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Self-Assembly

Self-Assembly. Ho-Lin Chen Nov 8 2005. 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

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Self-Assembly

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  1. Self-Assembly Ho-Lin Chen Nov 8 2005

  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

  3. Applications of Self-Assembly • Building blocks of nano-machines. • DNA computing. • Small electrical devices such as FLASH memory. [Black et. Al. ’03] • Nanostructures which “steer” light in the same way computer chips steer electrons. [Percec et. Al. ’03]

  4. Self-Assembly of DNA [Winfree]

  5. Abstract System Model

  6. DNA Tiles G4 G3 = G1 G2 [Fu and Seeman, ’93] Glues = sticky ends Tiles = molecules

  7. abstract Tile Assembly Model: [Rothemund, Winfree, ’2000] Temperature: A positive integer. (Usually 1 or 2) A set of tile types: Each tile is an oriented rectangle with glues on its corners. Each glue has a non-negative strength (0, 1 or 2). An initial assembly (seed). A tile can attach to an assembly iff the combined strength of the “matched glues” is greater or equal than the temperature. x z x y

  8. Example: Sierpinski System [Winfree, ’96] 0 1 0 0 1 1 0 1 T=2 0 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0

  9. Example: Sierpinski System 0 1 0 0 1 1 0 1 T=2 0 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0

  10. Example: Sierpinski System 0 1 0 0 1 1 0 1 T=2 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0

  11. Example: Sierpinski System 0 1 0 0 1 1 0 1 T=2 0 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0

  12. Example: Sierpinski System 0 1 0 0 1 1 0 1 T=2 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 0

  13. Example: Sierpinski System 0 1 0 0 1 1 0 1 T=2 0 0 1 0 0 1 1 1

  14. DAO-E Sierpinski triangle experiments Paul Rothemund, Nick Papadakis, Erik Winfree, PLoS Biology 2: e424 (2004) 340nm

  15. Theoretical Results • Efficiently assembling basic shapes with precisely controlled size and pattern. • Constructing N X N squares with O(log n/log log n) tiles. [Adleman, Cheng, Goel, Huang, ’01] • Perform universal computation by simulating BCA. [Winfree ’99] • Assemble arbitrary shape by O( Kolmogorov complexity) tiles with scaling. [Soloveichik, Winfree ’04]

  16. Block Cellular Automata f(X, Y) g(X, Y) X Y

  17. Simulating BCA T=2 g(X,Y) f(X,Y) A series of tiles with format: X Y Growth direction seed

  18. Assemble Arbitrary Shapes Replace each tile by a block. Size of block = O(computation time) computation

  19. Tile System Design • 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]

  20. Kinetic System Model

  21. kinetic Tile Assembly Model: [Winfree, 1998] A tile can attach at any location. The rate of attachment rf = constant. The rate of detachment rr,b = c e-bG

  22. Kinetic model => Abstract model • We set the temperature and concentration to rr,T+1 << rr,T < rf << rr,T-1 • If a tile attaches with strength < T-1, it is likely to fall off very fast. • If a tile is held by strength at least T+1, it is unlikely to fall off

  23. Error Correction

  24. Robustness Designs • Use biological mechanisms in the process. • Add extra structure/modification on the process of DNA self-assembly. • Add combinatorial structures to tile systems. • Use the original erroneous process, but add more structure to the tile system to do error correction.

  25. Using Biological Mechanisms • Use strand invasion [Chen, Cheng, Goel, Huang, Moisset de espanes, ’04] • Add protecting tiles [Fujibayashi and Murata, ’04]

  26. Strand Invasion

  27. Strand Invasion

  28. Strand Invasion

  29. Strand Invasion

  30. Strand Invasion

  31. Strand Invasion

  32. Strand Invasion

  33. Strand Invasion

  34. Strand Invasion

  35. Strand Invasion

  36. Strand Invasion

  37. Strand Invasion

  38. Strand Invasion

  39. Strand Invasion

  40. Strand Invasion

  41. Strand Invasion

  42. Strand Invasion

  43. Strand Invasion

  44. Strand Invasion

  45. Strand Invasion

  46. Strand Invasion (cont) Strand Invasion

  47. Strand Invasion

  48. Strand Invasion

  49. Example T=2

  50. Example T=2

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