Algorithmic Self-Assembly at the Nano-Scale by rll15525

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									    Algorithmic Self-Assembly at the Nano-Scale


                                          Ashish Goel
  1    1     1                         Stanford University
  1    1     0
                                    http://www.stanford.edu/~ashishg
  1    1     0
  1    0     1            Joint work with Len Adleman, Holin Chen, Qi Cheng,
                          Ming-Deh Huang, Pablo Moisset, Paul Rothemund,
  1    0     1            Rebecca Schulman, Erik Winfree
  1    0     0
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       2
                         A Matter of Scale
Question: Why an algorithmic study of “molecular” self-
 assembly 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 sub-
       discipline of distributed algorithms, artificial intelligence etc.

                          Ashish Goel, ashishg@stanford.edu                   3
       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         b           Single bar: strength 1 glue
                            Double bar: strength 2 glue
           d
   – Tiles floating on an infinite grid; Temperature 
   – A tile can add to an existing assembly if
            total strength of matching glues  
                                                            d
       f            b
                        c                      b                a   τ=2
       a                       b                        c


                    Ashish Goel, ashishg@stanford.edu                     4
                  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   5
      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          6
Rothemund’s DNA Origami
        A self-folded virus!!




             QuickTime™ and a
         TIFF (LZW) decompressor
      are neede d to see this picture.




    Ashish Goel, ashishg@stanford.edu    7
                       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        8
          Is Self-Assembly Just Crystallization?
   Crystals do not grow into unique terminal structures
       A sugar crystal does not grow to precisely 20nm
   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
       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                  9
          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                    10
     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
       Entropy, Equilibria, and Error Rates
       Reversibility
   Connections to experiments
   Self-assembly as a machine
       Not just assemble something, but perform work
       Much less understood than the first three

                            Ashish Goel, ashishg@stanford.edu          11
Can we create efficient counters?




        Ashish Goel, ashishg@stanford.edu   12
      Can we create efficient counters?


         Yes! Eg. Using “Chinese remaindering”
T=2




              Ashish Goel, ashishg@stanford.edu   13
      Can we create efficient counters?


         Yes! Eg. Using “Chinese remaindering”
T=2




              Ashish Goel, ashishg@stanford.edu   14
      Can we create efficient counters?


         Yes! Eg. Using “Chinese remaindering”
T=2




              Ashish Goel, ashishg@stanford.edu   15
      Can we create efficient counters?

         Yes! Eg. Using “Chinese remaindering”
T=2




              Ashish Goel, ashishg@stanford.edu   16
      Can we create efficient counters?


         Yes! Using “Chinese remaindering”
T=2




              Ashish Goel, ashishg@stanford.edu   17
      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                          18
Molecular machines




       QuickTime™ and a
   TIFF (LZW) decompressor
are neede d to see this picture.




 Ashish Goel, ashishg@stanford.edu   19
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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