Algorithmic self-assembly has been proposed as a mechanism for autonomous DNA computation and for bottom-up fabrication of complex nanodevices. Whereas much previous work has investigated self-assembly programs using an abstract model of irreversible, errorless assembly, experimental studies as well as more sophisticated reversible kinetic models indicate that algorithmic self-assembly is subject to several kinds of errors. Previously, it was shown that proofreading tile sets can reduce the occurrence of mismatch and facet errors. Here, we introduce the zig-zag tile set, which can reduce the occurrence of spurious nucleation errors. The zig-zag tile set takes advantage of the fact that assemblies must reach a critical size before their growth becomes favorable. By using a zig-zag tile set of greater width, we can increase the critical size of spurious assemblies without increasing the critical size of correctly seeded assemblies, exponentially reducing the spurious nucleation rate. In combination with proofreading results, this result indicates that algorithmic self-assembly can be performed with low error rates without a significant reduction in assembly speed. Furthermore, our zig-zag boundaries suggest methods for exquisite detection of DNA strands and for the replication of inheritable information without the use of enzymes.
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