Staged Self-Assembly and Polyomino Context-Free Grammars

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

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

3. Self-Assembly 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. Input Output (polyomino) (small staged assembly system)

28. Input n

32. Θ(n) system size

34. Θ(log(n)) system size

35. n Θ(n) Θ(log(n))

36. Input

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

39. Rule

40. Grammar

41. One dimension Ο(1) ? ? ? ? ? ? Ο(#glues2) Ω(n1/2/log(n)), Ο(n2/3) Staged System Grammar E. D. Demaine, S. Eisenstat, M. Ishaque, A. Winslow, One-dimensional staged self-assembly, DNA 17, 2011.

42. ? ? ? ?

43. Polyomino Grammar

44. Two dimensions Ο(log(n)) w/scaling Macrotile … … Ω(n/log3n) Grammar Staged System A. Winslow, Staged Self-Assembly and Polyomino Context-Free Grammars, DNA 19, 2013.

45. ? ? ? ? ? ?

46. Values

47. Values are distinct Values are contiguous

48. Activation

49. Activation