Error Tolerant DNA Self-Assembly Using ( $hbox{2}k-hbox{1}$)$times$( $hbox{2}k-hbox{1}$) Snake Tile Sets

DNA self-assembly has been advocated as a possible technique for bottom-up manufacturing of scaffolds for computing systems in the nanoscale region. However, self-assembly is affected by different types of errors (such as growth and facet roughening) that severely limit its applicability. Different methods for reducing the error rate of self-assembly using tiles as basic elements have been proposed. A particularly effective method relies on snake tile sets that utilize a square block of even size (i.e., 2k times 2k tiles, k = 2, 3,.. .). In this paper, an odd-sized square block [i.e., (2k -1) times (2k - 1)] is proposed as basis for the snake tile set. Compared with other tile sets, the proposed snake tile sets achieve a considerable reduction in error rate at a very modest reduction in growth rate. Growth and facet roughening errors are considered and analytical results are presented to prove the reduction in error rate compared with an even-sized snake tile set. Simulation results are provided.