Techniques for the Generation of Arbitrary Three-Dimensional Shapes in Tile-Based Self-Assembly Systems

A big challenge in nanorobotics is the construction of nanoscale objects. DNA is a bio-compatible tool to reliably and constructively create objects at the nanoscale. A possible tool to build nano-sized structures are tile-based self-assembly systems on the basis of DNA. It is challenging and time-consuming to efficiently design blueprints for the desired objects. This paper presents basic algorithms for the creation of tilesets for nxnxn-cubes in the aTAM model. Only few publications focus on three-dimensional DNA crystals. Three-dimensional shapes are likely to be of more use in nanorobotics. We present three variations: hollow cubes, cube-grids and filled cubes. The paper also presents a basic algorithm to create arbitrary, finite, connected, three-dimensional and predefined shapes at temperature 1, as well as ideas for more efficient algorithms. Among those are algorithms for spheres, ellipsoids, red blood cells and other promising designs. The algorithms and tilesets are tested/verified using a software that has been developed for the purpose of verifying three-dimensional sets of tiletypes and was influenced by the tool ISU TAS. Others can use the simulator and the algorithms to quickly create sets of tiletypes for their desired nanostructures. A long learning process may thus be omitted.