Self-Healing Tile Sets

Biology provides the synthetic chemist with a tantalizing and frustrating challenge: to create complex objects, defined from the molecular scale up to meters, that construct themselves from elementary components, and perhaps even reproduce themselves. This is the challenge of bottom-up fabrication. The most compelling answer to this challenge was formulated in the early 1980s by Ned Seeman, who realized that the information carried by DNA strands provides a means to program molecular self-assembly, with potential applications including DNA scaffolds for crystallography [19] or for molecular electronic circuits [15]. This insight opened the doors to engineering with the rich set of phenomena available in nucleic acid chemistry [20]

Toward reliable algorithmic self-assembly of DNA tiles: A fixed-width cellular automaton pattern

Bottom-up fabrication of nanoscale structures relies on chemical processes to direct self-assembly. The complexity, precision, and yield achievable by a one-pot 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 one-pot 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 self-assembly may be sufficient to create a wide range of complex objects in one-pot reactions

Two computational primitives for algorithmic self-assembly: Copying and counting

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 per-tile error rates in such crystals is roughly 10%, this work demonstrates the potential of algorithmic self-assembly to create complex nanoscale patterns of technological interest. A subset of the tiles for counting form information-bearing DNA tubes that copy bit strings from layer to layer along their length

Self-replication and evolution of DNA crystals

Is it possible to create a simple physical system that is capable of replicating itself? Can such a system evolve interesting behaviors, thus allowing it to adapt to a wide range of environments? This paper presents a design for such a replicator constructed exclusively from synthetic DNA. The basis for the replicator is crystal growth: information is stored in the spatial arrangement of monomers and copied from layer to layer by templating. Replication is achieved by fragmentation of crystals, which produces new crystals that carry the same information. Crystal replication avoids intrinsic problems associated with template-directed mechanisms for replication of one-dimensional polymers. A key innovation of our work is that by using programmable DNA tiles as the crystal monomers, we can design crystal growth processes that apply interesting selective pressures to the evolving sequences. While evolution requires that copying occur with high accuracy, we show how to adapt error-correction techniques from algorithmic self-assembly to lower the replication error rate as much as is required

Reducing facet nucleation during algorithmic self-assembly

Algorithmic self-assembly, a generalization of crystal growth, has been proposed as a mechanism for bottom-up fabrication of complex nanostructures and autonomous DNA computation. In principle, growth can be programmed by designing a set of molecular tiles with binding interactions that enforce assembly rules. In practice, however, errors during assembly cause undesired products, drastically reducing yields. Here we provide experimental evidence that assembly can be made more robust to errors by adding redundant tiles that "proofread" assembly. We construct DNA tile sets for two methods, uniform and snaked proofreading. While both tile sets are predicted to reduce errors during growth, the snaked proofreading tile set is also designed to reduce nucleation errors on crystal facets. Using atomic force microscopy to image growth of proofreading tiles on ribbon-like crystals presenting long facets, we show that under the physical conditions we studied the rate of facet nucleation is 4-fold smaller for snaked proofreading tile sets than for uniform proofreading tile sets

An information-bearing seed for nucleating algorithmic self-assembly

Self-assembly creates natural mineral, chemical, and biological structures of great complexity. Often, the same starting materials have the potential to form an infinite variety of distinct structures; information in a seed molecule can determine which form is grown as well as where and when. These phenomena can be exploited to program the growth of complex supramolecular structures, as demonstrated by the algorithmic self-assembly of DNA tiles. However, the lack of effective seeds has limited the reliability and yield of algorithmic crystals. Here, we present a programmable DNA origami seed that can display up to 32 distinct binding sites and demonstrate the use of seeds to nucleate three types of algorithmic crystals. In the simplest case, the starting materials are a set of tiles that can form crystalline ribbons of any width; the seed directs assembly of a chosen width with >90% yield. Increased structural diversity is obtained by using tiles that copy a binary string from layer to layer; the seed specifies the initial string and triggers growth under near-optimal conditions where the bit copying error rate is 17 kb of sequence information. In sum, this work demonstrates how DNA origami seeds enable the easy, high-yield, low-error-rate growth of algorithmic crystals as a route toward programmable bottom-up fabrication

Programmable Control of Nucleation for Algorithmic Self-Assembly

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.Comment: 37 pages, 14 figure