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Algorithms for Robust Self-Assembly

1. 1. 0. 0. 1. 1. 0. 0. 0. Algorithms for Robust Self-Assembly. Ho-Lin Chen holin@stanford.edu Ashish Goel Qi Cheng. 1. 1. 1. 1. 1. 0. 1. 1. 1. Counter made by self-assembly [ Adleman, Cheng, Goel, Huang ’ 01]. ( Chen, Goel , Cheng). Self-Assembly.

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Algorithms for Robust Self-Assembly

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  1. 1 1 0 0 1 1 0 0 0 Algorithms for Robust Self-Assembly Ho-Lin Chen holin@stanford.edu Ashish Goel Qi Cheng 1 1 1 1 1 0 1 1 1 Counter made by self-assembly [Adleman, Cheng, Goel, Huang ’01] (Chen, Goel, Cheng)

  2. Self-Assembly • Self-Assembly is the process by which simple objects autonomously assemble into complexes. • Geometry, dynamics, combinatorics are all important • Inorganic: Crystals, supramolecules • Organic: Proteins, DNA, cells, organisms • Goals: Understand self-assembly, design self-assembling systems • A key problem in nano-technology, molecular robotics, molecular computation (Chen, Goel, Cheng)

  3. Applications of Self-Assembly • Self-assembly can be used to create small electrical devices such as FLASH memory. [Black et. Al. ’03] • Self-assembly can create nanostructures which “steer” light in the same way computer chips steer electrons. [Percec et. Al. ’03] • DNA strands can self-assemble into tiles and those tiles can further self-assemble into larger structures. This has many potential applications. [Winfree ’96] DNA “rug” by Winfree (Chen, Goel, Cheng)

  4. DNA Tiles [Winfree] Glues = sticky ends Tiles = molecules (Chen, Goel, Cheng)

  5. Tile System: [Rothemund, Winfree, ’2000] Temperature: A positive integer. A set of tile types: Each tile is an oriented square with glues on its edges. Each glue has a non-negative strength. An initial assembly (seed). A tile can attach to an assembly iff the combined strength of the “matchings glues” is greater or equal than the temperature. (Chen, Goel, Cheng)

  6. Example of a tile system Temperature: 2 Set of tile types: Seed: (Cheng, Goel, Cheng)

  7. Example of a SA process Temperature: 2 Set of tile types: Seed: (Cheng, Goel, Cheng)

  8. Example of a SA process Temperature: 2 Set of tile types: Seed: (Cheng, Goel, Cheng)

  9. Example of a SA process Temperature: 2 Set of tile types: Seed: (Cheng, Goel, Cheng)

  10. Theoretical and Algorithmic Issues • Efficiently assembling basic shapes with precisely controlled size and pattern • Constructing N X N squares with Ω(log n/log log n) tiles [Adleman, Cheng, Goel, Huang, ’01] • Perform universal computation by simulating BCA [Winfree ’99] • Library of primitives to use in designing nano-scale structures [Adleman, Cheng, Goel, Huang, ’01] • Automate the design process [Adleman, Cheng, Goel, Huang, Kempe, Moisset de espanes, Rothemund ’01] • Robustness (Cheng, Goel, Cheng)

  11. Robustness • In practice, self-assembly is a thermodynamic process. When T=2, tiles with 0 or 1 matches also attach; tiles held by total strength 2 also fall off at a small rate. • Currently, there are 1-10% errors observed in experimental self-assembly. [Winfree, Bekbolatov, ’03] • Possible schemes for error correction • Biochemistry tricks • Coding theory and error correction (Cheng, Goel, Cheng)

  12. Error-Reducing Designs • Biochemistry tricks • Strand Invasion mechanism [Chen, Cheng, Goel, Huang, Moisset de espanes, ’04] • Coding theory and error correction • Proofreading tiles [Winfree, Bekbolatov,’03] • Snake tiles [Chen, Goel 05] (Cheng, Goel, Cheng)

  13. Strand Invasion (Cheng, Goel, Cheng)

  14. Strand Invasion (Cheng, Goel, Cheng)

  15. Strand Invasion (Cheng, Goel, Cheng)

  16. Strand Invasion (Cheng, Goel, Cheng)

  17. Strand Invasion (Cheng, Goel, Cheng)

  18. Strand Invasion (Cheng, Goel, Cheng)

  19. Strand Invasion (Cheng, Goel, Cheng)

  20. Strand Invasion (Cheng, Goel, Cheng)

  21. Strand Invasion (Cheng, Goel, Cheng)

  22. Strand Invasion (Cheng, Goel, Cheng)

  23. Strand Invasion (Cheng, Goel, Cheng)

  24. Strand Invasion (Cheng, Goel, Cheng)

  25. Strand Invasion (Cheng, Goel, Cheng)

  26. Strand Invasion (Cheng, Goel, Cheng)

  27. Strand Invasion (Cheng, Goel, Cheng)

  28. Strand Invasion (Cheng, Goel, Cheng)

  29. Strand Invasion (Cheng, Goel, Cheng)

  30. Strand Invasion (Cheng, Goel, Cheng)

  31. Strand Invasion (Cheng, Goel, Cheng)

  32. Strand Invasion (Cheng, Goel, Cheng)

  33. Strand Invasion (cont) Strand Invasion (Cheng, Goel, Cheng)

  34. Strand Invasion (Cheng, Goel, Cheng)

  35. Example T=2 (Cheng, Goel, Cheng)

  36. Example T=2 (Cheng, Goel, Cheng)

  37. Example T=2 (Cheng, Goel, Cheng)

  38. What can go wrong? T=2 (Cheng, Goel, Cheng)

  39. What can go wrong? T=2 (Cheng, Goel, Cheng)

  40. Why it may not matter: T=2 (Cheng, Goel, Cheng)

  41. Why it may not matter: T=2 (Cheng, Goel, Cheng)

  42. What can go really wrong? T=2 (Cheng, Goel, Cheng)

  43. What can go really wrong? T=2 (Cheng, Goel, Cheng)

  44. What can go really wrong? T=2 (Cheng, Goel, Cheng)

  45. Safe attachments and invadable systems Safe Unsafe Definition: A tile system is an invadable system iff for all assemblies that can be grown from the initial assembly, all possible attachments are safe. (Cheng, Goel, Cheng)

  46. Can we create efficient counters? (Cheng, Goel, Cheng)

  47. Can we create efficient counters? Yes! Using “Chinese remaindering” T=2 (Cheng, Goel, Cheng)

  48. Can we create efficient counters? Yes! Using “Chinese remaindering” T=2 (Cheng, Goel, Cheng)

  49. Can we create efficient counters? Yes! Using “Chinese remaindering” T=2 (Cheng, Goel, Cheng)

  50. Can we create efficient counters? Yes! Using “Chinese remaindering” T=2 (Cheng, Goel, Cheng)

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