Analysis of punctures in DNA self-assembly under forward growth

This paper deals with the characterization and analysis of intentionally induced punctures on a DNA self-assembly. Based on forward growth, punctures are utilized to remove errors in DNA tiles from the self-assembly. Initially, a Markov model is proposed by considering different types of punctures under various bonding conditions in the tiles. For different values of on and off rates (as corresponding to the parameters G(se) and G(mc)), it is shown that the proposed models can assess the types of puncture for removing mismatched tiles as errors. Subsequently, a novel model of puncturing is introduced to establish the condition by which a generic aggregate can utilize punctures for error resilience. It is proven that by using the correct puncture(s), errors as frozen mismatched tiles are moved toward the boundaries, thus ensuring the generation of the target assembly and ease in removal of the errors. As an example, the Sierpinski tile set is analyzed based on the proposed models to fully assess the appropriate type of puncture for this pattern. Simulation results are provided as evidence that the proposed models are effective.