In Appendix Table 3 of this article, the entries '85, 205, 335; 130, 200, 280' in the first and second rows were incorrect and should have been '85, 245, 415; 110, 210, 300.'The incorrect and corrected versions of Table 3 are given below.

Abstract Chemical systems have the potential to direct the next generation of dynamic materials if they can be integrated with a material while acting as the material’s own regulatory network. Chemical networks that use DNA and RNA strand displacement coupled with RNA synthesis and degradation, such as genelets, are promising chemical systems for this role. Genelets can produce a range of dynamic behaviors that respond to unique sets of environmental inputs. While a number of networks that generate specific types of outputs which vary in both time and amplitude have been developed, there are fewer examples of networks that recognize specific types of inputs in time and amplitude. Advanced chemical circuits in biology are capable of reading a given substrate concentration with relatively high accuracy to direct downstream function, demonstrating that such a chemical circuit is possible. Taking inspiration from this, we designed a genelet circuit which responds to a range of inputs by delivering a binary output based on the input concentration, and tested the network’s performance using an in silico model of circuit behavior. By modifying the concentrations of two circuit elements, we demonstrated that such a network topography could yield various target input concentration profiles to which a given circuit is sensitive. The number of unique elements in the final network topography as well as the individual circuit element concentrations are commensurate with properties of circuits that have been demonstrated experimentally. These factors suggest that such a network could be built and characterized in the laboratory.

As biology demonstrates, evolutionary algorithms are an extraordinarily powerful way to design complex nanoscale systems. While we can harness the biological apparatus for replicating and selecting DNA sequences to evolve enzymes and to some extent, organisms, we would like to build replication machinery that would allow us to evolve designs for a much wider variety of materials and systems. Here we describe work that uses techniques from the new field of structural DNA nanotechnology to modularly design nanoscale components that together can be assembled into a system for self-replicating a new form of chemical information or genome, and thus for evolving a new type of chemical sequence.

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.