The self-assembly process for bottom-up construction of nanostructures is of key importance to the emerging of the new scientific discipline of Nanoscience. For example, the self-assembly 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, self-assemblies at the molecular scale are prone to a quite high rate of error, and the key barrier to large-scale experimental implementation of DNA tiling is the high error rate in the self-assembly process. One major challenge to nanostructure self-assembly is to eliminate/limit these errors. The goals of this paper are to develop theoretical methods for compact error-resilient self-assembly, to analyze these by stochastic analysis and computer simulation (at a future date we also intend to demonstrate these error-resilient self-assembly methods by a series of laboratory experiments). Prior work by Winfree provided a innovative approach to decrease tiling self-assembly 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 error-resilient 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 error-resilient tiling using 2-way 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...

Abstract. For robust molecular implementation of tile-based algorithmic self-assembly, 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 (ε) can be reduced to an arbitrarily low rate – but at the cost of reduced speed (r) for the self-assembly process. For tile sets directly implementing blocked cellular automata, it was shown that r ≈ βε 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 ≈ βε and better. This suggests that existing DNA-based 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

Abstract. Algorithmic self-assembly, a generalization of crystal growth processes, has been proposed as a mechanism for autonomous DNA computation and for bottom-up 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 self-assembly 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 self-assembly 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 “zig-zag ” 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 zig-zag 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 self-assembly can proceed both efficiently and with an arbitrarily low error rate, even in a model where local growth rules are probabilistic.

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 razor-sharp 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 Cairns-Smith. His unconventional thoughts about the first life on earth were the catalyst for this work on self-replication. 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

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 a DNA mechanical device that is capable of universal computation, by mimicking the operation of a universal Turing machine. Building on our prior theoretical designs and a prototype experimental construction of autonomous unidirectional DNA walking devices that move along linear tracks, we present in this paper the design of a nanomechanical DNA device that autonomously mimics the operation of a 2-state 5color universal Turing machine. Our autonomous nanomechanical device, which we call an Autonomous DNA Turing Machine, is thus capable of universal computation and hence complex translational motion which we define as universal translational motion.

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My acquaintance with Ned Seeman began in the Caltech library sometime during 1992. At the time I was trying to design a DNA computer and was collecting papers in an attempt to learn all the biochemical tricks ever performed with DNA. Among the papers was Ned and Junghuei Chen’s beautiful construction of a DNA cube [1]. I had no idea how to harness such a marvel for computation – the diagrams explaining the cube were in a visual language that I could not parse and its static structure, once formed, did not seem to allow further information processing. However, I was in awe of the cube and wondered what kind of mad and twisted genius had conjured it. Ned’s DNA sculptures did turn out to have a relationship to computation. In 1994 Len Adleman’s creation of a DNA computer [2] showed that linear DNA self-assembly, together with operations such as PCR, could tackle NP-complete computational problems. Excited by this result, Erik Winfree quickly forged an amazing link that showed how the self-assembly of geometrical DNA objects, alone, can perform universal computation [3]. The

Abstract. DNA complexes, like the double crossover, are used as building blocks for the assembly of higher-order structures. Currently, the number of experimentally proven reliable complexes is small. We have begun work on expanding the collection of such complexes. Here we report on our design concepts and initial experiments. In particular, we present experimental evidence of two new complexes: quadruple crossovers and triangles. In principle, quadruple crossovers can be extended to three-dimensional, spacefilling lego brick complexes, while triangles are capable of hexagonally tiling the plane. 1

DNA is a crucial construction material for molecular scale objects with nano-scale features. Diverse synthetic DNA objects hold great potential for applications such as nanofabrication, nano-robotics, nano-computing, and nano-electronics. The construction of DNA objects is generally carried out via self-assembly. During self-assembly, DNA strands are guided by their sequence information into secondary structures to maximize WatsonCrick pairing of their bases and thus minimize the free energy of the resultant structures. A crucial computational problem in constructing DNA objects is the design of DNA sequences that can correctly assemble into desired DNA secondary structures. However, existing software packages only provide unintuitive text-line interfaces and generally require the user to step through the entire sequence selection process, which could be time-consuming and tedious. TileSoft described in this manuscript improves on previous software by delivering the following features: 1) Its graphical user interface renders the molecular architect the ability to define DNA secondary structure and accompanying designing constraints directly on the interface as well as the ability to view the optimized sequence information pictorially. 2) Its fully automatic optimization module relieves the user of the drudgery of manually dictating the sequence selection process, and its evolutionary algorithm produces satisfactory results efficiently. 3) Its graphical user interface and its optimization module are smoothly integrated from user's perspective, while they are at the same time well separated in terms of software architecture, making each amenable to future improvements without negatively affecting the other.

Winfree’s pioneering work led the foundations in the area of errorreduction in algorithmic self-assembly (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 error-resilient schemes that maintained the original size of the assemblies, but required certain restrictions on the Boolean functions to be used in the algorithmic self-assembly. 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 error-resilient 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