1 / 95

Complexities for Generalized Models of Self-Assembly

Complexities for Generalized Models of Self-Assembly. Gagan Aggarwal Stanford University Michael H. Goldwasser St. Louis University Ming-Yang Kao Northwestern University Robert T. Schweller Northwestern University. Some results were obtained independantly by Cheng, Espanes 2003.

ciel
Télécharger la présentation

Complexities for Generalized Models of Self-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. Complexities for Generalized Models of Self-Assembly Gagan Aggarwal Stanford University Michael H. Goldwasser St. Louis University Ming-Yang Kao Northwestern University Robert T. Schweller Northwestern University Some results were obtained independantly by Cheng, Espanes 2003

  2. Outline • Importance of DNA Self-Assembly • Synthesis of Nanostructures • DNA Computing • Tile Self-Assembly • DNA Word Design

  3. TILE

  4. TILE G C A T C G C G T A G C

  5. TILE G C A T C G C G T A G C

  6. TILE

  7. Super Small Circuits, Built Autonomously

  8. Molecular-scale pattern for a RAM memory with demultiplexed addressing (Winfree, 2003)

  9. DNA Computers + Output! Computer Program Input

  10. DNA Computers + Output! Computer Program Input Program

  11. DNA Computers + Output! Computer Program Input + Input Program

  12. DNA Computers + Output! Computer Program Input + Output! Input Program

  13. Outline • Importance of DNA Self-Assembly • Tile Self-Assembly (Generalized Models) • Tile Complexity • Shape Verification • Error Resistance • DNA Word Design

  14. Tile Model of Self-Assembly (Rothemund, Winfree STOC 2000) Tile System: t : temperature, positive integer G: glue function T: tileset s: seed tile

  15. How a tile system self assembles G(y,y) = 2 G(g,g) = 2 G(r, r) = 2 G(b,b) = 2 G(p,p) = 1 G(w,w) = 1 t = 2 T =

  16. How a tile system self assembles G(y,y) = 2 G(g,g) = 2 G(r, r) = 2 G(b,b) = 2 G(p,p) = 1 G(w,w) = 1 t = 2 T =

  17. How a tile system self assembles G(y,y) = 2 G(g,g) = 2 G(r, r) = 2 G(b,b) = 2 G(p,p) = 1 G(w,w) = 1 t = 2 T =

  18. How a tile system self assembles G(y,y) = 2 G(g,g) = 2 G(r, r) = 2 G(b,b) = 2 G(p,p) = 1 G(w,w) = 1 t = 2 T =

  19. How a tile system self assembles G(y,y) = 2 G(g,g) = 2 G(r, r) = 2 G(b,b) = 2 G(p,p) = 1 G(w,w) = 1 t = 2 T =

  20. How a tile system self assembles G(y,y) = 2 G(g,g) = 2 G(r, r) = 2 G(b,b) = 2 G(p,p) = 1 G(w,w) = 1 t = 2 T =

  21. How a tile system self assembles G(y,y) = 2 G(g,g) = 2 G(r, r) = 2 G(b,b) = 2 G(p,p) = 1 G(w,w) = 1 t = 2 T =

  22. How a tile system self assembles G(y,y) = 2 G(g,g) = 2 G(r, r) = 2 G(b,b) = 2 G(p,p) = 1 G(w,w) = 1 t = 2 T =

  23. How a tile system self assembles G(y,y) = 2 G(g,g) = 2 G(r, r) = 2 G(b,b) = 2 G(p,p) = 1 G(w,w) = 1 t = 2 T =

  24. New Models • Multiple Temperature Model • temperature may go up and down • Flexible Glue Model • Remove the restriction that G(x, y) = 0 for x!=y • Multiple Tile Model • tiles may cluster together before being added • Unique Shape Model • unique shape vs. unique supertile

  25. New Models • Multiple Temperature Model • temperature may go up and down • Flexible Glue Model • Remove the restriction that G(x, y) = 0 for x!=y • Multiple Tile Model • tiles may cluster together before being added • Unique Shape Model • unique shape vs. unique supertile

  26. New Models • Multiple Temperature Model • temperature may go up and down • Flexible Glue Model • Remove the restriction that G(x, y) = 0 for x!=y • Multiple Tile Model • tiles may cluster together before being added • Unique Shape Model • unique shape vs. unique supertile

  27. New Models • Multiple Temperature Model • temperature may go up and down • Flexible Glue Model • Remove the restriction that G(x, y) = 0 for x!=y • Multiple Tile Model • tiles may cluster together before being added • Unique Shape Model • unique shape vs. unique supertile

  28. Focus • Multiple Temperature Model • Adjust temperature during assembly • Flexible Glue Model • Remove the restriction that G(x, y) = 0 for x!=y Goal: Reduce Tile Complexity

  29. Our Tile Complexity Results Multiple temperature model: (our paper) k x N rectangles: beats standard model: (our paper) Flexible Glue: N x N squares: (our paper) (Adleman, Cheng, Goel, Huang STOC 2001) beats standard model:

