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January 18, 2010

Shape Replication through Self-Assembly and Rnase Enzymes

Zachary Abel Harvard UniversityNadia Benbernou Massachusetts Institute of TechnologyMirela Damian Villanova UniversityErik D. Demaine Massachusetts Institute of TechnologyMartin Demaine Massachusetts Institute of TechnologyRobin Flatland Siena CollegeSkott D. Kominers Harvard UniversityRobert Schweller University of Texas Pan American

Read: Replicate:

2

Outline

• Basic Model• RNA enzyme model• Shape replication

• Precise yield shape replication• Infinite yield shape replication

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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

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)

5

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

t = 2d

e

x ed

cba

Tile Assembly Model(Rothemund, Winfree, Adleman)

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

t = 2d

e

x ed

cba

b c

Tile Assembly Model(Rothemund, Winfree, Adleman)

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

t = 2d

e

x ed

cba

b c

Tile Assembly Model(Rothemund, Winfree, Adleman)

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

t = 2d

e

x ed

cba

b c

Tile Assembly Model(Rothemund, Winfree, Adleman)

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

t = 2d

e

x ed

cba

b ca

Tile Assembly Model(Rothemund, Winfree, Adleman)

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

t = 2d

e

x ed

cba

b ca

Tile Assembly Model(Rothemund, Winfree, Adleman)

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

t = 2d

e

x ed

cba

b ca

Tile Assembly Model(Rothemund, Winfree, Adleman)

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

t = 2d

e

x ed

cba

b ca

Tile Assembly Model(Rothemund, Winfree, Adleman)

13

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)

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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)

15

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)

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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)

17

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)

18

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

(Basic)Tile Assembly Model(Rothemund, Winfree, Adleman)

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Outline

• Basic Model• RNA enzyme model• Shape replication

• Precise yield shape replication• Infinite yield shape replication

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RNA enzyme Self-Assembly(suggested by Rothemund, Winfree 2000)

RNA tile types DNA tile types

RNA assembly model: • Assembly occurs over a number of stages.

• At each stage you may:1) Add a new collection of tile types

- Allow for further growth- All added types have infinite count

2) Add an Rnase enzyme- Dissolve all RNA tile types- May break apart assemblies

All tile types are of either DNA or RNA makeup:

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RNA enzyme Self-Assembly

Stage 1:

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RNA enzyme Self-Assembly

Stage 1:

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RNA enzyme Self-Assembly

Stage 1:

Stage 2:

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RNA enzyme Self-Assembly

Stage 1:

Stage 2:

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RNA enzyme Self-Assembly

Stage 1:

Stage 2:

Stage 3: Enzyme

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RNA enzyme Self-Assembly

Stage 1:

Stage 2:

Stage 3: Enzyme

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RNA enzyme Self-Assembly

Stage 1:

Stage 2:

Stage 3: Enzyme

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RNA enzyme Self-Assembly

Stage 1:

Stage 2:

Stage 3: Enzyme

Stage 4:

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RNA enzyme Self-Assembly

Stage 1:

Stage 2:

Stage 3: Enzyme

Stage 4:

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RNA enzyme Self-Assembly

Stage 1:

Stage 2:

Stage 3: Enzyme

Stage 4:

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RNA enzyme Self-Assembly

Stage 1:

Stage 2:

Stage 3: Enzyme

Stage 4:

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RNA enzyme Self-AssemblyMetrics for efficiency:

• Tile complexity: total number of distinct tile types used in the system.

• Stage complexity: total number of distinct stages used.

Stage 1:

Stage 2:

Stage 3: Enzyme

Stage 4:

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Outline

• Basic Model• RNA enzyme model• Shape replication

• Precise yield shape replication• Infinite yield shape replication

Shape Replication Problem

Design an assembly system (algorithm) that will replicate a large number of copies given a single copy of a pre-assembled input shape.

Precise Yield: Replicate exactly n copies for a given n

Infinite Yield: Replicate infinite copies-in practice, the number of copies should only be limited by the volume of particles available.

