A self-assembly model of time-dependent glue strength

Self-assembly is a ubiquitous process in which small objects selforganize into larger and complex structures. In 2000, Rothemund and Winfree proposed a Tile Assembly Model as a mathematical model for theoretical studies of self-assembly.We propose a refined self-assembly model in which the glue strength between two juxtaposed tiles is a function of the time they have been in neighboring positions. We then present an implementation of our model using strand displacement reactions on DNA tiles. Under our model, we can demonstrate and study catalysis and self-replication in the tile assembly. We then study the tile complexity for assembling shapes in our model and show that a thin rectangle of size k × N can be assembled using O((log(N))/ log log(N)) types of tiles, demonstrating the glue model has additional capabilities over the prior tiling assembly model.We also describe a method to implement with DNA tiles our model of time-dependant glue strength.

Duke Scholars

Author John H. Reif Computer Science