NDLI: Programmable Control of Nucleation for Algorithmic Self-Assembly

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Winfree, Erik Schulman, Rebecca
Copyright Year	2009
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.
Starting Page	1581
Ending Page	1616
Page Count	36
File Format	PDF
ISSN	00975397
DOI	10.1137/070680266
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4
Volume Number	39
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-12-04
Access Restriction	Subscribed
Subject Keyword	nucleation theory Nonnumerical algorithms Crystals DNA nanotechnology Analysis of algorithms algorithmic self-assembly
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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