New Graph Theory from and for Nanoconstruct Design Strategies

Joanna Ellis-Monaghan, Professor of Mathematics, Saint Michael's College
Greta Pangborn, Associate Professor of Computer Science, Saint Michael's College

New work in nanotechnology holds promise for a diverse range of applications including biomolecular computing, drug delivery and biosensors (see [Adl94CS91LL07See07]). DNA is an ideal material for building nanostructures because Watson-Crick complementarity allows for self-assembly of molecules, with single of strands of DNA bonding to complementary strands to form larger molecules.

Several different graphs have been constructed from self-assembling DNA molecules, including cubes [CS91], truncated octahedra [ZS94], rigid octahedra [SQJ04], and tetrahedra, dodecahedra, and buckyballs [H+08]. A 3D crystalline lattice has also been constructed [Z+09]. Recent origami methods have resulted in DNA folding into 2D images and designs (see [Rot06,HLS09]), and these methods are adaptable to 3D structures [DDS09].

We are particularly interested in questions related to optimal design strategies for a number of different self-assembly techniques.  For example: What is the minimum number of branched junction molecule types needed to create a particular polytope?  What is the best way to thread a target polytope or lattice to create the target molecule using a DNA origami technique?