Staged Self-Assembly:Nanomanufacture of Arbitrary Shapes with O(1) Glues

TL;DR

This paper introduces a staged self-assembly model for nanomanufacturing that enables the creation of arbitrary shapes using only a constant number of glue types, overcoming traditional limitations.

Contribution

It presents a novel staged assembly framework that encodes shapes in the staging process, allowing complex structures with minimal glue types, relevant for practical nanofabrication.

Findings

Enables arbitrary shape assembly with O(1) glues

Breaks traditional lower bounds in tile self-assembly

Applicable to practical bioengineering scenarios

Abstract

We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are motivated by a practical nanofabrication scenario through protein-based bioengineering. Staging allows us to break through the traditional lower bounds in tile self-assembly by encoding the shape in the staging algorithm instead of the tiles. All of our results are based on the practical assumption that only a constant number of glues, and thus only a constant number of tiles, can be engineered, as each new glue type requires significant biochemical research and experiments. Under this assumption, traditional tile self-assembly cannot even manufacture an n*n square; in contrast, we show how staged assembly enables manufacture of arbitrary orthogonal shapes in a variety of precise formulations of the model.