Controlling Errors in the Process of Molecular Self-Assembly

The problem of controlling errors in the process of molecular self-assembly is of central importance in biomolecular computation. The stochastic nature of the self-assembly process leads to assembly errors, i.e., deviations from ideal growth of the assembly. Many different constructions of proofreading tile sets have been proposed in the literature to reduce the effect of such assembly errors. Another major error mechanism affecting the self-assembly process in practice is that of imperfections within the tiles themselves. This source of error has, surprisingly, received little prior attention. In this work, We consider 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). The simulation results show that some tile set constructions show greater error-resilience in the presence of malformed tiles than others. But, most notably, the snaked proodreading tile set of Chen and Goel fails to form even moderately-sized tile assemblies when malformed tiles are present. We present modifications of the snaked proofreading construction that indicate that it is possible to design tile sets that are not just robust with respect to errors intrinsic to the self-assembly process, but also with respect to malformed tiles.