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Outline

• Basic Model• RNA enzyme model• Shape replication

• Precise yield shape replication• Infinite yield shape replication

Precise Yield: rectangles

Precise Yield: rectangles

a a a aaaaaaa

a a a a

aaaaaa

Precise Yield: rectangles

n n n neeeeee

wwwwww

s s ss

Precise Yield: rectangles

n n n neeeeee

wwwwww

s s ss

n

w

x xyy

Precise Yield: rectangles

n n n neeeeee

wwwwww

s s ss

nw

Precise Yield: rectangles

n n n neeeeee

wwwwww

s s ss

nw n

e

sw s

e

Precise Yield: rectangles

n n n neeeeee

wwwwww

s s ss

nw

ne

sw s

e

Precise Yield: rectangles

n n n neeeeee

ww

w

w

ww

s s ss

a

wa

a

a

Precise Yield: rectangles

n ne

e

w

wss

Step 1: Coat shape with layer of RNA

Precise Yield: rectangles

n ne

e

w

wss

Step 2: Coat shape with layer of DNAStep 1: Coat shape with layer of RNA

Precise Yield: rectanglesStep 2: Coat shape with layer of DNA.Step 3: Add enzyme.

Step 1: Coat shape with layer of RNA.

Precise Yield: rectanglesStep 2: Coat shape with layer of DNA.Step 3: Add enzyme.

Step 1: Coat shape with layer of RNA.

Precise Yield: rectanglesStep 2: Coat shape with layer of DNA.Step 3: Add enzyme.Step 4: Coat frame with layer of RNA.

Step 1: Coat shape with layer of RNA.

Precise Yield: rectanglesStep 2: Coat shape with layer of DNA.Step 3: Add enzyme.Step 4: Coat frame with layer of RNA.

Step 1: Coat shape with layer of RNA.

Precise Yield: rectanglesStep 2: Coat shape with layer of DNA.Step 3: Add enzyme.Step 4: Coat frame with layer of RNA.Step 5: Fill frame with DNA.

Step 1: Coat shape with layer of RNA.

Precise Yield: rectanglesStep 2: Coat shape with layer of DNA.Step 3: Add enzyme.Step 4: Coat frame with layer of RNA.Step 5: Fill frame with DNA.

Step 1: Coat shape with layer of RNA.

Precise Yield: rectanglesStep 2: Coat shape with layer of DNA.Step 3: Add enzyme.Step 4: Coat frame with layer of RNA.Step 5: Fill frame with DNA.Step 6: Add enzyme.

Step 1: Coat shape with layer of RNA.

Precise Yield: rectanglesStep 2: Coat shape with layer of DNA.Step 3: Add enzyme.Step 4: Coat frame with layer of RNA.Step 5: Fill frame with DNA.Step 6: Add enzyme.

Step 1: Coat shape with layer of RNA.

Precise Yield: General Shapes

Precise Yield: General Shapes

Precise Yield: General Shapes

Precise Yield: rectangles

Tile types O(1)

Stages O(log n)

Precise Yield:n copies

Precise Yield: rectangles

Tile types O(log n)

Stages O(1)

Precise Yield:n copies

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Outline

• Basic Model• RNA enzyme model• Shape replication

• Precise yield shape replication• Infinite yield shape replication

Infinite Yield: Rectangles

n n n neeeeee

wwwwww

s s ss

Infinite Yield: Rectangles

n n n neeeeee

wwwwww

s s ss

sw

a

Infinite Yield: Rectangles

as

bs

bs

a

b

s sa

s

Stair step tiles:

xx

Infinite Yield: Rectangles

as

bs

bs

a

b

s s

Stair step tiles:

xx

bx

Infinite Yield: Rectangles

as

bs

bs

a

b

s s

Stair step tiles:

xx

a

b

Infinite Yield: Rectangles

as

bs

bs

a

b

s

s

Stair step tiles:

xx

ab

Infinite Yield: Rectangles

as

bs

bs

a

b

s

Stair step tiles:

xx

b

a

b

Infinite Yield: Rectangles

as

bs

bs

a

b

s

Stair step tiles:

xx

b

a

b

Infinite Yield: Rectangles

as

bs

bs

a

b

s

Stair step tiles:

xx

b

a

b

Infinite Yield: Rectangles

as

bs

bs

a

b

Stair step tiles:

xx

b

bb

a

Infinite Yield: Rectangles

as

bs

bs

a

b

Stair step tiles:

xx

Infinite Yield: Rectangles

as

bs

bs

a

b

Stair step tiles:

xx

Infinite Yield: Rectangles

as

bs

bs

a

b

Stair step tiles:

xx

…

Infinite Yield: Rectangles

…

Tile types O(1)

Stages O(1)

