Protein Sequencing and Identification by Mass Spectrometry

Transcription

1 Protein Sequencing and Identification by Mass Spectrometry

2 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 Different Amino Acid Have Different Masses H...-HN-CH-CO-NH-CH-CO-NH-CH-CO- OH N-terminus R i-1 R i R i+1 C-terminus AA residue i-1 AA residue i AA residue i+1

4 Peptide Fragmentation Collision Induced Dissociation H...-HN-CH-CO... NH-CH-CO-NH-CH-CO- OH R i-1 R i R i+1 H + Prefix Fragment Suffix Fragment Peptides tend to fragment along the backbone. Mass spectrometer is a sophisticated (and rather expensive!) scale to measure the masses of these fragments

5 Breaking Protein into Peptides and Peptides into Fragment Ions Most mass spectrometers can only measure masses of short peptides (e.g., 20 amino acids or less) 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.

6 N- and C-terminal Peptides

7 Terminal peptides and ion types Peptide Mass (D) = 415

8 Masses of fragment ions Peptide Mass (D) = 415 Peptide without Mass (D) = 397

9 N- and C-terminal Peptides

10 N- and C-terminal Peptides

11 Theoretical Spectrum Reconstruct peptide from the set of masses of fragment ions (mass-spectrum)

12 Reconstructing Peptides Reconstruct peptide from the set of masses of fragment ions (mass-spectrum)

13 Reconstructing Peptides Reconstruct peptide from the set of masses of fragment ions (mass-spectrum)

14 Reconstructing Peptides Reconstruct peptide from the set of masses of fragment ions (mass-spectrum)

15 Peptide Fragmentation b 2 -H 2 O b 3 - NH 3 a 2 b 2 a 3 b 3 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 y 3 y 2 y 1 y 3 -H 2 O y 2 - NH 3

16 H 2 O Mass Spectra G V D L K 57 Da = K L G 99 Da = V D V G 0 mass The peaks in the mass spectrum: Prefix and Suffix Fragments. Fragments with neutral losses (-H 2 O, -NH 3 ) Noise and missing peaks.

17 Intensity Protein Identification with MS/MS Protein database MS/MS Peptide Identification 0 mass

18 Relative Abundance 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 S#: 1708 RT: AV: 1 NL: 5.27E6 T: + c d Full ms [ ] m/z

19 Tandem Mass-Spectrometry

20 Breaking Proteins into Peptides MPSERGTDIMRPAKID... protein GTDIMR PAKID MPSER peptides HPLC To MS/MS

21 Mass Spectrometry Matrix-Assisted Laser Desorption/Ionization (MALDI) From lectures by Vineet Bafna (UCSD)

22 Relative Abundance Relative Abundance Relative Abundance Tandem Mass Spectrometry RT: LC Time (min) NL: 1.52E8 Base Peak F: + c Full ms [ ] S#: 1707 RT: AV: 1 NL: 2.41E7 F: + c Full ms [ ] MS Scan m/z S#: 1708 RT: AV: 1 NL: 5.27E6 T: + c d Full ms [ ] Ion Source MS-1 collision cell MS MS/MS Scan m/z

23 Relative Abundance Protein Identification by Tandem Mass Spectrometry (MS/MS) S e q u e n c e MS/MS instrument database search Sequest, Mascot, etc 0 de novo interpretation Lutefisk, Peaks, etc S#: 1708 RT: AV: 1 NL: 5.27E6 T: + c d Full ms [ ] m/z

24 S#: 1708 RT: AV: 1 NL: 5.27E6 T: + c d Full ms [ ] Relative Abundance m/z De Novo vs. Database Search Database Search De Novo Database of known peptides MDERHILNM, KLQWVCSDL, PTYWASDL, ENQIKRSACVM, TLACHGGEM, NGALPQWRT, HLLERTKMNVV, GGPASSDA, GGLITGMQSD, MQPLMNWE, ALKIIMNVRT, AVGELTK, HEWAILF, GHNLWAMNAC, GVFGSVLRA, EKLNKAATYIN.. Mass, Score W Database of all peptides = 20 n A V AAAAAAAA,AAAAAAAC,AAAAAAAD,AAAAAAAE, L G T AAAAAAAG,AAAAAAAF,AAAAAAAH,AAAAAAI, E P C L K AVGELTI, AVGELTK W, AVGELTL, AVGELTM, D T YYYYYYYS,YYYYYYYT,YYYYYYYV,YYYYYYYY R AVGELTK

25 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.

26 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 % of the text. Suppose you search for a word in a text. Would it be possible to ignore % 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.

27 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 % of the text. Suppose you search for a word in a text. Would it be possible to ignore % 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 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 % of the text. Filtration algorithms (like FASTA or BLAST) ignore % of the text. Finding spelling errors. Sequence alignment algorithms (like Smith- Waterman) do it in quadratic time

29 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 % of the database. Suppose you compare a spectrum against a database. Would it be possible to ignore % 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.

