a large enough fragment (logarithmic in the size of the desired assembly for the case of counters and squares) is left intact. Molecular selfassembly has emerged as an important tool for nanoscale fabrication, molecular computation, crystallography, and nanomachines. On the experimental side, the combinatorial nature of DNA molecules, their relatively simple geometry (compared to smaller molecules such as the protein), and the existence of well developed laboratory techniques for creating and manipulating DNA molecules have made DNA an
Capabilities and Limits of Compact Error Resilience Methods for Algorithmic SelfAssembly
 REIF@CS.DUKE.EDU
, 2007
"... Winfree’s pioneering work led the foundations in the area of errorreduction in algorithmic selfassembly (Winfree and Bekbolatov in DNA Based Computers 9, LNCS, vol. 2943, pp. 126–144, 2004), but the construction resulted in increase of the size of assembly. Reif et al. (Nanotechnol. Sci. Comput. 79 ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Winfree’s pioneering work led the foundations in the area of errorreduction in algorithmic selfassembly (Winfree and Bekbolatov in DNA Based Computers 9, LNCS, vol. 2943, pp. 126–144, 2004), but the construction resulted in increase of the size of assembly. Reif et al. (Nanotechnol. Sci. Comput. 79–103, 2006) contributed further in this area with compact errorresilient schemes that maintained the original size of the assemblies, but required certain restrictions on the Boolean functions to be used in the algorithmic selfassembly. It is a critical challenge to improve these compact error resilient schemes to incorporate arbitrary Boolean functions, and to determine how far these prior results can be extended under different degrees of restrictions on the Boolean functions. In this work we present a considerably more complete theory of compact errorresilient schemes for algorithmic selfassembly in two and three dimensions. In our error model, ɛ is defined to be the probability that there is a mismatch between the neighboring sides of two juxtaposed tiles and they still stay together in the equilibrium. This probability is independent of any other match or mismatch and hence we term this probabilistic model as the
A self assembly model of timedependent glue strength
 In Proc. 11th International Meeting on DNA Computing
, 2005
"... Abstract Selfassembly is a ubiquitous process in which small objects selforganize into larger and complex structures. In 2000, Rothemund and Winfree proposed a Tile Assembly Model as a mathematical model for theoretical studies of selfassembly. We propose a refined selfassembly model in which the ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Abstract Selfassembly is a ubiquitous process in which small objects selforganize into larger and complex structures. In 2000, Rothemund and Winfree proposed a Tile Assembly Model as a mathematical model for theoretical studies of selfassembly. We propose a refined selfassembly model in which the glue strength between two juxtaposed tiles is a function of the time they have been in neighboring positions. We then present an implementation of our model using strand displacement reactions on DNA tiles. Under our model, we can demonstrate and study catalysis and selfreplication in the tile assembly. We then study the tile complexity for assembling shapes in our model and show that a thin rectangle of size k × N can be assembled using O((log(N)) / log log(N)) types of tiles, demonstrating the glue model has additional capabilities over the prior tiling assembly model. We also describe a method to implement with DNA tiles our model of timedependant glue strength.