Computational complexity and pragmatic solutions for flexible tile based DNA self-assembly

TL;DR

This paper explores the computational complexity of designing DNA nanostructures using branched junctions, demonstrating NP-completeness and offering practical algorithms for specific structures like platonic solids and nanotubes.

Contribution

It introduces graph theory-based methods to address DNA self-assembly design challenges and provides both heuristic and optimal solutions for key target structures.

Findings

Optimal design strategies are NP-complete.

Pragmatic programs for special cases.

Provably optimal solutions for specific structures.

Abstract

Branched junction molecule assembly of DNA nanostructures, pioneered by Seeman's laboratory in the 1980s, has become increasingly sophisticated, as have the assembly targets. A critical design step is finding minimal sets of branched junction molecules that will self-assemble into target structures without unwanted substructures forming. We use graph theory, which is a natural design tool for self-assembling DNA complexes, to address this problem. After determining that finding optimal design strategies for this method is generally NP-complete, we provide pragmatic solutions in the form of programs for special settings and provably optimal solutions for natural assembly targets such as platonic solids, regular lattices, and nanotubes. These examples also illustrate the range of design challenges.