30 Three Solutions Comparing a million spectra against a database. InsPecT (Tanner et al., Anal. Chem, 2005) MS/MS database search without even looking at % of the database. 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)

31 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?

32 Relative Abundance De novo Peptide Sequencing S#: 1708 RT: AV: 1 NL: 5.27E6 T: + c d Full ms [ ] m/z Sequence

33 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

34 b-ions (prefix or N-terminal ions) S E Q U E N C E Mass/Charge (M/Z)

35 a-ions = b-ions - CO = b-ions - 28 S E Q U E N C E Mass/Charge (M/Z)

36 Shifting Peaks: a-ions = b-ions - CO = b-ions - 28 S E Q U E N C E Mass/Charge (M/Z)

37 y-ions (suffix of C-terminal ions) E C N E U Q E S Mass/Charge (M/Z)

38 Intensity An Introduction to Bioinformatics Algorithms Mass/Charge (M/Z)

39 Intensity An Introduction to Bioinformatics Algorithms Mass/Charge (M/Z)

40 noise Mass/Charge (M/Z)

41 Intensity MS/MS Spectrum Mass/Charge (M/z)

42 Some Mass Differences between Peaks Correspond to Amino Acids u s e s e c e q n q u u e e e n n q c c e e s e

43 Some Mass Differences between Peaks Correspond to Amino Acids u s e s e c e q n q u u e e e n n q c c e e s e

44 Ion Types Some masses correspond to fragment ions, others are just random noise Knowing ion types Δ={δ 1, δ 2,, δ k } allows one to 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.

45 Example of Ion Type Δ={δ 1, δ 2,, δ k } Ion types correspond to {b, b-nh 3, b-h 2 O, b-co} 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

46 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

47 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

48 Shifting Peaks: a-ions = b-ions - CO = b-ions - 28 S E Q U E N C E Mass/Charge (M/Z)

49 Reverse Shifts Shift in H 2 O Shift in H 2 O+NH 3

50 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}

51 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)

52 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

53 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 sєs p(p, s)

54 Peak Score For a position t that represents ion type d j : p(p,s t ) = q j, if peak is generated at t 1-q j, otherwise

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

56 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: p(p',s) max P p(p,s) Peptides = paths in the spectrum graph P = the optimal path in the spectrum graph

57 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

58 Ions and Probabilities A peptide has all k peaks with probability k q i i 1 and no peaks with probability i k 1 (1 q i ) A peptide also produces a ``random noise'' with uniform probability q R in any position.

59 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: q R q q R (1 (1 q q q R ) ) q q R

60 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 probability q j. is generated with R=T- U T i - set of positions that are not associated with any partial peptides (noise).

61 Probabilistic Model For a position t δj T i the probability p(t, P,S) that peptide P produces a peak at position t. P( t, P, S) 1 q j q j if a peak is generatedat position t otherwise j Similarly, for t R, the probability that P produces a random noise peak at t is: P R ( t) 1 q R q R if a peak is generatedat position t otherwise

62 Probabilistic Score For a peptide P with n amino acids, the score for the whole peptides is expressed by the following ratio test: n i k j i R i R j j t p S P t p S p S P p 1 1 ) ( ),, ( ) ( ), (

63 S#: 1708 RT: AV: 1 NL: 5.27E6 T: + c d Full ms [ ] Relative Abundance m/z De Novo vs. Database Search Database Search De Novo Database of known peptides MDERHILNM, KLQWVCSDL, PTYWASDL, ENQIKRSACVM, TLACHGGEM, NGALPQWRT, HLLERTKMNVV, GGPASSDA, GGLITGMQSD, MQPLMNWE, ALKIIMNVRT, AVGELTK, HEWAILF, GHNLWAMNAC, GVFGSVLRA, EKLNKAATYIN.. A C L V G P W W E T L R T D K AVGELTK

64 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?

65 Why Not Sequence De Novo? De novo sequencing is not very accurate: Algorithm Amino Acid Accuracy Less than 30% of the peptides sequenced were completely correct! Whole Peptide Accuracy Lutefisk, SHERENGA, Peaks, PepNovo,

66 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.

67 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

68 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

69 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.

70 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

71 Post-Translational Modifications Proteins are involved in cellular signaling and metabolic regulation. They are subject to a large number of biological modifications. Most protein sequences are post-translationally modified and 600 types (!) of modifications of amino acid residues are known.

72 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.

