1. Solving Edge-Matching Puzzles Using DNA Computing Mohammed AlShamrani Department of Computer Science Concordia University March 23, 2011

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9. Phosphate Sugar (deoxyribose ) Hydrogen bonds

10. Solving Edge-Matching Puzzles Using DNA Computing 5-GACACTCACTGTCA-3 3-CTGTGAGTGACAGT-5 =

11. 5- CCAAGTTGATTGAGAA Solving Edge-Matching Puzzles Using DNA Computing 5- TAACTCTTTTCTCAAT-3 1. Synthesis What we can do with DNA … 2. Hybridization pH AAGAGTTATATGGGCT -3 3. Ligation 4. Replication (PCR) …………….. Exponential Growth

12. Solving Edge-Matching Puzzles Using DNA Computing 1 copy 2 copies 4 copies 8 copies Sd Jj

13. Solving Edge-Matching Puzzles Using DNA Computing DNA Computing is new perspective If DNA strands are made to represent objects/relations, then new knowledge can result from the application of these operations (synthesis, hyb., ligation, PCR, etc). This is DNA Computing.

14. Solving Edge-Matching Puzzles Using DNA Computing Example: Six degrees of Separation The claim is that any two people in the world are connected, on average, by 6 people who are connected by the is-a-friend-of relation. So you are a friend of X 1 who is a friend of X 2 … who is a friend of X 6 who is a friend of Nelson Mandela.

15. Solving Edge-Matching Puzzles Using DNA Computing Example: Six degrees of Separation So you are a friend of X 1 who is a friend of X 2 … who is a friend of X 6 who is a friend of Nelson Mandela. 5-CCAAGTTGATTGAGAAAAGAGTTATATGGGCT-3 5-TAACTCTTTTCTCAAT-3 1. Synthesis 2. Hybridization 3. Ligation Unit Computation

16. Solving Edge-Matching Puzzles Using DNA Computing Example: Six degrees of Separation So you are a friend of X 1 who is a friend of X 2 … who is a friend of X 6 who is a friend of Nelson Mandela. 1. Synthesis 2. Hybridization 3. Ligation Post-Ligation Product 4. Replication: Replicate sequences that begin withYou and end with Nelson Mandela

17. Solving Edge-Matching Puzzles Using DNA Computing Example: Six degrees of Separation So you are a friend of X 1 who is a friend of X 2 … who is a friend of X 6 who is a friend of Nelson Mandela. 1. Synthesis 2. Hybridization 3. Ligation 4. Replication Sequence encoding 6 people between you and Mandela Post-Replication product: sequences of different lengths but all begin with you and end with Mandela

18. Solving Edge-Matching Puzzles Using DNA Computing Example: Six degrees of Separation So you are a friend of X 1 who is a friend of X 2 … who is a friend of X 6 who is a friend of Nelson Mandela. 1. Synthesis 2. Hybridization 3. Ligation 4. Replication Sequence encoding 6 people between you and Mandela Post-Replication product: sequences of different lengths but all begin with you and end with Mandela

19. Solving Edge-Matching Puzzles Using DNA Computing Example: Six degrees of Separation So you are a friend of X 1 who is a friend of X 2 … who is a friend of X 6 who is a friend of Nelson Mandela. 1. Synthesis 2. Hybridization 3. Ligation 4. Replication 5. Gel Electrophoresis Your best chance of meeting Mandela Reference ladder

20. Solving Edge-Matching Puzzles Using DNA Computing Challenge: pack a collection of square tiles on a square board such that: 1)All abutting edges match in color 2)All boundary edges are grey

21. Solving Edge-Matching Puzzles Using DNA Computing Relevance: Complexity: EMPs are NP-Complete Turing-universality: 2-Dimensional growth of tiles can simulate the execution of any Turing machine. Nanotechnology: Tiles can serve as definitional motifs for nano-technological constructions: given a desired 2D shape, what set of tiles (preferably minimal) can grow to that shape? 5 + 9 = 14 59 14

22. Solving Edge-Matching Puzzles Using DNA Computing To solve an EMP with DNA, we need to: 1. Define the problem2. Formulate an algorithm3. Implement a DNA lab protocol

23. 2. Formulate an algorithm3. Implement a DNA lab protocol1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing

24. To solve an EMP with DNA, we need to: 2. Formulate an algorithm3. Implement a DNA lab protocol1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Diagonal-wise tile stacking: The algorithm succeeds if it makes a series of correct choices: at each step, find diagonal sets of tiles that can fit legally.

