May 3, 2006

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