Download Molecular Self-assembly

Algorithmic Self-Assembly at the Nano-Scale
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Ashish Goel
Stanford University
http://www.stanford.edu/~ashishg
Joint work with Len Adleman, Holin Chen, Qi Cheng,
Ming-Deh Huang, Pablo Moisset, Paul Rothemund,
Rebecca Schulman, Erik Winfree
Counter made by self-assembly
[Rothemund, Winfree ’00] [Adleman, Cheng, Goel, Huang ’01] [Cheng, Goel, Moisset ‘04]
Molecular Self-assembly


Self-assembly is the spontaneous formation of a complex
by small (molecular) components under simple
combination rules

Geometry, dynamics, combinatorics are all important

Inorganic: Crystals, supramolecules

Organic: Proteins, DNA
Goals: Understand self-assembly, design self-assembling
systems

A key problem in nano-technology, molecular robotics,
molecular computation
Ashish Goel, ashishg@stanford.edu
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A Matter of Scale
Question: Why an algorithmic study of “molecular” selfassembly specifically?
Answer: The scale changes everything

Consider assembling micro-level (or larger) components, eg.
robot swarms. Can attach rudimentary computers, motors,
radios to these structures.
• Can now implement an intelligent distributed algorithm.

In molecular self-assembly, we have nano-scale components.
No computers. No radios. No antennas.
• Need local rules such as “attach to another component if it has a
complementary DNA strand”

Self-assembly at larger scales is interesting, but is more a subdiscipline of distributed algorithms, artificial intelligence etc.
Ashish Goel, ashishg@stanford.edu
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The Tile Model of Self-Assembly
Oriented Tiles with a glue on each side [Wang ’61]
– Each glue is labeled by a strength
a
b
Single bar: strength 1 glue
Double bar: strength 2 glue
b
d
– Tiles floating on an infinite grid; Temperature 
– A tile can add to an existing assembly if
total strength of matching glues  
d
f
a
b
b
c
b
Ashish Goel, ashishg@stanford.edu
a
τ=2
c
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Synthesized Tile Systems – I

Styrene molecules attaching to a Silicon substrate

Coat Silicon substrate with Hydrogen

Remove one Hydrogen atom and bombard with Styrene
molecules

One Styrene molecule attaches, removes another Hydrogen
atom, resulting in a chain

Suggested use: Self-assembled molecular wiring on electronic
circuits
[Wolkow et al. ’00]
Ashish Goel, ashishg@stanford.edu
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Synthesized Tile Systems - II
A DNA “rug” assembled using DNA “tiles”
The rug is roughly 500 nm wide, and is assembled using
DNA tiles roughly 12nm by 4nm (false colored)
(Due to Erik Winfree, Caltech)
Ashish Goel, ashishg@stanford.edu
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Rothemund’s DNA Origami
A self-folded virus!!
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Ashish Goel, ashishg@stanford.edu
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Abstract Tile Systems

Tile: the four glues and their strengths

Tile System:

K tiles
• Infinitely many copies available of each tile


Temperature 
Accretion Model:

Assembly starts with a single seed tile, and proceeds by
repeated addition of single tiles e.g. Crystal growth

Are interested primarily in tile systems that assemble into a
unique terminal structure
[Rothemund and Winfree ‘00] [Wang ‘61]
Ashish Goel, ashishg@stanford.edu
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Is Self-Assembly Just Crystallization?

Crystals do not grow into unique terminal structures


Crystals are typically made up of a small number of different types
of components


Two types of proteins; a single Carbon molecule
Crystals have regular patterns


A sugar crystal does not grow to precisely 20nm
Computer circuits, which we would like to self-assemble, don’t
Molecular Self-assembly = combinatorics + crystallization

Can count, make interesting patterns

Nature doesn’t count too well, so molecular self-assembly is a genuinely
new engineering paradigm. Think engines. Think semiconductors.
Ashish Goel, ashishg@stanford.edu
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DNA and Algorithmic Self-Assembly
We will tacitly assume that the tiles are made of DNA strands woven
together, and that the glues are really free DNA strands

DNA is combinatorial, i.e., the functionality of DNA is determined largely
by the sequence of ACTG bases. Can ignore geometry to a first order.
• Trying to “count” using proteins would be hell

Proof-of-concept from nature: DNA strands can attach to “combinatorially”
matching sequences

DNA tiles have been constructed in the lab, and DNA computation has been
demonstrated

Can simulate arbitrary tile systems, so we do not lose any theoretical
generality, but we get a concrete grounding in the real world

The correct size (in the nano-range)
Ashish Goel, ashishg@stanford.edu
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A Roadmap for Algorithmic Self-Assembly

Self-assembly as a combinatorial process

The computational power of self-assembly

Self-assembling interesting shapes and patterns, efficiently
• Automating the design process?


Analysis of program size and assembly time
Self-assembly as a chemical reaction
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Entropy, Equilibria, and Error Rates
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Reversibility

Connections to experiments

Self-assembly as a machine
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Not just assemble something, but perform work

Much less understood than the first three
Ashish Goel, ashishg@stanford.edu
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Can we create efficient counters?
Ashish Goel, ashishg@stanford.edu
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Can we create efficient counters?
Yes! Eg. Using “Chinese remaindering”
T=2
Ashish Goel, ashishg@stanford.edu
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Can we create efficient counters?
Yes! Eg. Using “Chinese remaindering”
T=2
Ashish Goel, ashishg@stanford.edu
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Can we create efficient counters?
Yes! Eg. Using “Chinese remaindering”
T=2
Ashish Goel, ashishg@stanford.edu
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Can we create efficient counters?
Yes! Eg. Using “Chinese remaindering”
T=2
Ashish Goel, ashishg@stanford.edu
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Can we create efficient counters?
Yes! Using “Chinese remaindering”
T=2
Ashish Goel, ashishg@stanford.edu
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Can we create efficient counters?
Yes! Eg. Using “Chinese remaindering”
T=2
Generalizing:
Say p1, p2, …, pk
are distinct primes.
We can use i pi tiles
to assemble a
k £ (i pi) rectangle.
Ashish Goel, ashishg@stanford.edu
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Molecular machines
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Ashish Goel, ashishg@stanford.edu
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand Invasion
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Strand
Invasion
Strand
Invasion
(cont)
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Strand Invasion
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