explorations of theory and programming in self-assembly
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Explorations of Theory and Programming in Self-Assembly. Matthew J. Patitz Department of Computer Science University of Texas-Pan American 10/19/2010. Introduction to self-assembly. Q: What is self-assembly?. - PowerPoint PPT PresentationTRANSCRIPT
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Matthew J. Patitz
Explorations of Theory and Programming in Self-Assembly
Matthew J. PatitzDepartment of Computer ScienceUniversity of Texas-Pan American
10/19/2010
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Matthew J. Patitz
Introduction to self-assembly
A: The process by which relatively simple components in a disorganized state autonomously combine to form more complex objects
Q: What is self-assembly?
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Matthew J. Patitz
Introduction to self-assembly
Q: What self-assembles?A: Many structures at many scales! Examples include:
• Crystals (such as snowflakes)• Biological structures (e.g. viruses)• Cosmic structures (e.g. galaxies)
Images courtesy of SnowCrystals.com
Image courtesy of NSF.gov Image courtesy of hubblesite.org
A: The process by which relatively simple components in a disorganized state autonomously combine to form more complex objects
Q: What is self-assembly?
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Matthew J. Patitz
Introduction to self-assembly
Q: What self-assembles?A: Many structures at many scales! Examples include:
• Crystals (such as snowflakes)• Biological structures (e.g. viruses)• Galaxies
A: The process by which relatively simple components in a disorganized state autonomously combine to form more complex objects
Q: What is self-assembly?
Q: Why study self-assembly?A: Several reasons:
• Better understand origin and functioning of living systems• Mathematically interesting properties• Eventual creation of ‘fantastic’ technologies
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Matthew J. Patitz
Directions in self-assembly research
Toward atomically-precise manufacturingIBM-Caltech collaboration to use self-assembled molecules to guide design of smaller processors
Credit: PRNewsFoto/IBM
Nano biomedical devicesAarhus University Center for DNA Nanotechnology’s box with programmable lid
Credit: : Ebbe S. Andersen, Aarhus University
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Matthew J. Patitz
Researchers study both natural and artificial self-assembling systems
Theoretical as well as experimental work
My focus is on theoretical research into an artificial model, which I will now introduce…
Directions in self-assembly research
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Matthew J. Patitz
Tile Assembly Model
Erik Winfree introduced the Tile Assembly Model (TAM) in 1998
It was later refined by Paul Rothemund
The TAM is based on experimental work with DNA molecules by Ned Seeman
* Both Winfree and Rothemund have both been named MacArthur Fellows
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Matthew J. Patitz
Tile Assembly Model
DNA molecules formed into shapes such as Holliday junctions can be treated logically as 2-dimensional squares
Molecular structure of a Holliday junction(Image courtesy of Wikipedia)
Schematic view of Holliday junction with extended
‘sticky ends’
With the ‘sticky ends’ treated as glues, these molecules can be
thought of as square ‘tiles’
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Matthew J. Patitz
Tile Assembly Model
Fundamental components are 2-D square tilesEach side has an associated glue, with:
A type (usually represented by a string value)An integer-valued strength (usually 0, 1, or 2)
Tiles can also have labels (non-functional, for convenience)Tiles cannot be rotatedFinite number of different tile types
An infinite supply of each tile typeAbutting sides of tiles bind if both glue strengths and values match
Those sides bind with that shared strengthA tile can bind to an assembly if the sum of binding strengths is at least equal to the “temperature” value of the system (usually 1 or 2)
Assembly begins from a “seed” tile or assembly and grows 1 tile at a time
Strength 0 Strength 1 Strength 2
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Matthew J. Patitz
Temperature value = 2Seed = (S, (0,0))
Tile assembly example
Strength 0 Strength 1 Strength 2
Tile set:
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Matthew J. Patitz
Tile assembly example
Attachment by 2 strength-1 bonds is a form of “cooperation” between multiple tiles that gives the model great power
5
4
3
2
1
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Matthew J. Patitz
Tile Assembly Model
A tile assembly system (TAS) is an ordered triple T =(T,σ,)
T is the tile set (a set of tile types)σ defines the seed assembly (tile types and locations)is an integer value specifying the temperature (the minimum total binding strength required for a tile to adhere to an assembly)
A TAS is directed if it has a single, unique final assembly
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Matthew J. Patitz
Self-assembly of shapes
Any finite shape can trivially be self-assembled by creating a hard-coded tile type for every position in the shape.
