Exploring Lower Bounds of Self-Assembled DNA Complexes

DNA self-assembly is a tool that allows for the creation of various nanostructures. We model these nanostructures within the flexible-tile model that omits geometric restrictions on the DNA-stranded arms. To create structures, we use a collection of tiles known as a pot, which we restrict to explore the cases in which the pot realizes a graph of each order greater than some minimum order. We provide an algorithm that calculates the lower bounds and tile distributions of these restricted pots, which allows for discovering important relationships. By utilizing graph and number theoretic tools, we show that a closed formula exists for the minimum order of particular pots.