Upload
bioinformaticsinstitute
View
257
Download
2
Embed Size (px)
DESCRIPTION
Citation preview
www.bioalgorithms.infoAn Introduction to Bioinformatics Algorithms
Protein Sequencing and
Identification by Mass
Spectrometry
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Outline• Tandem Mass Spectrometry
• De Novo Peptide Sequencing
• Spectrum Graph
• Protein Identification via Database Search
• Identifying Post Translationally Modified Peptides
• Spectral Convolution
• Spectral Alignment
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Different Amino Acid Have Different Masses
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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Peptide Fragmentation
• Peptides tend to fragment along the backbone.
• Mass spectrometer is a sophisticated
(and rather expensive!) scale to measure
the masses of these fragments
H...-HN-CH-CO . . . NH-CH-CO-NH-CH-CO-…OH
Ri-1 Ri Ri+1
H+
Prefix Fragment Suffix Fragment
Collision Induced Dissociation
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Breaking Protein into Peptides and
Peptides into Fragment Ions• Most mass spectrometers can only measure masses of
short peptides (e.g., 20 amino acids 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.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
N- and C-terminal Peptides
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Terminal peptides and ion types
Peptide
Mass (D) 57 + 97 + 147 + 114 = 415
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Masses of fragment ions
Peptide
Mass (D) 57 + 97 + 147 + 114 = 415
Peptide
Mass (D) 57 + 97 + 147 + 114 – 18 = 397
without
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
N- and C-terminal Peptides
415
486
301
154
57
71
185
332
429
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
N- and C-terminal Peptides
415
486
301
154
57
71
185
332
429
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Theoretical Spectrum
415
486
301
154
57
71
185
332
429
Reconstruct peptide from the set of masses of fragment ions
(mass-spectrum)
57 71 154 185 301 332 415 429 486
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Reconstructing Peptides
Reconstruct peptide from the set of masses of fragment ions
(mass-spectrum)
57 71 154 185 301 332 415 429 486
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Reconstructing Peptides
Reconstruct peptide from the set of masses of fragment ions
(mass-spectrum) 57 71 81 100 112 131 160 172 177 185 201 221 235 301 312 325 332 370 387 409 415 423 429 460 472 486154
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Reconstructing Peptides
Reconstruct peptide from the set of masses of fragment ions
(mass-spectrum) 57 71 81 100 112 131 160 172 177 185 201 221 235 301 312 325 370 387 409 415 423 429 460 472 486
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Peptide Fragmentation
y3
b2
y2 y1
b3a2 a3
HO NH3+
| |
R1 O R2 O R3 O R4
| || | || | || |
H -- N --- C --- C --- N --- C --- C --- N --- C --- C --- N --- C -- COOH
| | | | | | |
H H H H H H H
b2-H2O
y3 -H2O
b3- NH3
y2 - NH3
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Mass Spectra
G V D L K
mass
0
57 Da = „G‟ 99 Da = „V‟LK D V G
• The peaks in the mass spectrum:
• Prefix
• Fragments with neutral losses (-H2O, -NH3)
• Noise and missing peaks.
and Suffix Fragments.
D
H2O
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Protein Identification with MS/MS
mass
0
Inte
nsity
mass
0
MS/MS
Peptide
Identification
Protein database
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Tandem Mass Spectrum• Tandem Mass Spectrometry mainly generates N-
and C-terminal fragment ions
• Chemical noise often complicates the spectrum.
• Represented in 2-D: mass/charge axis vs. intensity
axisS#: 1708 RT: 54.47 AV: 1 NL: 5.27E6
T: + c d Full ms2 638.00 [ 165.00 - 1925.00]
200 400 600 800 1000 1200 1400 1600 1800 2000
m/z
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Re
lative
Ab
un
da
nce
850.3
687.3
588.1
851.4425.0
949.4
326.0524.9
589.2
1048.6397.1226.9
1049.6489.1
629.0
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Tandem Mass-Spectrometry
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Breaking Proteins into Peptides
peptides
MPSER
……
GTDIMR
PAKID
……
HPLCTo
MS/MSMPSERGTDIMRPAKID......
