Abstract
The standard abstract model for analyzing DNA self-assembly, aTAM, assumes that single tiles attach one by one to a larger structure. In practice, tiles may attach to each other forming structures called polyominoes and then attach to the assembly using bonds from multiple tiles. Such polyominoes may cause errors in systems designed with only aTAM in mind. In this paper, we first present a formal definition of when one tile system is a “block replacement” of another. Then we present a block replacement scheme for making any system that admits non-trivial block replacement polyomino-safe. In addition, we present a smaller block replacement scheme that makes the Chinese Remainder counter polyomino-safe and prove that the question of whether a system is polyomino-safe (or other similar properties) is undecidable. Finally, we show that applying our polyomino-safe system produces self-healing systems when applied to most self-healing systems.
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This research was supported in part by NSF grants 1104592 and 1097249.
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Luhrs, C. Polyomino-safe DNA self-assembly via block replacement. Nat Comput 9, 97–109 (2010). https://doi.org/10.1007/s11047-009-9125-0
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DOI: https://doi.org/10.1007/s11047-009-9125-0