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Presentation on theme: "Www.bioalgorithms.infoAn Introduction to Bioinformatics Algorithms Protein Sequencing and Identification by Mass Spectrometry 1."— Presentation transcript:

1 Introduction to Bioinformatics Algorithms Protein Sequencing and Identification by Mass Spectrometry 1

2 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Outline Introduction to Protein Structure Peptide Mass Spectra De Novo Peptide Sequencing Spectrum Graphs Protein Identification via Database Search Spectral Convolution Spectral Alignment Problem 2 TK modified for WMU CS 6030

3 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Why are proteins and their sequences important? Necessary in order to understand how cells and their biochemical pathways function. A unique set of proteins is involved in each function Each organism has a unique set of expressed proteins Each type of cell / tissue has a unique set of expressed proteins A key to understanding how the brain or liver works is to determine what proteins they produce 3 TK Added for WMU CS 6030

4 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Basic Summary of Protein Structure A polypeptide is a polymer of amino acid residues, a linear chain based on amino acids A polypeptide can be completely specified by indicating the sequence of amino acids A protein is a collection of one more peptides bonded together 4

5 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info The Amino Acids 5

6 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Amino Acids – the basic building block 6

7 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Two amino acids can combine to form a dipeptide Formation of polypeptides Structure in blue is a peptide link If many amino acids are joined, we call it a polypeptide 7

8 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Note that a polypeptide is a chain of amino acid residues (water molecule is lost). End of chain with –NH 2 is the N-terminal End of chain with –COOH is the C-terminal Ends of the polypeptide chain 8

9 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Polypeptides -> Proteins 9

10 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Proteins can be complex structures 10

11 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Break proteins into peptide chain fragments Use enzymes to cut into pieces Further break apart peptide chains using mass spectrometry Peptide chains will break up in a manner predictable by molecular physics The masses of the molecular fragments will collectively deliver a “mass spectrum” from which the sequence can be derived First, we’ll explore the ways that mass spectrometry can break peptides apart De Novo Sequencing Strategy 11 TK added for WMU CS 6030

12 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Masses of Amino Acid Residues 12

13 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info The Periodic Table (part of it!) 13

14 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Protein Backbone 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 14

15 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Peptide Fragmentation Peptides tend to fragment along the backbone. Fragments can also loose neutral chemical groups like NH 3 and H 2 O. 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 15

16 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Breaking Protein into Peptides and Peptides into Fragment Ions Proteases, e.g. trypsin, break protein into 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. 16

17 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info N- and C-terminal Peptides N-terminal peptides C-terminal peptides 17

18 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Terminal peptides and ion types Peptide Mass (D) = 415 Peptide Mass (D) – 18 = 397 without 18

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

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

21 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 21

22 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 22

23 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Protein Identification with MS/MS GVDLK mass 0 Intensity mass 0 MS/MS Peptide Identification: 23

24 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Tandem Mass-Spectrometry 24

25 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Breaking Proteins into Peptides peptides MPSER …… GTDIMR PAKID …… HPLC To MS/MS MPSERGTDIMRPAKID protein 25

26 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 26

27 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Tandem Mass Spectrum Tandem Mass Spectrometry (MS/MS): mainly generates partial N- and C-terminal peptides Spectrum consists of different ion types because peptides can be broken in several places. Chemical noise often complicates the spectrum. Represented in 2-D: mass/charge axis vs. intensity axis 27

28 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 28

29 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info De Novo vs. Database Search: A Paradox The database of all peptides is huge ≈ O(20 n ). The database of all known peptides is much smaller ≈ O(10 8 ). 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 search space to find best one. De novo eliminates the need to scan database of all peptides by modeling the problem as a graph search. 29

30 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info De novo Peptide Sequencing Sequence 30

31 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Theoretical Spectrum 31

32 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Theoretical Spectrum (cont’d) 32

33 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Theoretical Spectrum (cont’d) 33