protein
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Mass SpectrometryMatrix-Assisted Laser Desorption/Ionization (MALDI)
From lectures by Vineet Bafna (UCSD)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Tandem Mass SpectrometryRT: 0.01 - 80.02
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Time (min)
0
10
20
30
40
50
60
70
80
90
100
Rela
tive A
bundance
13891991
1409 21491615
1621
14112147
1611
199516551593
138721551435
19872001 2177
1445 16611937
22051779 2135
20171313 22071307
23291105 17071095
2331
NL:
1.52E8
Base Peak F: +
c Full ms [
300.00 -
2000.00]
S#: 1708 RT: 54.47 AV: 1 NL: 5.27E6
T: + c d Full ms2 638.00 [ 165.00 - 1925.00]
200 400 600 800 1000 1200 1400 1600 1800 2000
m/z
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Re
lative
Ab
un
da
nce
850.3
687.3
588.1
851.4425.0
949.4
326.0524.9
589.2
1048.6397.1226.9
1049.6489.1
629.0
Scan 1708
LC
S#: 1707 RT: 54.44 AV: 1 NL: 2.41E7
F: + c Full ms [ 300.00 - 2000.00]
200 400 600 800 1000 1200 1400 1600 1800 2000
m/z
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Re
lative
Ab
un
da
nce
638.0
801.0
638.9
1173.8
872.3 1275.3
687.6944.7 1884.51742.11212.0783.3 1048.3 1413.9 1617.7
Scan 1707
MS
MS/MSIon
Source
MS-1collision
cell MS-2
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Protein Identification by Tandem
Mass Spectrometry (MS/MS)
S
e
q
u
e
n
c
e
S#: 1708 RT: 54.47 AV: 1 NL: 5.27E6
T: + c d Full ms2 638.00 [ 165.00 - 1925.00]
200 400 600 800 1000 1200 1400 1600 1800 2000
m/z
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Re
lative
Ab
un
da
nce
850.3
687.3
588.1
851.4425.0
949.4
326.0524.9
589.2
1048.6397.1226.9
1049.6489.1
629.0
MS/MS instrument
database search
•Sequest, Mascot, etc
de novo interpretation
•Lutefisk, Peaks, etc
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
De Novo vs. Database Search S#: 1708 RT: 54.47 AV: 1 NL: 5.27E6
T: + c d Full ms2 638.00 [ 165.00 - 1925.00]
200 400 600 800 1000 1200 1400 1600 1800 2000
m/z
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Rel
ativ
e A
bund
ance
850.3
687.3
588.1
851.4425.0
949.4
326.0524.9
589.2
1048.6397.1226.9
1049.6489.1
629.0
WR
A
C
V
GE
K
DW
LP
T
L T
WR
A
C
VG
E
K
DW
LP
T
L T
De Novo
AVGELTK
Database
Search
Database of all peptides = 20n
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..
Database of
known peptides
MDERHILNM, KLQWVCSDL,
PTYWASDL, ENQIKRSACVM, TLACHGGEM, NGALPQWRT,
HLLERTKMNVV, GGPASSDA,
GGLITGMQSD, MQPLMNWE,
ALKIIMNVRT, AVGELTK,
HEWAILF, GHNLWAMNAC, GVFGSVLRA, EKLNKAATYIN..
Mass, Score
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
De Novo vs. Database Search: A Paradox
• The database of all peptides is huge ≈ 20n peptides of length n
• The database of all known peptides is much smaller ≈ 108 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 knownpeptides to find best one.
• De novo eliminates the need to scan database of all peptides by modeling the problem as a graph search.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Three Algorithmic Problems• Searching for a million words in a text. Suppose it takes
1 sec to find a word in a text. How much time would it take to find 1 million words in the text?
• Searching for a word without even looking at 99.999% of the text. Suppose you search for a word in a text. Would it be possible to ignore 99.999% of the text, scan only the remaining part and guarantee that the word you are looking for will be found?
• Finding spelling errors in a book written in an unknown language. Given a book (in an unknown language) and a misspelled word (with insertions, deletions, and substitutions of letters) correct spelling errors in the word.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Three Algorithmic Problems• Searching for a million words in a text. Suppose it takes
1 sec to find a word in a text. How much time would it take to find 1 million words in the text? 1 million seconds?
• Searching for a word without even looking at 99.999% of the text. Suppose you search for a word in a text. Would it be possible to ignore 99.999% of the text, scan only the remaining part and guarantee that the word you are looking for will be found?
• Finding spelling errors in a book written in an unknown language. Given a book (in an unknown language) and a misspelled word (with insertions, deletions, and substitutions of letters) correct spelling errors in the word.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Genomics: Problems Solved. • Searching for a million words in a text.
Aho-Corasik algorithm takes roughly the same time with a million words as it takes with a single word.
• Searching for a word without even looking at 99.999% of the text.
Filtration algorithms (like FASTA or BLAST) ignore 99.999% of the text.
• Finding spelling errors.
Sequence alignment algorithms (like Smith-Waterman) do it in quadratic time
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Proteomics: Three Problems• Comparing a million spectra against a database. Suppose it
takes 1 sec to interpret a spectrum. How much time would it take to
interpret 1 million spectra?
• Mass-spectrometry database search without even looking at
99.999% of the database. Suppose you compare a spectrum
against a database. Would it be possible to ignore 99.999% of the
database, scan only the remaining part and guarantee that you still
can identify a peptide of interest?
• Blind PTM search and discovery of new PTM types. Given a
spectrum of a peptide with unknown PTM types, find this peptide in
the database. Discover new PTM types by data mining of large
MS/MS datasets.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Three Solutions• Comparing a million spectra against a database.
InsPecT (Tanner et al., Anal. Chem, 2005)
• MS/MS database search without even looking at
99.999% of the database.
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)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Filtration: Combining De Novo Sequencing and
Database Search in Mass-Spectrometry
• So far de novo and database search were presented as two separate techniques
• Database search is rather slow: many labs generate more than 100,000 spectra per day. SEQUEST takes approximately 1 minute to compare a single spectrum against SWISS-PROT (54Mb) on a desktop.
• It will take SEQUEST more than 2 months to analyze the MS/MS data produced in a single day.
