Negative Glues and Non-determinism in Nanocomputations by Self-assembly

Abstract

Tile-based self-assembly is a model of ”algorithmic crystal growt” in which square ”tiles” represent molecules that bind to each other via highly-specific bonds on their four sides, driven by random mixing in solution but constrained by the local binding rules of the tile bonds. Winfree defined a model of tile-based self-assembly known as the abstract Tile Assembly Model (aTAM), [4]. The fundamental components of this model are un-rotatable, but translatable square ”tile types” whose sides are labeled with ”glues” representing binding sites. Two tiles that are placed next to each other are attracted with strength determined by the glues where they abut, and, in the aTAM, a tile binds to an assembly if it is attracted on all matching sides with total strength at least a certain threshold value τ. Assembly begins from a ”seed” tile and progresses in a stepwise fashion until no more tiles may attach. In his aTAM model Winfree postulated negative (i.e., repulsive) interactions between tiles to be physically plausible and, subsequently, Reif, Sahu, and Yin, [3], studied negative interactions in the context of reversible attachment operations.