A Metric for Assessing the Error Tolerance of Tile Sets for Punctured DNA Self-Assemblies

This paper presents a novel metric by which the effectiveness of punctures (as corrective action for error tolerance) can be assessed with respect to tile sets for DNA self- assembly in nano-manufacturing. Initially, the conditions for correct binding of a tile to an existing aggregate are analyzed using a Markovian approach; based on this analysis, it is proved that correct aggregation (as identified with a so-called Ideal Tile Set) is not always met for existing tile sets for nano-manufacturing. Hence, a metric is proposed for assessing tile sets by utilizing punctures. Tile sets are investigated and assessed with respect to features such error (mismatched tile) movement, punctured area and bond types. Subsequently, it is shown that the proposed metric can comprehensively assess the effectiveness of a type of a puncture for a tile set and its capability to attain error tolerance for the desired pattern. Extensive simulation results are provided.