Error Tolerance of DNA Self-Healing Assemblies by Puncturing

Self-assembly is affected by high error rates due to incorrect tiles in nano-technology manufacturing. Tile sets that can heal (fully or partially) an erroneous assembly have been proposed. Self-healing requires growth to be restarted such that erroneous tiles can be removed and the correct tiles to bind to the aggregate. Punctures can be used for this purpose. The goal of this paper is to characterize an intentionally induced puncture (and its relevant properties) on an erroneous tile site in the assembly. This allows to propagate any newly generated error away from the source of growth (i.e. the seed tile), such that self-assembly can continue along specific directions. Different types of puncture are considered with respect to growth direction, error and aggregate types. Puncture resilience is analyzed using a new characterization metric; different tile sets are investigated in detail. Analytical and simulation results are provided.