Tile Based Modeling of DNA Self-Assembly for Two Graph Families with Appended Paths

TL;DR

This paper models DNA self-assembly using a tile-based approach to efficiently construct specific graph-structured nanostructures, minimizing the types of molecules needed for complex target graphs.

Contribution

It introduces a flexible tile model for DNA assembly, providing minimum molecule and end-type counts for tadpole and lollipop graph families under various constraints.

Findings

Minimum molecule types for tadpole graphs determined

Minimum end types for lollipop graphs established

Challenges in optimal assembly strategies discussed

Abstract

Branched molecules of deoxyribonucleic acid (DNA) can self-assemble into nanostructures through complementary cohesive strand base pairing. The production of DNA nanostructures is valuable in targeted drug delivery and biomolecular computing. With theoretical efficiency of laboratory processes in mind, we use a flexible tile model for DNA assembly. We aim to minimize the number of different types of branched junction molecules necessary to assemble certain target structures. We represent target structures as discrete graphs and branched DNA molecules as vertices with half-edges. We present the minimum numbers of required branched molecule and cohesive-end types under three levels of restrictive conditions for the tadpole and lollipop graph families. These families represent cycle and complete graphs with a path appended via a single cut-vertex. We include three general lemmas regarding such vertex-induced path subgraphs. Through proofs and examples, we demonstrate the challenges that can arise in determining optimal construction strategies.