Natural Computing

, Volume 7, Issue 3, pp 347–370

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

  • Erik D. Demaine
  • Martin L. Demaine
  • Sándor P. Fekete
  • Mashhood Ishaque
  • Eynat Rafalin
  • Robert T. Schweller
  • Diane L. Souvaine
Article

DOI: 10.1007/s11047-008-9073-0

Cite this article as:
Demaine, E.D., Demaine, M.L., Fekete, S.P. et al. Nat Comput (2008) 7: 347. doi:10.1007/s11047-008-9073-0

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 × 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.

Keywords

Self-assembly Tiling Nanotechnology DNA computing DNA self-assembly 

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • Martin L. Demaine
    • 1
  • Sándor P. Fekete
    • 2
  • Mashhood Ishaque
    • 3
  • Eynat Rafalin
    • 4
  • Robert T. Schweller
    • 5
  • Diane L. Souvaine
    • 3
  1. 1.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA
  2. 2.Department of Computer ScienceBraunschweig University of TechnologyBraunschweigGermany
  3. 3.Department of Computer ScienceTufts UniversityMedfordUSA
  4. 4.Google Inc.Mountain ViewUSA
  5. 5.Department of Computer ScienceUniversity of Texas-Pan AmericanEdinburgUSA

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