A Chinese Postman Problem Based on DNA Computing Z. Yin, F. Zhang, and J. Xu* J. Chem. Inf. Comput. Sci. 2002, 42, Summarized by Shin, Soo-Yong

© 2002, SNU BioIntelligence Lab, Chinese Postman Problem (CPP) Similar with TSP CPP has to visit all edges in the graph, but can visit same edges more than twice.  cf) TSP for all vertexes.

© 2002, SNU BioIntelligence Lab, Algorithm for CPP The same as Adleman’s algorithm 1. Generate a random closed walk 2. Keep only those closed walks that begins with fixed vertices and end with fixed vertices 3. Keep only those closed walks that enter all of the edges of the given graph at least once. 4. Find the shortest path 5. Determine

© 2002, SNU BioIntelligence Lab, Implementation Step 1  Edge weights are represented by the length.  Vertex : 20mer  Edge : 10mer for starting, 10mer for ending, 10* w ij for weight

© 2002, SNU BioIntelligence Lab, Implementation Step 2  PCR with rear 10 bp of ‘0’ and former 10 bp of ‘0’ Step 3  Affinity-purification for all edges Step 4  Gel electrophoresis Step 5  Sequencing

© 2002, SNU BioIntelligence Lab, 참고사항 실험 없음. Journal of Chemical Information and Computer Science  Core SCI! impact factor is (1998)

DNA Solution of a Graph Coloring Problem Y. Liu, J. Xu*, L. Pan, and S. Wang J. Chem. Inf. Comput. Sci. 2002, 42, Summarized by Shin, Soo-Yong

© 2002, SNU BioIntelligence Lab, Graph Coloring Problem Find minimum number of color to paint a different color for the adjacent vertexes.

© 2002, SNU BioIntelligence Lab, Algorithm Convert to the problem an ensemble of all rearrangements of the required colors.  Ex) (2,1,5,3,6,5) (1,2,3,1,2,3) (2,3,4,2,3,4)  Wrong answer : (1,1,3,1,2,3) Delete illegal answer Sort the answer (find minimum length)

© 2002, SNU BioIntelligence Lab, Representation dsDNA strands Color section ( C i ) and name section ( N i )  N 1 & N 7 for PCR, N i : 20 bp  C i : j if C i = j ( j = 1,2,…,6)  380 bp for , 230 bp for

© 2002, SNU BioIntelligence Lab, Representation Initial fragment

© 2002, SNU BioIntelligence Lab, Making a pool Parallel overlap assembly (POA)

© 2002, SNU BioIntelligence Lab, Delete illegal answer Illegal answer template  (x, x, *, *, *, *), (x, *, x, *, *, *), (x, *, *, *, x, *), (x, *, *, *, *, x), (*, x, x, *, *, *), (*, x, *, x, *, *), (*, x, *, *, *, x), (*, *, x, x, *, *), (*, *, x, *, x, *), (*, *, *, x, x, *), (*, *, *, x, *, x), (*, *, *, *, x, x) Divide into two tubes  T1 cut out by restriction enzyme (1, *, *, *, *, *)  T2 cut out (*, 1, *, *, *, *) Combine T1 and T2 Repeat all strings for given templates.

© 2002, SNU BioIntelligence Lab, Experimental Results Product of POA and PCR Final product

© 2002, SNU BioIntelligence Lab, To reduce errors Digesting the ssDNA with S 1 nuclease before restriction digestions Two cycles of digestion-PCR Avoid accidental homologies longer than 4 bp