  30. Building k x N Rectangles k-digit, base N(1/k) counter: k N

  31. Building k x N Rectangles k-digit, base N(1/k) counter: k N Tile Complexity:

  32. Build a 4 x 256 rectangle: t = 2 S3 0 S2 0 S1 0 S g g g p C0 C1 C2 C3 S

  33. Build a 4 x 256 rectangle: t = 2 S3 0 g S2 0 0 1 2 3 0 0 g S1 0 S g g g p C0 C1 C2 C3 0 S3 0 S2 0 0 S1 g g p S C1 C2 C3

  34. Build a 4 x 256 rectangle: t = 2 g g 0 1 0 1 S3 0 p r g S2 0 0 1 2 3 0 0 g S1 0 S g g g p C0 C1 C2 C3 S3 0 0 S2 0 0 S1 0 0 p S C1 C2 C3

  35. Build a 4 x 256 rectangle: t = 2 g g 0 1 0 1 S3 0 p r g S2 0 0 1 2 3 0 0 g S1 0 S g g g p C0 C1 C2 C3 S3 0 0 S2 0 0 g g S1 0 0 0 1 S C1 C2 C3

  36. Build a 4 x 256 rectangle: t = 2 g g 0 1 0 1 S3 0 p r g S2 0 0 1 2 3 0 0 g S1 0 S g g g p C0 C1 C2 C3 S3 0 0 0 0 S2 0 0 0 0 S1 0 0 0 1 p S C1 C2 C3 C0 C1 C2 C3

  37. Build a 4 x 256 rectangle: t = 2 g g 0 1 0 1 S3 0 p r g S2 0 0 1 2 3 0 0 1 2 g S1 0 S g g g p 2 3 C0 C1 C2 C3 S3 0 0 0 0 0 0 S2 0 0 0 0 0 0 S1 0 0 0 1 1 1 p S C1 C2 C3 C0 C1 C2 C3

  38. Build a 4 x 256 rectangle: t = 2 g g 0 1 0 1 S3 0 p r g S2 0 0 1 2 3 0 0 1 2 g S1 0 p r S P R g g g p 3 0 2 3 p r C0 C1 C2 C3 S3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 S2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 S1 0 0 0 1 1 1 1 2 2 2 2 3 3 3 p S C1 C2 C3 C0 C1 C2 C3 C0 C1 C2 C3 C0 C1 C2 C3

  39. Build a 4 x 256 rectangle: t = 2 g g 0 1 0 1 S3 0 p r g S2 0 0 1 2 3 0 0 1 2 g S1 0 p r S P R g g g p 3 0 2 3 p r C0 C1 C2 C3 S3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 S2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 S1 0 0 0 1 1 1 1 2 2 2 2 3 3 3 P S C1 C2 C3 C0 C1 C2 C3 C0 C1 C2 C3 C0 C1 C2 C3

  40. Build a 4 x 256 rectangle: t = 2 g g 0 1 0 1 S3 0 p r g S2 0 0 1 2 3 0 0 1 2 g S1 0 p r S P R g g g p 3 0 2 3 p r C0 C1 C2 C3 S3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 S2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 S1 0 0 0 1 1 1 1 2 2 2 2 3 3 3 P S C1 C2 C3 C0 C1 C2 C3 C0 C1 C2 C3 C0 C1 C2 C3

  41. Build a 4 x 256 rectangle: t = 2 g g 0 1 0 1 S3 0 p r g S2 0 0 1 2 3 0 0 1 2 g S1 0 p r S P R g g g p 3 0 2 3 p r C0 C1 C2 C3 S3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 S2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 S1 0 0 0 1 1 1 1 2 2 2 2 3 3 3 P R S C1 C2 C3 C0 C1 C2 C3 C0 C1 C2 C3 C0 C1 C2 C3

  42. Build a 4 x 256 rectangle: t = 2 g g 0 1 0 1 S3 0 p r g S2 0 0 1 2 3 0 0 1 2 g S1 0 p r S P R g g g p 3 0 2 3 p r C0 C1 C2 C3 S3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 S2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 S1 0 0 0 1 1 1 1 2 2 2 2 3 3 3 P R … S C1 C2 C3 C0 C1 C2 C3 C0 C1 C2 C3 C0 C1 C2 C3 C0 C1 C2

  43. Build a 4 x 256 rectangle: t = 2 g g 0 1 0 1 S3 0 p r g S2 0 0 1 2 3 0 0 1 2 g S1 0 p r S P R g g g p 3 0 2 3 p r C0 C1 C2 C3 S3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 S2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 … S1 0 0 0 1 1 1 1 2 2 2 2 3 3 3 P R 0 0 S C1 C2 C3 C0 C1 C2 C3 C0 C1 C2 C3 C0 C1 C2 C3 C0 C1 C2

  44. Build a 4 x 256 rectangle: t = 2 g g 0 1 0 1 S3 0 p r g S2 0 0 1 2 3 0 0 1 2 g S1 0 p r S P R g g g p 3 0 2 3 p r C0 C1 C2 C3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 P 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 P 3 3 P R 0 0 0 1 1 1 1 2 2 2 2 3 3 3 P C1 C2 C3 C0 C1 C2 C3 C0 C1 C2 C3 C0 C1 C2 C3 C0 C1 C2 C3

  45. Building k x N Rectangles k-digit, base N(1/k) counter: k N Tile Complexity:

  46. 2-temperature model t= 4 3 1 3 3

  47. 2-temperature model t = 4 6

More Related