Modeling Self-Assembled DNA Nanotubes

Emerging laboratory techniques have been developed using the Watson-Crick complementarity properties of DNA strands to achieve self-assembly of graphical complexes. One recent focus in DNA nanotechnology is the formation of nanotubes, which we model with a two-dimensional lattice that wraps around to form a tube. The vertices of the lattice graph represent k-armed branched junction molecules, called tiles. Using concepts from graph theory, we seek to determine the minimum number of tile and bond-edge types necessary to create a desired self-assembled complex. Results are known for certain infinite classes of graphs, but are yet to be found for several other classes. Specifically, results are unknown for lattice graphs which motivates our study of triangle and hexagonal lattice graphs. While some laboratory settings allow for the possibility of the formation of smaller complexes using the same set of tiles, we examine the problem under the restriction that no smaller complete complex may be formed