Self-Assembly of Arbitrary Shapes Using RNAse Enzymes: Meeting the Kolmogorov Bound with Small Scale Factor (extended abstract)

TL;DR

This paper introduces a novel self-assembly method using RNAse enzymes that significantly reduces the scale factor needed to construct arbitrary shapes, achieving near-optimal efficiency related to the shape's Kolmogorov complexity.

Contribution

It demonstrates that a single destruction operation enables efficient shape assembly with minimal scaling, improving upon previous methods that required larger scale factors.

Findings

Single RNAse enzyme use reduces scale factor to logarithmic in shape size.

Shapes can be constructed with a number of tile types proportional to Kolmogorov complexity.

Efficient construction is possible for a large class of shapes without scaling.

Abstract

We consider a model of algorithmic self-assembly of geometric shapes out of square Wang tiles studied in SODA 2010, in which there are two types of tiles (e.g., constructed out of DNA and RNA material) and one operation that destroys all tiles of a particular type (e.g., an RNAse enzyme destroys all RNA tiles). We show that a single use of this destruction operation enables much more efficient construction of arbitrary shapes. In particular, an arbitrary shape can be constructed using an asymptotically optimal number of distinct tile types (related to the shape's Kolmogorov complexity), after scaling the shape by only a logarithmic factor. By contrast, without the destruction operation, the best such result has a scale factor at least linear in the size of the shape, and is connected only by a spanning tree of the scaled tiles. We also characterize a large collection of shapes that can be constructed efficiently without any scaling.