Optimizing Tile Concentrations to Minimize Errors and Time for DNA Tile Self-Assembly Systems

TL;DR

This paper investigates how adjusting tile concentrations in DNA self-assembly can reduce errors and assembly time, providing theoretical proofs and simulation methods for optimal concentration settings.

Contribution

It introduces a method to set tile concentrations proportional to the square root of their frequency, minimizing errors and assembly time in DNA tile systems.

Findings

Optimal concentrations are proportional to the square root of tile frequency.

The proposed concentrations minimize growth errors in rectilinear systems.

Expected assembly time can be approximated efficiently with simulations.

Abstract

DNA tile self-assembly has emerged as a rich and promising primitive for nano-technology. This paper studies the problems of minimizing assembly time and error rate by changing the tile concentrations because changing the tile concentrations is easy to implement in actual lab experiments. We prove that setting the concentration of tile $T_i$ proportional to the square root of $N_i$ where $N_i$ is the number of times $T_i$ appears outside the seed structure in the final assembled shape minimizes the rate of growth errors for rectilinear tile systems. We also show that the same concentrations minimize the expected assembly time for a feasible class of tile systems. Moreover, for general tile systems, given tile concentrations, we can approximate the expected assembly time with high accuracy and probability by running only a polynomial number of simulations in the size of the target shape.