Shape replication through self-assembly and RNase enzymes
Author(s)Abel, Zachary Ryan; Benbernou, Nadia M.; Damian, Mirela; Demaine, Erik D.; Demaine, Martin L.; Flatland, Robin; Kominers, Scott Duke; Schweller, Robert; ... Show more Show less
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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.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Mathematics
Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2010
Society for Industrial and Applied Mathematics
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.
Author's final manuscript