34 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Exhaustive Search Involves analysis of 20 L sequences of length L Branch and bound advisable, but success has been limited Analysis of Spectrum Graph Based on experimental spectrum rather than all possible matches to possible spectra Two approaches to determining sequence from the mass spectra 34 TK added slide for WMU CS 6030

35 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 paths How to find best path 35

36 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. 36

37 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} correspond to Δ={0, 17, 18} This is a set of masses of chemical groups frequently cleaved from peptide fragments during bombardment of molecules with electrons in the mass spectrometer collision cell *Note: In reality the δ value of ion type b is -1 but we will “hide” it for the sake of simplicity 37 TK modified slide for WMU CS 6030

38 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info The theoretical spectra of peptide P is designated as T(P) T(P) can be calculated by subtracting all possible ion types Δ={δ 1, δ 2,…, δ k } from all possible partial peptides of P Every partial peptide will have k masses in T(P) Theoretical Spectra 38 TK added slide for WMU CS 6030

39 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 (S) and theoretical spectra (T) is defined similarly 39

40 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 m: parent mass Output: P: peptide with mass m, whose theoretical spectrum T matches the experimental S spectrum the best 40

41 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Vertices of 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} 41

42 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Edges of Spectrum Graph Two vertices with mass difference corresponding to an amino acid A: Connect with an edge labeled by A 42

43 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info A possible peptide sequence is identified by finding a path from mass 0 to parent mass m in the resulting DAG Many possible sequences (paths) will typically be identified in the DAG The “best path” is identified by scoring using probabilities that are based on experimental data Peptide Sequences 43 TK added slide for WMU CS 6030

44 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 (mass) s Scoring = computing probabilities p(P,S) = π s є S p(P, s) 44

45 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 45

46 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 46

47 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 47

48 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 48

49 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. 49

50 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: 50

51 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). 51

52 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: 52

53 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: 53

54 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Graph experimental spectrum S = {s 1,…,s q } Label directed edges in graph that correspond to the mass of a single amino acid Find all possible peptide sequences, which are paths from 0 to m in the DAG Score possible sequences using probabilities of specific ion masses occurring Select the sequence with the maximum score Summary of Steps for Peptide Sequencing using a Spectrum Graph (8.12) 54 TK added slide for WMU CS 6030

55 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info De novo sequencing is often not feasible with experimental data because the resulting spectra may be incomplete However, de novo algorithm is much faster! Since thousands of proteins have been sequenced, a database search is possible Database search is therefore a more practical solution in most cases May save time in assay/experiment design SEQUEST is a program that implements database search algorithm Protein Identification via Database Search (8.13) 55 Added by TK for WMU CS 6030 References:

56 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 in the search space to find best one. De novo eliminates the need to scan all peptides by modeling the problem as a graph search. Why not sequence de novo? 56

57 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 m: parent mass Output: A peptide with mass m, whose theoretical spectrum matches the experimental S spectrum the best 57

58 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 m: parent mass Output: A peptide of mass m from the database whose theoretical spectrum matches the experimental S spectrum the best 58

59 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info MS/MS Database Search Database search in mass-spectrometry has been very 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. 59

60 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. 60

61 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 pathways of proteins. 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 61

62 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 200 types of modifications of amino acid residues are known. 62

63 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. 63

64 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. 64

65 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. 65

66 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 m: parent mass Output: A peptide of mass m from the database whose theoretical spectrum matches the experimental S spectrum the best 66

67 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 m: parent mass Parameter k (# of mutations/modifications) Output: A peptide of mass m that is at most k mutations/modifications apart from a database peptide and whose theoretical spectrum matches the experimental S spectrum the best 67

68 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Database Search: Sequence Analysis vs. MS/MS Analysis 68

69 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. 69

70 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. 70

71 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 71

72 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Convolution 72

73 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 73

74 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info The simplest approach is to base comparison only on SPC A more sophisticated, but still naïve, approach is to consider the mass differences that correspond to a known peptide modification. A high multiplicity of such a difference would indicate a possible match. Naïve approaches to using Spectral Convolution 74 Added by TK for WMU CS 6030 References:

