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95
Proofreading tile sets: Error correction for algorithmic selfassembly
 DNA Computers
"... Abstract. For robust molecular implementation of tilebased algorithmic selfassembly, methods for reducing errors must be developed. Previous studies suggested that by control of physical conditions, such as temperature and the concentration of tiles, errors (") can be reduced to an arbitrar ..."
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Cited by 57 (10 self)
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Abstract. For robust molecular implementation of tilebased algorithmic selfassembly, methods for reducing errors must be developed. Previous studies suggested that by control of physical conditions, such as temperature and the concentration of tiles, errors (") can be reduced to an arbitrarily low rate { but at the cost of reduced speed (r) for the selfassembly process. For tile sets directly implementing blocked cellular automata, it was shown that r "2 was optimal. Here, we show that an improved construction, which we refer to as proofreading tile sets, can in principle exploit the cooperativity of tile assembly reactions to dramatically improve the scaling behavior to r " and better. This suggests that existing DNAbased molecular tile approaches may be improved to produce macroscopic algorithmic crystals with few errors. Generalizations and limitations of the proofreading tile set construction are discussed. 1
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 ..."
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Cited by 56 (10 self)
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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...
Programmable control of nucleation for algorithmic selfassembly
, 2009
"... Algorithmic selfassembly, a generalization of crystal growth processes, has been proposed as a mechanism for autonomous DNA computation and for bottomup fabrication of complex nanostructures. A “program” for growing a desired structure consists of a set of molecular “tiles” designed to have speci ..."
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Cited by 43 (11 self)
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Algorithmic selfassembly, a generalization of crystal growth processes, has been proposed as a mechanism for autonomous DNA computation and for bottomup fabrication of complex nanostructures. A “program” for growing a desired structure consists of a set of molecular “tiles” designed to have specific binding interactions. A key challenge to making algorithmic selfassembly practical is designing tile set programs that make assembly robust to errors that occur during initiation and growth. One method for the controlled initiation of assembly, often seen in biology, is the use of a seed or catalyst molecule that reduces an otherwise large kinetic barrier to nucleation. Here we show how to program algorithmic selfassembly similarly, such that seeded assembly proceeds quickly but there is an arbitrarily large kinetic barrier to unseeded growth. We demonstrate this technique by introducing a family of tile sets for which we rigorously prove that, under the right physical conditions, linearly increasing the size of the tile set exponentially reduces the rate of spurious nucleation. Simulations of these “zigzag” tile sets suggest that under plausible experimental conditions, it is possible to grow large seeded crystals in just a few hours such that less than 1 percent of crystals are spuriously nucleated. Simulation results also suggest that zigzag tile sets could be used for detection of single DNA strands. Together with prior work showing that tile sets can be made robust to errors during properly initiated growth, this work demonstrates that growth of objects via algorithmic selfassembly can proceed both efficiently and with an arbitrarily low error rate, even in a model where local growth rules are probabilistic.
Selfreplication and evolution of DNA crystals
 Advances in Artificial Life: 8th European Conference (ECAL), volume LNCS 3630
, 2005
"... I came to Caltech a scatterbrained but enthusiastic young scientist. Without the constant nurturing and tutelage of my PhD advisor, Erik Winfree, I can’t imagine what would have happened. Erik’s gifts are many – a generous spirit, stratospheric intellectual standards, a razorsharp intuition for the ..."
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Cited by 17 (7 self)
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I came to Caltech a scatterbrained but enthusiastic young scientist. Without the constant nurturing and tutelage of my PhD advisor, Erik Winfree, I can’t imagine what would have happened. Erik’s gifts are many – a generous spirit, stratospheric intellectual standards, a razorsharp intuition for the truth, and a boundless imagination. It has been a pleasure and a privilege to work with him, to hear his constant feedback on my own imperfect thoughts. I hope in the future I can honor a tiny portion of his gifts to me by teaching others. As a PhD student I have been privileged to stand on the shoulders of other both brilliant and kind intellectual giants, without whom this work would never have been. First and foremost, my thesis work owes an unpayable intellectual debt to the work of Graham CairnsSmith. His unconventional thoughts about the first life on earth were the catalyst for this work on selfreplication. I am flattered and grateful for his continued support in the form of visits, talks, and letters during his retirement. No one was more honest about the rigors of the PhD process and a life in science than Paul Rothemund. As human and as good a friend as Paul has been, he also been someone to aspire to be like. Simply, Paul is a whiz, and a big friendly intellectual giant. I am excited about everything
Design of DNA origami
 In ICCAD ’05: Proceedings of the 2005 IEEE/ACM International conference on Computeraided design
, 2005
"... Abstract — The generation of arbitrary patterns and shapes at very small scales is at the heart of our effort to miniaturize circuits and is fundamental to the development of nanotechnology. Here I review a recently developed method for folding long single strands of DNA into arbitrary twodimension ..."
