"Graph Theory & DNA Self-Assembly"

Recent advances in DNA self-assembly have resulted in nanoscale graphs: cubes, octahedrons, truncated octahedra, and even buckyballs, as well as ultra-fine meshes. These constructs serve emergent applications in biomolecular computing, nanoelectronics, biosensors, drug delivery systems, and organic synthesis. One construction method uses k-armed branched junction molecules, called tiles, whose arms are double strands of DNA with one strand extending beyond the other, forming a ‘sticky end’ at the end of the arm that can bond to any other sticky end with complementary Watson-Crick bases. Another construction method, called DNA origami, ‘threads’ a single strand of DNA through the target structure and then uses short ‘staple’ strands to fold the DNA into the desired geometric shape. A third method uses circular single strands of DNA to trace the faces of a structure. Often the underlying structure is a graph, and in this case we use graph theory to determine optimal design strategies for chemists and biologists producing these nanostructures. This is joint work with Greta Pangborn, with undergraduate research participation.