1. DNA Computing: Implications for Theoretical Computer Science Lila Kari Dept. of Computer Science University of Western Ontario London, ON, Canada http://www.csd.uwo.ca/~lila/ lila@csd.uwo.ca

2. DNATCS From DNA to TCS The genetic code Splicing systems Optimal encodings for DNA Computing Sticker systems Watson-Crick automata Combinatorics on DNA words Cellular computing DNA computation by self-assembly

3. 1953: Watson and Crick discover DNA structure

4. DNA DNA structure

5. The RNA Tie Club 1954 “Solve the riddle of the RNA structure and to understand how it builds proteins” (clockwise from upper left: Francis Crick, L. Orgel, James Watson, Al. Rich) There are 20 aminoacids that build up proteins

6. The Diamond Code G.Gamow - double stranded DNA acts as a template for protein synthesis: various combinations of bases could form distinctively shaped cavities into which the side chains of aminoacids might fit

7. Comma-Free Codes (the prettiest wrong idea in 20-th century science) The RNA piglet model

8. The prettiest wrong idea in all of 20 th century science Suckling-pig model of protein synthesis Construct a code in which when two sense codons (triplets) are catenated, the subword codons are nonsense codons If CGU and AAG are sense codons, then GUA and UAA must be nonsense because they appear in CGUAAG

9. Comma-free codes (Crick 1957) How many words can a comma-free code include? For n=4 and k=3 the size of a maximal comma-free code is the magic number 20 For an alphabet of n letters grouped into k- letter words, if k is prime, the number of maximal comma-free codes is (n^k –n)/k For n=4 and k=3 this equals 408

10. Reality Intrudes News from the lab bench: [Nirenberg,Matthaei ’61] synthesize RNA, namely poly-U, coding for phenylalanine By 1965 the genetic code was solved The code resembled none of the theoretical notions The “extra” codons are merely redundant

11. The Genetic Code

12. Splicing Systems (Head 1987) 5’ CCCCCTCGACCCCC 3’ 3’GGGGGAGCTGGGGG5’ + 5’AAAAAGCGCAAAAA 3’ 3’ TTTTTCGCGTTTTT 5’ + Enzyme 1 + Enzyme 2 5’TCGA3’ 5’GCGC3’ 3’AGCT5’ 3’CGCG5’

13. Splicing Systems 5’ CCCCCT CGACCCCC 3’ 3’GGGGGAGC TGGGGG5’ + 5’AAAAAG CGCAAAAA 3’ 3’ TTTTTCGC GTTTTT 5’ DNA strands with compatible sticky ends recombine to produce two new strands

14. Splicing operation

15. Splicing system sample results Theorem (Paun’95, Freund,Kari,Paun,’99) Every type-0 language can be generated by a splicing system with finitely many axioms and finitely many rules. Theorem (Freund,Kari,Paun ’99) For every given alphabet T there exists a splicing system, with finitely many axioms and finitely many rules, that is universal for the class of systems with terminal alphabet T.

16. DNATCS From DNA to TCS The genetic code Splicing systems Optimal encodings for DNA Computing Sticker systems Watson-Crick automata Combinatorics on DNA words Cellular computing DNA computation by self-assembly

17. DNA Computing (Adleman’94) Input / Output (DNA) –Data encoded using the DNA alphabet {A, C, G, T} and synthesized as DNA strands Bio-operations –Cut –Paste –Recombination –Anneal / Melt –Copy

18. Biomolecular (DNA) Computing Hamiltonian Path Problem [Adleman, Science, 1994] DNA-based addition [Guarnieri et al, Science, 1996] Maximal Clique Problem [Ouyang et al, Science, 1997] DNA computing by self-assembly [Winfree et al, Nature 1998] Computations by circular insertions, deletions [Daley, Kari, Gloor, Siromoney, SPIRE’99] DNA computing on surfaces [Liu et al, Nature, 2000] Molecular computation by DNA hairpin formation[Sakamoto et al, Science, 2000] 20-variable Satisfiability [Braich et al., Science 2002] An autonomous molecular computer for logical control of gene expression [Benenson et al, Nature, 2004] Folding DNA to create nanoscale shapes and patterns [Rothemund, Nature, 2006] Efficient Turing-universal computation with DNA polymers [Qian, Soloveichik, Winfree, DNA Computing and Molecular Programming, 2010] Molecular robots guided by prescriptive landscapes [Lund et al., Nature, 2010]

19. Encoding Information for DNA Computing DNA strands should form desired bonds DNA strands should be free of undesirable intra-molecular bonds DNA strands should be free of undesirable inter-molecular bonds

20. Intramolecular Bonds

21. Intra- and inter-molecular bonds

22. DNA-complementarity model (Kari,Kitto,Thierrin’02)

23. Bond-free languages Bonds between DNA strands

24. Sample Results (Hussini/Kari/Konstantinidis/Losseva/Sosik ‘03)

25. Sticker Systems (Freund,Paun,Rozenberg,Salomaa’98, Kari,Paun,Rozenberg,Salomaa,Yu’98, Hoogeboom,van Vugt’00, Kuske,Weigel’04, Paun,Rozenberg ‘98) Given a complementarity relation, define an alphabet of double-stranded columns

