Synthesizing Small and Reliable Tile Sets for Patterned DNA Self-assembly

We consider the problem of finding, for a given 2D pattern of coloured tiles, a minimal set of tile types self-assembling to this pattern in the abstract Tile Assembly Model of Winfree (1998). This Patterned self-Assembly Tile set Synthesis (PATS) problem was first introduced by Ma and Lombardi (2008), and subsequently studied by Göös and Orponen (2011), who presented an exhaustive partition-search branch-and-bound algorithm (briefly PS-BB) for it. However, finding the true minimal tile sets is very time consuming, and the algorithm PS-BB is not well-suited for finding small but not necessarily minimal solutions. In this paper, we modify the basic partitionsearch framework by using a heuristic to optimize the order in which the algorithm traverses its search space. We find that by running several parallel executions of the modified algorithm PS-H, the search time for small tile sets can be shortened considerably. Additionally, we suggest a new approach, answer set programmin (ASP), to solving the PATS problem. We also introduce a method for computing the reliability of a given tile set, i.e. the probability of its error-free self-assembly to the desired target tiling, based on Winfree’s analysis of the kinetic Tile Assembly Model (1998). We present empirical data on the reliability of tile sets found by the PS-BB and PS-H algorithms and find that also here the PS-H algorithm constitutes a significant improvement over the earlier PS-BB algorithm.