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Statistical Significance for Peptide Identification by Tandem Mass Spectrometry. Nathan Edwards Center for Bioinformatics and Computational Biology University of Maryland, College Park. Mass Spectrometry for Proteomics. Measure mass of many (bio)molecules simultaneously High bandwidth - PowerPoint PPT Presentation
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Statistical Significance for
Peptide Identification by
Tandem Mass Spectrometry
Statistical Significance for
Peptide Identification by
Tandem Mass SpectrometryNathan EdwardsCenter for Bioinformatics and Computational BiologyUniversity of Maryland, College Park
2
Mass Spectrometry for Proteomics
• Measure mass of many (bio)molecules simultaneously• High bandwidth
• Mass is an intrinsic property of all (bio)molecules• No prior knowledge required
3
Mass Spectrometry for Proteomics
• Measure mass of many molecules simultaneously• ...but not too many, abundance bias
• Mass is an intrinsic property of all (bio)molecules• ...but need a reference to compare to
4
High Bandwidth
100
0250 500 750 1000
m/z
% I
nte
nsit
y
5
Mass is fundamental!
6
Mass Spectrometry for Proteomics
• Mass spectrometry has been around since the turn of the century...• ...why is MS based Proteomics so new?
• Ionization methods• MALDI, Electrospray
• Protein chemistry & automation• Chromatography, Gels, Computers
• Protein sequence databases• A reference for comparison
7
Sample Preparation for Peptide Identification
Enzymatic Digestand
Fractionation
8
Single Stage MS
MS
m/z
9
Tandem Mass Spectrometry(MS/MS)
Precursor selection
m/z
m/z
10
Tandem Mass Spectrometry(MS/MS)
Precursor selection + collision induced dissociation
(CID)
MS/MS
m/z
m/z
11
Peptide Fragmentation
H…-HN-CH-CO-NH-CH-CO-NH-CH-CO-…OH
Ri-1 Ri Ri+1
AA residuei-1 AA residuei AA residuei+1
N-terminus
C-terminus
Peptides consist of amino-acids arranged in a linear backbone.
12
Peptide Fragmentation
13
Peptide Fragmentation
-HN-CH-CO-NH-CH-CO-NH-
RiCH-R’
bi
yn-iyn-i-1
bi+1
R”
i+1
i+1
14
Peptide Fragmentation
Peptide: S-G-F-L-E-E-D-E-L-K
y1
y2
y3
y4
y5
y6
y7
y8
y9
ion
1020
907
778
663
534
405
292
145
88
MW
762SGFL EEDELKb4
389SGFLEED ELKb7
MWion
633SGFLE EDELKb5
1080S GFLEEDELKb1
1022SG FLEEDELKb2
875SGF LEEDELKb3
504SGFLEE DELKb6
260SGFLEEDE LKb8
147SGFLEEDEL Kb9
15
Peptide Fragmentation
100
0250 500 750 1000
m/z
% I
nte
nsit
y
K1166
L1020
E907
D778
E663
E534
L405
F292
G145
S88 b ions
147260389504633762875102210801166 y ions
16
Peptide Fragmentation
K1166
L1020
E907
D778
E663
E534
L405
F292
G145
S88 b ions
100
0250 500 750 1000
m/z
% I
nte
nsit
y
147260389504633762875102210801166 y ions
y6
y7
y2 y3 y4
y5
y8 y9
b3
b5 b6 b7b8 b9
b4
17
Peptide Identification
• For each (likely) peptide sequence1. Compute fragment masses2. Compare with spectrum3. Retain those that match well
• Peptide sequences from protein sequence databases• Swiss-Prot, IPI, NCBI’s nr, ...
• Automated, high-throughput peptide identification in complex mixtures
18
High Quality Peptide Identification: E-value < 10-8
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Moderate quality peptide identification: E-value < 10-3
20
Amino-Acid Molecular Weights
Amino-Acid Residual MW Amino-Acid Residual MW
A Alanine 71.03712 M Methionine 131.04049
C Cysteine 103.00919 N Asparagine 114.04293
D Aspartic acid 115.02695 P Proline 97.05277
E Glutamic acid 129.04260 Q Glutamine 128.05858
F Phenylalanine 147.06842 R Arginine 156.10112
G Glycine 57.02147 S Serine 87.03203
H Histidine 137.05891 T Threonine 101.04768
I Isoleucine 113.08407 V Valine 99.06842
K Lysine 128.09497 W Tryptophan 186.07932
L Leucine 113.08407 Y Tyrosine 163.06333
21
Peptide Identification
• Peptide fragmentation by CID is poorly understood
• MS/MS spectra represent incomplete information about amino-acid sequence• I/L, K/Q, GG/N, …
• Correct identifications don’t come with a certificate!
