Snaked Proofreading

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In [1], Chen and Goel demonstrated a tile set transformation which provided improvements over the previous proofreading technique. In fact, their snaked proofreading technique not only provides substantial improvements in error correction, it also provides for "provably good" assembly time, or specifically that it allows for close to linear assembly time (within a logarithmic factor of irreversible error-free growth). Snaked proofreading relies on a block replacement scheme similar to the proofreading of Winfree and Bekbolatov [2], but with a different internal bond structure. An example of the difference can be seen in Figure 1 (below). The general technique is to force multiple insufficient attachments to occur and be locked into place before an error can persist.

Especially notable is the fact that snaked proofreading does not only provide benefits in simulations of the kTAM, but in [3] Chen, Schulman, Goel, and Winfree actually created a tile set which utilized the technique and experimented with it in a wet-lab setting. They created tile sets which self-assembled into long ribbons, some which were designed to implement snaked proofreading and some which were not, and were able to verify via atomic force microscopy that the snaked proofreading tile sets experienced a 4-fold reduction in facet nucleation errors.

Sierpinski Growth Error
A tile type from the original, unaltered tile set.
Red cartouche
The block used as a replacement in standard proofreading.
not sure
The block used as a replacement in snaked proofreading.
Figure 1. A comparison of the block replacement transformations used in standard proofreading and snaked proofreading

References

  1. Ho-Lin Chen, Ashish Goel - Error Free Self-Assembly using Error Prone Tiles
    Proceedings of the 10th International Meeting on DNA Based Computers pp. 274--283,2004
    Bibtex
    Author : Ho-Lin Chen, Ashish Goel
    Title : Error Free Self-Assembly using Error Prone Tiles
    In : Proceedings of the 10th International Meeting on DNA Based Computers -
    Address :
    Date : 2004
  2. Erik Winfree, Renat Bekbolatov - Proofreading Tile Sets: Error Correction for Algorithmic Self-Assembly
    DNA 2943:126-144,2003
    http://dblp.uni-trier.de/db/conf/dna/dna2003.html#WinfreeB03
    Bibtex
    Author : Erik Winfree, Renat Bekbolatov
    Title : Proofreading Tile Sets: Error Correction for Algorithmic Self-Assembly
    In : DNA -
    Address :
    Date : 2003
  3. Ho-Lin Chen, Rebecca Schulman, Ashish Goel, Erik Winfree - Reducing Facet Nucleation during Algorithmic Self-Assembly
    Nano Letters 7(9):2913--2919, September 2007
    http://dx.doi.org/10.1021/nl070793o
    Bibtex
    Author : Ho-Lin Chen, Rebecca Schulman, Ashish Goel, Erik Winfree
    Title : Reducing Facet Nucleation during Algorithmic Self-Assembly
    In : Nano Letters -
    Address :
    Date : September 2007