Analysis and Algorithmic Construction of Self-Assembled DNA Complexes

TL;DR

This paper explores the use of graph theory to analyze and algorithmically construct DNA self-assembled complexes, focusing on pots with a single bond-edge type to determine possible structures and develop construction algorithms.

Contribution

It introduces a graph-theoretic framework for DNA self-assembly and provides two algorithms for constructing complete complexes from pots with one bond-edge type.

Findings

Identifies the relationship between graph order and tile arms in DNA complexes.

Provides algorithms for constructing complete DNA complexes from specific pots.

Analyzes the types and sizes of structures possible with single bond-edge type pots.

Abstract

DNA self-assembly is an important tool that has a wide range of applications such as building nanostructures, the transport of target virotherapies, and nano-circuitry. Tools from graph theory can be used to encode the biological process of DNA self-assembly. The principle component of this process is to examine collections of branched junction molecules, called pots, and study the types of structures that can be constructed. We restrict our attention to pots which contain one set of complementary cohesive-ends, i.e. a single bond-edge type, and we identify the types and sizes of structures that can be built from such a pot. In particular, we show a dependence between the order of graphs in the output of the pot and the number of arms on the corresponding tiles. Furthermore, we provide two algorithms which will construct complete complexes for a pot with a single bond-edge type.