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A Self-assembly Model of Time-Dependent Glue Strength

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Algorithmic Bioprocesses

Part of the book series: Natural Computing Series ((NCS))

Abstract

Self-assembly is a ubiquitous process in which small objects self-organize into larger and complex structures. In 2000, Rothemund and Winfree proposed a Tile Assembly Model as a mathematical model for theoretical studies of self-assembly. We propose a refined self-assembly model in which the glue strength between two juxtaposed tiles is a function of the time they have been in neighboring positions. We then present an implementation of our model using strand displacement reactions on DNA tiles. Under our model, we can demonstrate and study catalysis and self-replication in the tile assembly. We then study the tile complexity for assembling shapes in our model and show that a thin rectangle of size k×N can be assembled using O((log (N))/log log (N)) types of tiles, demonstrating the glue model has additional capabilities over the prior tiling assembly model. We also describe a method to implement with DNA tiles our model of time-dependant glue strength.

Sudheer Sahu was a PhD student in Duke University when this research was conducted.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Duke University, Box 90129, Durham, NC, 27708, USA

    Sudheer Sahu & John H. Reif

  2. Department of Computer Science, Department of Bioengineering, Center for Biological Circuit Design, Caltech, Pasadena, CA, 91125, USA

    Peng Yin

Authors
  1. Sudheer Sahu
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  2. Peng Yin
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  3. John H. Reif
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Corresponding author

Correspondence to Sudheer Sahu .

Editor information

Editors and Affiliations

  1. Dept. Computer Science, University of British Columbia, Main Mall 201-2366, Vancouver, V6T 1Z4, Canada

    Anne Condon

  2. Dept. Applied Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel

    David Harel

  3. Leiden Inst. Advanced Computer Science, Leiden University, Niels Bohrweg 1, Leiden, 2333 CA, Netherlands

    Joost N. Kok

  4. Turku Centre for Computer Science, Lemminkaisenkatu 14 A, Turku, 20520, Finland

    Arto Salomaa

  5. Computer Science, Computation,, California Inst. of Technology, Pasadena, 91125, U.S.A.

    Erik Winfree

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Sahu, S., Yin, P., Reif, J.H. (2009). A Self-assembly Model of Time-Dependent Glue Strength. In: Condon, A., Harel, D., Kok, J., Salomaa, A., Winfree, E. (eds) Algorithmic Bioprocesses. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88869-7_11

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  • DOI: https://doi.org/10.1007/978-3-540-88869-7_11

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  • Print ISBN: 978-3-540-88868-0

  • Online ISBN: 978-3-540-88869-7

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