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The RNA Maximum Base Pair Matching Problem

The RNA Maximum Base Pair Matching Problem

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The RNA Maximum Base Pair Matching Problem

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  1. The RNA Maximum Base Pair Matching Problem 報告者:99366076顧家源

  2. Introduce • G • A • C • C • U • RNA由4種鹼基構成: {A, G, C, U} • Base Pair: 可降低RNA的自由能量, 使其結構更穩定{A – U, G – C, G - U} • RNASequence:R = A – G – G – C – C – U – U – C – C – U • Secondary Structure:

  3. In 3D Presentation

  4. Constraint • 每組Base Pair的兩個鹼基必須間隔4以上 • Example:

  5. Structure & Free Energy

  6. Problem Statement • 已知一RNA序列R • 找出含有最多Base Pair的SecondaryStructureof R • 設定參數: • A– U, G – C, G – U的權重均為+1

  7. Max. #Base Pairs

  8. Step. 1 – Compute ρ(ri, rj)

  9. Step. 2– Set M(i, i~i+3) = 0

  10. Case 1 No match! ri rj-1 rj Si,j-1

  11. Case 2 ri match rj ri rj-1 rj ri+1 Si+1,j-1

  12. Case 3 rk match rj ri rj-1 rj rk Si,k-1 Sk+1,j-1 k = i + 1 to j - 4

  13. Step. 3– Compute all M(i, j)

  14. Step. 3– Compute all M(i, j)

  15. Step. 3 - M1,10

  16. Result

  17. Route 1

  18. Route 2

  19. Route 3

  20. Algorithm • Input:R = r1r2…rn • Output: a secondary structure of R with the maximum #base pairs. • Step1: /* Computation of ρ(ri, rj), 1 ≤ i < j ≤ n */WW = {(A, U), (U, A), (G, C), (C, G), (G, U), (U, G)};fori = 1 tondoforj = itondoif (ri, rj) WW thenρ(ri, rj) = 1; elseρ(ri, rj) = 0;end forend for Time Complexity = O(n2)

  21. Algorithm • Step2: /* Initialization of Mi,j for j – i≤ 3 */fori = 1 tondoforj = itoi + 3 doif j ≤ nthenMi,j = 0;end forend for Time Complexity = O(n)

  22. Algorithm • Step3: /* Calculation of Mi,j for j – i > 3 */forh = 4 ton - 1 dofori = 1 ton - hdoj = i + h;case1 = Mi,j-1;case2 = (1 + Mi+1,j-1) ρ(ri, rj);case3 = ;Mi,j = max{ case1, case2, case3 };end forend for Time Complexity = O(n3)

  23. Case 1 No match! ri rj-1 rj Si,j-1

  24. Case 2 ri match rj ri rj-1 rj ri+1 Si+1,j-1

  25. Case 3 rk match rj ri rj-1 rj rk Si,k-1 Sk+1,j-1 k = i + 1 to j - 4

  26. Time Complexity • Step. 1 • Step. 2 • Step. 3

  27. Errata • P. 273 • Since we want to find the k between i + 1 and j + 4 such that Mi,j is the maximum, … • “j + 4” correct to “j - 4”. • P. 282 • Next, we analyze the time complexity… • Step 1 is O(n2) • Step 2 is O(n) • Step 3 is O(n3)

  28. Comparison • 前面幾節所介紹的Dynamic Programming,其運作模式如右: • Ai,j表示a提供a1~aib提供b1~bj的local optimal

  29. Comparison • 本節的方式則如右: • Mi,j表示ri~rj的local optimal • 主要的差異在於RNA的「折疊」 • 時間複雜的的差異來自較多的候補

  30. Resources • 線上RNA結構預測網頁(CGI):http://rna.tbi.univie.ac.at/cgi-bin/RNAfold.cgi • 視覺化RNA結構呈現軟體-RnaDv:http://rna-dv.sourceforge.net/