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Optimum coding framework for error detection in the self-assembly of the Sierpinski triangle

Optimum coding framework for error detection in the self-assembly of the Sierpinski triangle

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© The Institution of Engineering and Technology
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This study presents a coding framework by which DNA self-assembly can be analysed for error detection. The proposed framework relies on coding and mapping functions that allow establishing the correctness of bonding each tile based on the codes of the tiles along a so-called traversal path. This method is different from the one that relies on comparing the pattern to be assembled (as defined by the tile set) and the current aggregate (as resulting from previously assembled tiles). As a widely used pattern and instantiation of this process, the Sierpinski triangle self-assembly is analysed in detail. The Sierpinski triangle is therefore utilised as an example to show the application of the proposed method. Different properties are proposed and its optimum coding is achieved for error detection. Simulation results are presented.

Inspec keywords: molecular biophysics; aggregation; biology computing; DNA; nanobiotechnology; self-assembly; error detection

Other keywords: aggregate; DNA self-assembly; bonding; Sierpinski triangle; error detection; optimum coding framework; tile; traversal path

Subjects: Macromolecular configuration (bonds, dimensions); Biology and medical computing; Biomolecular structure, configuration, conformation, and active sites; Model reactions in molecular biophysics

References

    1. 1)
      • Hashempour, M., Mashreghian Arani, Z., Lombardi, F.:: `Error tolerance of DNA self-healing assemblies by puncturing', Twenty-Second IEEE Int. Symp. on Defect and Fault Tolerance in VLSI Systems (DFT'07), 26–28 September 2007, Rome, Italy, p. 400–408.
    2. 2)
      • Winfree, E., Bekbolatov, R.: `Proofreading tile sets: error correction for algorithmic self-assembly', Proc. Ninth Int. Meeting on DNA Based Computers, June 2003, Madison, Wisconsin, p. 126–144, (LNCS, 2943) (Springer, Berlin, 2004).
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    4. 4)
      • Reif, J.H., Sahu, S., Yin, P.: `Compact error-resilient computational DNA tiling assemblies', DNA Computing 10, 2004, Berlin, Heidelberg.
    5. 5)
      • Chen, H.-L., Goel, A.: `Error free self-assembly using error prone tiles', DNA Computing 10, 2005, p. 62–75, (LNCS, 3384).
    6. 6)
      • Hashempour, M., Mashreghian Arani, Z., Lombardi, F.:: `Robust self-assembly of interconnects by parallel DNA growth', IEEE/ACM Symp. on Nanoscale Architectures (NANOARCH'07), San Jose, CA, USA, p. 21–22 October 2007, 70–76.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-nbt.2010.0037
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