Staged self assembly and polyomino context free grammars
This presentation is the property of its rightful owner.
Sponsored Links
1 / 73

Staged Self-Assembly and Polyomino Context-Free Grammars PowerPoint PPT Presentation


  • 51 Views
  • Uploaded on
  • Presentation posted in: General

Staged Self-Assembly and Polyomino Context-Free Grammars. Andrew Winslow. Defense Edition. Self-Assembly. S imple particles coalescing into complex superstructures. Self-Assembly. S imple particles coalescing into complex superstructures. Self-Assembly.

Download Presentation

Staged Self-Assembly and Polyomino Context-Free Grammars

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Staged self assembly and polyomino context free grammars

Staged Self-Assembly andPolyomino Context-Free Grammars

Andrew Winslow

Defense Edition


Self assembly

Self-Assembly

Simple particles coalescing into

complex superstructures.


Self assembly1

Self-Assembly

Simple particles coalescing into

complex superstructures.


Self assembly2

Self-Assembly

Simple particles coalescing into

complex superstructures.


Self assembly3

Self-Assembly

Simple particles coalescing into

complex superstructures.


Staged self assembly and polyomino context free grammars

Crystallization


Staged self assembly and polyomino context free grammars

Morphogenesis


Staged self assembly and polyomino context free grammars

Natural Self-Assembly


Staged self assembly and polyomino context free grammars

Synthetic Self-Assembly with DNA


Staged self assembly and polyomino context free grammars

Tile


Staged self assembly and polyomino context free grammars

Glues


Our work

Our work:

Study an abstract self-assembly model

based on DNA tile systems.


Staged self assembly and polyomino context free grammars

Tile


Staged self assembly and polyomino context free grammars

Glues


Staged self assembly and polyomino context free grammars

Assembly


Staged self assembly and polyomino context free grammars

Mixing


Staged self assembly and polyomino context free grammars

Bin


Staged self assembly and polyomino context free grammars

Reagents


Staged self assembly and polyomino context free grammars

Products


Staged self assembly and polyomino context free grammars

Size


Staged self assembly and polyomino context free grammars

Staged self-assembly


Staged self assembly and polyomino context free grammars

Input

Output

(polyomino)

(small staged assembly system)


Staged self assembly and polyomino context free grammars

Input

n


Staged self assembly and polyomino context free grammars

Θ(n) system size


Staged self assembly and polyomino context free grammars

Θ(log(n)) system size


Staged self assembly and polyomino context free grammars

n

Θ(n)

Θ(log(n))


Staged self assembly and polyomino context free grammars

Input


Staged self assembly and polyomino context free grammars

Finding small systems is (NP-)hard.

Study a simplified model.


Staged self assembly and polyomino context free grammars

Rule


Staged self assembly and polyomino context free grammars

Grammar


One dimension

One dimension

Ο(1)

? ? ?

? ? ?

Ο(#glues2)

Ω(n1/2/log(n)), Ο(n2/3)

Staged System

Grammar

E. D. Demaine, S. Eisenstat, M. Ishaque, A. Winslow, One-dimensional staged self-assembly, DNA 17, 2011.


Staged self assembly and polyomino context free grammars

? ? ? ?


Staged self assembly and polyomino context free grammars

Polyomino Grammar


Two dimensions

Two dimensions

Ο(log(n))

w/scaling

Macrotile

Ω(n/log3n)

Grammar

Staged System

A. Winslow, Staged Self-Assembly and Polyomino Context-Free Grammars, DNA 19, 2013.


Staged self assembly and polyomino context free grammars

?

?

?

?

?

?


Staged self assembly and polyomino context free grammars

Values


Values are distinct

Values are distinct

Values are contiguous


Staged self assembly and polyomino context free grammars

Activation


Staged self assembly and polyomino context free grammars

Activation


Staged self assembly and polyomino context free grammars

? ? ?


Staged self assembly and polyomino context free grammars

? ? ?


Staged self assembly and polyomino context free grammars

? ? ?


Staged self assembly and polyomino context free grammars

[1..3] +4

Shifting


Staged self assembly and polyomino context free grammars

[4..6] +4

Shifting


Staged self assembly and polyomino context free grammars

[1..3] +4

Shifting

Activation


Staged self assembly and polyomino context free grammars

? ? ?


Staged self assembly and polyomino context free grammars

[2..5] +3


Staged self assembly and polyomino context free grammars

? ? ?


Staged self assembly and polyomino context free grammars

[1..4] +2


Staged self assembly and polyomino context free grammars

? ? ?


Staged self assembly and polyomino context free grammars

[1..4] +4


Staged self assembly and polyomino context free grammars

Product

Activated reagent 1

Activated & shifted reagent 2

Shifted reagent 2

Reagent 1

Reagent 2


Staged self assembly and polyomino context free grammars

?

?

?

?

?

?


Staged self assembly and polyomino context free grammars

A R1

A & S R2

S R2

A R1

A & S R2

S R2

A R1

A & S R2

S R2


Staged self assembly and polyomino context free grammars

A R1

A R1

A R1

A & S R2

A & S R2

A & S R2

S R2

S R2

S R2

Ο(log(n))

w/scaling


Staged self assembly and polyomino context free grammars

Ω(n/log3n)


Staged self assembly and polyomino context free grammars

Ω(n/loglog(n))

Ο(loglog(n))


Staged self assembly and polyomino context free grammars

Ω(n/log2n)

Ο(log(n))


Staged self assembly and polyomino context free grammars

Ω(n/log2n)

Ο(log(n))


Staged self assembly and polyomino context free grammars

Grammar

Staged System

Grammars are small,

staged systems are always smaller

Ο(log(n))

Ο(1)

Ω(n1/2/log(n)), Ο(n2/3)

Ω(n/log3n)

w/scaling


Thank you

Thank you

Committee:

Collaborators:

Lenore Cowen

Sarah Eisenstat

Erik Demaine

MashhoodIshaque

Ben Hescott

Matthew Patitz

Diane Souvaine

Robert Schweller

Hyunmin Yi

Damien Woods

NSF grants 0941538 and 0830734


  • Login