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Hierarchical self assembly of patterns from the Robinson tilings: DNA tile design in an enhanced Tile Assembly Model

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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.

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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.

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  1. Monrovia, CA, 91016, USA

    Jennifer E. Padilla

  2. Department of Chemistry, New York University, New York, NY, 10003, USA

    Wenyan Liu & Nadrian C. Seeman

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  1. Jennifer E. Padilla
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  2. Wenyan Liu
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Correspondence to Jennifer E. Padilla.

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Padilla, J.E., Liu, W. & Seeman, N.C. Hierarchical self assembly of patterns from the Robinson tilings: DNA tile design in an enhanced Tile Assembly Model. Nat Comput 11, 323–338 (2012). https://doi.org/10.1007/s11047-011-9268-7

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