The Effect of Malformed Tiles on Tile Assemblies within kTAM

Abstract

Many different constructions of proofreading tile sets have been proposed in the literature to reduce the effect of deviations from ideal behaviour of the dynamics of the molecular tile self-assembly process. In this paper, we consider the effect on the tile assembly process of a different kind of non-ideality, namely, imperfections in the tiles themselves. We assume a scenario in which some small proportion of the tiles in a tile set are malformed. We study, through simulations, the effect of such malformed tiles on the self-assembly process within the kinetic Tile Assembly Model (kTAM). Our simulation results show that some tile set constructions show greater error-resilience in the presence of malformed tiles than others. For example, the 2- and 3-way overlay compact proofreading tile sets of Reif et al. [4] are able to handle malformed tiles quite well. On the other hand, the snaked proodreading tile set of Chen and Goel [1] fails to form even moderately-sized tile assemblies when malformed tiles are present. We show how the Chen-Goel construction may be modified to yield snaked proofreading tile sets that show good resistance to the effect of malformed tile.