January 18, 2010
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Transcript of January 18, 2010
1
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:
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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)
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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)
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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)
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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)
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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)
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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)
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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
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
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
107
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
109
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
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