Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues

Authors:
Erik D. Demaine;Martin L. Demaine;Sándor P. Fekete;Mashhood Ishaque;Eynat Rafalin;Robert T. Schweller;Diane L. Souvaine
Affiliations:
MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, USA 02139;MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, USA 02139;Department of Computer Science, Braunschweig University of Technology, Braunschweig, Germany 38116;Department of Computer Science, Tufts University, Medford, USA 02155;Google Inc., Mountain View, USA 94043;Department of Computer Science, University of Texas-Pan American, Edinburg, USA 78539;Department of Computer Science, Tufts University, Medford, USA 02155
Venue:
Natural Computing: an international journal
Year:
2008

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Abstract

We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are motivated by a practical nanofabrication scenario through protein-based bioengineering. Staging allows us to break through the traditional lower bounds in tile self-assembly by encoding the shape in the staging algorithm instead of the tiles. All of our results are based on the practical assumption that only a constant number of glues, and thus only a constant number of tiles, can be engineered. Under this assumption, traditional tile self-assembly cannot even manufacture an n 脳 n square; in contrast, we show how staged assembly in theory enables manufacture of arbitrary shapes in a variety of precise formulations of the model.