Everybody Wants to Be a Seed: Arbitrary Single-Tile Seeds in the Abstract Tile Assembly Model

Winfree’s abstract Tile Assembly Model (aTAM) is one of the most popular abstract models for DNA nano-computing. This papers presents a seedless version of the aTAM. Instead of a designated seed assembly, any single isolated tile can initiate the assembly. This paper shows that such system can simulate any aTAM system at constant scale and it presents a tile set to do so. All systems can be simulated at scale at most 10 and most of them can be simulated at scale 5, provided that their seeds are large enough. Removing the need for seed in self-assembly is a new way of solving the nucleation problem, that is, the problem of controlling the initialisation of any self-assembly process. It also allows for a convergence of the aTAM towards other classical tiling models, such as Wang’s. The systems presented are based on independent modules made of tiles. The modules are carefully designed so they act kind of like stem cells. When a module self-assembles from an isolated tile, it grows a pseudo-seed which represents the seed of the simulated system with a Hamiltonian cycle along the borders of the corresponding macrotiles. The other modules, which appear later on during the simulation as components of the "regular" macrotiles, depend on each other to self-assemble. In such cases, the assembly is synchronised in a way so that the growth of any pseudo-seed is blocked. This ensures that a macrotile self-assembles only when interacting either with the pseudo-seed or with previously completed macrotiles.