22
Peptide Identification
• High-throughput workflows demand we analyze all spectra, all the time.
• Spectra may not contain enough information to be interpreted correctly• …bad static on a cell phone
• Peptides may not match our assumptions• …its all Greek to me
• “Don’t know” is an acceptable answer!
23
Peptide Identification
• Rank the best peptide identifications
• Is the top ranked peptide correct?
24
Peptide Identification
• Rank the best peptide identifications
• Is the top ranked peptide correct?
25
Peptide Identification
• Rank the best peptide identifications
• Is the top ranked peptide correct?
26
Peptide Identification
• Incorrect peptide has best score• Correct peptide is missing?• Potential for incorrect conclusion• What score ensures no incorrect
peptides?• Correct peptide has weak score
• Insufficient fragmentation, poor score• Potential for weakened conclusion• What score ensures we find all correct
peptides?
27
Statistical Significance
• Can’t prove particular identifications are right or wrong...• ...need to know fragmentation in advance!
• A minimal standard for identification scores...• ...better than guessing.• p-value, E-value, statistical significance
28
Pin the tail on the donkey…
29
Probability Concepts
Throwing darts• One at a time• Blindfolded
Uniform distribution?Independent?Identically distributed?
Pr [ Dart hits 20 ] = 0.05
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Probability Concepts
Throwing darts• One at a time• Blindfolded• Three darts
Pr [Hitting 20 3 times] = 0.05 * 0.05 * 0.05
Pr [Hit 20 at least twice] = 0.007125 + 0.000125
0 times 0.857375
1 times 0.135375
2 times 0.007125
3 times 0.000125
31
Probability Concepts
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability 0.857375 0.135375 0.007125 0.000125
0 1 2 3
32
Probability Concepts
Throwing darts• One at a time• Blindfolded• 100 darts
Pr [Hitting 20 3 times] = 0.139575
Pr [Hit 20 at least twice] = 0.9629188
0 times 0.005920
1 times 0.031160
2 times 0.081181
3 times 0.139575
33
Probability ConceptsHistogram of rbinom(10000, 100, 0.05)
rbinom(10000, 100, 0.05)
Fre
qu
en
cy
0 5 10 15
05
00
10
00
15
00
34
Match Score
• Dartboard represents the mass range of the spectrum
• Peaks of a spectrum are “slices”• Width of slice corresponds to mass tolerance
• Darts represent • random masses
• masses of fragments of a random peptide• masses of peptides of a random protein• masses of biomarkers from a random class
• How many darts do we get to throw?
35
Match Score
100
0250 500 750 1000 m/z
% I
nte
nsit
y
270
755 580
550
330
870
• What is the probability that we match at least 5 peaks?
36
Match Score
• Pr [ Match ≥ s peaks ] = Binomial( p , n ) ≈ Poisson( p n ), for small p and large n
p is prob. of random mass / peak match,n is number of darts (fragments in our answer)
37
Match Score
Theoretical distribution• Used by OMSSA• Proposed, in various forms, by many.
• Probability of random mass / peak match• IID (independent, identically distributed)• Based on match tolerance
38
Match Score
Theoretical distribution assumptions• Each dart is independent
• Peaks are not “related”
• Each dart is identically distributed• Chance of random mass / peak match is
the same for all peaks
39
Tournament Size
0 2 4 6 8 10 12
0.00
0.05
0.10
0.15
0 2 4 6 8 10 12
0.00
0.05
0.10
0.15
0 5 10 15
0.00
0.05
0.10
0.15
0 5 10 15
0.00
0.05
0.10
0.15
100
Dar
ts, #
20’
s
100 people 1000 people10000 people 100000 people
40
Tournament Size10
0 D
arts
, # 2
0’s
100 people 1000 people10000 people 100000 people
10 12 14 16 18
010
2030
4050
10 12 14 16 18
010
2030
4050
10 12 14 16 18
010
2030
4050
10 12 14 16 18
010
2030
4050
41
Number of Trials
• Tournament size == number of trials• Number of peptides tried• Related to sequence database size
• Probability that a random match score is ≥ s• 1 – Pr [ all match scores < s ]• 1 – Pr [ match score < s ] Trials (*)• Assumes IID!
