1. www.bioalgorithms.infoAn Introduction to Bioinformatics Algorithms Protein Sequencing and Identification by Mass Spectrometry

2. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Outline Tandem Mass Spectrometry De Novo Peptide Sequencing Spectrum Graph Protein Identification via Database Search Identifying Post Translationally Modified Peptides Spectral Convolution Spectral Alignment

3. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Masses of Amino Acid Residues

4. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Different Amino Acid Have Different Masses H...-HN-CH-CO-NH-CH-CO-NH-CH-CO-…OH R i-1 RiRi R i+1 AA residue i-1 AA residue i AA residue i+1 N-terminus C-terminus

5. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Peptide Fragmentation Peptides tend to fragment along the backbone. Mass spectrometer is a sophisticated (and rather expensive!) scale to measure the masses of these fragments H...-HN-CH-CO... NH-CH-CO-NH-CH-CO-…OH R i-1 RiRi R i+1 H+H+ Prefix FragmentSuffix Fragment Collision Induced Dissociation

6. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Breaking Protein into Peptides and Peptides into Fragment Ions Most mass spectrometers can only measure masses of short peptides (e.g., 20 amino acids) rather than masses of entire proteins (usually hundreds of amino acids). That’s why: Proteases, e.g. trypsin, break protein into short peptides. A Tandem Mass Spectrometer further breaks the peptides down into fragment ions and measures the mass of each piece. Mass Spectrometer accelerates the fragmented ions; heavier ions accelerate slower than lighter ones. Mass Spectrometer measure mass/charge ratio of an ion.

7. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info N- and C-terminal Peptides N-terminal peptides C-terminal peptides

8. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Terminal peptides and ion types Peptide Mass (D) 57 + 97 + 147 + 114 = 415

9. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Masses of fragment ions Peptide Mass (D) 57 + 97 + 147 + 114 = 415 Peptide Mass (D) 57 + 97 + 147 + 114 – 18 = 397 without

10. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info N- and C-terminal Peptides N-terminal peptides C-terminal peptides 415 486 301 154 57 71 185 332 429

11. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info N- and C-terminal Peptides N-terminal peptides C-terminal peptides 415 486 301 154 57 71 185 332 429

12. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Theoretical Spectrum 415 486 301 154 57 71 185 332 429 Reconstruct peptide from the set of masses of fragment ions (mass-spectrum) 57 71 154 185 301 332 415 429 486

13. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Reconstructing Peptides Reconstruct peptide from the set of masses of fragment ions (mass-spectrum) 57 71 154 185 301 332 415 429 486

14. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Reconstructing Peptides Reconstruct peptide from the set of masses of fragment ions (mass-spectrum) 57 71 81 100 112 131 154 160 172 177 185 201 221 235 301 312 325 332 370 387 409 415 423 429 460 472 486

15. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Reconstructing Peptides Reconstruct peptide from the set of masses of fragment ions (mass-spectrum) 57 71 81 100 112 131 160 172 177 185 201 221 235 301 312 325 370 387 409 415 423 429 460 472 486

16. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Peptide Fragmentation y3y3 b2b2 y2y2 y1y1 b3b3 a2a2 a3a3 HO NH 3 + | | R 1 O R 2 O R 3 O R 4 | || | || | || | H -- N --- C --- C --- N --- C --- C --- N --- C --- C --- N --- C -- COOH | | | | | | | H H H H H H H b2-H2Ob2-H2O y 3 -H 2 O b 3 - NH 3 y 2 - NH 3

17. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Mass Spectra GVDLK mass 0 57 Da = ‘G’ 99 Da = ‘V’ L K DVG The peaks in the mass spectrum: Prefix Fragments with neutral losses (-H 2 O, -NH 3 ) Noise and missing peaks. and Suffix Fragments. D H2OH2O

18. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Protein Identification with MS/MS GVDLK mass 0 Intensity mass 0 MS/MS Peptide Identification

19. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Tandem Mass Spectrum Tandem Mass Spectrometry mainly generates N- and C-terminal fragment ions Chemical noise often complicates the spectrum. Represented in 2-D: mass/charge axis vs. intensity axis

20. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Tandem Mass-Spectrometry

21. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Breaking Proteins into Peptides peptides MPSER …… GTDIMR PAKID …… HPLC To MS/MS MPSERGTDIMRPAKID...... protein

22. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Mass Spectrometry Matrix-Assisted Laser Desorption/Ionization (MALDI) From lectures by Vineet Bafna (UCSD)

23. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Tandem Mass Spectrometry Scan 1708 LC Scan 1707 MS MS/MS Ion Source MS-1 collision cell MS-2

24. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Protein Identification by Tandem Mass Spectrometry (MS/MS) Sequence MS/MS instrument database search Sequest, Mascot, etc de novo interpretation Lutefisk, Peaks, etc

25. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info De Novo vs. Database Search W R A C V G E K D W L P T L T W R A C V G E K D W L P T L T De Novo AVGELTK Database Search Database of all peptides = 20 n AAAAAAAA,AAAAAAAC,AAAAAAAD,AAAAAAAE, AAAAAAAG,AAAAAAAF,AAAAAAAH,AAAAAAI, AVGELTI, AVGELTK, AVGELTL, AVGELTM, YYYYYYYS,YYYYYYYT,YYYYYYYV,YYYYYYYY Database of known peptides MDERHILNM, KLQWVCSDL, PTYWASDL, ENQIKRSACVM, TLACHGGEM, NGALPQWRT, HLLERTKMNVV, GGPASSDA, GGLITGMQSD, MQPLMNWE, ALKIIMNVRT, AVGELTK, HEWAILF, GHNLWAMNAC, GVFGSVLRA, EKLNKAATYIN.. Mass, Score

26. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info De Novo vs. Database Search: A Paradox The database of all peptides is huge ≈ 20 n peptides of length n The database of all known peptides is much smaller ≈ 10 8 peptides However, de novo algorithms can be much faster, even though their search space is much larger! A database search scans all peptides in the database of all known peptides to find best one. De novo eliminates the need to scan database of all peptides by modeling the problem as a graph search.

27. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Three Algorithmic Problems Searching for a million words in a text. Suppose it takes 1 sec to find a word in a text. How much time would it take to find 1 million words in the text? Searching for a word without even looking at 99.999% of the text. Suppose you search for a word in a text. Would it be possible to ignore 99.999% of the text, scan only the remaining part and guarantee that the word you are looking for will be found? Finding spelling errors in a book written in an unknown language. Given a book (in an unknown language) and a misspelled word (with insertions, deletions, and substitutions of letters) correct spelling errors in the word.

28. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Three Algorithmic Problems Searching for a million words in a text. Suppose it takes 1 sec to find a word in a text. How much time would it take to find 1 million words in the text? 1 million seconds? Searching for a word without even looking at 99.999% of the text. Suppose you search for a word in a text. Would it be possible to ignore 99.999% of the text, scan only the remaining part and guarantee that the word you are looking for will be found? Finding spelling errors in a book written in an unknown language. Given a book (in an unknown language) and a misspelled word (with insertions, deletions, and substitutions of letters) correct spelling errors in the word.

29. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Genomics: Problems Solved. Searching for a million words in a text. Aho-Corasik algorithm takes roughly the same time with a million words as it takes with a single word. Searching for a word without even looking at 99.999% of the text. Filtration algorithms (like FASTA or BLAST) ignore 99.999% of the text. Finding spelling errors. Sequence alignment algorithms (like Smith- Waterman) do it in quadratic time

30. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Proteomics: Three Problems Comparing a million spectra against a database. Suppose it takes 1 sec to interpret a spectrum. How much time would it take to interpret 1 million spectra? Mass-spectrometry database search without even looking at 99.999% of the database. Suppose you compare a spectrum against a database. Would it be possible to ignore 99.999% of the database, scan only the remaining part and guarantee that you still can identify a peptide of interest? Blind PTM search and discovery of new PTM types. Given a spectrum of a peptide with unknown PTM types, find this peptide in the database. Discover new PTM types by data mining of large MS/MS datasets.

31. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Three Solutions Comparing a million spectra against a database. InsPecT (Tanner et al., Anal. Chem, 2005) MS/MS database search without even looking at 99.999% of the database. PepNovoTag+InsPecT (Tanner et al., Anal. Chem, 2005) Blind PTM search and discovery of new PTM types. Given a spectrum of a peptide with unknown PTM types, find this peptide in the database. Discover new PTM types by data mining of large MS/MS datasets. MS-Alignment (Tsur et al., Nature Biotech., 2005)

32. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Filtration: Combining De Novo Sequencing and Database Search in Mass-Spectrometry So far de novo and database search were presented as two separate techniques Database search is rather slow: many labs generate more than 100,000 spectra per day. SEQUEST takes approximately 1 minute to compare a single spectrum against SWISS-PROT (54Mb) on a desktop. It will take SEQUEST more than 2 months to analyze the MS/MS data produced in a single day. Can slow database search be combined with fast de novo analysis?

33. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info De novo Peptide Sequencing Sequence

34. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Theoretical Spectrum

35. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Theoretical Spectrum (cont’d)

36. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Theoretical Spectrum (cont’d)

37. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Building Spectrum Graph How to create vertices (from masses) How to create edges (from mass differences) How to score vertices How to score paths How to find the best path

38. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info S E Q U E N C E b-ions (prefix or N-terminal ions) Mass/Charge (M/Z)

39. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info a-ions = b-ions - CO = b-ions - 28 Mass/Charge (M/Z) S E Q U E N C E

40. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info S E Q U E N C E Mass/Charge (M/Z) Shifting Peaks: a-ions = b-ions - CO = b-ions - 28

41. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info y-ions (suffix of C-terminal ions) Mass/Charge (M/Z) E C N E U Q E S

42. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Mass/Charge (M/Z) Intensity

43. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Mass/Charge (M/Z) Intensity

44. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info noise Mass/Charge (M/Z)

45. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info MS/MS Spectrum Mass/Charge (M/z) Intensity

46. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Some Mass Differences between Peaks Correspond to Amino Acids s s s e e e e e e e e q q q u u u n n n e c c c

47. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Some Mass Differences between Peaks Correspond to Amino Acids s s s e e e e e e e e q q q u u u n n n e c c c

48. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Ion Types Some masses correspond to fragment ions, others are just random noise Knowing ion types Δ={δ 1, δ 2,…, δ k } lets us distinguish fragment ions from noise We can learn ion types δ i and their probabilities q i by analyzing a large test sample of annotated spectra.

49. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Example of Ion Type Δ={δ 1, δ 2,…, δ k } Ion types {b, b-NH 3, b-H 2 O, b-CO} correspond to Δ={0, 17, 18, 28} *Note: In reality the δ value of ion type b is -1 but we will “hide” it for the sake of simplicity

50. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Match between Spectra and the Shared Peak Count The match between two spectra is the number of masses (peaks) they share (Shared Peak Count or SPC) In practice mass-spectrometrists use the weighted SPC that reflects intensities of the peaks Match between experimental and theoretical spectra is defined similarly

51. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Peptide Sequencing Problem Goal: Find a peptide with maximal match between an experimental and theoretical spectrum. Input: S: experimental spectrum Δ : set of possible ion types Output: A peptide whose theoretical spectrum matches the experimental spectrum the best

52. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Reverse Shifts Two peaks b-H 2 O and b are given by the Mass Spectrum With a +H 2 O shift, if two peaks coincide that is a possible vertex. Mass/Charge (M/Z) Intensity Red: Mass Spectrum Blue: shift (+H 2 O) b/b-H 2 O+H 2 O b-H 2 O b+H 2 O

53. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info S E Q U E N C E Mass/Charge (M/Z) Shifting Peaks: a-ions = b-ions - CO = b-ions - 28

54. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Reverse Shifts Shift in H 2 O+NH 3 Shift in H 2 O

55. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Vertices of the Spectrum Graph Masses of potential N-terminal peptides Vertices are generated by reverse shifts corresponding to ion types Δ={δ 1, δ 2,…, δ k } Every N-terminal peptide can generate up to k ions m-δ 1, m-δ 2, …, m-δ k Every mass s in an MS/MS spectrum generates k vertices V(s) = {s+δ 1, s+δ 2, …, s+δ k } corresponding to potential N-terminal peptides Vertices of the spectrum graph: {initial vertex}  V(s 1 )  V(s 2 ) ...  V(s m )  {terminal vertex}

56. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Edges of the Spectrum Graph Two vertices with mass difference corresponding to an amino acid A: Connect with an edge labeled by A Gap edges corresponding to the mass of pairs of amino acids (optional)

57. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Paths Paths in the labeled graph spell out amino acid sequences There are many paths, how to find the correct one? We need scoring to evaluate paths

58. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Path Score p(P,S) = probability that peptide P produces spectrum S= {s 1,s 2,…s q } p(P, s) = the probability that peptide P generates a peak s Scoring = computing probabilities p(P,S) = π s є S p(P, s)

59. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info For a position t that represents ion type d j : q j, if peak is generated at t p(P,s t ) = 1-q j, otherwise Peak Score

60. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Peak Score (cont’d) For a position t that is not associated with an ion type: q R, if peak is generated at t p R (P,s t ) = 1-q R, otherwise q R = the probability of a noisy peak that does not correspond to any ion type

61. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Finding Optimal Paths in the Spectrum Graph For a given MS/MS spectrum S, find a peptide P’ maximizing p(P,S) over all possible peptides P: Peptides = paths in the spectrum graph P’ = the optimal path in the spectrum graph

62. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Ions and Probabilities Tandem mass spectrometry is characterized by a set of ion types {δ 1,δ 2,..,δ k } and their probabilities {q 1,...,q k } δ i -ions of a partial peptide are produced independently with probabilities q i

63. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Ions and Probabilities A peptide has all k peaks with probability and no peaks with probability A peptide also produces a ``random noise'' with uniform probability q R in any position.

64. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Ratio Test Scoring for Partial Peptides Incorporates premiums for observed ions and penalties for missing ions. Example: for k=4, assume that for a partial peptide P’ we only see ions δ 1,δ 2,δ 4. The score is calculated as:

65. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Scoring Peptides T- set of all positions. T i ={t δ1,, t δ2,...,,t δk, }- set of positions that represent ions of partial peptides P i. A peak at position t δj is generated with probability q j. R=T- U T i - set of positions that are not associated with any partial peptides (noise).

66. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Probabilistic Model For a position t δj  T i the probability p(t, P,S) that peptide P produces a peak at position t. Similarly, for t  R, the probability that P produces a random noise peak at t is:

67. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Probabilistic Score For a peptide P with n amino acids, the score for the whole peptides is expressed by the following ratio test:

68. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info De Novo vs. Database Search W R A C V G E K D W L P T L T W R A C V G E K D W L P T L T De Novo AVGELTK Database Search Database of known peptides MDERHILNM, KLQWVCSDL, PTYWASDL, ENQIKRSACVM, TLACHGGEM, NGALPQWRT, HLLERTKMNVV, GGPASSDA, GGLITGMQSD, MQPLMNWE, ALKIIMNVRT, AVGELTK, HEWAILF, GHNLWAMNAC, GVFGSVLRA, EKLNKAATYIN..

69. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info De Novo vs. Database Search: A Paradox de novo algorithms are much faster, even though their search space is much larger! A database search scans all peptides to find the best one. De novo eliminates the need to scan all peptides by modeling the problem as a graph search. Why not sequence de novo?

70. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Why Not Sequence De Novo? De novo sequencing is not very accurate: Less than 30% of the peptides sequenced were completely correct! Algorithm Amino Acid Accuracy Whole Peptide Accuracy Lutefisk, 1997 0.5660.189 SHERENGA, 1999 0.6900.289 Peaks, 2003 0.6730.246 PepNovo, 2005 0.7270.296

71. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Pros and Cons of de novo Sequencing Advantage: Gets the sequences that are not necessarily in the database. An additional similarity search step using these sequences may identify the related proteins in the database. Disadvantage: Requires higher quality spectra to be accurate.

72. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Role of de novo Interpretation Interpreting MS/MS of novel peptides Automatic validation of MS/MS database matches. Leveraging homology matching across species

73. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Peptide Sequencing Problem Goal: Find a peptide with maximal match between an experimental and theoretical spectrum. Input: S: experimental spectrum Δ : set of possible ion types Output: A peptide whose theoretical spectrum matches the experimental S spectrum the best

74. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Peptide Identification Problem Goal: Find a peptide from the database with maximal match between an experimental and theoretical spectrum. Input: S: experimental spectrum database of peptides Δ : set of possible ion types Output: A peptide from the database whose theoretical spectrum matches the experimental S spectrum the best

75. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info De novo Peptide Sequencing Problem=Protein Identification Problem in the Database of ALL Peptides Although de novo peptide sequencing problem seems to be more difficult that peptide identification problem, the algorithms for the former problem are actually much faster!

76. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info MS/MS Database Search Database search in mass-spectrometry has been successful in identification of already known proteins. Experimental spectrum can be compared with theoretical spectra of database peptides to find the best fit. SEQUEST (Yates et al., 1995) But reliable algorithms for identification of modified peptides is a much more difficult problem.

77. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Functional Proteomics Problem: Given a large collection of uninterpreted spectra, find out which spectra correspond to similar peptides. A method that cross-correlates related spectra (e.g., from normal and diseased individuals) would be valuable in functional proteomics.

78. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info The dynamic nature of the proteome The proteome of the cell is changing Various extra-cellular, and other signals activate various protein pathways. A key mechanism of protein activation is post-translational modification (PTM) These pathways may lead to other genes being switched on or off Mass spectrometry is key to probing the proteome and detecting PTMs

79. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Post-Translational Modifications Proteins are involved in cellular signaling and metabolic regulation. They are subject to a large number of biological modifications. Almost all protein sequences are post- translationally modified and 600 types (!) of modifications of amino acid residues are known.

80. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Examples of Post-Translational Modification Post-translational modifications increase the number of “letters” in amino acid alphabet and lead to a combinatorial explosion in both database search and de novo approaches.

81. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Peptide Masses N-terminal peptides C-terminal peptides 415 486 301 154 57 71 185 332 429

82. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Peptide Masses: Modification +16 on N N-terminal peptides C-terminal peptides 415 486 301 154 57 71 185 332 429 +16

83. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Reconstructing Modified Peptides Reconstruct peptide from the set of masses of fragment ions (mass-spectrum) 57 71 154 185 301 332 415 429 486 +16 +16 +16 +16 +16 57 71 154 201 301 348 431 445 502

84. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Reconstructing Modified Peptides Reconstruct peptide from the set of masses of fragment ions (mass-spectrum) 57 71 81 100 112 131 154 160 172 177 185 201 221 235 301 312 325 332 370 387 409 415 423 429 460 472 486 57 71 81 100 112 131 154 160 172 177 185 201 221 235 301 312 325 332 348 387 409 415 423 431 445 472 502

85. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Sequencing of Modified Peptides De novo peptide sequencing is invaluable for identification of unknown proteins: However, de novo algorithms are designed for working with high quality spectra with good fragmentation and without modifications. Another approach is to compare a spectrum against a set of known spectra in a database.

86. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Search for Modified Peptides: Virtual Database Approach Yates et al.,1995: an exhaustive search in a virtual database of all modified peptides. Exhaustive search leads to a large combinatorial problem, even for a small set of modifications types. Problem (Yates et al.,1995). Extend the virtual database approach to a large set of modifications.

87. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Exhaustive Search for modified peptides. YFDSTDYNMAK 2 5 =32 possibilities, with 2 types of modifications! Phosphorylation? Oxidation? For each peptide, generate all modifications. Score each modification.

88. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Peptide Identification Problem Revisited Goal: Find a peptide from the database with maximal match between an experimental and theoretical spectrum. Input: S: experimental spectrum database of peptides Δ : set of possible ion types Output: A peptide from the database whose theoretical spectrum matches the experimental S spectrum the best

89. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Modified Peptide Identification Problem Goal: Find a modified peptide from the database with maximal match between an experimental and theoretical spectrum. Input: S: experimental spectrum database of peptides Δ : set of possible ion types Parameter k (# of mutations/modifications) Output: A peptide that is at most k mutations/modifications apart from a database peptide and whose theoretical spectrum matches the experimental S spectrum the best

90. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Search for Modified Peptides: Virtual Database Approach YFDSTDYNMAK 2 5 =32 possibilities, with 2 types of modifications! Phosphorylation? Oxidation? Yates et al.,1995: an exhaustive search in a virtual database of all modified peptides. Combinatorial explosion, even for a small set of modifications types. A larger set of spurious matches must be filtered out. It’s much more likely that incorrect matches will have high scores. Problem (Yates et al.,1995). Extend the virtual database approach to a large set of modifications.

91. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Restrictive vs Unrestrictive (Blind) Search for Modified Peptides Restrictive search requires the researcher to guess which modification types are present in the sample How would you feel if you were allowed to perform only 10 out of 20x19=380 possible point mutations (with all other forbidden) while aligning two proteins? This is exactly what restrictive PTM search algorithms does.

92. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Restrictive vs Unrestrictive (Blind) Search for Modified Peptides Restrictive search requires the researcher to guess which modification types are present in the sample Blind search performs an unrestrictive search for all possible modification offsets at once.

93. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Database Search: Sequence Analysis vs. MS/MS Analysis Sequence analysis: similar peptides (that a few mutations apart) have similar sequences MS/MS analysis: similar peptides (that a few mutations apart) have dissimilar spectra

94. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Peptide Identification Problem: Challenge Very similar peptides may have very different spectra! Goal: Define a notion of spectral similarity that correlates well with the sequence similarity. If peptides are a few mutations/modifications apart, the spectral similarity between their spectra should be high.

95. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Deficiency of the Shared Peaks Count Shared peaks count (SPC): intuitive measure of spectral similarity. Problem: SPC diminishes very quickly as the number of mutations increases. Only a small portion of correlations between the spectra of mutated peptides is captured by SPC.

96. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info SPC Diminishes Quickly S(PRTEIN) = {98, 133, 246, 254, 355, 375, 476, 484, 597, 632} S(PRTEYN) = {98, 133, 254, 296, 355, 425, 484, 526, 647, 682} S(PGTEYN) = {98, 133, 155, 256, 296, 385, 425, 526, 548, 583} no mutations SPC=10 1 mutation SPC=5 2 mutations SPC=2

97. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Convolution

98. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Elements of S 2 S 1 represented as elements of a difference matrix. The elements with multiplicity >2 are colored; the elements with multiplicity =2 are circled. The SPC takes into account only the red entries

99. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Convolution 1 2 3 4 5 0 -150 -100 -50 0 50 100 150 x Spectral Convolution: An Example

100. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Comparison: Difficult Case S = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100} Which of the spectra S’ = {10, 20, 30, 40, 50, 55, 65, 75,85, 95} or S” = {10, 15, 30, 35, 50, 55, 70, 75, 90, 95} fits the spectrum S the best? SPC: both S’ and S” have 5 peaks in common with S. Spectral Convolution: reveals the peaks at 0 and 5.

101. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Comparison: Difficult Case S S’ S S’’

102. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Limitations of the Spectrum Convolutions Spectral convolution does not reveal that spectra S and S’ are similar, while spectra S and S” are not. Clumps of shared peaks: the matching positions in S’ come in clumps while the matching positions in S” don't. This important property was not captured by spectral convolution.

103. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Sequence Alignment=Path in a Grid Finding similarities between two peptides is equivalent to finding an optimal path in a Manhattan-like grid (sequence alignment).

104. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Sequence Alignment=Path in a Grid Finding similarities between two peptides is equivalent to finding an optimal path in a Manhattan-like grid (sequence alignment). Every horizontal/vertical segment in this path corresponds to insertion/deletion of an amino acid.

105. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Sequence Alignment=Path in a Grid Finding similarities between two peptides is equivalent to finding an optimal path in a Manhattan-like grid (sequence alignment). Every horizontal/vertical segment in this path corresponds to insertion/deletion of an amino acid. Can we find similarities between a spectrum and a peptide using a similar approach (spectral alignment)?

106. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Converting Spectra into 0-1 Sequences Convert spectrum into a 0-1 string with 1s corresponding to the positions of the peaks.

107. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Modified peptide Modifications are modeled as insertion (or deletions) of blocks of zeroes 000101001010000000110000001001 Spectrum 00010100001-----00010000001001 Peptide A modification with positive offset - inserting a block of 0s A modification with negative offset - deleting a block of 0s

108. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectra Comparison vs. String Comparison Comparison of theoretical and experimental spectra (represented as 0-1 strings) corresponds to a (somewhat unusual) edit distance/alignment between 0-1 strings where elementary edit operations are insertions and deletions of blocks of 0s Use sequence alignment algorithms!

109. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Alignment Graph Horizontal axis: Experimental spectrum Vertical axis: Theoretical spectrum of a peptide A B C D E

110. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Alignment Graph Like in alignment algorithms, every path in the spectral alignment graph represents a possible interpretation of a spectra. A path covering maximal number of 1s is the “best” interpretation of the spectrum. Vertical / horizontal segment in the optimal path are modifications A B C D E

111. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Alignment vs. Sequence Alignment Alignment graph with different alphabet and scoring. Movement can be diagonal (matching masses) or horizontal/vertical (insertions/deletions corresponding to PTMs). At most k horizontal/vertical moves.

112. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Alignment Algorithm Simultaneous analysis of N- and C-terminal ions Taking into account the intensities and charges Analysis of neutral losses Speed ………

113. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Enriching the model Fitting, seeded alignment Masses are prefix residue masses (PRMs) supported by b and/or y peaks and neutral losses Masses need not be integers Vertices have arbitrary scores: MassScore(v)

114. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Shifts A = {a 1 < … < a n } : an ordered set of natural numbers. A shift (i,  ) is characterized by two parameters, the position ( i ) and the length (  ). The shift (i,  ) transforms {a 1, …., a n } into {a 1, ….,a i-1,a i + ,…,a n +  }

115. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Shifts: An Example The shift (i,  ) transforms {a 1, …., a n } into {a 1, ….,a i-1,a i + ,…,a n +  } e.g. 10 20 30 40 50 60 70 80 90 10 20 30 35 45 55 65 75 85 10 20 30 35 45 55 62 72 82 shift (4, -5) shift (7,-3)

116. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Alignment Problem Find a series of k shifts that make the sets A={a 1, …., a n } and B={b 1,….,b n } as similar as possible. k -similarity between sets D(k) - the maximum number of elements in common between sets after k shifts.

117. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Comparing Spectra=Comparing 0-1 Strings A modification with positive offset corresponds to inserting a block of 0s A modification with negative offset corresponds to deleting a block of 0s Comparison of theoretical and experimental spectra (represented as 0-1 strings) corresponds to a (somewhat unusual) edit distance/alignment problem where elementary edit operations are insertions/deletions of blocks of 0s Use sequence alignment algorithms!

118. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Product A={a 1, …., a n } and B={b 1,…., b n } Spectral product A  B : two-dimensional matrix with nm 1s corresponding to all pairs of indices (a i,b j ) and remaining elements being 0s. 10 20 30 40 50 55 65 75 85 95  1 1 1 1 1 SPC: the number of 1s at the main diagonal.  -shifted SPC: the number of 1s on the diagonal (i,i+  )

119. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Alignment: k -similarity k -similarity between spectra: the maximum number of 1s on a path through this graph that uses at most k+1 diagonals. k -optimal spectral alignment = a path. The spectral alignment allows one to detect more and more subtle similarities between spectra by increasing k.

120. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info SPC reveals only D(0)=3 matching peaks. Spectral Alignment reveals more hidden similarities between spectra: D(1)=5 and D(2)=8 and detects corresponding mutations. Use of k-Similarity

121. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Black line represent the path for k=0 Red lines represent the path for k=1 Blue lines (right) represents the path for k=2

122. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Convolution’ Limitation The spectral convolution considers diagonals separately without combining them into feasible mutation scenarios. D(1) =10 shift function score = 10 D(1) =6 10 20 30 40 50 55 65 75 85 95 10 20 30 40 50 60 70 80 90 100 10 15 30 35 50 55 70 75 90 95 10 20 30 40 50 60 70 80 90 100 

123. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Dynamic Programming for Spectral Alignment D ij (k) : the maximum number of 1s on a path to (a i,b j ) that uses at most k+1 diagonals. (i’,j’) ~ (i,j): the points are located on the same diagonal Running time: O(n 4 k)

124. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Edit Graph for Fast Spectral Alignment diag(i,j) – the position of previous 1 on the same diagonal as (i,j)

125. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Fast Spectral Alignment Algorithm Running time: O(n 2 k)

126. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Alignment: Complications Spectra are combinations of an increasing (N- terminal ions) and a decreasing (C-terminal ions) number series. These series form two diagonals in the spectral product, the main diagonal and the perpendicular diagonal. The described algorithm deals with the main diagonal only.

127. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Alignment: Complications Simultaneous analysis of N- and C-terminal ions Taking into account the intensities and charges Analysis of minor ions

128. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info MS/MS and East-West Traveling Salesman Problem

129. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info PTM Frequency Matrix 50,000 spectra (IKKb sample) were searched in blind mode, and identifications with p-value <0.05 were retained Shading of the cell (x,y) reflects the number of annotations with modification: (offset x, amino acid y)

130. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info PTM Frequency Matrix 16 on W - Oxidation 16 on M - Oxidation 14 on K - Methylation 22 - Sodium 32 on M - Double oxidation 28 on K - Dimethylation

131. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Shadows in PTM Frequency Matrix 17 on M – ??? oxidation with shift off by 1 (possible error in parent mass and/or wrong assignments of isotopic peaks)

132. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Shadows in PTM Frequency Matrix 17 on M – ??? oxidation with offset off by 1 (possible error in parent mass and/or misassignment of isotopic peaks 14 on A ??? incorrectly placed methylation (A instead of closely located K)

133. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Removing Shadows Annotation is Δ-correct if it correctly predicts the offset but places it incorrectly on one of the neighboring amino acids (happens if fragmentation near the PTM site is poor). Shadows are removed by dealing with Δ- correct annotations in such a way that they are ‘explained away’ by the most frequent PTM

134. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Filtration in Similarity Searches Scoring Protein Query Sequence Alignment – Smith-Waterman Algorithm Sequence matches Protein Sequences Filtration Filtered Sequences Sequence Alignment: – BLAST Database actgcgctagctacggatagctgatcc agatcgatgccataggtagctgatcc atgctagcttagacataaagcttgaat cgatcgggtaacccatagctagctcg atcgacttagacttcgattcgatcgaat tcgatctgatctgaatatattaggtccg atgctagctgtggtagtgatgtaaga BLAST filters out very few correct matches and is almost as accurate as Smith – Waterman algorithm. Database actgcgctagctacggatagctgatcc agatcgatgccataggtagctgatcc atgctagcttagacataaagcttgaat cgatcgggtaacccatagctagctcg atcgacttagacttcgattcgatcgaat tcgatctgatctgaatatattaggtccg atgctagctgtggtagtgatgtaaga

135. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Filtration and MS/MS Scoring MS/MS spectrum Peptide Sequencing – SEQUEST / Mascot Sequence matches Peptide Sequences Filtration Peptide Sequences Database MDERHILNMKLQWVCSDLPT YWASDLENQIKRSACVMTLA CHGGEMNGALPQWRTHLLE RTYKMNVVGGPASSDALITG MQSDPILLVCATRGHEWAILF GHNLWACVNMLETAIKLEGVF GSVLRAEKLNKAAPETYIN..

136. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Filtration in MS/MS Sequencing Filtration in MS/MS is more difficult than in BLAST. Early approaches using Peptide Sequence Tags were not able to substitute the complete database search. Current filtration approaches are mostly used to generate additional identifications rather than replace the database search. Can we design a filtration based search that can replace the database search, and is orders of magnitude faster?

137. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Asking the Old Question Again: Why Not Sequence De Novo? De novo sequencing is still not very accurate! Algorithm Amino Acid Accuracy Whole Peptide Accuracy Lutefisk (Taylor and Johnson, 1997). 0.5660.189 SHERENGA (Dancik et. al., 1999). 0.6900.289 Peaks (Ma et al., 2003). 0.6730.246 PepNovo (Frank and Pevzner, 2005). 0.7270.296

138. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info So What Can be Done with De Novo? Given an MS/MS spectrum: Can de novo predict the entire peptide sequence? Can de novo predict partial sequences? Can de novo predict a set of partial sequences, that with high probability, contains at least one correct tag? A Covering Set of Tags - No! (accuracy is less than 30%). - No! (accuracy is 50% for GutenTag and 80% for PepNovo ) - Yes!

139. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Peptide Sequence Tags A Peptide Sequence Tag is short substring of a peptide. Example: G V D L K G V DG V D V D L D L KD L K Tags:

140. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Filtration with Peptide Sequence Tags Peptide sequence tags can be used as filters in database searches. The Filtration: Consider only database peptides that contain the tag (in its correct relative mass location). First suggested by Mann and Wilm (1994). Similar concepts also used by: GutenTag - Tabb et. al. 2003. MultiTag - Sunayev et. al. 2003. OpenSea - Searle et. al. 2004.

141. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Why Filter Database Candidates? Filtration makes genomic database searches practical (BLAST). Effective filtration can greatly speed-up the process, enabling expensive searches involving post-translational modifications. Goal: generate a small set of covering tags and use them to filter the database peptides.

142. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Tag Generation - Global Tags Parse tags from de novo reconstruction. Only a small number of tags can be generated. If the de novo sequence is completely incorrect, none of the tags will be correct. W R A C V G E K D W L P T L T AVGELTK TAG Prefix Mass AVG 0.0 VGE 71.0 GEL 170.1 ELT 227.1 LTK 356.2

143. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Tag Generation - Local Tags Extract the highest scoring subspaths from the spectrum graph. Sometimes gets misled by locally promising-looking “garden paths”. W R A C V G E K D W L P T L T TAG Prefix Mass AVG 0.0 WTD 120.2 PET 211.4

144. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Ranking Tags Each additional tag used to filter increases the number of database hits and slows down the database search. Tags can be ranked according to their scores, however this ranking is not very accurate. It is better to determine for each tag the “probability” that it is correct, and choose most probable tags.

145. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Reliability of Amino Acids in Tags For each amino acid in a tag we want to assign a probability that it is correct. Each amino acid, which corresponds to an edge in the spectrum graph, is mapped to a feature space that consists of the features that correlate with reliability of amino acid prediction, e.g. score reduction due to edge removal

146. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Score Reduction Due to Edge Removal The removal of an edge corresponding to a genuine amino acid usually leads to a reduction in the score of the de novo path. However, the removal of an edge that does not correspond to a genuine amino acid tends to leave the score unchanged. W R A C V G K D W L P T L T W R A C V G K D W L P T L T W R A C V G K D W L P T L T E W W R A C V G K D L P T L T

147. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Probabilities of Tags How do we determine the probability of a predicted tag ? We use the predicted probabilities of its amino acids and follow the concept: a chain is only as strong as its weakest link

148. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Experimental Results Length 3Length 4Length 5 Algorithm \ #tags1101 1 GlobalTag 0.800.940.730.870.660.80 LocalTag+ 0.75 0.96 0.700.900.570.80 GutenTag 0.490.890.410.780.310.64

149. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Tag-based Database Search Tag filterSignificanceScore Tag extension De novo Db 55M peptides Candidate Peptides (700)

150. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Matching Multiple Tags Matching of a sequence tag against a database is fast Even matching many tags against a database is fast k tags can be matched against a database in time proportional to database size, but independent of the number of tags. keyword trees (Aho-Corasick algorithm) Scan time can be amortized by combining scans for many spectra all at once. build one keyword tree from multiple spectra

151. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Keyword Trees YAK S N N F F AT YFAK YFNS FNTA …..Y F R A Y F N T A…..

152. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Tag Extension FilterSignificanceScoreExtension De novo Db 55M peptides Candidate Peptides (700)

153. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Given: tag with prefix and suffix masses xyz match in the database Compute if a suffix and prefix match with allowable modifications. Compute a candidate peptide with most likely positions of modifications (attachment points). Fast Extension xyz

154. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Scoring Modified Peptides FilterSignificanceScoreExtension De novo Db 55M peptides

155. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Scoring Input: Candidate peptide with attached modifications Spectrum Output: Score function that normalizes for length, as variable modifications can change peptide length.

156. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Assessing Reliability of Identifications FilterSignificanceScoreextension De novo Db 55M peptides

157. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Selecting Features for Separating Correct and Incorrect Predictions Features: Score S: as computed Explained Intensity I: fraction of total intensity explained by annotated peaks. b-y score B: fraction of b+y ions annotated Explained peaks P: fraction of top 25 peaks annotated. Each of I,S,B,P features is normalized (subtract mean and divide by s.d.) Problem: separate correct and incorrect identifications using I,S,B,P

158. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Separating power of features

159. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Separating power of features Quality scores: Q = w I I + w S S + w B B + w P P The weights are chosen to minimize the mis-classification error

160. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Distribution of Quality Scores

161. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Results on ISB data-set All ISB spectra were searched. The top match is valid for 2978 spectra (2765 for Sequest) InsPecT-Sequest: 644 spectra (I-S dataset) Sequest-InsPecT: 422 spectra (S-I dataset) Average explained intensity of I-S = 52% Average explained intensity of S-I = 28% Average explained intensity I  S = 58% ~70 Met. Oxidations Run time is 0.7 secs. per spectrum (2.7 secs. for Sequest)

162. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Filtration Results The search was done against SWISS-PROT (54Mb). With 10 tags of length 3: The filtration is 1500 more efficient. Less than 4% of spectra are filtered out. The search time per spectrum is reduced by two orders of magnitude as compared to SEQUEST. PTMsTag Length # TagsFiltrationInsPecT Runtime SEQUEST Runtime None313.4×10 -7 0.17 sec> 1 minute 3101.6×10 -6 0.27 sec Phosphory lation 315.8×10 -7 0.21 sec> 2 minutes 3102.7×10 -6 0.38 sec

163. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info SPIDER: Yet Another Application of de novo Sequencing Suppose you have a good MS/MS spectrum of an elephant peptide Suppose you even have a good de novo reconstruction of this spectra However, until elephant genome is sequenced, it is hard to verify this de novo reconstruction Can you search de novo reconstruction of a peptide from elephant against human protein database? SPIDER algorithm addresses this comparative proteomics problem Slides from Bin Ma, University of Western Ontario

164. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Common de novo sequencing errors GG N and GG have the same mass

165. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info From de novo Reconstruction to Database Candidate through Real Sequence Given a sequence with errors, search for the similar sequences in a DB. (Seq) X: LSCFAV (Real) Y: SLCFAV (Match) Z: SLCF-V sequencing error (Seq) X: LSCF-AV (Real) Y: EACF-AV (Match) Z: DACFKAV mass(LS)=mass(EA) Homology mutations

166. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Alignment between de novo Candidate and Database Candidate If real sequence Y is known then: d(X,Z) = seqError(X,Y) + editDist(Y,Z) (Seq) X: LSCF-AV (Real) Y: EACF-AV (Match) Z: DACFKAV

167. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Alignment between de novo Candidate and Database Candidate If real sequence Y is known then: d(X,Z) = seqError(X,Y) + editDist(Y,Z) If real sequence Y is unknown then the distance between de novo candidate X and database candidate Z: d(X,Z) = min Y ( seqError(X,Y) + editDist(Y,Z) ) (Seq) X: LSCF-AV (Real) Y: EACF-AV (Match) Z: DACFKAV

168. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Alignment between de novo Candidate and Database Candidate If real sequence Y is known then: d(X,Z) = seqError(X,Y) + editDist(Y,Z) If real sequence Y is unknown then the distance between de novo candidate X and database candidate Z: d(X,Z) = min Y ( seqError(X,Y) + editDist(Y,Z) ) Problem: search a database for Z that minimizes d(X,Z) The core problem is to compute d(X,Z) for given X and Z. (Seq) X: LSCF-AV (Real) Y: EACF-AV (Match) Z: DACFKAV

169. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Computing seqError(X,Y) Align X and Y (according to mass). A segment of X can be aligned to a segment of Y only if their mass is the same! For each erroneous mass block (X i,Y i ), the cost is f(X i,Y i )=f(mass(X i )). f(m) depends on how often de novo sequencing makes errors on a segment with mass m. seqError(X,Y) is the sum of all f(mass(X i )). X Y Z seqError editDist (Seq) X: LSCFAV (Real) Y: EACFAV

170. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Computing d(X,Z) Dynamic Programming: Let D[i,j]=d(X[1..i], Z[1..j]) We examine the last block of the alignment of X[1..i] and Z[1..j]. (Seq) X: LSCF-AV (Real) Y: EACF-AV (Match) Z: DACFKAV

171. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Dynamic Programming: Four Cases Cases A, B, C - no de novo sequencing errors Case D: de novo sequencing error D[i,j]=D[i,j-1]+indel D[i,j]=D[i-1,j]+indel D[i,j]=D[i-1,j-1]+dist(X[i],Z[j])D[i,j]=D[i’-1,j’-1]+alpha(X[i’..i],Z[j’..j]) D[i,j] is the minimum of the four cases.

172. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Computing alpha(.,.) alpha(X[i’..i],Z[j’..j]) = min m(y)=m(X[i’..i]) [seqError (X[i’..i],y)+editDist(y,Z[j’..j])] = min m(y)=m[i’..i] [f(m[i’..i])+editDist(y,Z[j’..j])]. = f(m[i’..i]) + min m(y)=m[i’..i] editDist(y,Z[j’..j]). This is like to align a mass with a string. Mass-alignment Problem: Given a mass m and a peptide P, find a peptide of mass m that is most similar to P (among all possible peptides)

173. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Solving Mass-Alignment Problem

174. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Improving the Efficiency Homology Match mode: Assumes tagging (only peptides that share a tag of length 3 with de novo reconstruction are considered) and extension of found hits by dynamic programming around the hits. Non-gapped homology match mode: Sequencing error and homology mutations do not overlap. Segment Match mode: No homology mutations. Exact Match mode: No sequencing errors and homology mutations.

175. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Experiment Result The correct peptide sequence for each spectrum is known. The proteins are all in Swissprot but not in Human database. SPIDER searches 144 spectra against both Swissprot and human databases

176. An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Example Using de novo reconstruction X=CCQWDAEACAFNNPGK, the homolog Z was found in human database. At the same time, the correct sequence Y, was found in SwissProt database. Seq(X): CCQ[W ]DAEAC[AF] K Real(Y): CCK AD DAEAC FA VE GP K Database(Z): CCK[AD]DKETC[FA] K sequencing errors homology mutations