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.

Main Author: Abel, Zachary.
Other Authors: Benbernou, Nadia., Damian, Mirela., Demaine, Erik D., Demaine, Martin L., Flatland, Robin., Kominers, Scott D., Schweller, Robert.
Language: English
Published: 2010
Online Access: http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:175701