25. To solve an EMP with DNA, we need to: 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Diagonal-wise tile stacking: But couldnt there be more than correct choice at each step? Yes: non-determinism. NP-Complete

26. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Diagonal-wise tile stacking: Observation : at any given step, only two edges of each tile are involved in constraint validation.

27. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Diagonal-wise tile stacking: Observation: at any given step, only two edges of each tile are involved in constraint validation Conceptually: a tile is the union of two half tiles.

28. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Diagonal-wise half-tile stacking: Conceptually: a tile is the union of two half tiles. The algorithm succeeds if it makes a series of correct choices: at each step, find diagonal sets of half-tiles that can fit perfectly.

29. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Diagonal-wise half-tile stacking: Tile dissection along the diagonals produces two pairs of half tiles Pairs of half-tiles

30. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Diagonal-wise half-tile stacking: The union of a pair on the tiling grid reproduces the tile in one orientation U U UU

31. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Diagonal-wise half-tile stacking: Formalizations What is a half-tile? What is the relation between half-tiles? Is the solution with the set of half-tiles equivalent to that of tiles? Can we proof it? What is the union of two half-tiles? What is the relation (bridging) between diagonal sets of half-tiles (lanes)? What is a valid lane ?

32. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Diagonal-wise half-tile stacking: Formalizations

33. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Diagonal-wise half-tile stacking: Why ? In the correct solution, diagonal sets of half-tiles have two useful properties: 1. All diagonal sets of half-tiles are of odd length 1 half-tile 3 half-tiles 5 half-tiles 7 half-tiles

34. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Diagonal-wise half-tile stacking: Why ? In the correct solution, diagonal sets of half-tiles have two useful properties: 1. All diagonal sets of half-tiles are of odd length 2. All diagonal sets of half-tiles are begin and end with grey

35. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Diagonal-wise half-tile stacking: Why ? In the correct solution, diagonal sets of half-tiles have two useful properties: 1. All diagonal sets of half-tiles are of odd length 2. All diagonal sets of half-tiles are begin and end with grey Gel Electrophoresis as a computational heuristic Polymerase Chain Reaction (PCR) as a computational heuristic and a processing power

36. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Ultimately we seek to find the set of DNA lanes that encode the full solution to the puzzle: 1. Enumerate DNA lanes (stapling) 2. Build DNA grid by stacking lanes (bridging) DNA Grid

37. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Step 1: Associate half-tiles to random ssDNA sequences (synthesis) 5-ATGGGTGAAGAAGATG GTAGAAGAGAAATAAG -3 GAATAAAGCTAGCGGC-3

38. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing 5-ATGGGTGAAGAAGATG GTAGAAGAGAAATAAG-3 GAATAAAGCTAGCGGC-3 3-TCTTCTACCATCTTCT-5 3-CTTTATTCCTTATTTC-5 Red staple Blue staple Step 2: Mix half-tiles strands with stapler strands to generate random lanes

39. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Step 3: Keep only lanes of beginning and ending with grey (PCR)

40. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Step 4: Keep only lanes of length 1, 3, 5, and 7 half-tiles (Gel Electrophoresis).

41. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Step 5: Bridge lanes. 5………..XXXXXTGTATATGTGTGGGAACAGGTTTAATXXXXX………3 3-.........XXXXXXAAGAGTTATATGA CTCCTGAAATGGAXXXXX…..5 CCACACATATACA-3 5-ATTAAACCTGTTC 5-TTCTCAATATACT GAGGACTTTACCT-3 Bridging strands

42. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Step 5: Bridge lanes. Bridging is a sensitive and labor-intensive process: 3-D shape of the double-helix must be taken into account: design constraints Migration of bridged assemblies on gel is tricky

43. 2. Formulate an algorithm3. Implement a DNA lab protocol 1. Define the problem Solving Edge-Matching Puzzles Using DNA Computing Puzzle Solution =

44. Solving Edge-Matching Puzzles Using DNA Computing Concluding remarks: NP-Completeness of EMPs: we can measure processing power of DNA Computing Half-tile Assembly Model: Turing-complete PCR-powered model for DNA nanotechnological fabrication

45. Solving Edge-Matching Puzzles Using DNA Computing http://users.encs.concordia.ca/~mo_alsha/thesis/