Counting by DNA Self-Assembly in the Presence of Rotated Tiles

This paper deals with counting in the presence of tile rotation in DNA self-assembly using the so-called binary counter tile set. Initially, it is shown that when considering tile rotation under the assumption of no (zero) mismatch, self-assembly may result in a different counting pattern than normally expected. A relation between counting and tile rotation is established with respect to the angle of rotation as well as the location of the rotated tile. The binary counter tile set is analyzed using a graph model, which captures the rotational and transition features of the bonding process. Simulation results using Xgrow confirm the validity of the analysis.