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Staged Self-Assembly andPolyomino Context-Free
GrammarsAndrew Winslow
Defense Edition
Simple particles coalescing into complex superstructures.
Self-Assembly
Self-AssemblySimple particles coalescing into
complex superstructures.
Self-AssemblySimple particles coalescing into
complex superstructures.
Self-AssemblySimple particles coalescing into
complex superstructures.
Crystallization
Morphogenesis
Natural Self-Assembly
Synthetic Self-Assembly with DNA
Tile
Glues
Our work:Study an abstract self-assembly model
based on DNA tile systems.
Tile
Glues
Assembly
Mixing
Bin
Reagents
Products
Size
Staged self-assembly
Input Output
(polyomino)
(small staged assembly system)
n
Input
Θ(n) system size
Θ(log(n)) system size
n
Θ(n) Θ(log(n))
Input
Study a simplified model.
Finding small systems is (NP-)hard.
Rule
Grammar
Ο(#glues2)Ω(n1/2/log(n)), Ο(n2/3)
Staged System
? ? ?
One dimension
Ο(1)
E. D. Demaine, S. Eisenstat, M. Ishaque, A. Winslow, One-dimensional staged self-assembly, DNA 17, 2011.
Grammar
? ? ?
? ? ? ?
Polyomino Grammar
w/scaling
Two dimensions
Grammar Staged System
……
A. Winslow, Staged Self-Assembly and Polyomino Context-Free Grammars, DNA 19, 2013.