1. Physical Mapping Problem D7526010@csie.ntu.edu.tw

2. Problem Definition • Physical mapping的定義

3. H J DNA A B Q C P D O N E M F G L H K J Fragment of DNA

4. Why We Need Physical Mapping • 可以利用這個地圖將DNA做完全排序 • 可以知道基因到底如何對人類產生作用 • 利用人造蛋白質...等等來改進遺傳體質

5. 人類染色體(約 bp) Physical map (約 bp) AGACTAGTCGTAACGATCGCTAATTTAAGGCTACT..... DNA Sequencing (約 bp)

6. Why We Need Physical Mapping • 可以利用這個地圖將DNA做完全排序 • 可以知道基因到底如何對人類產生作用 • 利用人造蛋白質...等等來改進遺傳體質 • 可以得知基因(或標記)的大約位置 • 對於一些遺傳疾病可以得到較多的資訊 • 可以幫助偵測是否具有遺傳疾病

7. DNA A B Q C P D O N E M F G L H K J Fragment of DNA H J α

9. target DNA 加入酵素

10. Partial Digest Problem • by single enzyme A • restriction sites: a1< a2< a3<.....< ap • multiset of fragment lengths {aj-ai,i<j}

11. target DNA

12. Double Digest Problem (DDP) • Clones first completely digested by enzyme A,then by B, finally A and B together • restriction sites: • by A: a1< a2< a3<.....< ap • by B: b1< b2< b3 <.....< bq • by A+B : c1< c2< c3 <.....< cp+q • Reconstruct the restriction sites from these multisets

13. Example : DDP Enzyme A+B 1 2 3 3 5 6 7 Enzyme A 3 6 8 10 Enzyme B 4 5 7 11

14. Solution

15. Double Digest Problem (DDP)

16. target DNA ........

17. By Probe Approach

18. target DNA ................. ........ ATGCGCTAACTGGACTTCAAGCCTAAACTGCATCAGACTT TACGCGATTGACCTGAAGT Complementary probe The Spirit of Hybridization

19. target DNA A B 1 2 3 4 5 C D E F G H I J

22. J D F I E G A C H B 1 2 3 4 5

24. 1 A、B、C C、D、E 2 3 E、F F、G 4 G、H、I 5 6 I、J、K False Negative 1 A、C C、D、E 2 3 E、F A、F、G 4 G、H、I 5 6 E、F、I、J、K

25. 1 A、B、C C、D、E 2 3 E、F F、G 4 G、H、I 5 6 I、J、K False Positive 1 A、C C、D、E 2 3 E、F A、F、G 4 G、H、I 5 6 E、F、I、J、K

26. Chimeric Clones 1 A、C 1 A、B、C C、D、E 2 C、D、E 2 3 E、F 3 E、F A、F、G 4 F、G 4 G、H、I 5 G、H、I 5 6 E、F、I、J、K 6 I、J、K

27. 5 A、B、C C、D、E 6 3 E、F F、G 4 I、J、K 1 2 G、H、I Clones 1 2 3 4 5 6 A B Probes C D E F G H I J K

28. Clones 1 2 3 4 5 6 A 5 A、B、C B Probes C、D、E 6 C 3 E、F、K D I、J、K、F、G E 4 F I、J、K 1 G H 2 G、H、I I J K

29. How To Use Traveling Salesman Problem to Solve Physical Mapping Problem

30. How to Convert to TSP? • Hamming distance

32. How to Convert to TSP? • Hamming distance • Cycle weight = number of gaps transitions +2n

34. How to Convert to TSP? • Hamming distance • Cycle weight = number of gaps transitions +2n • So, minimize the cycle weight is to the gap number

37. Our approach • We also convert it to optimization problem • Using more complicated model • Using Genetic Algorithm to solve it. F(A) = X*C(A)+Y*P(A)+Z*N(A)+T*M(A)+ P*L(A).

38. The results of our approach tested on simulated data. • (a) (b) • The false negative rate is set as 0.1. The false positive rate is 0.05. • The false negative rate is set as 0.1. The false positive rate is 0.01.

39. Experimental Results of our GA tested on Real data from chromosome 1 (a) It shows the results of our GA run with the data which is a contig with about 95 clones and about 120 probes (b) It shows the results of our GA run with the data which is a contig with about 172 clones and about 136 probes