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Algorithmic Self-Assembly at the Nano-Scale

1. 1. 0. 0. 1. 1. 0. 0. 0. Algorithmic Self-Assembly at the Nano-Scale. Ashish Goel Stanford University http://www.stanford.edu/~ashishg Joint work with Len Adleman, Holin Chen, Qi Cheng, Ming-Deh Huang, Pablo Moisset, Paul Rothemund, Rebecca Schulman, Erik Winfree. 1. 1. 1. 1. 1.

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Algorithmic Self-Assembly at the Nano-Scale

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  1. 1 1 0 0 1 1 0 0 0 Algorithmic Self-Assembly at the Nano-Scale Ashish GoelStanford University http://www.stanford.edu/~ashishg Joint work with Len Adleman, Holin Chen, Qi Cheng, Ming-Deh Huang, Pablo Moisset, Paul Rothemund, Rebecca Schulman, Erik Winfree 1 1 1 1 1 0 1 1 1 Counter made by self-assembly [Rothemund, Winfree ’00] [Adleman, Cheng, Goel, Huang ’01] [Cheng, Goel, Moisset ‘04]

  2. 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:Understandself-assembly,designself-assembling systems • A key problem in nano-technology, molecular robotics, molecular computation Ashish Goel, ashishg@stanford.edu

  3. 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

  4. The Tile Model of Self-Assembly [Wang ’61] Ashish Goel, ashishg@stanford.edu

  5. 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

  6. 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

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

  8. Abstract Tile Systems • Tile: the four glues and their strengths • Tile System: • K tiles • Infinitely many copies available of each tile • Temperature t • 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

  9. 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

  10. 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

  11. 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

  12. Can we create efficient counters? 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! Eg. Using “Chinese remaindering” T=2 Ashish Goel, ashishg@stanford.edu

  17. Can we create efficient counters? Yes! Using “Chinese remaindering” T=2 Ashish Goel, ashishg@stanford.edu

  18. 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

  19. Molecular machines Ashish Goel, ashishg@stanford.edu

  20. Strand Invasion Ashish Goel, ashishg@stanford.edu

  21. Strand Invasion Ashish Goel, ashishg@stanford.edu

  22. Strand Invasion Ashish Goel, ashishg@stanford.edu

  23. Strand Invasion Ashish Goel, ashishg@stanford.edu

  24. Strand Invasion Ashish Goel, ashishg@stanford.edu

  25. Strand Invasion Ashish Goel, ashishg@stanford.edu

  26. Strand Invasion Ashish Goel, ashishg@stanford.edu

  27. Strand Invasion Ashish Goel, ashishg@stanford.edu

  28. Strand Invasion Ashish Goel, ashishg@stanford.edu

  29. Strand Invasion Ashish Goel, ashishg@stanford.edu

  30. Strand Invasion Ashish Goel, ashishg@stanford.edu

  31. Strand Invasion Ashish Goel, ashishg@stanford.edu

  32. Strand Invasion Ashish Goel, ashishg@stanford.edu

  33. Strand Invasion Ashish Goel, ashishg@stanford.edu

  34. Strand Invasion Ashish Goel, ashishg@stanford.edu

  35. Strand Invasion Ashish Goel, ashishg@stanford.edu

  36. Strand Invasion Ashish Goel, ashishg@stanford.edu

  37. Strand Invasion Ashish Goel, ashishg@stanford.edu

  38. Strand Invasion Ashish Goel, ashishg@stanford.edu

  39. Strand Invasion Ashish Goel, ashishg@stanford.edu

  40. Strand Invasion Strand Invasion (cont) Ashish Goel, ashishg@stanford.edu

  41. Strand Invasion Ashish Goel, ashishg@stanford.edu

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