Infinite Yield:Rectangles

Infinite Yield: General Shapes

Infinite Yield: General ShapesStep 1: Coat with RNA

Infinite Yield: General ShapesStep 2: Create rectangular DNA encasing

Infinite Yield: Binary counter tool

c c c cc c c c c c c c c c c c c c c cc c cc

Infinite Yield: Binary counter tool

1 c c c cc c c c c c c c c c c c c c c cc c cm

0

0 10 0 1 1nn

nn

0 11 0 0 1cc

nc

1 m

m

xx

Binary counter tiles:

c01 mm

n

1

Infinite Yield: Binary counter tool

1 c c c cc c c c c c c c c c c c c c cc c c0 0

m

0

0 10 0 1 1nn

nn

0 11 0 0 1cc

nc

1 m

m

xx

Binary counter tiles:

c01 mm

n

1

Infinite Yield: Binary counter tool

1 c c c cc c c c c c c c c c c c c cc c c0

m

1 1n

0

0 10 0 1 1nn

nn

0 11 0 0 1cc

nc

1 m

m

xx

Binary counter tiles:

c01 mm

n

1

Infinite Yield: Binary counter tool

1 c c c cc c c c c c c c c c c c c cc c c

0

0 10 0 1 1nn

nn

0 11 0 0 1cc

nc

1 m

m

xx

Binary counter tiles:

c

0

0

m

1 1

1 mmn

1

1

Infinite Yield: Binary counter tool

1 c c c cc c c c c c c c c c c c cc c c

0

0 10 0 1 1nn

nn

0 11 0 0 1cc

nc

1 m

m

xx

Binary counter tiles:

c

0

0

1

1 mmn

10 0cm

1

Infinite Yield: Binary counter tool

1 c c c cc c c c c c c c c c c c cc c c

0

0 10 0 1 1nn

nn

0 11 0 0 1cc

nc

1 m

m

xx

Binary counter tiles:

c

0

0

m

1

1 mmn

10 0

10 0

1

Infinite Yield: Binary counter tool

1 c c c c c c c c c c c c c c c cc c c

0

0 10 0 1 1nn

nn

0 11 0 0 1cc

nc

1 m

m

xx

Binary counter tiles:

c

0

0

m

1

1 mmn

10

10 0

1 1n

1

Infinite Yield: Binary counter tool

1 c c c c c c c c c c c c c c c cc c c

0

0 10 0 1 1nn

nn

0 11 0 0 1cc

nc

1 m

m

xx

Binary counter tiles:

c

0

0

m

1

1 mmn

10

10

1 1

n0 0

1

Infinite Yield: Binary counter tool

1 c c c c c c c c c c c c c c c cc c c

0

0 10 0 1 1nn

nn

0 11 0 0 1cc

nc

1 m

m

xx

Binary counter tiles:

c

0

0

m

1

1 mmn

10

10

1 1

0 01

1

Infinite Yield: Binary counter tool

1

0

0 10 0 1 1nn

nn

0 11 0 0 1cc

nc

1 m

m

xx

Binary counter tiles:

c

0

0

1

1 mmn

10

10

101

011

111

000

100

010

101

1 1 1 1

011

111

1 1

0001

0 100

010

101

011

111

0 0 0 01 1 1 1

01

11

000

100

010

101

011

11

11

11

11

Infinite Yield: General Shapes

…

…

Infinite Yield: General Shapes

1 1 1 1 0 0 0 0 0 0

1 1 1 1 1 1

1 1 1 1 1

1 1 1 1 1 0 0 0 0 0 0

1 1 1 1 1 1

0 0 0 0 0 0

0 0 0 0

1 1 1 1

1 1 1 1 …

…

Infinite Yield: General Shapes

1 1 1 1 0 0 0 0 0 01 1 1 1 1 1

1 1 1 1 11 1 1 1 1 0 0 0 0 0 0

1 1 1 1 1 1

0 0 0 0 0 00 0 0 01 1 1 1

1 1 1 11 1 1 1 11 1 1 1 1

0 0 0 0 0 1 1 1 1 11 1 1 1 1

1 1 1 1 11 1 1 1 1

11

1 1 1 1 1 1 1 1 1 1 1 0 0 0 01 1 1 1

0 0 0 00 0 0 0

Infinite Yield: General Shapes

1 1 1 1 0 0 0 0 0 01 1 1 1 1 1

1 1 1 1 11 1 1 1 1 0 0 0 0 0 0

1 1 1 1 1 1

0 0 0 0 0 00 0 0 01 1 1 1

1 1 1 11 1 1 1 11 1 1 1 1

0 0 0 0 0 1 1 1 1 11 1 1 1 1

1 1 1 1 11 1 1 1 1

11

1 1 1 1 1 1 1 1 1 1 1 0 0 0 01 1 1 1

0 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 000 0 0 000 0 0 0

00

0 0 000 0 000 0 0 00 0 0 00 00 0 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 01 1 1 1 1