26. Sticking operation

27. Complex Sticker Systems Sakakibara,Kobayashi ‘01: Sticker systems based on hairpins Alhazov,Cavaliere ’05: Observable sticker systems

28. Watson-Crick Automata (Freund,Paun,Rozenberg,Salomaa’99;Paun,Rozenberg’98; MartinVide,Paun,Rozenberg,Salomaa’98;Czeizler,Czeizler 06; Paun,Paun’99;Czeizler,Czeizler,Kari,Salomaa’08)

29. DNATCS From DNA to TCS The genetic code Splicing systems Optimal encodings for DNA Computing Sticker systems Watson-Crick automata Combinatorics on DNA words Cellular computing DNA computation by self-assembly

30. Combinatorics on DNA Words IDEA: Consider the word w and its WK- complement, WK(w), as equivalent The word ACTG CAGT CAGT can be considered repetitive (periodic) because it can be written as ACGT WK(ACGT) 2 Generalize classical notions such as power of a word, border, primitive word, palindrome, conjugacy, commutativity

31. Identity => Antimorphic involution f Pseudo-palindrome (de Luca,De Luca’06, Kari,Mahalingam’09) u = f(u) Pseudo-commutativity (Kari,Mahalingam’08) u v = f(v) u Pseudo-bordered word (Kari,Mahalingam’07) w = v x = y f(v) Pseudoknot-bordered word (Kari,Seki’09) w = u v x = y f(u) f(v) Pseudo-conjugacy of u, v (Kari,Mahalingam’08) u x = f(x) v

32. Fine and Wilf Theorem

33. Extended Fine and Wilf Theorem

35. Lyndon-Schutzenberger Equation

36. Extended Lyndon-Schuzenberger

37. Extended Lyndon-Schutzenberger

38. Cellular Computing Photo courtesy of L.F. Landweber

39. Ciliates: Genetic Info Exchange Photo courtesy of L.F. Landweber

40. Ciliates: Gene Rearrangement Photo courtesy of L.F. Landweber

41. Ciliates: Bio-operations

42. Ciliate Computing Guided Recombination System = A formal computational model based on contextual circular insertions and deletions Such systems have the computational power of Turing Machines (Landweber,Kari ’99,Kari,Kari’99)

43. Other ciliate computing models * Ld, hi, dlad model (Harju,Rozenberg ’03, Harju,Petre,Rozenberg ’03, Prescott, Ehrenfeucht,Rozenberg’03) * Template guided recombination model (Angeleska,Jonoska,Saito,Landweber’07, Daley,McQuillan ’06, Kari,Rahman ’10) * RNA guided recombination model (Nowacki et. al, ’07)

44. DNATCS From DNA to TCS The genetic code Splicing systems Optimal encodings for DNA Computing Sticker systems Watson-Crick automata Combinatorics on DNA words Cellular computing DNA computation by self-assembly

45. DNA Computation by Self-Assembly (Mao, LaBean, Reif,, Seeman, Nature, 2000)

46. DNA self-assembly model (Adleman’00, Winfree’98) Tile = square with the edges labelled from a finite alphabet of glues (Wang ’61) Tiles cannot be rotated Two adjacent tiles on the plane stick if they have the same glue at the touching edges

47. Dynamic Self-Assembly Tile System T = Finite set of tiles, unlimited supply of each “tile type” Supertiles self-assemble with tiles from T   Start with an arbitrary single tile: “seed”   Proceed by incremental additions of single tiles that stick AB D C AA C B

48. Self-Assembly Problem “Given a tile system T, can arbitrarily large supertiles self-assemble with tiles from T?” Equivalent to: “Given a tile system T, does there exist an infinite ribbon of tiles from T?”

49. Sample Results Undecidability of existence of an infinite ribbon (L.Adleman, J.Kari, L.Kari, D.Reishus, P.Sosik ‘09) Consequence: Undecidability of existence of arbitrarily large supertiles that self-assemble from a given tile set, starting from an arbitrary “seed” Self-assembly model with variable strength and negative strength (repelling) glues (Doty, Kari, Masson, ‘10)

50. DNA Nanotechnology (Chen, Seeman, Nature, ‘01)

51. DNA Clonable Octahedron (Shih, Joyce, Nature ‘04)

52. Nanoscale DNA Tetrahedra ( Goodman, Turberfield, Science, ‘05)

53. DNA Origami (Rothemund, Nature, 2006)

54. DNATCS From DNA to TCS The genetic code Splicing systems Optimal encodings for DNA Computing Sticker systems Watson-Crick automata Combinatorics on DNA words Cellular computing DNA computation by self-assembly

55. Impact of DNA Computing on Theoretical Computer Science Novel computing paradigms abstracted from biological phenomena Alternative physical substrates on which to implement computations, e.g. DNA Viewing natural processes as computations has become essential, desirable, and inevitable These developments challenge our assumptions, and our very definition of computation “Biology and Computer Science – life and computation – are related” (Adleman)

56. Our Challenge Discover a new, broader notion of computation Understand the world around us in terms of information processing “Biology and Computer Science – life and computation – are related. I am confident that at their interface great discoveries await whose who seek them.” (Adleman’98)