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

Authors:
Jennifer E. Padilla;Wenyan Liu;Nadrian C. Seeman
Affiliations:
, Monrovia, USA 91016;Department of Chemistry, New York University, New York, USA 10003;Department of Chemistry, New York University, New York, USA 10003
Venue:
Natural Computing: an international journal
Year:
2012

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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.