Shape Replication Through Self-Assembly and RNase Enzymes

Published on: 2010/01/05

Abstract

We introduce the problem of shape replication in the Wang tile self-assembly model. Given an input shape, we consider the problem of designing a self-assembly system which will replicate that shape into either a specific number of copies, or an unbounded number of copies. Motivated by practical DNA implementations of Wang tiles, we consider a model in which tiles consisting of DNA or RNA can be dynamically added in a sequence of stages. We further permit the addition of RNase enzymes capable of disintegrating RNA tiles. Under this model, we show that arbitrary genus-0 shapes can be replicated infinitely many times using only \(O(1)\) distinct tile types and \(O(1)\) stages. Further, we show how to replicate precisely \(n\) copies of a shape using \(O(\log n)\) stages and \(O(1)\) tile types.

Authors

Zachary Abel, Nadia Benbernou, Mirela Damian, Erik Demaine, Martin Demaine, Robin Flatland, Scott Kominers, Robert Schweller

File

Shape Replication Through Self-Assembly and RNase Enzymes.pdf