• Can slow database search be combined with fast de novo analysis?
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
De novo Peptide Sequencing
S#: 1708 RT: 54.47 AV: 1 NL: 5.27E6
T: + c d Full ms2 638.00 [ 165.00 - 1925.00]
200 400 600 800 1000 1200 1400 1600 1800 2000
m/z
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Re
lative
Ab
un
da
nce
850.3
687.3
588.1
851.4425.0
949.4
326.0524.9
589.2
1048.6397.1226.9
1049.6489.1
629.0
Sequence
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Building Spectrum Graph
• How to create vertices (from masses)
• How to create edges (from mass differences)
• How to score vertices
• How to score paths
• How to find the best path
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
S E Q U E N C E
b-ions (prefix or N-terminal ions)
Mass/Charge (M/Z)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
a-ions = b-ions - CO = b-ions - 28
Mass/Charge (M/Z)
S E Q U E N C E
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
S E Q U E N C E
Mass/Charge (M/Z)
Shifting Peaks: a-ions = b-ions - CO = b-ions - 28
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
y-ions (suffix of C-terminal ions)
Mass/Charge (M/Z)
E C N E U Q E S
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Mass/Charge (M/Z)
Inte
nsi
ty
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Mass/Charge (M/Z)
Inte
nsi
ty
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
noise
Mass/Charge (M/Z)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
MS/MS Spectrum
Mass/Charge (M/z)
Inte
nsi
ty
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Some Mass Differences between Peaks
Correspond to Amino Acids
s
ss
e
ee
e
e
e
e
e
q
q
qu
u
u
n
n
n
e
c
c
c
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Some Mass Differences between Peaks
Correspond to Amino Acids
s
ss
e
ee
e
e
e
e
e
q
q
qu
u
u
n
n
n
e
c
c
c
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Ion Types
• Some masses correspond to fragment ions,
others are just random noise
• Knowing ion types Δ={δ1, δ2,…, δk} allows one to
distinguish fragment ions from noise
• We can learn ion types δi and their probabilities qi
by analyzing a large test sample of annotated
spectra.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Example of Ion Type
• Δ={δ1, δ2,…, δk}
• Ion types
{b, b-NH3, b-H2O, b-CO}
correspond to
Δ={0, 17, 18, 28}
*Note: In reality the δ value of ion type b is -1 but we will “hide” it for the sake of simplicity
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Match between Spectra and the
Shared Peak Count
• The match between two spectra is the number of masses (peaks)
they share (Shared Peak Count or SPC)
• In practice mass-spectrometrists use the weighted SPC that
reflects intensities of the peaks
• Match between experimental and theoretical spectra is defined
similarly
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Peptide Sequencing Problem
Goal: Find a peptide with maximal match between
an experimental and theoretical spectrum.
Input:
• S: experimental spectrum
• Δ: set of possible ion types
Output:
• A peptide whose theoretical spectrum
matches the experimental spectrum the best
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
S E Q U E N C E
Mass/Charge (M/Z)
Shifting Peaks: a-ions = b-ions - CO = b-ions - 28
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Reverse Shifts
Shift in H2O+NH3
Shift in H2O
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Vertices of the Spectrum Graph• Masses of potential N-terminal peptides
• Vertices are generated by reverse shifts corresponding to ion types
Δ={δ1, δ2,…, δk}
• Every N-terminal peptide can generate up to k ions
m-δ1, m-δ2, …, m-δk
• Every mass s in an MS/MS spectrum generates k vertices
V(s) = {s+δ1, s+δ2, …, s+δk}
corresponding to potential N-terminal peptides
• Vertices of the spectrum graph:
{initial vertex} V(s1) V(s2) ... V(sm) {terminal vertex}
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Edges of the Spectrum Graph
• Two vertices with mass difference corresponding to
an amino acid A:
• Connect with an edge labeled by A
• Gap edges corresponding to the mass of pairs of
amino acids (optional)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Paths
• Paths in the labeled graph spell out amino
acid sequences
• There are many paths, how to find the correct
one?
• We need scoring to evaluate paths
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Path Score
• p(P,S) = probability that peptide P produces spectrum S= {s1,s2,…sq}
• p(P, s) = the probability that peptide Pgenerates a peak s
• Scoring = computing probabilities
• p(P,S) = πsєS p(P, s)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
• For a position t that represents ion type dj :
qj, if peak is generated at t
p(P,st) =
1-qj , otherwise
Peak Score
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Peak Score (cont’d)
• For a position t that is not associated with an
ion type:
qR , if peak is generated at t
pR(P,st) =
1-qR , otherwise
• qR = the probability of a noisy peak that does
not correspond to any ion type
An Introduction to Bioinformatics Algorithms www.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
p(P,S)p(P',S) Pmax
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Ions and Probabilities
• Tandem mass spectrometry is characterized by a set of ion types {δ1,δ2,..,δk} and their probabilities {q1,...,qk}
• δi-ions of a partial peptide are produced independently with probabilities qi
An Introduction to Bioinformatics Algorithms www.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 qR in any position.
k
i
iq1
k
i
iq1
)1(
An Introduction to Bioinformatics Algorithms www.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 δ1,δ2,δ4.
