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  1. Complexities for the Design of Self-Assembly Systems May 3, 2006 Robert SchwellerElectrical Engineering and Computer Science Department Northwestern University Email: schwellerr@cs.northwestern.edu http://www.cs.northwestern.edu/~schwellerr/

  2. Outline • Background, Motivation • Model • Temperature Programming • Flexible Glue Self-Assembly • Shape Verification • Future Work

  3. Molecular Building Blocks T G C G A C G C

  4. Molecular Building Blocks [John Reif’s Group, Duke University]

  5. DNA Scaffolding [Sung Ha Park, Constantin Pistol, Sang Jung Ahn, John H. Reif, Alvin R. Lebeck, Chris Dwyer, and Thomas H. LaBean, 2006]

  6. Simulation of Cellular Automata Paul Rothemund, Nick Papadakis, Erik Winfree, PLoS Biology 2: e424 (2004) 340nm

  7. Outline • Background, Motivation • Model • Temperature Programming • Shape Verification • Flexible Glue Self-Assembly • Future Work

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

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

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

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

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

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

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

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

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

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

  18. Each Shape Requires a Distinct Tile Set

  19. Programmable, General Purpose Tile Set?

  20. Programmable, General Purpose Tile Set? . . .

  21. Outline • Background, Motivation • Model • Temperature Programming • Flexible Glue Self-Assembly • Shape Verification • Future Work

  22. Multiple Temperature Model Multiple Temperature Model - temperature may go up and down

  23. Multiple Temperature Model Multiple Temperature Model - temperature may go up and down t < t1 , t2 , ... , tr-1 , tr >

  24. Multiple Temperature Model Multiple Temperature Model - temperature may go up and down t < t1 , t2 , ... , tr-1 , tr > Tile Complexity: Number of Tiles Temperature Complexity: Number of Temperatures

  25. Building k x n Rectangles k-digit, base n(1/k) counter: k n

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

  27. two temperatures t= 4 3 1 3 3 n

  28. two temperatures t = 4 6 n

  29. two temperatures Tile Complexity: t = 4 6 n

  30. two temperatures Tile Complexity: t = 4 6 n Kolmogorov Complexity (Rothemund, Winfree STOC 2000) Beats Standard Model

  31. Programmable, General Purpose Tile Set? . . .

  32. High Level Approach Given: n 1011001 log n

  33. High Level Approach Given: n 1011001 log n 1 temp

  34. High Level Approach Given: n 1011001 log n 1 temp 1

  35. High Level Approach Given: n 1011001 log n 1 0 temp 1 0

  36. High Level Approach Given: n 1011001 log n 1 0 1 1 0 . . . . . . temp 1 0 1 1 0 0 1

  37. High Level Approach . . . 0 0 1 . . . temp 1 0 1 1 0 0 1

  38. High Level Approach . . . 0 0 1 . . . temp 1 0 1 1 0 0 1

  39. High Level Approach . . . 0 0 1 . . . temp 1 0 1 1 0 0 1

  40. Assembly of n x n Squares N - k k

  41. Assembly of n x n Squares n - k k

  42. Assembly of n x n Squares n - k k

  43. Assembly of n x n Squares n - k Complexity: k

  44. Assembly of n x n Squares n – log n Complexity: log n

  45. Assembly of n x n Squares n – log n Complexity: seed row log n

  46. Encoding a Single Bit 0 0 1 0 1 0’ 1’ z z 1 z Z g g g g g g g g a g g

  47. Encoding a Single Bit t = < 2 > 0 0 1 0 1 0’ 1’ z z 1 z Z g g g g g g g g a g g a

  48. Encoding a Single Bit t = < 2 > 0 0 1 0 1 0’ 1’ z z 1 z Z g g g g g g g g a g g a

  49. Encoding a Single Bit t = < 2 > 0 0 1 0 1 0’ 1’ z z 1 z Z g g g g g g g g a g g a

  50. Encoding a Single Bit t = < 2 > 0 0 1 0 1 0’ 1’ z z 1 z Z g g g g g g g g a g g a