To test the theoretical limits of the TAM, we explore infinite shapes
Self-similar fractals are interesting infinite shapes because of their complex, aperiodic nature
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Matthew J. Patitz
A (non-trivial) discrete self-similar fractal is a recursively defined, infinite set of integer lattice points having fractal dimension more than 1 but less than 2.
c
The second stage is the generator of the fractal.
Discrete self-similar fractals
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Matthew J. Patitz
Example Discrete Self-Similar Fractal:The Sierpinski Carpet
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Matthew J. Patitz
Self-assembly of discrete self-similar fractals
In Self-Assembly of Discrete Self-Similar Fractals, Patitz and Summers showed that there are classes of discrete self-similar fractals that don’t self-assemble in the TAM
We [Patitz and Summers] also proved that for an overlapping class, there are approximations that do self-assemble
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Matthew J. Patitz
Self-assembly of discrete self-similar fractals
A pinch point discrete self-similar fractal is a discrete self-similar fractal having a “special” kind of generator.
The generator must be connected.
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Matthew J. Patitz
Self-assembly of discrete self-similar fractals
Theorem. No pinch point discrete self-similar fractal strictly self-assembles in a directed tile assembly system (at any temperature).
Why? Because of the geometry of pinch point discrete self-similar fractals.
Question. Do any non-trivial discrete self-similar fractals strictly self-assemble?
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Matthew J. Patitz
Self-assembly of discrete self-similar fractals
A nice discrete self-similar fractal is any discrete self-similar fractal whose generator looks like this…
But NOT these…
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Matthew J. Patitz
Self-assembly of discrete self-similar fractals
For any nice self-similar fractal, we can apply “fiber” to it as follows.
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Matthew J. Patitz
Self-assembly of discrete self-similar fractals
Start with the third stage of any nice self-similar fractal.
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Matthew J. Patitz
Self-assembly of discrete self-similar fractals
Add some fiber.
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Matthew J. Patitz
Self-assembly of discrete self-similar fractals
Recursively build the next stage.
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Matthew J. Patitz
Self-assembly of discrete self-similar fractals
And repeat!
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Matthew J. Patitz
Fibered Sierpinski carpet
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Matthew J. Patitz
Theorem. Every nice self-similar fractal has a fibered version that strictly self-assembles and has the same fractal dimension as its non-fibered counter-part. [Patitz and Summers, 2008]
Self-assembly of discrete self-similar fractals
On to programming tools now…
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Matthew J. Patitz
Simulation of Self-Assembly in the Abstract Tile Assembly Model with ISU TAS
Matthew J. Patitz
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Matthew J. Patitz
(Iowa State University Tile Assembly Simulator)
Overview of ISU TAS
Open sourceC++ application based on wxWidgets
Cross platform (Windows, Linux, Mac)
Graphical tile set editorSimulator
Many debugging featuresSupports several variations of the model
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Matthew J. Patitz
Tile set editor
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Matthew J. Patitz
Provides a simple graphical representation of the tile set (separate from simulator)
Allows creation of new tiles and editing of existing tiles
Functionality for copying, pasting, rotating, searching, etc.
Displays tile set information such as which tiles are functional duplicates of each other, which tiles are used in the current assembly, etc.
Tile set editor
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Matthew J. Patitz
Simulator
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Matthew J. Patitz
3-D
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Matthew J. Patitz
Simulations of assemblies begin from a user-defined seed
Simulations can proceed in single steps or in fast-forward mode
Steps are cached, so simulations can also be ‘rewound’
User can set arbitrary zoom factorsAn overview window shows the entire assembly
Frontier locations can be highlighted and toggled
Simulator
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Matthew J. Patitz
Downloading the software
ISU TAS, the fractal generator, and other related software is all freely available (both the
executables and the source code) from the following web site:
http://www.cs.iastate.edu/~lnsa
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Matthew J. Patitz
Roadmap for the futureMany open problems in the TAM yet to explore
Collaborations will be keyFractals, temperature 1, computations vs. space requirements, fault tolerance, etc.
Moving beyond the TAMIt’s an elegant and powerful modelExtremely basic – doesn’t reflect complexity of biological systemsCreate new, more powerful models
Examples:2-handed assemblyDNA/RNA tiles model
“Reusable” space, greater impact of geometryDynamic, adaptable componentsEmphasis on experimental practicalityTheory, programming tools, and laboratory experimentation
Inter-disciplinary research – let’s implement them in the lab!
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Matthew J. Patitz
Thank you!