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29
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 41 (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.
The tile assembly model is intrinsically universal
 In Proceedings of the 53rd Symposium on Foundations of Computer Science
, 2012
"... We prove that the abstract Tile Assembly Model (aTAM) of nanoscale selfassembly is intrinsically universal. This means that there is a single tile assembly system U that, with proper initialization, simulates any tile assembly system T. The simulation is “intrinsic ” in the sense that the selfasse ..."
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Cited by 25 (14 self)
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We prove that the abstract Tile Assembly Model (aTAM) of nanoscale selfassembly is intrinsically universal. This means that there is a single tile assembly system U that, with proper initialization, simulates any tile assembly system T. The simulation is “intrinsic ” in the sense that the selfassembly process carried out by U is exactly that carried out by T, with each tile of T represented by an m×m “supertile ” of U. Our construction works for the full aTAM at any temperature, and it faithfully simulates the deterministic or nondeterministic behavior of each T. Our construction succeeds by solving an analog of the cell differentiation problem in developmental biology: Each supertile of U, starting with those in the seed assembly, carries the “genome ” of the simulated system T. At each location of a potential supertile in the selfassembly of U, a decision is made whether and how to express this genome, i.e., whether to generate a supertile and, if so, which tile of T it will represent. This decision must be achieved using asynchronous communication under incomplete information, but it achieves the correct
Parallelism and Time in Hierarchical SelfAssembly
, 2012
"... We study the role that parallelism plays in time complexity of variants of Winfree’s abstract Tile Assembly Model (aTAM), a model of molecular algorithmic selfassembly. In the “hierarchical ” aTAM, two assemblies, both consisting of multiple tiles, are allowed to aggregate together, whereas in the ..."
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Cited by 21 (8 self)
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We study the role that parallelism plays in time complexity of variants of Winfree’s abstract Tile Assembly Model (aTAM), a model of molecular algorithmic selfassembly. In the “hierarchical ” aTAM, two assemblies, both consisting of multiple tiles, are allowed to aggregate together, whereas in the “seeded” aTAM, tiles attach one at a time to a growing assembly. Adleman, Cheng, Goel, and Huang (Running Time and Program Size for SelfAssembled Squares, STOC 2001) showed how to assemble an n×n square in O(n) time in log n the seeded aTAM using O ( ) unique tile types, where log log n both of these parameters are optimal. They asked whether the hierarchical aTAM could allow a tile system to use the ability to form large assemblies in parallel before they attach to break the Ω(n) lower bound for assembly time. We show log n that there is a tile system with the optimal O ( ) tile log log n types that assembles an n×n square using O(log 2 n) parallel “stages”, which is close to the optimal Ω(log n) stages, forming the final n×n square from four n/2×n/2 squares, which are themselves recursively formed from n/4 × n/4 squares, etc. However, despite this nearly maximal parallelism, the system requires superlinear time to assemble the square. We extend the definition of partial order tile systems studied by Adleman et al. in a natural way to hierarchical assembly and show that no hierarchical partial order tile system can build any shape with diameter N in less than time Ω(N), demonstrating that in this case the hierarchical model affords no speedup whatsoever over the seeded model. We also strengthen the Ω(N) time lower bound for deterministic seeded systems of Adleman et al. to nondeterministic seeded systems. Finally, we show that for infinitely many n, a tile system can assemble an n × n ′ rectangle, with n> n ′, in time O(n 4/5 log n), breaking the lineartime lower bound that applies to all seeded systems and partial order hierarchical systems.
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
Rapid prototyping of 3D DNAorigami shapes with caDNAno. Nucleic Acids Res
, 2009
"... with caDNAno ..."
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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 13 (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].
Activatable Tiles: Compact, Robust Programmable Assembly and Other Applications
 in DNA Computing: DNA13 (edited by Max Garzon and Hao Yan), SpringerVerlag Lecture Notes for Computer Science (LNCS
, 2007
"... While algorithmic DNA selfassembly is, in theory, capable of forming complex patterns, its experimental demonstration has been limited by significant assembly errors. In this paper we describe a novel protection/deprotection strategy to strictly enforce the direction of tiling assembly growth to en ..."
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Cited by 11 (6 self)
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While algorithmic DNA selfassembly is, in theory, capable of forming complex patterns, its experimental demonstration has been limited by significant assembly errors. In this paper we describe a novel protection/deprotection strategy to strictly enforce the direction of tiling assembly growth to ensure the robustness of the assembly process. Tiles are initially inactive, meaning that each tile’s output pads are protected and cannot bind with other tiles. After other tiles bind to the tile’s input pads, the tile transitions to an active state and its output pads are exposed, allowing further growth. We describe abstract and kinetic models of activatable tile assembly and show that the error rate can be decreased significantly with respect to Winfree’s original kinetic tile assembly model without considerable decrease in assembly growth speed. We prove that an activatable tile set is an example of a compact, errorresilient and selfhealing tileset. We describe a DNA design of activatable tiles and a mechanism of deprotection using DNA polymerization and strand displacement. We conclude with a brief discussion on some applications of activatable tiles beyond computational tiling, both as a novel concentration system and a catalyst in chemical reactions. 1
Synthesizing minimal tile sets for patterned DNA selfassembly
 In DNA
, 2010
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Intrinsic universality in tile selfassembly requires cooperation
 In SODA 2014: Proceedings of the 25th Annual ACMSIAM Symposium on Discrete Algorithms
, 2014
"... We prove a negative result on the power of a model of algorithmic selfassembly for which finding general techniques and results has been notoriously difficult. Specifically, we prove that Winfree’s abstract Tile Assembly Model is not intrinsically universal when restricted to use noncooperative ti ..."
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Cited by 7 (4 self)
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We prove a negative result on the power of a model of algorithmic selfassembly for which finding general techniques and results has been notoriously difficult. Specifically, we prove that Winfree’s abstract Tile Assembly Model is not intrinsically universal when restricted to use noncooperative tile binding. This stands in stark contrast to the recent result that the abstract Tile Assembly Model is indeed intrinsically universal when cooperative binding is used (FOCS 2012). Noncooperative selfassembly, also known as “temperature 1”, is where all tiles bind to each other if they match on at least one side. On the other hand, cooperative selfassembly requires that some tiles bind on at least two sides. Our result shows that the change from noncooperative