The score is calculated as:RRRR q
q
q
q
q
q
q
q 4321
)1(
)1(
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Scoring Peptides
• T- set of all positions.
• Ti={t δ1,, t δ2,..., ,t δk,}- set of positions that represent ions of partial peptides Pi.
• A peak at position tδj is generated with probability qj.
• R=T- U Ti - set of positions that are not associated with any partial peptides (noise).
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Probabilistic Model
• For a position t δj Ti 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:
otherwise1
position tat generated ispeak a if),,(
j
j
j
q
qSPtP
otherwise1
position tat generated ispeak a if)(
R
R
Rq
qtP
An Introduction to Bioinformatics Algorithms www.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:
n
i
k
j iR
i
R j
j
tp
SPtp
Sp
SPp
1 1 )(
),,(
)(
),(
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
De Novo vs. Database Search S#: 1708 RT: 54.47 AV: 1 NL: 5.27E6
T: + c d Full ms2 638.00 [ 165.00 - 1925.00]
200 400 600 800 1000 1200 1400 1600 1800 2000
m/z
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Rel
ativ
e A
bund
ance
850.3
687.3
588.1
851.4425.0
949.4
326.0524.9
589.2
1048.6397.1226.9
1049.6489.1
629.0
WR
A
C
V
GE
K
DW
LP
T
L T
WR
A
C
VG
E
K
DW
LP
T
L T
De Novo
AVGELTK
Database
Search
Database of
known peptides
MDERHILNM, KLQWVCSDL,
PTYWASDL, ENQIKRSACVM, TLACHGGEM, NGALPQWRT,
HLLERTKMNVV, GGPASSDA,
GGLITGMQSD, MQPLMNWE,
ALKIIMNVRT, AVGELTK,HEWAILF, GHNLWAMNAC,
GVFGSVLRA, EKLNKAATYIN..
Database of
known peptides
MDERHILNM, KLQWVCSDL,
PTYWASDL, ENQIKRSACVM, TLACHGGEM, NGALPQWRT,
HLLERTKMNVV, GGPASSDA,
GGLITGMQSD, MQPLMNWE,
ALKIIMNVRT, AVGELTK,
HEWAILF, GHNLWAMNAC, GVFGSVLRA, EKLNKAATYIN..
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
De Novo vs. Database Search: A Paradox
• de novo algorithms are much faster, even though their search space is much larger!
• A database search scans all peptides to find the best one.
• De novo eliminates the need to scan all peptides by modeling the problem as a graph search.
Why not sequence de novo?
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Why Not Sequence De Novo?• De novo sequencing is not very accurate:
• Less than 30% of the peptides sequenced were completely correct!
Algorithm Amino
Acid
Accuracy
Whole Peptide
Accuracy
Lutefisk, 1997 0.566 0.189
SHERENGA, 1999 0.690 0.289
Peaks, 2003 0.673 0.246
PepNovo, 2005 0.727 0.296
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Pros and Cons of de novo Sequencing
• Advantage:• Gets the sequences that are not necessarily in the
database.
• An additional similarity search step using these sequences may identify the related proteins in the database.
• Disadvantage:• Requires higher quality spectra to be accurate.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Peptide Sequencing Problem
Goal: Find a peptide with maximal match between
an experimental and theoretical spectrum.
Input:
• S: experimental spectrum
• Δ: set of possible ion types
Output:
• A peptide whose theoretical spectrum
matches the experimental S spectrum the best
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Peptide Identification ProblemGoal: 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 Sspectrum the best
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
MS/MS Database Search
Database search in mass-spectrometry has been successful in identification of already known proteins.
Experimental spectrum can be compared with theoretical
spectra of database peptides to find the best fit.
SEQUEST (Yates et al., 1995)
But reliable algorithms for identification of modified
peptides is a much more difficult problem.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
The dynamic nature of the proteome
• The proteome of the cell is changing
• Various extra-cellular, and other signals activate various protein pathways.
• A key mechanism of protein activation is post-translational modification (PTM)
• These pathways may lead to other genes being switched on or off
• Mass spectrometry is key to probing the proteome and detecting PTMs
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
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.
An Introduction to Bioinformatics Algorithms www.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.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Peptide Masses
415
486
301
154
57
71
185
332
429
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Peptide Masses: Modification +16 on N
415
486
301
154
57
71
185
332
429
+16
+16
+16
+16
+16
+16
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Reconstructing Modified Peptides
Reconstruct peptide from the set of masses of fragment ions
(mass-spectrum)
57 71 154 185 301 332 415 429 486
+16 +16 +16 +16 +16
57 71 154 201 301 348 431 445 502
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Reconstructing Modified Peptides
Reconstruct peptide from the set of masses of fragment ions
(mass-spectrum) 57 71 81 100 112 131 154 160 172 177 185 201 221 235 301 312 325 332 370 387 409 415 423 429 460 472 486
57 71 81 100 112 131 154 160 172 177 185 201 221 235 301 312 325 332 348 387 409 415 423 431 445 472 502
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Peptide Identification Problem Revisited
Goal: Find a peptide from the database with maximal match between an experimental and theoretical spectrum.
