P ROTEIN SEONDARY & SUPER-SECONDARY STRUCTURE PREDICTION WITH HMM By En-Shiun Annie Lee

1. PROTEIN SEONDARY & SUPER-SECONDARY STRUCTURE PREDICTION WITH HMM By En-Shiun Annie Lee CS 882 Protein Folding Instructed by Professor Ming Li

2. 0. OUTLINE • Introduction • Problem • Methods (4) • HMM Examples (3) • Segmentation HMM • Profile HMM • Conditional Random Field • Proposal

3. 1. INTRODUCTION • Introduction * • Problem • Methods (4) • HMM Examples (3) • Segmentation HMM • Profile HMM • Conditional Random Field • Proposal

4. 1. Genomics • Achievements in Genomic • BLAST (Basic Local Alignment Search Tool) • most cited paper published in 1990s • more than 15,000 times • Human genome project • Completion April 2003

5. 1. Proteomics • Precedence to Proteomics • Protein Data Bank (PDB) • 40,132 structures • cited more than 6,000 times

6. 1. Proteomics Number of Protein Structures in Protein Data Bank

7. 1. Secondary Structure • Importance • The known secondary structure may be used as an input for the tertiary structure predictions.

8. 1. Protein Structure • Primary Structure

9. 1. Protein Structure • Secondary Structure

10. 1. Secondary Structure • α-helix • Interaction between i and (i+4)th residue

11. 1. Secondary Structure • β-sheet/strand • Parallel or Anti-parallel

12. 1. Secondary Structure • Coil (loop)

13. 1. Protein Structure • Tertiary Structure

14. 1. Protein Structure • Super-Secondary (2.5) Structure Super-Secondary (2.5) Structure

15. 1. Protein Structure • Quaternary Structure Super-Secondary (2.5) Structure

16. 2. PROBLEM • Introduction • Problem * • Methods (4) • HMM Examples (3) • Segmentation HMM • Profile HMM • Conditional Random Field • Proposal

17. 2. Secondary Structure • Problem • Given: • A primary sequence of amino acids • a1a2…an • Find: • Secondary structure of each ai as • α-helix = H • β-strand = E * • coil = C

18. 2. Secondary Structure • Example • Given: • Primary Sequence • GHWIATRGQLIREAYEDYRHFSSECPFIP • Find: • Secondary Structure Element • CEEEEECHHHHHHHHHHHCCCHHCCCCCC • Note: segments

19. 2. Prediction Quality • Three-state prediction accuracy • Q3 = # of correctly predicted residues total # of number of residues • Q, Qβ, Qc • Q3 for random prediction is 33% • Theoretical limit Q3=90%.

20. 2. Prediction Quality • Segment Overlap (SOV) • Higher penalties for core segment regions • Matthews Correlation Coefficients (MCC) • Prediction errors made for each state

21. 2. True Structures • Three dimensional PDB data • DSSP (Dictionary of Secondary Structure of Proteins) • 8 states • H = alpha helix H • G = 310 - helix H • I = 5 helix (pi helix) H • E = extended strand (beta ladder) E • B = residue in isolated beta-bridge E • T = hydrogen bonded turn C • S = bend C • C = coil C • STRIDE

22. 3. METHODS • Introduction • Problem • Methods (4) * • HMM Examples (3) • Segmentation HMM • Profile HMM • Conditional Random Field • Proposal

23. 3. Sliding Window • Sliding-Window

24. 3. Sliding Window • Sliding-Window

25. 3. Sliding Window • Sliding-Window

26. 3. Sliding Window • Sliding-Window

27. 3. Four Methods • Statistical Method • Neural Network • Support Vector Machine • Hidden Markov Model

28. 3a. Statistical Method • Propensity • Ex. Chou-Fasman 50~53%

29. 3b. Neural Network • Ex. PHD 71%

30. 3c. SVM • Ex. PSIPRED 76~78%

31. 3d. HMM Definition • State set Q • Output alphabet Σ

32. 3d. HMM Definition • Transition probabilities • probability of entering the state p from state q • Tq(p) •  q  Q •  p  Q

33. 3d. HMM Definition • Emission probabilities • probability emits each letter of Σ from state q • Eq(ai) •  ai  Σ •  q  Q

34. 3d. HMM Decoding • Problem • Given: • HMM = (Q,Σ,E,T) and • Sequence S • Where S = S1, S2, …, Sn • Find: • Most probable path of state gone through to get S • Where X = X1, X2, …, Xn = state sequence

35. 4. HMM Decoding • Optimize • Pr [ S , X ] • X = X1, X2, …, Xn = state sequence • S = S1, S2, …, Sn • Pr [ S | X ]

36. 4. HMM Decoding • Dynamic programming • Memoryless • Pr [Xn|Sn] = Pr [Xn-1|Sn-1] Tn-1[Xn] EXn[Sn]

37. 4. HMM EXAMPLES • Introduction • Problem • Methods (4) • HMM Examples (3) * • Segmentation HMM • Profile HMM • Conditional Random Field • Proposal

38. 4a. SEMI-HMM • Introduction • Problem • Methods (4) • HMM Examples (3) • Semi-HMM * • Profile HMM • Conditional Random Field • Proposal

39. 4a. Semi-HMM • Definition • Each state can emit a sequence • Move emission probabilities into states • Model secondary structure segments

40. 4a. Segmentation • Sequence Segments

41. 4a. Segmentation • Sequence Segments

42. 4a. Segmentation • Sequence Segments • T = secondary structural type of the segment, {H, E, L} • S = ends of each individual structural segments • R = known amino acid sequence

43. 4a. Segmentation • Sequence Segments • T2 = E = β-strand • S2 = 9 • R2 = S1 + 1 : S2

44. 4a. Bayesian • Bayesian Formulation • R = Sequence of ALL amino acid residues • S = End of the segments • T = Secondary structural type of the segments • {H, E, L}

45. 4a. Bayesian • Bayesian Formulation    • Likelihood • Priori Probability • Constant  (S,T)   dropped

46. 4a. Bayesian • Likelihood • m = Total number of segments • Sj = End of the jth segments • Tj = Secondary structural type of the jth segments

47. 4a. Bayesian • Likelihood

48. 4a. Bayesian • Likelihood

49. 4a. Bayesian •  Likelihood N-terminus Internal C-terminus

50. 4a. BSPPS • Bayesian Segmentation PPS