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

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Phosphate Sugar (deoxyribose ) Hydrogen bonds

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

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

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

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.

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.

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

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

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

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

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

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

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? =

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

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

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.

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

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.

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.

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.

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

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

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 ?

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

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

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

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

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

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

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

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)

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).

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……… XXXXXXAAGAGTTATATGA CTCCTGAAATGGAXXXXX…..5 CCACACATATACA-3 5-ATTAAACCTGTTC 5-TTCTCAATATACT GAGGACTTTACCT-3 Bridging strands

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

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

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

Solving Edge-Matching Puzzles Using DNA Computing