The effect of malformed tiles on tile assemblies within the kinetic tile assembly model

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. (DNA Computing 10, Lecture Notes in Computer Science, vol 3384. Springer, 2005) are able to handle malformed tiles quite well. On the other hand, the snaked proofreading tile set of Chen and Goel (DNA Computing 10, Lecture Notes in Computer Science, vol 3384. Springer, 2005) 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 new snaked proofreading tile sets that are resilient not only to errors intrinsic to the assembly process, but also to errors caused by malformed tiles.