73 Peptide Masses

74 Peptide Masses: Modification +16 on N

75 Reconstructing Modified Peptides Reconstruct peptide from the set of masses of fragment ions (mass-spectrum)

76 Reconstructing Modified Peptides Reconstruct peptide from the set of masses of fragment ions (mass-spectrum)

77 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

78 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

79 Search for Modified Peptides: Virtual Database Approach Yates et al.,1995: an exhaustive search in a virtual database of all modified peptides. YFDSTDYNMAK 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. Extend the virtual database approach to a large set of modifications. Oxidation? Phosphorylation? 2 5 =32 possibilities, with 2 types of modifications!

80 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 the restrictive PTM search algorithms do.

81 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.

82 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

83 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.

84 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.

85 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

86 Spectral Convolution S2 Number of S1 {s2 pairs s1 ( S 2 s1:s1 S1,s2 S2 } S1, s2 S2with s2 S )( x) 1 s 1 x : The shared peaks count ( S S )(0) 2 1 (SPC peak):

87 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

88 Spectral Convolution: An Example x

89 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.

90 Spectral Comparison: Difficult Case S S S S

91 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.

92 Sequence Alignment=Path in a Grid Finding similarities between two peptides A R N G A L R A 1 1 R 1 1 N 1 G 1 Z A 1 1 L 1 R 1 1 is equivalent to finding an optimal path in a Manhattan-like grid (sequence alignment).

93 Sequence Alignment=Path in a Grid Finding similarities between two peptides A R N G A L R A 1 1 R 1 1 N 1 G 1 Z A 1 1 L 1 R 1 1 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.

94 Sequence Alignment=Path in a Grid A R N G A L R A 1 1 R 1 1 N 1 G 1 Z A 1 1 L 1 R 1 1 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)?

95 Converting Spectra into 0-1 Sequences Convert spectrum into a 0-1 string with 1s corresponding to the positions of the peaks.

96 Modified peptide Modifications are modeled as insertion (or deletions) of blocks of zeroes Spectrum Peptide A modification with positive offset - inserting a block of 0s A modification with negative offset - deleting a block of 0s

97 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!

98 Spectral Alignment Graph A B C D E Horizontal axis: Experimental spectrum Vertical axis: Theoretical spectrum of a peptide

99 Spectral Alignment Graph A B C D E 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

100 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.

101 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 into {a 1,., a n } {a 1,.,a i-1,a i +,,a n + }

102 Shifts: An Example The shift (i, ) transforms {a 1,., a n } into {a 1,.,a i-1,a i +,,a n + } e.g shift (4, -5) shift (7,-3)

103 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.

104 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!

105 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 SPC: the number of 1s at the main diagonal. -shifted SPC: the number of 1s on the diagonal (i,i+ )

106 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.

107 Use of k-similarity 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.

108 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

109 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

110 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. D ij ( k) max ( i', j') ( i, j) { D i' j' D i' j' ( k) 1, if ( i', D( k) max D ( k) j') ~ ( i, j) ( k 1) 1, otherwise ij ij (i,j ) ~ (i,j): the points are located on the same diagonal Running time: O(n 4 k)

111 Edit Graph for Fast Spectral Alignment diag(i,j) the position of previous 1 on the same diagonal as (i,j)

112 Fast Spectral Alignment Algorithm Running time: O(n 2 k) M D M ij ij ij ( k) max Di ' j' ( k) ( k) ( i', j') max max ( i, j) D M M M diag( i, j) i 1, j D ij i 1, j i, j 1 ( k) 1 ( k) ( k ( k) ( k) ( k) 1 1) 1

113 Spectral Alignment: Complications Spectra are combinations of an increasing (Nterminal 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.

114 Spectral Alignment: Complications Simultaneous analysis of N- and C-terminal ions Taking into account the intensities and charges Analysis of minor ions

115 MS/MS and East-West Traveling Salesman Problem

116 Anti-symmetric paths De-novo problem Input: Output: Spectrum graph Anti-symmetric longest path E D T E S S S S E T D E E Anti-symmetric path problem (Tim Chen, SODA 2001) avoids reusing the same peak twice (as both b- and y-ions) in the optimal path Without anti-symmetric condition, the correct peptide SETDE would be missed and the algorithm would output a symmetric peptide: Why? ESESE

117 PTM Frequency Matrix A C D E F G H I K L M N P Q R S T V W Y ## ## ## ## ## ## ,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)

118 PTM Frequency Matrix 14 on K - Methylation 16 on M - Oxidation A C D E F G H I K L M N P Q R S T V W Y ## ## ## ## ## ## on W - Oxidation 22 - Sodium 28 on K - Dimethylation 32 on M - Double oxidation

119 Filtration in Similarity Searches Sequence Alignment: Smith-Waterman BLAST Algorithm Protein Query Sequence matches Filtration Scoring Database actgcgctagctacggatagctgatcc agatcgatgccataggtagctgatcc atgctagcttagacataaagcttgaat cgatcgggtaacccatagctagctcg atcgacttagacttcgattcgatcgaat tcgatctgatctgaatatattaggtccg atgctagctgtggtagtgatgtaaga BLAST filters out very few correct matches and is almost as accurate as Smith Waterman algorithm.

