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Staged Self-Assembly and Polyomino Context-Free Grammars

This work explores a novel approach to self-assembly using simple particles that coalesce into complex superstructures. Focusing on DNA tile systems and their application in synthetic and natural self-assembly, the study presents an abstract model based on polyomino context-free grammars. We analyze staged self-assembly mechanisms, establish rules, and evaluate the computational complexity of small system configurations. Key insights include the challenges of finding solutions in NP-hard scenarios and the efficiency of one-dimensional staged systems as compared to two-dimensional grammars.

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Staged Self-Assembly and Polyomino Context-Free Grammars

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  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

  10. Tile

  11. Glues

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

  13. Tile

  14. Glues

  15. Assembly

  16. Mixing

  17. Bin

  18. Reagents

  19. Products

  20. Size

  21. Staged self-assembly

  22. Input Output (polyomino) (small staged assembly system)

  23. Input n

  24. Θ(n) system size

  25. Θ(log(n)) system size

  26. n Θ(n) Θ(log(n))

  27. Input

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

  29. Rule

  30. Grammar

  31. 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.

  32. ? ? ? ?

  33. Polyomino Grammar

  34. 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.

  35. ? ? ? ? ? ?

  36. Values

  37. Values are distinct Values are contiguous

  38. Activation

  39. Activation

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