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, MA;MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, MA;Institut für Mathematische Optimierung, Technische Universität Braunschweig, Braunschweig, Germany;Department of Computer Science, Tufts University, Medford, MA;Google Inc.,;Department of Computer Science, University of Texas Pan American, Edinburg, Texas;Department of Computer Science, Tufts University, Medford, MA

  • Venue:
  • DNA13'07 Proceedings of the 13th international conference on DNA computing
  • Year:
  • 2007

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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, as each new glue type requires significant biochemical research and experiments. Under this assumption, traditional tile self-assembly cannot even manufacture an n×n square; in contrast, we show how staged assembly enables manufacture of arbitrary orthogonal shapes in a variety of precise formulations of the model.