1 1 1 1 11 1 1 1 1 0 0 0 0 0 0

1 1 1 1 1 1

0 0 0 0 0 00 0 0 01 1 1 1

1 1 1 1

0 0 0 00 0 0 000 0 0 00 0 0 0

00

0 0 000 0 000 0 0 0 0 0 00 00 0 0 0 0 0

01

1

0

0 0 0 0 0 01 1 1 1 1 1

0 0 0 0 0 0

0 0 0 00 0

0 01 1

0 0

0 0

1 1 1 100 0 000 0 000 0 0

1000

Step 3: Label each face with unique binary code

Infinite Yield: General Shapes

1 1 1 1 0 0 0 0 0 01 1 1 1 1 1

1 1 1 1 11 1 1 1 1 0 0 0 0 0 0

1 1 1 1 1 1

0 0 0 0 0 00 0 0 01 1 1 1

1 1 1 11 1 1 1 11 1 1 1 1

0 0 0 0 0 1 1 1 1 11 1 1 1 1

1 1 1 1 11 1 1 1 1

11

1 1 1 1 1 1 1 1 1 1 1 0 0 0 01 1 1 1

0 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 000 0 0 000 0 0 0

00

0 0 000 0 000 0 0 00 0 0 00 00 0 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 01 1 1 1 1

1 1 1 1 11 1 1 1 1 0 0 0 0 0 0

1 1 1 1 1 1

0 0 0 0 0 00 0 0 01 1 1 1

1 1 1 1

0 0 0 00 0 0 000 0 0 00 0 0 0

00

0 0 000 0 000 0 0 0 0 0 00 00 0 0 0 0 0

01

1

0

0 0 0 0 0 01 1 1 1 1 1

0 0 0 0 0 0

0 0 0 00 0

0 01 1

0 0

0 0

1 1 1 100 0 000 0 000 0 0

1000

Step 4: Enzyme.

Infinite Yield: General Shapes

0 0 0 01 1 1 1

1 1 1 1

0 0 0 0

…

0 0 0 01 1 1 1

1 1 1 1

0 0 0 0

0 0 0 01 1 1 1

1 1 1 1

0 0 0 0

0 0 0 01 1 1 1

1 1 1 1

0 0 0 0

0 0 0 01 1 1 1

1 1 1 1

0 0 0 0

Step 5: Infinitely replicate all labeled rectangles

Infinite Yield: General Shapes

1 1 1 1 0 0 0 0 0 01 1 1 1 1 1

1 1 1 1 11 1 1 1 1 0 0 0 0 0 0

1 1 1 1 1 1

0 0 0 0 0 00 0 0 01 1 1 1

1 1 1 11 1 1 1 11 1 1 1 1

0 0 0 0 0 1 1 1 1 11 1 1 1 1

1 1 1 1 11 1 1 1 1

11

1 1 1 1 1 1 1 1 1 1 1 0 0 0 01 1 1 1

0 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 000 0 0 000 0 0 0

00

0 0 000 0 000 0 0 00 0 0 00 00 0 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 01 1 1 1 1

1 1 1 1 11 1 1 1 1 0 0 0 0 0 0

1 1 1 1 1 1

0 0 0 0 0 00 0 0 01 1 1 1

1 1 1 1

0 0 0 00 0 0 000 0 0 00 0 0 0

00

0 0 000 0 000 0 0 0 0 0 00 00 0 0 0 0 0

01

1

0

0 0 0 0 0 01 1 1 1 1 1

0 0 0 0 0 0

0 0 0 00 0

0 01 1

0 0

0 0

1 1 1 100 0 000 0 000 0 0

1000

Infinite Yield: General ShapesReassembly?

0 0 0 01 1 1 1

1 1 1 1

0 0 0 0

0 0 0 0 0 01 1 1 1 1 1

0 0 0 0 0 0

0 0 0 00 0

Infinite Yield: General ShapesReassembly?

0 0 0 11 1 1 1

1 1 1 0

0 0 0 0

0 0 0 0 0 01 1 1 1 1 1

0 0 0 0 0 1

0 0 0 00 0

Infinite Yield: General ShapesReassembly?

0 0 0 11 1 1 1

1 1 1 0

0 0 0 0

0 0 0 0 0 01 1 1 1 1 1

0 0 0 0 0 1

0 0 0 00 0

Infinite Yield: General ShapesReassembly?