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Cited by 16 (0 self)
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Abstract — The generation of arbitrary patterns and shapes at very small scales is at the heart of our effort to miniaturize circuits and is fundamental to the development of nanotechnology. Here I review a recently developed method for folding long single strands of DNA into arbitrary twodimensional shapes using a raster fill technique – ‘scaffolded DNA origami’. Shapes up to 100 nanometers in diameter can be approximated with a resolution of 6 nanometers and decorated with patterns of roughly 200 binary pixels at the same resolution. Experimentally verified by the creation of a dozen shapes and patterns, the method is easy, high yield, and lends itself well to automated design and manufacture. So far, CAD tools for scaffolded DNA origami are simple, require handdesign of the folding path, and are restricted to two dimensional designs. If the method gains wide acceptance, better CAD tools will be required. I.
The Power of Nondeterminism in SelfAssembly
"... We investigate the role of nondeterminism in Winfree’s abstract tile assembly model, which was conceived to model artificial molecular selfassembling systems constructed from DNA. By nondeterminism we do not mean a magical ability such as that possessed by a nondeterministic algorithm to search an ..."
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Cited by 15 (7 self)
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We investigate the role of nondeterminism in Winfree’s abstract tile assembly model, which was conceived to model artificial molecular selfassembling systems constructed from DNA. By nondeterminism we do not mean a magical ability such as that possessed by a nondeterministic algorithm to search an exponentialsize space in polynomial time. Rather, we study realistically implementable systems that retain a different sense of determinism in that they are guaranteed to produce a unique shape but are nondeterministic in that they do not guarantee which tile types will be placed where within the shape. We show a “molecular computability ” result: there is an infinite shape S that is uniquely assembled by a tile system but not by any deterministic tile system. We show a “molecular complexity ” result: there is a finite shape S that is uniquely assembled by a tile system with c tile types, but every deterministic tile system that uniquely assembles S has more than c tile types. In fact we extend the technique to derive a stronger (classical complexity theoretic) result, showing that the problem of finding the minimum number of tile types that uniquely assemble a given finite shape is Σ P 2complete. In contrast, the problem of finding the minimum number of deterministic tile types that uniquely assemble a shape is NPcomplete [5].
Design of an autonomous DNA nanomechanical device capable of universal computation and universal translational motion
, 2004
"... Abstract. Intelligent nanomechanical devices that operate in an autonomous fashion are of great theoretical and practical interest. Recent successes in building large scale DNA nanostructures, in constructing DNA mechanical devices, and in DNA computing provide a solid foundation for the next step ..."
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Cited by 13 (5 self)
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Abstract. Intelligent nanomechanical devices that operate in an autonomous fashion are of great theoretical and practical interest. Recent successes in building large scale DNA nanostructures, in constructing DNA mechanical devices, and in DNA computing provide a solid foundation for the next step forward: designing autonomous DNA mechanical devices capable of arbitrarily complex behavior. One prototype system towards this goal can be an autonomous DNA mechanical device capable of universal computation, by mimicking the operation of a universal Turing machine. Building on our prior theoretical design and prototype experimental construction of an autonomous unidirectional DNA walking device moving along a linear track, we present here the design of a nanomechanical DNA device that autonomously mimics the operation of a 2state 5color universal Turing machine. Our autonomous nanomechanical device, called an Autonomous DNA Turing Machine (ADTM), is thus capable of universal computation and hence complex translational motion, which we define as universal translational motion. 1
A thermodynamic approach to designing structurefree combinatorial DNA word sets
 Nucleic Acids Res
, 2005
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Twisted duality for embedded graphs
"... Abstract. We consider two operations on an edge of an embedded graph (or equivalently a ribbon graph): giving a halftwist to the edge, and taking the partial dual with respect to the edge. These two operations give rise to an action of S3 E(G),theribbon group, onG. The action of the ribbon group ..."
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Cited by 9 (5 self)
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Abstract. We consider two operations on an edge of an embedded graph (or equivalently a ribbon graph): giving a halftwist to the edge, and taking the partial dual with respect to the edge. These two operations give rise to an action of S3 E(G),theribbon group, onG. The action of the ribbon group on embedded graphs extends the concepts of duality, partial duality, and Petrie duality. We show that this ribbon group action gives a complete characterization of duality in that if G is any cellularly embedded graph with medial graph Gm, then the orbit of G under the group action is precisely the set of all graphs with medial graphs isomorphic (as abstract graphs) to Gm. We provide characterizations of special sets of twisted duals (such as the partial duals) of embedded graphs in terms of medial graphs, and we show how different kinds of graph isomorphism give rise to these various notions of duality. The ribbon group action then leads to a deeper understanding of the properties of, and relationships among, various graph polynomials via the generalized transition polynomial which interacts naturally with the ribbon group action. 1.
Synthesizing minimal tile sets for patterned DNA selfassembly
 In DNA
, 2010
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