Optimizing the Construction of Self-Assembled DNA Windmill Graphs

Laboratory techniques have been developed using the Watson- Crick complementary properties of DNA strands to achieve self- assembly of DNA complexes. Since modeling the self- assembly process requires designing the component molecular building blocks, construction methods developed with concepts from graph theory have resulted in significantly increased efficiency. The vertices of the graph of some degree k represent k-armed branched junction molecules, called tiles. Each branch of a tile has a cohesive end of some bond- edge type. We seek to determine the minimum number of distinct tile and bond- edge types necessary to create a target self- assembled complex. Although many results are known for a few infinite classes of graphs, many classes of graphs remain unsolved. With this poster, we present results for the minimum number of tile and bond- edge types for windmill graphs