Shape replication through self-assembly and RNase enzymes
Name
Demaine_Shape replication.pdf
Size
1.37 MB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Abel, Zachary Ryan
Benbernou, Nadia M.
Damian, Mirela
Demaine, Erik D.
Demaine, Martin L.
Flatland, Robin
Kominers, Scott Duke
Schweller, Robert
Date Issued
January 2010
Journal
Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2010
Publisher
Society for Industrial and Applied Mathematics
Citation
Abel, Zachary et al. "Shape Replication through Self-Assembly and RNase Enzymes." Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2010, Jan. 17-19, Hyatt Regency Austin, Austin, TX.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
www.siam.org/proceedings/soda/2010/SODA10_085_abelz.pdf
