1 / 22

Introduction to Tiling Assembly

Discover the intricate process of self-assembly where simple objects autonomously form complex structures. Learn the significance of geometry, dynamics, and combinatorics in inorganic crystals, supramolecules, organic proteins, DNA, cells, and organisms. Gain insights into designing self-assembling systems for nano-technology, molecular robotics, and molecular computation. Explore applications such as nano-machines, DNA computing, FLASH memory, and light-steering nanostructures. Delve into abstract system models, DNA tiles, and kinetic tile assembly models in this fascinating field with vast potential.

ksanderson
Télécharger la présentation

Introduction to Tiling Assembly

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction to Tiling Assembly Ho-Lin Chen Nov 8 2005 (Chen)

  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)

  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] (Chen)

  4. Self-Assembly of DNA [Winfree] (Chen)

  5. Abstract System Model (Chen)

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

  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 (Chen)

  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 (Chen)

  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 (Chen)

  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 (Chen)

  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 (Chen)

  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 (Chen)

  13. Example: Sierpinski System 0 1 0 0 1 1 0 1 T=2 0 0 1 0 0 1 1 1 (Chen)

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

  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] (Chen)

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

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

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

  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] (Chen)

  20. Kinetic System Model (Chen)

  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 (Chen)

  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 (Chen)

More Related