Search Methods for Tile Sets in Patterned DNA Self-Assembly

TL;DR

This paper investigates search algorithms for designing minimal tile sets in DNA self-assembly to replicate specific patterns, addressing an NP-hard problem with practical solution methods.

Contribution

It introduces and evaluates various search techniques for efficiently finding small or minimal tile sets in the PATS problem, considering kinetic assembly reliability.

Findings

Several search methods can produce small tile sets for given patterns.

Some algorithms reliably find minimal or near-minimal solutions.

Assessment of solution quality based on the kinetic Tile Assembly Model.

Abstract

The Pattern self-Assembly Tile set Synthesis (PATS) problem, which arises in the theory of structured DNA self-assembly, is to determine a set of coloured tiles that, starting from a bordering seed structure, self-assembles to a given rectangular colour pattern. The task of finding minimum-size tile sets is known to be NP-hard. We explore several complete and incomplete search techniques for finding minimal, or at least small, tile sets and also assess the reliability of the solutions obtained according to the kinetic Tile Assembly Model.