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Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues

This paper explores the staged self-assembly process to create complex nanostructures using a minimal number of glues. The goal is to efficiently build target shapes with low bin and stage complexity.

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Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues

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  1. Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Thirteenth International Meeting on DNA Computers June 5, 2007 Eric Demaine Massachusetts Institute of Technology Martin Demaine Massachusetts Institute of Technology Sandor Fekete Technische Universität Braunschweig Mashood Ishaque Tufts University Eynat Rafalin Google Robert SchwellerUniversity of Texas Pan American Diane Souvaine Tufts University

  2. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T = Glue Function: Tile Set: Temperature:

  3. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T = e d

  4. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T = e d

  5. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T = e d b c

  6. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T = e d b c

  7. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T = e d b c

  8. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T = e d a b c

  9. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T = e d a b c

  10. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T = e d a b c

  11. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T = e d a b c

  12. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T = e d a b c

  13. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T = e x d a b c

  14. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e e x d a b c G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T =

  15. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e e x x d a b c G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T =

  16. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e x e x x d a b c G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T =

  17. Tile Assembly Model (Rothemund, Winfree, Adleman) a b c x d e x x e x x d a b c G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 T =

  18. Non-Staged Assembly BEAKER Start with initial Tileset • Assembly occurs within 1 single container • - Assembly occurs within 1 single stage

  19. Non-Staged Assembly BEAKER BEAKER After some time... Start with initial Tileset Various Producible Supertiles exist in solution • Assembly occurs within 1 single container • - Assembly occurs within 1 single stage

  20. Non-Staged Assembly BEAKER BEAKER BEAKER After some time... After enough time... Start with initial Tileset Various Producible Supertiles exist in solution Only Terminally Produced assemblies remain • Assembly occurs within 1 single container • - Assembly occurs within 1 single stage

  21. Staged Assembly

  22. Staged Assembly • Pour multiple bins into a single bin

  23. Staged Assembly • Pour multiple bins into a single bin • Split contents of any given bin among multiple new bins

  24. Staged Assembly • Pour multiple bins into a single bin • Split contents of any given bin among multiple new bins

  25. Staged Assembly

  26. Staged Assembly • Assembly occurs in a sequence of stages, and assemblies can be separated into separate bins Bin Complexity: 4 Mix pattern: Stage Complexity: 3

  27. Staged Assembly • Assembly occurs in a sequence of stages, and assemblies can be separated into separate bins Bin Complexity: 4 Bins = Space Complexity Stages = Time Complexity Stage Complexity: 3

  28. Staged Assembly • Our Goal: Given a target shape, design mixing algorithms that: • Use only O(1) tiles/glues to build target shape. • Are efficient in terms of: • Bin complexity • Stage complexity. • Assembly occurs in a sequence of stages, and assemblies can be separated into separate bins Bin Complexity: 4 Stage Complexity: 3

  29. Simple Example: 1 x n line

  30. Simple Example: 1 x n line

  31. Simple Example: 1 x n line

  32. Simple Example: 1 x n line stage i stage i+3

  33. Simple Example: 1 x n line stage i stage i+3 Staged Assembly 1 x n line

  34. Simple Example: 1 x n line stage i stage i+3 Staged Assembly 1 x n line Non-Staged Model 1 x n line

  35. n x n Square

  36. n x n Square Staged Assembly n x n square Base Case 1 x n line: Use line algorithm

  37. n x n Square: unstable?

  38. n x n Square: unstable?

  39. n x n Square: unstable?

  40. n x n Square: FullConnectivity [Rothemund, Winfree STOC 2000] FullConnectivity Constraint: All adjacent tiles in assembled shape must share a full strength bond

  41. n x n Square: FullConnectivity FullConnectivity Constraint: All adjacent tiles in assembled shape must share a full strength bond

  42. n x n Square: FullConnectivity FullConnectivity Constraint: All adjacent tiles in assembled shape must share a full strength bond Shifting Problem

  43. n x n Square: FullConnectivity FullConnectivity Constraint: All adjacent tiles in assembled shape must share a full strength bond Jigsaw Technique: Use Geometry to enforce proper binding. Shifting Problem

  44. n x n Square: FullConnectivity FullConnectivity Constraint: All adjacent tiles in assembled shape must share a full strength bond Jigsaw Technique: Use Geometry to enforce proper binding.

  45. n x n Square: FullConnectivity FullConnectivity Constraint: All adjacent tiles in assembled shape must share a full strength bond Jigsaw Technique: Use Geometry to enforce proper binding.

  46. n x n Square: FullConnectivity Staged Assembly Fully Connected n x n square Non-Staged Model Fully Connected n x n square [adleman, cheng, goel, huang STOC 2001]

  47. Arbitrary Shapes • Spanning Tree Method • Jigsaw Method for non-hole Shapes • Simulation Method

  48. Simulate Large Tilesets

  49. Simulate Large Tilesets 0000 0001 0010 0011 0100 0101 0110

  50. Simulate Large Tilesets 0000 0001 0 0010 0011 1 0100 0101 0110

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