Input:
• S: experimental spectrum
• database of peptides
• Δ: set of possible ion types
Output:
• A peptide from the database whose theoretical spectrum matches the experimental Sspectrum the best
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Modified Peptide Identification ProblemGoal: 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Search for Modified Peptides:
Virtual Database Approach
• YFDSTDYNMAK
• 25=32 possibilities, with
2 types of modifications!
Phosphorylation?Oxidation?
Yates et al.,1995: an exhaustive search in a
virtual database of all modified peptides.
Combinatorial explosion, even for a small
set of modifications types.
A larger set of spurious matches must be
filtered out. It‟s much more likely that
incorrect matches will have high scores.
Problem. Extend the virtual database
approach to a large set of modifications.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Restrictive vs Unrestrictive (Blind)
Search for Modified Peptides• Restrictive search requires the researcher to
guess which modification types are present in
the sample
• How would you feel if you were allowed to
perform only 10 out of 20x19=380 possible
point mutations (with all other forbidden)
while aligning two proteins?
• This is exactly what the restrictive PTM
search algorithms do.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Restrictive vs Unrestrictive (Blind) Search
for Modified Peptides
• Restrictive search requires the researcher to guess which modification types are present in the sample
• Blind search performs an unrestrictive search for all
possible modification offsets at once.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Database Search:
Sequence Analysis vs. MS/MS Analysis
Sequence analysis:
similar peptides (that a few mutations apart) have similar sequences
MS/MS analysis:
similar peptides (that a few mutations apart) have dissimilar spectra
An Introduction to Bioinformatics Algorithms www.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.
An Introduction to Bioinformatics Algorithms www.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.
An Introduction to Bioinformatics Algorithms www.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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Spectral Convolution
)0)((
))((
,
12
12
122211
22111212
:
SS
xSS
ssSsSs
}S,sS:ss{sSS
x
:peak) (SPC count peaks shared The
with pairs of Number
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Elements of S2 S1 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
1
2
3
4
5
0
-150 -100 -50 0 50 100
150
x
Spectral Convolution: An Example
An Introduction to Bioinformatics Algorithms www.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.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Spectral Comparison: Difficult Case
S S’
S S’’
An Introduction to Bioinformatics Algorithms www.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.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
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).
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
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.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
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)?
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Converting Spectra into 0-1 Sequences
• Convert spectrum into a 0-1 string with 1s
corresponding to the positions of the peaks.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Modified peptide
Modifications are modeled as insertion (or deletions)
of blocks of zeroes
000101001010000000110000001001 Spectrum
00010100001-----00010000001001 Peptide
A modification with positive offset - inserting a block of 0s
A modification with negative offset - deleting a block of 0s
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Spectra Comparison vs. String Comparison
• Comparison of theoretical and
experimental spectra (represented as 0-1
strings) corresponds to a (somewhat
unusual) edit distance/alignment
between 0-1 strings where elementary
edit operations are insertions and
deletions of blocks of 0s
• Use sequence alignment algorithms!
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Spectral Alignment Graph
0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
0
0
0
0
1 1 1 1 1 1
0
0
0
0
1 1 1 1 1 1
0
0
1 1 1 1 1 1
0
0
0
0
1 1 1 1 1 1
0
0
0
0
1 1 1 1 1 1
Horizontal axis:
Experimental spectrum
Vertical axis:
Theoretical spectrum of a
peptide
A
B
C
D
E
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Spectral Alignment Graph0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
0
0
0
0
1 1 1 1 1 1
0
0
0
0
1 1 1 1 1 1
0
0
1 1 1 1 1 1
0
0
0
0
1 1 1 1 1 1
0
0
0
0
1 1 1 1 1 1
Like in alignment algorithms,
every path in the spectral
alignment graph represents a
possible interpretation of a
spectra.
A path covering maximal
number of 1s is the “best”
interpretation of the spectrum.
Vertical / horizontal segment
in the optimal path are
modifications
A
B
C
D
E
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Spectral Alignment vs. Sequence Alignment
• Alignment graph with different alphabet and
scoring.
• Movement can be diagonal (matching
masses) or horizontal/vertical
(insertions/deletions corresponding to PTMs).
• At most k horizontal/vertical moves.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Shifts
A = {a1 < … < an} : an ordered set of natural
numbers.
A shift (i, ) is characterized by two parameters,
the position (i) and the length ( ).
The shift (i, ) transforms
{a1, …., an}
into
{a1, ….,ai-1,ai+ ,…,an+ }
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Shifts: An Example
The shift (i, ) transforms {a1, …., an}
into {a1, ….,ai-1,ai+ ,…,an+ }
e.g.
10 20 30 40 50 60 70 80 90
10 20 30 35 45 55 65 75 85
10 20 30 35 45 55 62 72 82
shift (4, -5)
shift (7,-3)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Spectral Alignment Problem
• Find a series of k shifts that make the sets
A={a1, …., an} and B={b1,….,bn}
as similar as possible.
• k-similarity between sets
• D(k) - the maximum number of elements in
common between sets after k shifts.
An Introduction to Bioinformatics Algorithms www.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!
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Spectral ProductA={a1, …., an} and B={b1,…., bn}
Spectral product A B: two-dimensional matrix with nm 1s corresponding to all pairs of
indices (ai,bj) and remaining
elements being 0s.
