Shape replication through self-assembly and RNase enzymes

Authors:
Zachary Abel;Nadia Benbernou;Mirela Damian;Erik D. Demaine;Martin L. Demaine;Robin Flatland;Scott D. Kominers;Robert Schwelle
Affiliations:
Harvard University, Cambridge, MA;MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, MA;Villanova University, PA;MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, MA;MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, MA;Siena College, NY;Harvard University, Cambridge, MA;University of Texas-Pan American, Edinburg, TX
Venue:
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Year:
2010

Citing 6
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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.