Randomized Self-Assembly

We use the abstract tile assembly model of Winfree [6], which models the aggregation of monomers called tiles that attach one at a time to a growing structure, starting from a single seed tile, in which bonds (“glues”) on the tile are specific (glues only stick to glues of the same type on other tiles) and cooperative (so that multiple weak glues are necessary to attach a tile). The general idea of randomized self-assembly is to use the inherent randomness of self-assembly to help the assembly process. If multiple types of tiles are able to bind to a single binding site, then we assume that their relative concentrations determine the probability that each succeeds. With careful design, we can use the same tile set to create different structures, by changing the concentrations to affect what is likely to assemble. Another use of randomness is in reducing the number of different tile types required to assemble a shape.