10 20 30 40 50 55 65 75 85 95
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
SPC: the number of 1s at the main diagonal.
-shifted SPC: the number of 1s on the diagonal (i,i+ )
An Introduction to Bioinformatics Algorithms www.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.
An Introduction to Bioinformatics Algorithms www.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
An Introduction to Bioinformatics Algorithms www.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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Spectral Convolution’ Limitation
The spectral convolution considers diagonals separately without combining them into feasible
mutation scenarios.
D(1) =10 shift function score = 10 D(1) =6
10 20 30 40 50 55 65 75 85 95
10
20
30
40
50
60
70
80
90
100
10 15 30 35 50 55 70 75 90 95
10
20
30
40
50
60
70
80
90
100
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Dynamic Programming for Spectral Alignment
Dij(k): the maximum number of 1s on a path to
(ai,bj) that uses at most k+1 diagonals.
(i’,j’) ~ (i,j): the points are located on the same diagonal
Running time: O(n4 k)
otherwisekD
jijiifkDkD
ji
ji
jijiij ,1)1(
),(~)','(,1)(max)(
''
''
),()','({
)(max)( kDkD ijij
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Edit Graph for Fast Spectral Alignment
diag(i,j) – the position
of previous 1 on the
same diagonal as (i,j)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Fast Spectral Alignment Algorithm
1)1(
1)(max)(
1,1
),(
kM
kDkD
ji
jidiag
ij
)(max)( ''),()','(
kDkM jijiji
ij
)(
)(
)(
max)(
1,
,1
kM
kM
kD
kM
ji
ji
ij
ij
Running time: O(n2 k)
An Introduction to Bioinformatics Algorithms www.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.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Spectral Alignment: Complications
• Simultaneous analysis of N- and C-terminal ions
• Taking into account the intensities and charges
• Analysis of minor ions
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
MS/MS and East-West Traveling Salesman Problem
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
EE SE E SE D E SE D T E S
129
244
345
47487
216
317
432
E D T
ESS
E S
T D EE
S
Anti-symmetric paths
E D T
ESS
E S
T D EE
S
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:
ESESEWhy?
De-novo problemInput: Spectrum graph
Output: Anti-symmetric longest path
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
PTM Frequency Matrix
A C D E F G H I K L M N P Q R S T V W Y
10 1 1 3 2 0 4 0 0 2 1 1 0 7 2 3 5 4 3 0 0
11 7 2 0 1 1 6 0 1 1 1 1 2 0 0 0 7 2 1 0 1
12 2 2 1 1 6 3 1 0 5 2 3 1 0 5 0 2 1 3 0 0
13 4 0 3 2 0 5 1 4 4 5 3 1 0 2 2 5 4 2 2 1
14 12 2 5 16 1 12 0 7 ## 4 43 3 5 2 2 13 4 20 0 3
15 5 0 3 2 2 8 0 7 16 7 18 5 3 4 1 6 1 12 0 1
16 6 0 20 63 2 21 5 73 2 63 ## 14 10 18 2 7 8 10 ## 6
17 5 0 7 8 3 9 2 18 2 23 ## 32 5 18 0 8 2 5 29 3
18 0 3 3 3 3 10 1 6 4 9 15 7 43 5 1 5 3 5 2 1
19 2 0 0 3 0 7 1 3 9 4 3 3 7 1 0 7 1 12 4 0
20 3 3 0 3 2 5 0 2 3 3 1 3 2 1 0 4 0 0 0 0
21 8 0 1 3 0 3 0 1 1 5 0 1 1 4 2 2 1 2 1 2
22 12 0 25 25 15 39 8 20 5 25 1 29 7 27 1 39 27 22 1 13
23 1 1 3 6 0 14 0 3 4 5 0 26 6 2 1 3 2 0 0 2
24 0 0 1 2 0 6 1 4 1 2 0 0 1 1 4 6 1 3 0 1
25 1 6 2 0 1 4 1 0 3 8 0 0 0 4 1 6 0 8 0 0
26 1 2 1 2 2 5 0 1 0 4 0 2 4 3 1 6 2 3 0 1
27 2 1 1 2 0 4 0 2 3 3 1 1 1 3 0 2 2 3 1 0
28 5 5 2 2 4 1 1 12 ## 29 2 2 4 1 6 40 1 56 0 2
29 4 0 0 1 4 3 2 4 28 5 1 6 1 0 3 11 1 9 0 1
30 6 1 1 3 3 20 0 6 13 1 2 3 2 13 1 6 4 4 1 1
31 3 3 4 1 4 6 1 8 8 9 7 1 2 19 2 7 8 6 0 0
32 5 3 0 0 4 7 1 2 1 5 ## 3 1 4 9 1 2 6 43 0
33 1 1 0 1 2 6 1 1 3 9 33 2 0 4 2 6 1 1 8 3
34 5 0 2 2 2 8 4 7 9 19 3 7 1 5 4 4 1 0 0 2
