Modeling facet roughening errors in self-assembly by snake tile sets

Self-assembly by DNA tiles has been advocated as a possible technique for bottom-up manufacturing of scaffolds in the nanoscale region. However, self-assembly is severely affected by facet roughening errors. A particularly effective error tolerant method utilizes snake tile sets with a square block of even dimension (i.e. 2 k times 2 k) of tiles. Snake tile sets of odd dimension (i.e. (2 k - 1) x (2k - 1)) have also been proposed. To analyze error tolerant mechanism of snake tile sets, this paper presents an analytical Markov model for facet roughening errors. A generalized model is proposed and used to analyze snake tile sets for the realistic cases of k = 2 and 3. Closed form solutions are attained in the analysis. Simulation results are presented to confirm that snake tile sets of odd dimension are more tolerant to facet errors than other tile sets for self-assembly.