Molecular Algorithms -- Overview

1. 1 1 0 0 1 1 0 0 0 Molecular Algorithms -- Overview Ashish GoelStanford University http://www.stanford.edu/~ashishg Joint work with Len Adleman, Holin Chen, Qi Cheng, Ming-Deh Huang, Chris Luhrs, 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. Adleman’s Experiment • Use DNA strands to code information • Can solve Hamiltonian paths • NP complete • Lots of press • Ingenious experiment • Started an entire community (eg. The DNA computing workshop) • Not practical, as an alternative to modern computers • Today: Brief overview • Molecular self-assembly • Molecular machines • People/Funding/Current status • Short term and long term directions Ashish Goel, ashishg@stanford.edu

3. 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

4. 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

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

6. 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

7. 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

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

9. 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

10. 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

11. 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

12. 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

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

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

19. 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

20. Also, binary From Cheng, Moisset, Goel; Optimal self-assembly of counters at temperature 2 (basic ideas developed over many papers) Ashish Goel, ashishg@stanford.edu

21. Interesting fact • Binary counter is combinatrorially equivalent to a de-multiplexer • If we could make large counters effiiciently, we would have a combinatorial template for a computer memory • Molecularly precise • Around 4X improvement over Silicon • Futuristic? Yes, but not as much as you might think Ashish Goel, ashishg@stanford.edu

22. Experiment by Barish et al • Made a counter (very similar to the one described above) • Unfortunately, lots of errors • Error-correction: huge challenge • Self-healing • Coding theory techniques vs bio-chemistry techniques Ashish Goel, ashishg@stanford.edu

23. The Source of Errors: Thermodynamics GA = Activation energy GB = Bond energy + 2GB GB GA GA Correct Growth Incorrect Growth Rate of correct growth ¼ exp(-GA) Probability of incorrect growth ¼ exp(-GA + GB) Constraint: 2 GB > GA (system goes forward) ) Rate has quadratic dependence on error probability ) Time to reliably assemble an n £ n square ¼ n5 Ashish Goel, ashishg@stanford.edu

24. Snake Tiles G2 G3 G1 G2a G2b G4 X2 G3b G1b X1 X3 Each tile in the original system corresponds to four tiles in the new system The internal glues are unique to this block G3a G1a G4a G4b Ashish Goel, ashishg@stanford.edu

25. How does this help? First tile attaches with a weak binding strength Ashish Goel, ashishg@stanford.edu

26. How does this help? First tile attaches with a weak binding strength Second tile attaches and secures the first tile Ashish Goel, ashishg@stanford.edu

27. How does this help? First tile attaches with a weak binding strength Second tile attaches and secures the first tile No Other tiles can attach without another nucleation error Ashish Goel, ashishg@stanford.edu

28. Preliminary Experimental Results (Obtained by Chen, Goel, Schulman, Winfree) Ashish Goel, ashishg@stanford.edu

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33. Four by Four Snake Tiles Ashish Goel, ashishg@stanford.edu

34. Four by Four Snake Tiles Ashish Goel, ashishg@stanford.edu

35. Four by Four Snake Tiles Ashish Goel, ashishg@stanford.edu

36. Four by Four Snake Tiles Ashish Goel, ashishg@stanford.edu

37. Four by Four Snake Tiles Ashish Goel, ashishg@stanford.edu

38. Four by Four Snake Tiles Ashish Goel, ashishg@stanford.edu

39. Four by Four Snake Tiles Ashish Goel, ashishg@stanford.edu

40. Four by Four Snake Tiles Ashish Goel, ashishg@stanford.edu

41. Four by Four Snake Tiles Ashish Goel, ashishg@stanford.edu

42. Four by Four Snake Tiles Ashish Goel, ashishg@stanford.edu

43. Four by Four Snake Tiles Ashish Goel, ashishg@stanford.edu

44. Four by Four Snake Tiles Ashish Goel, ashishg@stanford.edu

45. Analysis • Snake tile design extends to 2k£2k blocks. • Prevents tile propagation even after k+1 nucleation/growth errors • The error probability changes from p to roughly pk • We can assemble an N£N square in time O(N polylog N) and it remains stable for time W(N) (with high probability). • Resolution loss of O(log N) • Assuming tiles held by strength 3 do not fall off • Matches the time for ideal, irreversible assembly • Compare to N3 for basic proof-reading and N5 with no error-correction in the thermodynamic model [Chen, Goel; DNA ‘04] • Extensions, variations by Reif’s group, Winfree’s group, our group, and others • Recent result: Simple combinatorial criteria; Can avoid resolution loss by using third dimension[Chen, Goel, Luhrs; SODA ‘08] Ashish Goel, ashishg@stanford.edu

46. Open problem • Techniques for error reduction • Understand underlying bio-chemical primitives • Algorithms and combinatorial analysis • Probabilistic analysis • Serious simulations • Experimental verification • Challenges: What else could we do with self-assembly? • Antennas? Inductors? Origami followed by micro-scale assembly? Ashish Goel, ashishg@stanford.edu

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

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

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

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