35 0 1 0 2 1 7 0 1 5 2 1 2 2 1 0 2 2 3 0 2
50,000 spectra (IKKb sample)
were searched in blind mode,
and identifications with p-value
<0.05 were retained
Shading of the cell (x,y) reflects
the number of annotations with
modification:
(offset x, amino acid y)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
PTM Frequency Matrix
A C D E F G H I K L M N P Q R S T V W Y
10 1 1 3 2 0 4 0 0 2 1 1 0 7 2 3 5 4 3 0 0
11 7 2 0 1 1 6 0 1 1 1 1 2 0 0 0 7 2 1 0 1
12 2 2 1 1 6 3 1 0 5 2 3 1 0 5 0 2 1 3 0 0
13 4 0 3 2 0 5 1 4 4 5 3 1 0 2 2 5 4 2 2 1
14 12 2 5 16 1 12 0 7 ## 4 43 3 5 2 2 13 4 20 0 3
15 5 0 3 2 2 8 0 7 16 7 18 5 3 4 1 6 1 12 0 1
16 6 0 20 63 2 21 5 73 2 63 ## 14 10 18 2 7 8 10 ## 6
17 5 0 7 8 3 9 2 18 2 23 ## 32 5 18 0 8 2 5 29 3
18 0 3 3 3 3 10 1 6 4 9 15 7 43 5 1 5 3 5 2 1
19 2 0 0 3 0 7 1 3 9 4 3 3 7 1 0 7 1 12 4 0
20 3 3 0 3 2 5 0 2 3 3 1 3 2 1 0 4 0 0 0 0
21 8 0 1 3 0 3 0 1 1 5 0 1 1 4 2 2 1 2 1 2
22 12 0 25 25 15 39 8 20 5 25 1 29 7 27 1 39 27 22 1 13
23 1 1 3 6 0 14 0 3 4 5 0 26 6 2 1 3 2 0 0 2
24 0 0 1 2 0 6 1 4 1 2 0 0 1 1 4 6 1 3 0 1
25 1 6 2 0 1 4 1 0 3 8 0 0 0 4 1 6 0 8 0 0
26 1 2 1 2 2 5 0 1 0 4 0 2 4 3 1 6 2 3 0 1
27 2 1 1 2 0 4 0 2 3 3 1 1 1 3 0 2 2 3 1 0
28 5 5 2 2 4 1 1 12 ## 29 2 2 4 1 6 40 1 56 0 2
29 4 0 0 1 4 3 2 4 28 5 1 6 1 0 3 11 1 9 0 1
30 6 1 1 3 3 20 0 6 13 1 2 3 2 13 1 6 4 4 1 1
31 3 3 4 1 4 6 1 8 8 9 7 1 2 19 2 7 8 6 0 0
32 5 3 0 0 4 7 1 2 1 5 ## 3 1 4 9 1 2 6 43 0
33 1 1 0 1 2 6 1 1 3 9 33 2 0 4 2 6 1 1 8 3
34 5 0 2 2 2 8 4 7 9 19 3 7 1 5 4 4 1 0 0 2
35 0 1 0 2 1 7 0 1 5 2 1 2 2 1 0 2 2 3 0 2
16 on W - Oxidation
16 on M - Oxidation14 on K - Methylation
22 - Sodium
32 on M - Double oxidation
28 on K - Dimethylation
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Filtration in Similarity Searches
Scoring
Protein Query
Sequence Alignment –Smith-Waterman Algorithm
Sequence matches
Filtration
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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Filtration and MS/MS
Scoring
MS/MS spectrum
Peptide Sequencing – SEQUEST / Mascot
Sequence matches
Filtration
Database
MDERHILNMKLQWVCSDLPT
YWASDLENQIKRSACVMTLACHGGEMNGALPQWRTHLLE
RTYKMNVVGGPASSDALITG
MQSDPILLVCATRGHEWAILFGHNLWACVNMLETAIKLEGVF
GSVLRAEKLNKAAPETYIN..
Database
MDERHILNMKLQWVCSDLPT
YWASDLENQIKRSACVMTLACHGGEMNGALPQWRTHLLE
RTYKMNVVGGPASSDALITG
MQSDPILLVCATRGHEWAILFGHNLWACVNMLETAIKLEGVF
GSVLRAEKLNKAAPETYIN..
An Introduction to Bioinformatics Algorithms www.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.
• Can we design a filtration based search that can replacethe database search, and is orders of magnitude faster?
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Asking the Old Question Again: Why
Not Sequence De Novo?• De novo sequencing is still not very accurate!
Algorithm Amino Acid
Accuracy
Whole Peptide
Accuracy
Lutefisk (Taylor and Johnson, 1997). 0.566 0.189
SHERENGA (Dancik et. al., 1999). 0.690 0.289
Peaks (Ma et al., 2003). 0.673 0.246
PepNovo (Frank and Pevzner, 2005). 0.727 0.296
An Introduction to Bioinformatics Algorithms www.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!
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Peptide Sequence Tags
• A Peptide Sequence Tag is short substring of
a peptide.
Example: G V D L K
G V D
V D L
D L K
Tags:
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Filtration with Peptide Sequence Tags• Peptide sequence tags can be used as filters in
database searches.
• The Filtration: Consider only database peptides that contain the tag (in its correct relative mass location).
• First suggested by Mann and Wilm (1994).
