@article{45a39fec7f2842119f54274fdf2470f0,
title = "Hierarchical self assembly of patterns from the Robinson tilings: DNA tile design in an enhanced Tile Assembly Model",
abstract = "We introduce a hierarchical self assembly algorithm that produces the quasiperiodic patterns found in the Robinson tilings and suggest a practical implementation of this algorithm using DNA origami tiles. We modify the abstract Tile Assembly Model (aTAM), to include active signaling and glue activation in response to signals to coordinate the hierarchical assembly of Robinson patterns of arbitrary size from a small set of tiles according to the tile substitution algorithm that generates them. Enabling coordinated hierarchical assembly in the aTAM makes possible the efficient encoding of the recursive process of tile substitution.",
keywords = "Algorithmic assembly, DNA origami, Hierarchical assembly, Quasiperiodicity, Recursion, Robinson tiling, Self assembly, Substitution tiling, Tile Assembly Model",
author = "Padilla, {Jennifer E.} and Wenyan Liu and Seeman, {Nadrian C.}",
note = "Funding Information: Fig. 14 Schematic representation of the four recursive Robinson tiles made from DNA and their signaling pathways. Binding sites (?, -), neutral seesaws (S), transducers (T, t), and activation strands (A) are indicated on each of the four tiles. Inactive binding sites are indicated with pale colors and two-way arrows between them and seesaw elements (S) on the Highway and Junction Tiles. The direction of propagation of energetically favorable signal cascades is indicated with arrows. Seesaw pathways that can go in either direction are indicated with arrow heads in both directions. Positions of elements are based on the locations of free staple strand ends. a The Input Tile contains only binding sites that are already active. b Activation signals entering the Decision Tile from bound neighbors are indicated in orange. Each neighbor bound to the Decision Tile activates one of the signals on each of the adjacent edges. This arrangement means that two of the three other edges must be bound before a given edge of Acknowledgments We thank Natasha Jonoska for helpful discussions and anonymous reviewers for helpful suggestions. This research has been supported by the following grants to NCS: GM-29554 from the National Institute of General Medical Sciences, CTS-0608889 and CCF-0726378 from the National Science Foundation, W911NF-11-1-0024 and W911NF-07-1-0439 from the Army Research Office, N000140910181 and N000140911118 from the Office of Naval Research and a grant from the W.M. Keck Foundation.",
year = "2012",
month = jun,
doi = "10.1007/s11047-011-9268-7",
language = "English (US)",
volume = "11",
pages = "323--338",
journal = "Natural Computing",
issn = "1567-7818",
publisher = "Springer Netherlands",
number = "2",
}