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 which 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 by introducing a family of tile sets for which we rigorously prove that, under the right physical conditions, increasing the size of the tile set by a constant amount 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 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. Along with prior work on constructing tile sets that are robust to assembly errors during growth, this work is a step toward understanding how algorithmic self-assembly can be performed with low error rates without a significant reduction in assembly speed.