75 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. 75

76 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Comparison: Difficult Case S S’ S S’’ 76

77 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. 77

78 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 +  } 78

79 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 shift (4, -5) shift (7,-3) 79

80 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. 80

81 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Summary Introduction to Protein Structure Peptide Mass Spectra De Novo Peptide Sequencing Spectrum Graphs Protein Identification via Database Search Spectral Convolution Spectral Alignment Problem 81 TK modified for WMU CS 6030

82 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info References Jones, Neil C., and Pevzner, Pavel A., An Introduction to Bioinformatics Algorithms, chapter 8, and Mass Spectrometry slides at Russell, Peter J., iGenetics, A Molecular Approach, chapter 6 (Gene Expression: Translation) Hoppe, Pamela (WMU), lecture slides from BIOS 2500 (General Genetics) “The Structure of Proteins”, SEQUEST site, 82 TK added for WMU CS 6030

83 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Additional Slides from Bioinformatics.info 83 TK modified for WMU CS 6030

84 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Representing Spectra in 0-1 Alphabet Convert spectrum to a 0-1 string with 1s corresponding to the positions of the peaks. 84

85 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! 85

86 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Spectral Alignment vs. Sequence Alignment Manhattan-like 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. 86

87 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  SPC: the number of 1s at the main diagonal.  -shifted SPC: the number of 1s on the diagonal (i,i+  ) 87

88 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. 88

89 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 89

90 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 90

91 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) =  91

92 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. Running time: O(n 4 k) 92

93 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) 93

94 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Fast Spectral Alignment Algorithm Running time: O(n 2 k) 94

95 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. 95

96 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 96

97 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Filtration: Combining de novo 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? 97

98 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Why Filtration ? 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 98

99 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.. 99

100 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? 100

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

102 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! 102

103 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: 103

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

105 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. 105

106 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 ELT LTK

107 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 PET

108 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. 108

109 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 109

110 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 110

111 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 111

112 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Experimental Results Results are for 280 spectra of doubly charged tryptic peptides from the ISB and OPD datasets. Length 3Length 4Length 5 Algorithm \ #tags GlobalTag LocalTag GutenTag

113 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Tag-based Database Search Tag filterSignificanceScore Tag extension De novo Db 55M peptides Candidate Peptides (700) 113

114 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 114

115 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….. 115

116 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Tag Extension FilterSignificanceScoreExtension De novo Db 55M peptides Candidate Peptides (700) 116

117 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 117

118 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Scoring Modified Peptides FilterSignificanceScoreExtension De novo Db 55M peptides 118

119 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. 119

120 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Assessing Reliability of Identifications FilterSignificanceScoreextension De novo Db 55M peptides 120

121 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 121

122 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Separating power of features 122

123 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 123

124 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Distribution of Quality Scores 124

125 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) 125

126 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Results for Mus-IMAC data-sets The Alliance for Cellular signalling is looking at proteins phosphorylated in specific signal transduction pathways spectra are searched with upto 4 modifications (upto 3 Met. Oxidation and upto 2 Phos.) 281 phosphopeptides with P-value <

127 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info 127

128 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× sec> 1 minute × sec Phosphory lation 315.8× sec> 2 minutes × sec 128

129 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Conclusion With 10 tags of length 3: The filtration is 1500 more efficient than using only the parent mass alone. Less than 4% of the positive peptides are filtered out. The search time per spectrum is reduced from over a minute (SEQUEST) to 0.4 seconds. 129

130 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 (Han, Ma, Zhang ) addresses this comparative proteomics problem Slides from Bin Ma, University of Western Ontario 130

131 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Common de novo sequencing errors GG N and GG have the same mass 131

132 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 132

133 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 133

134 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 134

135 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 135

136 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 136

137 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 137

138 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. 138

139 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) 139

140 An Introduction to Bioinformatics Algorithmswww.bioalgorithms.info Solving Mass-Alignment Problem 140

141 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. 141

142 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 142

143 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 143


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