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1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts

Mar 29, 2015

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1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts Institute of Technology Martin DemaineMassachusetts Institute of Technology Sandor FeketeTechnische Universitt Braunschweig Mashood IshaqueTufts University Eynat RafalinGoogle Robert SchwellerUniversity of Texas Pan American Diane SouvaineTufts University Slide 2 2 Tile Assembly Model (Rothemund, Winfree, Adleman) T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 Tile Set: Glue Function: Temperature: x ed cba Slide 3 3 T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 d e x ed cba Tile Assembly Model (Rothemund, Winfree, Adleman) Slide 4 4 T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 d e x ed cba Tile Assembly Model (Rothemund, Winfree, Adleman) Slide 5 5 T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 d e x ed cba bc Tile Assembly Model (Rothemund, Winfree, Adleman) Slide 6 6 T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 d e x ed cba bc Tile Assembly Model (Rothemund, Winfree, Adleman) Slide 7 7 T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 d e x ed cba bc Tile Assembly Model (Rothemund, Winfree, Adleman) Slide 8 8 T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 d e x ed cba bca Tile Assembly Model (Rothemund, Winfree, Adleman) Slide 9 9 T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 d e x ed cba bca Tile Assembly Model (Rothemund, Winfree, Adleman) Slide 10 10 T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 d e x ed cba bca Tile Assembly Model (Rothemund, Winfree, Adleman) Slide 11 11 T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 d e x ed cba bca Tile Assembly Model (Rothemund, Winfree, Adleman) Slide 12 12 T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 x ed cba abc d e Tile Assembly Model (Rothemund, Winfree, Adleman) Slide 13 13 T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 x ed cba x abc d e Tile Assembly Model (Rothemund, Winfree, Adleman) Slide 14 14 T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 abc d e x x ed cba Tile Assembly Model (Rothemund, Winfree, Adleman) Slide 15 15 T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 x ed cba abc d e xx Tile Assembly Model (Rothemund, Winfree, Adleman) Slide 16 16 T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 x ed cba abc d e xx x Tile Assembly Model (Rothemund, Winfree, Adleman) Slide 17 17 T = G(y) = 2 G(g) = 2 G(r) = 2 G(b) = 2 G(p) = 1 G(w) = 1 t = 2 x ed cba abc d e xx xx Tile Assembly Model (Rothemund, Winfree, Adleman) Slide 18 18 BEAKER Start with initial Tileset Non-Staged Assembly -Assembly occurs within 1 single container - Assembly occurs within 1 single stage Slide 19 19 BEAKER After some time... Start with initial Tileset Various Producible Supertiles exist in solution Non-Staged Assembly -Assembly occurs within 1 single container - Assembly occurs within 1 single stage Slide 20 20 BEAKER After some time... After enough time... Start with initial Tileset Various Producible Supertiles exist in solution Only Terminally Produced assemblies remain Non-Staged Assembly -Assembly occurs within 1 single container - Assembly occurs within 1 single stage Slide 21 21 Staged Assembly Slide 22 22 Staged Assembly -Pour multiple bins into a single bin Slide 23 23 Staged Assembly -Pour multiple bins into a single bin -Split contents of any given bin among multiple new bins Slide 24 24 Staged Assembly -Pour multiple bins into a single bin -Split contents of any given bin among multiple new bins Slide 25 25 Staged Assembly Slide 26 26 Staged Assembly Assembly occurs in a sequence of stages, and assemblies can be separated into separate bins Bin Complexity: 4 Stage Complexity: 3 Mix pattern: Slide 27 27 Staged Assembly Assembly occurs in a sequence of stages, and assemblies can be separated into separate bins Bins = Space Complexity Stages = Time Complexity Bin Complexity: 4 Stage Complexity: 3 Slide 28 28 Staged Assembly Assembly occurs in a sequence of stages, and assemblies can be separated into separate bins Bin Complexity: 4 Stage Complexity: 3 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. Slide 29 29 Simple Example: 1 x n line Slide 30 30 Simple Example: 1 x n line Slide 31 31 Simple Example: 1 x n line Slide 32 32 Simple Example: 1 x n line stage i stage i+3 Slide 33 33 Simple Example: 1 x n line stage i stage i+3 tiles / gluesO(1) = 3 BinsO(1) StagesO(log n) Staged Assembly 1 x n line Slide 34 34 Simple Example: 1 x n line stage i stage i+3 tiles / gluesO(1) = 3 BinsO(1) StagesO(log n) Staged Assembly 1 