• Similar concepts also used by:• GutenTag - Tabb et. al. 2003.
• MultiTag - Sunayev et. al. 2003.
• OpenSea - Searle et. al. 2004.
An Introduction to Bioinformatics Algorithms www.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.
An Introduction to Bioinformatics Algorithms www.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
VG
E
K
DW
LP
T
LT
AVGELTK
TAG Prefix Mass
AVG 0.0
VGE 71.0
GEL 170.1
ELT 227.1
LTK 356.2
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Tag Generation - Local Tags
• Extract the highest scoring subspaths from the spectrum graph.
• Sometimes gets misled by locally
promising-looking “garden paths”.
WR
A
C
V
GE
K
DW
LP
T
L T
TAG Prefix Mass
AVG 0.0
WTD 120.2
PET 211.4
An Introduction to Bioinformatics Algorithms www.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.
An Introduction to Bioinformatics Algorithms www.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
An Introduction to Bioinformatics Algorithms www.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 notcorrespond to a genuine amino acid tends to leave the score unchanged.
WR
A
C
VG
K
DWL
P
T
L T
WR
A
C
VG
K
DWL
P
T
L T
WR
A
C
VG
K
DWL
P
T
L TE
W
WR
A
C
VG
K
DL
P
T
L T
An Introduction to Bioinformatics Algorithms www.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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Experimental ResultsLength 3 Length 4 Length 5
Algorithm \ #tags 1 10 1 10 1 10
GlobalTag 0.80 0.94 0.73 0.87 0.66 0.80
LocalTag+ 0.75 0.96 0.70 0.90 0.57 0.80
GutenTag 0.49 0.89 0.41 0.78 0.31 0.64
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Tag-based Database Search
Tag filter SignificanceScoreTag
extension
De novo
Db55M peptides
Candidate Peptides (700)
An Introduction to Bioinformatics Algorithms www.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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Keyword Trees
Y A K
SN
N
F
F
AT
YFAK
YFNS
FNTA
…..Y F R A Y F N T A…..
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Tag Extension
Filter SignificanceScoreExtension
De novo
Db55M peptides
CandidatePeptides(700)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
• Given: • tag with prefix and suffix masses <mP> xyz <mS>
• 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<mP>xyz<mS>
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Scoring Modified Peptides
Filter SignificanceScoreExtension
De novo
Db55M peptides
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Scoring
• Input:
• Candidate peptide with attached modifications
• Spectrum
• Output:
• Score function that normalizes for length, as
variable modifications can change peptide length.
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Assessing Reliability of Identifications
Filter SignificanceScoreextension
De novo
Db55M peptides
An Introduction to Bioinformatics Algorithms www.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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Separating power of features
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Separating power of features
Quality scores:
Q = wI I + wS S + wB B + wP P
The weights are chosen to minimize
the mis-classification error
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Distribution of Quality Scores
An Introduction to Bioinformatics Algorithms www.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)
An Introduction to Bioinformatics Algorithms www.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.
PTMs Tag
Length
# Tags Filtration InsPecT
Runtime
SEQUEST
Runtime
None 3 1 3.4 10-7 0.17 sec > 1 minute
3 10 1.6 10-6 0.27 sec
Phosphory
lation
3 1 5.8 10-7 0.21 sec > 2 minutes
3 10 2.7 10-6 0.38 sec
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
SPIDER: Yet Another Application of de novoSequencing
• Suppose you have a good MS/MS spectrum of an elephant peptide
• Suppose you even have a good de novoreconstruction 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
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Common de novo sequencing errors
GG
N and GG
have the
same mass
An Introduction to Bioinformatics Algorithms www.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-Vsequencing error
(Seq) X: LSCF-AV
(Real) Y: EACF-AV
(Match) Z: DACFKAV mass(LS)=mass(EA)
Homology mutations
An Introduction to Bioinformatics Algorithms www.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
An Introduction to Bioinformatics Algorithms www.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) = minY ( seqError(X,Y) + editDist(Y,Z) )
(Seq) X: LSCF-AV
(Real) Y: EACF-AV
(Match) Z: DACFKAV
An Introduction to Bioinformatics Algorithms www.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) = minY ( 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
An Introduction to Bioinformatics Algorithms www.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 (Xi,Yi), the cost is
f(Xi,Yi)=f(mass(Xi)).
• 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(Xi)).X
Y
Z
seqError
editDist
(Seq) X: LSCFAV
(Real) Y: EACFAV
An Introduction to Bioinformatics Algorithms www.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
An Introduction to Bioinformatics Algorithms www.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.
An Introduction to Bioinformatics Algorithms www.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)
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info
Solving Mass-Alignment Problem
])[,()])1..([),((min
)])1..([,(
])..[),((min
min])..[,(
jZydistjiZymm
indeljiZm
indeljiZymm
jiZm
y
y
An Introduction to Bioinformatics Algorithms www.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.
An Introduction to Bioinformatics Algorithms www.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
An Introduction to Bioinformatics Algorithms www.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]<NN><PG>K
Real(Y): CCK AD DAEAC FA VE GP K
Database(Z): CCK[AD]DKETC[FA]<EE><GK>K
sequencing errors
homology mutations