Tile Model of Self-Assembly

Abstract

Self assembly is the process by which an organized structure can spontaneously form from simple parts. It describes the assembly of diverse structures such as crystals, DNA helices and microtubules and has promising applications in nano-fabrication of molecular structures and DNA computing. Adleman and Rothemund and Winfree suggested the currently leading computational model, the two-dimensional tile assembly model. In this model a tile is an oriented unit square. Each edge has an associated bond type that interacts with a certain strength with matching sides of other tiles. A new tile can adsorb to a growing complex when the total interaction strength with its neighbors exceeds a certain parameter t. We present a generalization to the existing tile assembly model, that enables more flexibility in design and fabrication of complex shapes, and that has better complexity properties.