x n line tiles / glues (n) Bins1 Stages1 Non-Staged Model 1 x n line Slide 35 35 n x n Square Slide 36 36 n x n Square Base Case 1 x n line: Use line algorithm tiles / gluesO(1) BinsO(1) StagesO(log n) Staged Assembly n x n square Slide 37 37 n x n Square: unstable? Slide 38 38 n x n Square: unstable? Slide 39 39 n x n Square: unstable? Slide 40 40 n x n Square: Full Connectivity Full Connectivity Constraint: All adjacent tiles in assembled shape must share a full strength bond [Rothemund, Winfree STOC 2000] Slide 41 41 n x n Square: Full Connectivity Full Connectivity Constraint: All adjacent tiles in assembled shape must share a full strength bond Slide 42 42 n x n Square: Full Connectivity Shifting Problem Full Connectivity Constraint: All adjacent tiles in assembled shape must share a full strength bond Slide 43 43 n x n Square: Full Connectivity Shifting Problem Jigsaw Technique: Use Geometry to enforce proper binding. Full Connectivity Constraint: All adjacent tiles in assembled shape must share a full strength bond Slide 44 44 n x n Square: Full Connectivity Jigsaw Technique: Use Geometry to enforce proper binding. Full Connectivity Constraint: All adjacent tiles in assembled shape must share a full strength bond Slide 45 45 n x n Square: Full Connectivity Jigsaw Technique: Use Geometry to enforce proper binding. Full Connectivity Constraint: All adjacent tiles in assembled shape must share a full strength bond Slide 46 46 n x n Square: Full Connectivity tiles / gluesO(1) BinsO(1) StagesO(log n) Temperature1 Staged Assembly Fully Connected n x n square tiles / glues (log n / log log n) Bins1 Stages1 Temperature2 Non-Staged Model Fully Connected n x n square [adleman, cheng, goel, huang STOC 2001] Slide 47 47 Arbitrary Shapes Spanning Tree Method Jigsaw Method for non-hole Shapes Simulation Method Slide 48 48 Simulate Large Tilesets Slide 49 49 Simulate Large Tilesets 0000 0001 0010 0011 0100 0101 0110 Slide 50 50 Simulate Large Tilesets 0000 0001 0010 0011 0100 0101 0110 0 1 Slide 51 51 Simulate Large Tilesets 0001 0000 0001 0011 0001 0011 0011 0000 0001 0010 0011 0100 0101 0110 Slide 52 52 Simulate Large Tilesets 001 0011 0000 0001 0010 0011 0100 0101 0110 1 Slide 53 53 Simulate Large Tilesets 00 0011 0000 0001 0010 0011 0100 0101 0110 10 Slide 54 54 Simulate Large Tilesets Slide 55 55 c Simulate Large Tilesets b a... Slide 56 56 Simulate Large Tilesets c b a 001 0011 1 0 0 1 0 0 10 0 001 0011 1 0 0 1 0 0 10 0 001 0011 1 0 0 1 0 0 10 0... tiles / gluesO(1) BinsO(|T|) StagesO(log log |T|) Simulate temp=1 tileset T tiles / gluesO(1) BinsO(n) StagesO(log log n) ScaleO(log n) Arbitrary n tile Shape Slide 57 57 Arbitrary Shape Assembly Spanning Tree Method Jigsaw Method for non-hole Shapes Simulation Method tiles / gluesO(1) BinsO(n) StagesO(n) Connectivity FULL Scale2 GeneralityHole Free Jigsaw Method tiles / gluesO(1) BinsO(log n) StagesO(diameter) Connectivity Partial Scale1 GeneralityALL Spanning Tree Method tiles / gluesO(1) BinsO(n) StagesO(log log n) Connectivity FULL ScaleO(log n) GeneralityALL Simulation Method Slide 58 58 tiles / gluesO(1) BinsO(1) StagesO(log n) Staged Assembly n x n square First Result: What if we have B bins? Near Optimal Tradeoff: Bins versus Stages (Crazy Mixing) Slide 59 59 tiles / gluesO(1) BinsO(1) StagesO(log n) Staged Assembly n x n square First Result: What if we have B bins? B^2 edges, Can encode B^2 Bits of information Per stage. Near Optimal Tradeoff: Bins versus Stages (Crazy Mixing) Slide 60 60 Near Optimal Tradeoff: Bins versus Stages (Crazy Mixing) tiles / gluesO(1) BinsB Stages ( log n / B^2) Lower Bound for almost all n tiles / gluesO(1) BinsB Stages ( log n / B^2 + log B) Upper Bound Assembly of n x n squares with B bins: Upper bound technique: -Encode B^2 bits describing target square at each stage -Combine with Simulation macro tiles. Slide 61 61 Staged Assembly permits various techniques for the assembly of arbitrary shapes with O(1) tiles/glues. For some shapes (squares) we achieve near optimal tradeoffs in bin versus stage complexity. Staged assembly may shed light on natural assembly systems Cells of body perhaps serve as bins Staged assembly emphasizes importance of geometric shape for bonding, perhaps similar to protein shape determining function. Conclusions Slide 62 62 Problems with model? Applications in DNA code design using synthetic DNA words? Incorporating produced structures as well as terminally produced structures Experiments, simulations Apply more intense mixing patterns to general shapes Tradeoffs between tile complexity and bin/stage complexity. Simulation of t=2 systems Future Work 001 0011 1 Slide 63 63 Thanks for listening. Questions?