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.
Natural Self-Assembly
Synthetic Self-Assembly with DNA
Our work:Study an abstract self-assembly model
based on DNA tile systems.
Staged self-assembly
Input Output
(polyomino)
(small staged assembly system)
Θ(log(n)) system size
Study a simplified model.
Finding small systems is (NP-)hard.
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.
Ω(n/log3n)
Ο(log(n))
Macrotile
Values are distinct
Values are contiguous
Shifting
[1..3] +4
Shifting
[4..6] +4
Activation
Shifting
[1..3] +4
Reagent 1
Reagent 2
Product
Activated reagent 1
Shifted reagent 2
Activated & shifted reagent 2
A R1
S R2
A & S R2
A R1
S R2
A & S R2
A R1
S R2
A & S R2
A R1
S R2
A & S R2
A R1
S R2
A & S R2
A R1
S R2
A & S R2
w/scalingΟ(log(n))
Ο(loglog(n))
…
Ω(n/loglog(n))
…
……
Ο(log(n))Ω(n/log2n)
Ο(log(n))
…
Ω(n/log2n)
…
Grammar Staged System Ο(1)
Ω(n1/2/log(n)), Ο(n2/3)
w/scaling
Ο(log(n))
Ω(n/log3n)
Grammars are small,staged systems are always
smaller
Thank youCommittee:
Diane Souvaine
Erik DemaineBen Hescott
Lenore Cowen
Hyunmin Yi
Collaborators:
Matthew Patitz
Sarah Eisenstat
Robert Schweller
Mashhood Ishaque
Damien Woods
NSF grants 0941538 and 0830734