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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 Demaine Massachusetts Institute of Technology Martin Demaine Massachusetts Institute of Technology Sandor Fekete Technische Universität Braunschweig Mashood Ishaque Tufts University Eynat Rafalin Google Robert Schweller University of Texas Pan American Diane Souvaine Tufts University
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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.

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

1

Thirteenth International Meeting on DNA Computers

June 5, 2007

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

Eric Demaine Massachusetts Institute of TechnologyMartin Demaine Massachusetts Institute of TechnologySandor Fekete Technische Universität BraunschweigMashood Ishaque Tufts UniversityEynat Rafalin GoogleRobert Schweller University of Texas Pan AmericanDiane Souvaine Tufts University

Page 2: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

2

Tile Assembly Model(Rothemund, Winfree, Adleman)

T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

Tile Set:

Glue Function:

Temperature:

x ed

cba

Page 3: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

d

e

x ed

cba

Tile Assembly Model(Rothemund, Winfree, Adleman)

Page 4: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

4

T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

d

e

x ed

cba

Tile Assembly Model(Rothemund, Winfree, Adleman)

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

5

T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

d

e

x ed

cba

b c

Tile Assembly Model(Rothemund, Winfree, Adleman)

Page 6: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

d

e

x ed

cba

b c

Tile Assembly Model(Rothemund, Winfree, Adleman)

Page 7: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

d

e

x ed

cba

b c

Tile Assembly Model(Rothemund, Winfree, Adleman)

Page 8: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

8

T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

d

e

x ed

cba

b ca

Tile Assembly Model(Rothemund, Winfree, Adleman)

Page 9: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

d

e

x ed

cba

b ca

Tile Assembly Model(Rothemund, Winfree, Adleman)

Page 10: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

10

T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

d

e

x ed

cba

b ca

Tile Assembly Model(Rothemund, Winfree, Adleman)

Page 11: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

d

e

x ed

cba

b ca

Tile Assembly Model(Rothemund, Winfree, Adleman)

Page 12: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

x ed

cba

a b c

d

e

Tile Assembly Model(Rothemund, Winfree, Adleman)

Page 13: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

x ed

cba

x

a b c

d

e

Tile Assembly Model(Rothemund, Winfree, Adleman)

Page 14: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

a b c

d

e

x

x ed

cba

Tile Assembly Model(Rothemund, Winfree, Adleman)

Page 15: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

x ed

cba

a b c

d

e

x x

Tile Assembly Model(Rothemund, Winfree, Adleman)

Page 16: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

16

T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

x ed

cba

a b c

d

e

x x

x

Tile Assembly Model(Rothemund, Winfree, Adleman)

Page 17: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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T = G(y) = 2G(g) = 2G(r) = 2G(b) = 2G(p) = 1G(w) = 1

t = 2

x ed

cba

a b c

d

e

x x

x x

Tile Assembly Model(Rothemund, Winfree, Adleman)

Page 18: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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BEAKER

Start with initial Tileset

Non-Staged Assembly

-Assembly occurs within 1 single container

- Assembly occurs within 1 single stage

Page 19: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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BEAKERBEAKER

Aftersome time...

Start with initial Tileset Various Producible Supertilesexist in solution

Non-Staged Assembly

-Assembly occurs within 1 single container

- Assembly occurs within 1 single stage

Page 20: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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BEAKERBEAKER BEAKER

Aftersome time...

After enough time...

Start with initial Tileset Various Producible Supertilesexist in solution

Only Terminally Producedassemblies remain

Non-Staged Assembly

-Assembly occurs within 1 single container

- Assembly occurs within 1 single stage

Page 21: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Staged Assembly

Page 22: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Staged Assembly

-Pour multiple bins into a single bin

Page 23: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Staged Assembly

-Pour multiple bins into a single bin-Split contents of any given bin among multiple new bins

Page 24: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Staged Assembly

-Pour multiple bins into a single bin-Split contents of any given bin among multiple new bins

Page 25: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Staged Assembly

Page 26: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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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:

Page 27: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Staged Assembly• Assembly occurs in a sequence of stages, and

assemblies can be separated into separate bins

Bins = Space ComplexityStages = Time Complexity

Bin Complexity: 4

Stage Complexity: 3

Page 28: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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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.

Page 29: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Simple Example: 1 x n line

Page 30: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Simple Example: 1 x n line

Page 31: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Simple Example: 1 x n line

Page 32: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Simple Example: 1 x n line

stage i

stage i+3

Page 33: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Simple Example: 1 x n line

stage i

stage i+3

tiles / glues O(1) = 3

Bins O(1)

Stages O(log n)

Staged Assembly1 x n line

Page 34: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Simple Example: 1 x n line

stage i

stage i+3

tiles / glues O(1) = 3

Bins O(1)

Stages O(log n)

Staged Assembly1 x n line

tiles / glues (n)

Bins 1

Stages 1

Non-Staged Model1 x n line

Page 35: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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n x n Square

Page 36: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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n x n Square

Base Case1 x n line:Use linealgorithm

tiles / glues O(1)

Bins O(1)

Stages O(log n)

Staged Assemblyn x n square

Page 37: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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n x n Square: unstable?