• Expect value • E = Trials * Pr [ match ≥ s ]• Corresponds to Bonferroni bound on (*)
42
Better Dart Throwers
43
Better Random Models
• Comparison with completely random model isn’t really fair
• Match scores for real spectra with real peptides obey rules
• Even incorrect peptides match with non-random structure!
44
Better Random Models
• Want to generate random fragment masses (darts) that behave more like the real thing:• Some fragments are more likely than others• Some fragments depend on others
• Theoretical models can only incorporate this structure to a limited extent.
45
Better Random Models
• Generate random peptides• Real looking fragment masses• No theoretical model!• Must use empirical distribution• Usually require they have the correct
precursor mass
• Score function can model anything we like!
46
Better Random Models
Fenyo & Beavis, Anal. Chem., 2003
47
Better Random Models
Fenyo & Beavis, Anal. Chem., 2003
48
Better Random Models
• Truly random peptides don’t look much like real peptides
• Just use peptides from the sequence database!
• Caveats:• Correct peptide (non-random) may be included• Peptides are not independent
• Reverse sequence avoids only the first problem
49
Extrapolating from the Empirical Distribution
• Often, the empirical shape is consistent with a theoretical model
Geer et al., J. Proteome Research, 2004 Fenyo & Beavis, Anal. Chem., 2003
50
False Positive Rate Estimation
• Each spectrum is a chance to be right, wrong, or inconclusive.• How many decisions are wrong?
• Given identification criteria:• SEQUEST Xcorr, E-value, Score, etc., plus...• ...threshold
• Use “decoy” sequences• random, reverse, cross-species• Identifications must be incorrect!
51
False Positive Rate Estimation
• # FP in real search = # hits in decoy search• Need same size database, or rate conversion
• FP Rate: # decoy hits # real hits
• FP Rate: 2 x # decoy hits . (# real hits + # decoy hits)
52
False Positive Rate Estimation
• A form of statistical significance• In “theory”, E-value and a FP rate are the
same.• Search engine independent
• Easy to implement• Assumes a single threshold for all
spectra• Spectrum/Peptide Identification scores are
not iid!...• ...but E-values, in principle, are.
53
Peptide Prophet
• From the Institute for Systems Biology• Keller et al., Anal. Chem. 2002
• Re-analysis of SEQUEST results
• Spectra are trials • Assumes that many of the spectra are
not correctly identified
54
Peptide Prophet
Distribution of spectral scores in the results
Keller et al., Anal. Chem. 2002
55
Peptide Prophet
• Assumes a bimodal distribution of scores, with a particular shape
• Ignores database size• …but it is included implicitly
• Like empirical distribution for peptide sampling, can be applied to any score function• Can be applied to any search engines’ results
56
Peptide Prophet
• Caveats• Are spectra scores sampled from the same
distribution?• Is there enough correct identifications for second
peak?• Are spectra independent observations?• Are distributions appropriately shaped?
• Huge improvement over raw SEQUEST results
57
Peptides to Proteins
Nesvizhskii et al., Anal. Chem. 2003
58
Peptides to Proteins
59
Peptides to Proteins
• A peptide sequence may occur in many different protein sequences• Variants, paralogues, protein families
• Separation, digestion and ionization is not well understood
• Proteins in sequence database are extremely non-random, and very dependent
60
Publication Guidelines
61
Publication Guidelines
1. Computational parameters• Spectral processing• Sequence database• Search program• Statistical analysis
2. Number of peptides per protein• Each peptide sequence counts once!• Multiple forms of the same peptide
count once!
62
Publication Guidelines
3. Single-peptide proteins must be explicitly justified by
• Peptide sequence• N and C terminal amino-acids• Precursor mass and charge• Peptide Scores• Multiple forms of the peptide counted once!
4. Biological conclusions based on single-peptide proteins must show the spectrum
63
Publication Guidelines
5. More stringent requirements for PMF data analysis
• Similar to that for tandem mass spectra
6. Management of protein redundancy• Peptides identified from a different species?
7. Spectra submission encouraged
64
Summary
• Could guessing be as effective as a search?
• More guesses improves the best guess
• Better guessers help us be more discriminating
• Peptide to proteins is not as simple as it seems
• Publication guidelines reflect sound statistical principles.
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