1. Staged Self-Assembly and Polyomino Context-Free Grammars Andrew Winslow Defense Edition

2. Simple particles coalescing into complex superstructures. Self-Assembly

3. Simple particles coalescing into complex superstructures.

4. Self-Assembly Simple particles coalescing into complex superstructures.

5. Self-Assembly Simple particles coalescing into complex superstructures.

6. Crystallization

7. Morphogenesis

8. Natural Self-Assembly

9. Synthetic Self-Assembly with DNA

11. Tile

12. Glues

15. Our work: Study an abstract self-assembly model based on DNA tile systems.

16. Tile

17. Glues

18. Assembly

19. Mixing

20. Bin

21. Reagents

22. Products

24. Size

26. Staged self-assembly

27. InputOutput (polyomino) (small staged assembly system)

28. n Input

32. Θ( n) system size

34. Θ (log(n)) system size

35. n Θ (n) Θ (log(n))

36. Input

37. Study a simplified model. Finding small systems is (NP-)hard.

39. Rule

40. Grammar

41. Ο (#glues 2 ) Ω (n 1/2 /log(n)), Ο (n 2/3 ) Staged System ? ? ? One dimension Ο (1) E. D. Demaine, S. Eisenstat, M. Ishaque, A. Winslow, One-dimensional staged self-assembly, DNA 17, 2011. Grammar ? ? ?

42. ? ?

43. Polyomino Grammar

44. w/scaling Two dimensions GrammarStaged System … … A. Winslow, Staged Self-Assembly and Polyomino Context-Free Grammars, DNA 19, 2013. Ω (n/log 3 n) Ο (log(n)) Macrotile

45. ? ? ? ? ? ?

46. Values

47. Values are distinct Values are contiguous

48. Activation

52. ? ? ?

55. Shifting [1..3] +4

56. Shifting [4..6] +4

57. Activation Shifting [1..3] +4

58. ? ? ?

59. [2..5] +3

60. ? ? ?

61. [1..4] +2

62. ? ? ?

63. [1..4] +4

64. Reagent 1 Reagent 2 Product Activated reagent 1 Shifted reagent 2 Activated & shifted reagent 2

65. ? ? ? ? ? ?

66. A R1 S R2 A & S R2 A R1 S R2 A & S R2 A R1 S R2 A & S R2

67. A R1 S R2 A & S R2 A R1 S R2 A & S R2 A R1 S R2 A & S R2 w/scaling Ο (log(n))

68. … … Ω (n/log 3 n)

69. Ο (loglog(n)) … Ω (n/loglog(n)) …

70. … … Ο (log(n)) Ω (n/log 2 n)

71. Ο (log(n)) … Ω (n/log 2 n) …

72. GrammarStaged System Ο (1) Ω (n 1/2 /log(n)), Ο (n 2/3 ) w/scaling Ο (log(n)) Ω (n/log 3 n) Grammars are small, staged systems are always smaller

73. Thank you Committee: Diane Souvaine Erik Demaine Ben Hescott Lenore Cowen Hyunmin Yi Collaborators: Matthew Patitz Sarah Eisenstat Robert Schweller Mashhood Ishaque Damien Woods NSF grants 0941538 and 0830734