Page 38: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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n x n Square: unstable?

Page 39: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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n x n Square: unstable?

Page 40: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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n x n Square: Full Connectivity

Full Connectivity Constraint: All adjacent tiles inassembled shape mustshare a full strength bond

[Rothemund, Winfree STOC 2000]

Page 41: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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n x n Square: Full Connectivity

Full Connectivity Constraint: All adjacent tiles inassembled shape mustshare a full strength bond

Page 42: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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n x n Square: Full Connectivity

Shifting Problem

Full Connectivity Constraint: All adjacent tiles inassembled shape mustshare a full strength bond

Page 43: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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n x n Square: Full Connectivity

Shifting Problem

Jigsaw Technique:Use Geometryto enforce properbinding.

Full Connectivity Constraint: All adjacent tiles inassembled shape mustshare a full strength bond

Page 44: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

44

n x n Square: Full Connectivity

Jigsaw Technique:Use Geometryto enforce properbinding.

Full Connectivity Constraint: All adjacent tiles inassembled shape mustshare a full strength bond

Page 45: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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n x n Square: Full Connectivity

Jigsaw Technique:Use Geometryto enforce properbinding.

Full Connectivity Constraint: All adjacent tiles inassembled shape mustshare a full strength bond

Page 46: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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n x n Square: Full Connectivity

tiles / glues O(1)

Bins O(1)

Stages O(log n)

Temperature 1

Staged AssemblyFully Connected

n x n square

tiles / glues (log n / log log n)

Bins 1

Stages 1

Temperature 2

Non-Staged ModelFully Connected

n x n square

[adleman, cheng, goel, huang STOC 2001]

Page 47: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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

Page 48: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Simulate Large Tilesets

Page 49: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Simulate Large Tilesets

0000

0001

0010

0011

0100

0101

0110

Page 50: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Simulate Large Tilesets

0000

0001

0010

0011

0100

0101

0110

0

1

Page 51: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Simulate Large Tilesets

0 0 0 1

0 0 0 0

0 0 01

0 0 1 1

0 0 01

0 01 1

0 01 1

0000

0001

0010

0011

0100

0101

0110

Page 52: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Simulate Large Tilesets

0 01

0 01 1

0000

0001

0010

0011

0100

0101

0110

1

Page 53: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Simulate Large Tilesets

0 0

0 01 1

0000

0001

0010

0011

0100

0101

0110

10

Page 54: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Simulate Large Tilesets

0 01

0 01 1

1

00

1

00

1 0

0

Page 55: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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c

Simulate Large Tilesets

b

a

0 01

0 01 1

1

00

1

00

1 0

0

0 01

0 01 1

1

00

1

00

1 0

0

0 01

0 01 1

1

00

1

00

1 0

0

. . .

Page 56: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Simulate Large Tilesets

c

b

a

0 01

0 01 1

1

00

1

00

1 0

0

0 01

0 01 1

1

00

1

00

1 0

0

0 01

0 01 1

1

00

1

00

1 0

0

. . .

tiles / glues O(1)

Bins O(|T|)

Stages O(log log |T|)

Simulate temp=1 tileset T

tiles / glues O(1)

Bins O(n)

Stages O(log log n)

Scale O(log n)

Arbitrary n tile Shape

Page 57: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Arbitrary Shape Assembly

• Spanning Tree Method• Jigsaw Method for non-hole Shapes• Simulation Method

tiles / glues O(1)

Bins O(n)

Stages O(n)

Connectivity FULL

Scale 2

Generality Hole Free

Jigsaw Method

tiles / glues O(1)

Bins O(log n)

Stages O(diameter)

Connectivity Partial

Scale 1

Generality ALL

Spanning Tree Method

tiles / glues O(1)

Bins O(n)

Stages O(log log n)

Connectivity FULL

Scale O(log n)

Generality ALL

Simulation Method

Page 58: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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tiles / glues O(1)

Bins O(1)

Stages O(log n)

Staged Assemblyn x n square

First Result:

What if we have B bins?

Near Optimal Tradeoff: Bins versus Stages(Crazy Mixing)

Page 59: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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tiles / glues O(1)

Bins O(1)

Stages O(log n)

Staged Assemblyn x n square

First Result:

What if we have B bins?

B^2 edges, Can encode B^2Bits of informationPer stage.

Near Optimal Tradeoff: Bins versus Stages(Crazy Mixing)

Page 60: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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Near Optimal Tradeoff: Bins versus Stages(Crazy Mixing)

tiles / glues O(1)

Bins B

Stages ( log n / B^2)

Lower Bound for almost all n

tiles / glues O(1)

Bins B

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.

Page 61: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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

Page 62: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

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• 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

0 01

0 01 1

1

Page 63: 1 Thirteenth International Meeting on DNA Computers June 5, 2007 Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues Eric DemaineMassachusetts.

63

Thanks for listening. Questions?