Shape Replication Through Self-Assembly and RNase Enzymes

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.

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Zachary Abel, Nadia Benbernou, Mirela Damian, Erik Demaine, Robin Flatland, Skott Kominers, Robert Schweller, Martin Demaine
• Keywords: Discrete Algorithms, Distinct Tile Types, Shape Replication, SODA 2010, Wang Tile Self-assembly