0 0 0 11 1 1 1

1 1 1 0

0 0 0 0

0 0 0 0 0 01 1 1 1 1 1

0 0 0 0 0 1

0 0 0 00 00101

0 11 00 01 1

10

1

1

Infinite Yield: General Shapes

1 1 1 1 0 0 0 0 0 01 1 1 1 1 1

1 1 1 1 11 1 1 1 1 0 0 0 0 0 0

1 1 1 1 1 1

0 0 0 0 0 00 0 0 01 1 1 1

1 1 1 11 1 1 1 11 1 1 1 1

0 0 0 0 0 1 1 1 1 11 1 1 1 1

1 1 1 1 11 1 1 1 1

11

1 1 1 1 1 1 1 1 1 1 1 0 0 0 01 1 1 1

0 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 000 0 0 000 0 0 0

00

0 0 000 0 000 0 0 00 0 0 00 00 0 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 01 1 1 1 1

1 1 1 1 11 1 1 1 1 0 0 0 0 0 0

1 1 1 1 1 1

0 0 0 0 0 00 0 0 01 1 1 1

1 1 1 1

0 0 0 00 0 0 000 0 0 00 0 0 0

00

0 0 000 0 000 0 0 0 0 0 00 00 0 0 0 0 0

01

1

0

0 0 0 0 0 01 1 1 1 1 1

0 0 0 0 0 0

0 0 0 00 0

0 01 1

0 0

0 0

1 1 1 100 0 000 0 000 0 0

1000

Step 6: Reassemble, fill in frame, break out copies with enzyme.

Infinite Yield: General Shapes

1 1 1 1 0 0 0 0 0 01 1 1 1 1 1

1 1 1 1 11 1 1 1 1 0 0 0 0 0 0

1 1 1 1 1 1

0 0 0 0 0 00 0 0 01 1 1 1

1 1 1 11 1 1 1 11 1 1 1 1

0 0 0 0 0 1 1 1 1 11 1 1 1 1

1 1 1 1 11 1 1 1 1

11

1 1 1 1 1 1 1 1 1 1 1 0 0 0 01 1 1 1

0 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 000 0 0 000 0 0 0

00

0 0 000 0 000 0 0 00 0 0 00 00 0 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 01 1 1 1 1

1 1 1 1 11 1 1 1 1 0 0 0 0 0 0

1 1 1 1 1 1

0 0 0 0 0 00 0 0 01 1 1 1

1 1 1 1

0 0 0 00 0 0 000 0 0 00 0 0 0

00

0 0 000 0 000 0 0 0 0 0 00 00 0 0 0 0 0

01

1

0

0 0 0 0 0 01 1 1 1 1 1

0 0 0 0 0 0

0 0 0 00 0

0 01 1

0 0

0 0

1 1 1 100 0 000 0 000 0 0

1000

Tile types O(1)

Stages O(1)

Infinite Yield:Vertically convex

Infinite Yield: Non-vertically convex shapes

• Grow counter along surface of shape

000100100011

0100

0101

0110

0111

1000

1001

1010

• Grow counter along surface of shape

Start end

Infinite Yield: Non-vertically convex shapes

0001

0010

0011

0100

0101

0110

0111

1000

1001

1010

• Grow counter along surface of shape

• Break apart with enzyme

Infinite Yield: Non-vertically convex shapes

0001

0010

0011

0100

0101

0110

0111

1000

1001

1010

• Grow counter along surface of shape

• Break apart

with enzyme

• Replicate

Infinite Yield: Non-vertically convex shapes

0001

0010

0011

0100

0101

0110

0111

1000

1001

1010

• Grow counter along surface of shape

• Break apart

with enzyme

• Replicate

• Reassemble

Infinite Yield: Non-vertically convex shapes

0001

00100011

0100

0101

0110

0111

1000

1001

1010

• Grow counter along surface of shape

• Break apart

with enzyme

• Replicate

• Reassemble

Infinite Yield: Non-vertically convex shapes

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Tile types O(1)

Stages O(1)

Infinite Yield:

Infinite Yield: General Shapes

Future Work

• Replicate and improve-Hybrid algorithms for replication and modification

• Extension to 3D-Planarity/spacial constraint

• Replication of internal pattern

• Staged enzyme model for assembly from scratch- Seems to be very powerful for this

• Temperature changes to perform replication

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January 18, 2010

Thank you. Questions?

Zachary Abel Harvard UniversityNadia Benbernou Massachusetts Institute of TechnologyMirela Damian Villanova UniversityErik D. Demaine Massachusetts Institute of TechnologyMartin Demaine Massachusetts Institute of TechnologyRobin Flatland Siena CollegeSkott D. Kominers Harvard UniversityRobert Schweller University of Texas Pan American

Read: Replicate: