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13
Programmable control of nucleation for algorithmic selfassembly
 in DNA Computing 10, Lecture Notes in Comput. Sci. 3384
, 2005
"... Abstract. 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 ..."
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Cited by 30 (10 self)
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Abstract. 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 15 (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
Parallelism and Time in Hierarchical SelfAssembly ∗
"... 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 5 (1 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. 1
Communication, convergence, and stochastic stability in selfassembly
 In 49th IEEE Conference on Decision and Control (CDC). Ieee
, 2010
"... Abstract — Existing work on programmable selfassembly has focused on deterministic performance guarantees—stability of desirable states. In particular, for any acyclic target graph a binary rule set can be synthesized such that the target graph is the uniquely stable assembly. If the number of agen ..."
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Cited by 2 (1 self)
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Abstract — Existing work on programmable selfassembly has focused on deterministic performance guarantees—stability of desirable states. In particular, for any acyclic target graph a binary rule set can be synthesized such that the target graph is the uniquely stable assembly. If the number of agents is finite, communication and consensus algorithms are necessary for the dynamic process induced by the rule set to converge to a state with a maximum number of target assemblies. We suggest a selfassembly problem constrained so that communication can only occur between a pair of agents participating in a formation or severance event. We propose a stochastic decision policy for the agents that provides a performance guarantee in the form of stochastic stability for any finite number of agents and any acyclic target graph. In particular, the process will have a yield of desirable assemblies approaching 100 percent of the maximum as the number of agents increases. This is accomplished with a probability that can be made arbitrarily close to one. This result is established analytically and demonstrated via simulation. We argue that probabilistic performance criteria such as stochastic stability are relevant to the selfassembly problem. This approach allows for the analysis of robustness in the presence of uncertain disturbances to agent behavior. Another feature of probabilistic performance guarantees is the ability to model reversible processes. We also suggest how the presented process can be augmented with communications to provide stability. I.
Selfassembled DNA Nanostructures and DNA Devices
"... This chapter overviews the past and current state of the emerging research area in the field of nanoscience that make use of synthetic DNA to selfassemble into DNA nanostructures and to make operational molecularscale devices. Recently there have been a series of quite astonishing experimental res ..."
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Cited by 1 (1 self)
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This chapter overviews the past and current state of the emerging research area in the field of nanoscience that make use of synthetic DNA to selfassemble into DNA nanostructures and to make operational molecularscale devices. Recently there have been a series of quite astonishing experimental results which have taken the technology from a state of intriguing possibilities into demonstrated capabilities of quickly increasing scale and complexity. We discuss the design and demonstration of molecularscale devices that make use of DNA nanostructures to achieve: molecular patterning, molecular computation, amplified sensing and nanoscale transport. We particularly emphasize molecular devices that make use of techniques that seem most promising, namely ones that are programmable (the tasks executed can be modified without entirely redesigning the nanostructure) and autonomous (executing steps with no external mediation after starting). 1.
Polyominoes Simulating ArbitraryNeighborhood
, 1002
"... This paper provides a bridge between the classicaltiling theory and the complex neighborhood selfassembling situations that exist in practice. The neighborhood of a position in the plane is the set of coordinates which are considered adjacent to it. This includes classical neighborhoods of size fou ..."
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This paper provides a bridge between the classicaltiling theory and the complex neighborhood selfassembling situations that exist in practice. The neighborhood of a position in the plane is the set of coordinates which are considered adjacent to it. This includes classical neighborhoods of size four, as well as arbitrarily complex neighborhoods. A generalized tile system consists of a set of tiles, a neighborhood, and a relation which dictates which are the “admissible ” neighboring tiles of a given tile. Thus, in correctly formed assemblies,tilesareassignedpositionsoftheplaneinaccordancetothisrelation. We prove that any validly tiled path defined in a given but arbitrary neighborhood (a zipper) can be simulated by a simple “ribbon ” of microtiles. A ribbon is a special kind of polyomino, consisting of a nonselfcrossing sequence of tiles on the plane, in which successive tiles stick along their adjacent edge. Finally, we extend this construction to the case of traditional tilings, proving that we can simulate arbitraryneighborhood tilings by simpleneighborhood tilings, while preserving some of their essential properties.