120 Filtration and MS/MS Peptide Sequencing SEQUEST / Mascot MS/MS spectrum Sequence matches Filtration Scoring Database MDERHILNMKLQWVCSDLPT YWASDLENQIKRSACVMTLA CHGGEMNGALPQWRTHLLE RTYKMNVVGGPASSDALITG MQSDPILLVCATRGHEWAILF GHNLWACVNMLETAIKLEGVF GSVLRAEKLNKAAPETYIN..

121 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. Can we design a filtration based search that can replace the database search, and is orders of magnitude faster?

122 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) SHERENGA (Dancik et. al., 1999) Peaks (Ma et al., 2003) PepNovo (Frank and Pevzner, 2005)

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

124 Peptide Sequence Tags A Peptide Sequence Tag is short substring of a peptide. Example: Tags: G V D L K G V D V D L D L K

125 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 MultiTag - Sunayev et. al OpenSea - Searle et. al

126 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.

127 Tag Generation - Global Tags A C L V W G P W E T L T D R K AVGELTK TAG Prefix Mass AVG 0.0 VGE 71.0 GEL ELT LTK 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.

128 Tag Generation - Local Tags W R TAG Prefix Mass A C L V P W G E T L D T K AVG 0.0 WTD PET Extract the highest scoring subspaths from the spectrum graph. Sometimes gets misled by locally promising-looking garden paths.

129 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.

130 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

131 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

132 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

133 Experimental Results Length 3 Length 4 Length 5 Algorithm \ #tags GlobalTag LocalTag GutenTag

134 Tag-based Database Search Candidate Peptides (700) Db 55M peptides Tag filter Tag extension Score Significance De novo

135 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

136 Keyword Trees Y F A K N S F YFAK YFNS FNTA N T A..Y F R A Y F N T A..

137 Tag Extension Candidate Peptides (700) Db 55M peptides Filter Extension Score Significance De novo

138 Fast Extension Given: tag with prefix and suffix masses <m P > xyz <m S > match in the database <m P >xyz<m S > xyz Compute if a suffix and prefix match with allowable modifications. Compute a candidate peptide with most likely positions of modifications (attachment points).

139 Scoring Modified Peptides Db 55M peptides Filter Extension Score Significance De novo

140 Scoring Input: Candidate peptide with attached modifications Spectrum Output: Score function that normalizes for length, as variable modifications can change peptide length.

141 Assessing Reliability of Identifications Db 55M peptides Filter extension Score Significance De novo

142 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

143 Separating power of features

144 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

145 Distribution of Quality Scores

146 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)

147 Filtration Results PTMs Tag Length # Tags Filtration InsPecT Runtime SEQUEST Runtime None sec > 1 minute sec Phosphory sec > 2 minutes lation sec 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.

148 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

149 Common de novo sequencing errors N and GG have the same mass GG

150 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 Homology mutations (Seq) X: LSCF-AV (Real) Y: EACF-AV (Match) Z: DACFKAV mass(ls)=mass(ea)

151 Alignment between de novo Candidate and Database Candidate (Seq) X: LSCF-AV (Real) Y: EACF-AV (Match) Z: DACFKAV If real sequence Y is known then: d(x,z) = seqerror(x,y) + editdist(y,z)

152 Alignment between de novo Candidate and Database Candidate (Seq) X: LSCF-AV (Real) Y: EACF-AV (Match) Z: DACFKAV 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) )

153 Alignment between de novo Candidate and Database Candidate (Seq) X: LSCF-AV (Real) Y: EACF-AV (Match) Z: DACFKAV 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.

154 Computing seqerror(x,y) Align X and Y (according to mass). (Seq) X: LSCFAV (Real) Y: EACFAV 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

155 Computing d(x,z) (Seq) X: LSCF-AV (Real) Y: EACF-AV (Match) Z: DACFKAV 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].

156 Dynamic Programming: Four Cases D[i,j]=D[i,j-1]+indel D[i,j]=D[i-1,j]+indel Cases A, B, C - no de novo sequencing errors Case D: de novo sequencing error 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.

157 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)

158 Solving Mass-Alignment Problem ]) [, ( 1)])..( [ ), ( ( min 1)])..( [, ( ]).. [ ), ( ( min min ]).. [, ( j Z y dist j i Z y m m indel j i Z m indel j i Z y m m j i Z m y y

159 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.

160 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

161 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. sequencing errors Seq(X): CCQ[W ]DAEAC[AF]<NN><PG>K Real(Y): CCK AD DAEAC FA VE GP K Database(Z): CCK[AD]DKETC[FA]<EE><GK>K homology mutations