Design Optimization for DNA Nanostructures

Abstract

This paper is concerned with minimizing the cost of self-assembling DNA nanostructures by minimizing the number of different components used in the construction. We first describe the nanostructures, then give a combinatorial formalization of the assembly process and demonstrate that the octet truss provides an accurate geometric framework for current branched junction molecule assembly. We choose the octet truss because it is highly symmetric and has an appropriate number of edges for the application. We develop a method of differentiating among branched junction molecules, the basic building blocks of the nanostructures, within this structure. In the mathematical model, we represent the branched junction molecules graphically with „tiles‟. We use this approach to find the minimum number of tiles necessary to construct Platonic and Archimedean solids naturally occurring within the octet truss. This will be useful and cost efficient for the chemists and biologists who actually build these branched junction molecules because once a branched junction molecule is created, a lab can make many copies of it.