Bioalgo 2012-03-massspec

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 Identificationvia Database Search
• IdentifyingPost Translationally Modified Peptides
• Spectral Convolution
• Spectral Alignment

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

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

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.

N- and C-terminal Peptides

Terminal peptides and ion types
Peptide
Mass (D) 57 + 97 + 147 + 114 = 415

Masses of fragment ions
Peptide
Mass (D) 57 + 97 + 147 + 114 = 415
Peptide
Mass (D) 57 + 97 + 147 + 114 – 18 = 397
without

N- and C-terminal Peptides
415
486
301
154
57
71
185
332
429

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

Reconstructing Peptides
(mass-spectrum)
57 71 154 185 301 332 415 429 486

(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

(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

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

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

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

Tandem Mass Spectrum
• Tandem Mass Spectrometry mainly generates N-
and C-terminal fragment ions
• Chemical noise often complicates the spectrum.
• Represented in 2-D: mass/charge axis vs. intensity
axis
S#: 1708 RT: 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
RelativeAbundance
850.3
687.3
588.1
851.4
425.0
949.4
326.0
524.9
589.2
1048.6
397.1226.9
1049.6
489.1
629.0

Tandem Mass-Spectrometry

Breaking Proteins into Peptides
peptides
MPSER
……
GTDIMR
PAKID
……
HPLC
To
MS/MSMPSERGTDIMRPAKID......
protein

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

Tandem Mass Spectrometry
RT: 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
RelativeAbundance
1389
1991
1409 2149
1615 1621
1411
2147
1611
19951655
1593
1387
21551435 1987
2001 2177
1445 1661
1937
2205
1779 2135
2017
1313 22071307 2329
1105 17071095
2331
NL:
1.52E8
BasePeakF:+
cFullms[
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
RelativeAbundance
850.3
687.3
588.1
851.4
425.0
949.4
326.0
524.9
589.2
1048.6
397.1226.9
1049.6
489.1
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
RelativeAbundance
638.0
801.0
638.9
1173.8
872.3 1275.3
687.6
944.7 1884.51742.11212.0783.3 1048.3 1413.9 1617.7
Scan 1707
MS
MS/MS
Ion
Source
MS-1
collision
cell MS-2

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
RelativeAbundance
850.3
687.3
588.1
851.4
425.0
949.4
326.0
524.9
589.2
1048.6
397.1226.9
1049.6
489.1
629.0
MS/MS instrument
database search
•Sequest, Mascot, etc
de novo interpretation
•Lutefisk, Peaks, etc

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
RelativeAbundance
850.3
687.3
588.1
851.4
425.0
949.4
326.0
524.9
589.2
1048.6
397.1226.9
1049.6
489.1
629.0
W
R
A
C
V
G
E
K
DW
L
P
T
L T
W
R
A
C
V
G
E
K
DW
L
P
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
Mass, Score

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 known
peptides to find best one.
• De novo eliminates the need to scan database of all peptides by
modeling the problem as a graph search.

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.

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 millionseconds?
• 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.

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

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.

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)

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?

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
RelativeAbundance
850.3
687.3
588.1
851.4
425.0
949.4
326.0
524.9
589.2
1048.6
397.1226.9
1049.6
489.1
629.0
Sequence

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

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

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

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

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

Mass/Charge (M/Z)
Intensity

noise
Mass/Charge (M/Z)

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

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

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.

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

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

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

Reverse Shifts
Shift in H2O+NH3
Shift in H2O

Vertices of the Spectrum Graph
• Masses of potential N-terminalpeptides
• Vertices aregenerated by reverseshifts correspondingto ion types
Δ={δ1, δ2,…, δk}
• Every N-terminalpeptidecan generateup to k ions
m-δ1, m-δ2, …, m-δk
• Every mass s in an MS/MS spectrumgenerates k vertices
V(s) = {s+δ1, s+δ2, …, s+δk}
correspondingto potentialN-terminalpeptides
• Vertices of the spectrum graph:
{initialvertex} V(s1) V(s2) ... V(sm) {terminalvertex}

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)

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

Path Score
• p(P,S) = probability that peptide P produces
spectrum S= {s1,s2,…sq}
• p(P, s) = the probability that peptide P
generates a peak s
• Scoring = computing probabilities
• p(P,S) = πsєS p(P, s)

• For a position t that represents ion type dj :
qj, if peak is generated at t
p(P,st) =
1-qj , otherwise
Peak Score

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

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

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

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
iq
1
k
i
iq
1
)1(

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(

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).

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 tatgeneratedispeakaif
),,(
j
j
j
q
q
SPtP
otherwise1
position tatgeneratedispeakaif
)(
R
R
R
q
q
tP

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 )(
),,(
)(
),(

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
RelativeAbundance
850.3
687.3
588.1
851.4
425.0
949.4
326.0
524.9
589.2
1048.6
397.1226.9
1049.6
489.1
629.0
W
R
A
C
V
G
E
K
DW
L
P
T
L T
W
R
A
C
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G
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De Novo
AVGELTK
Database
Search
Database of
known peptides
Database of
known peptides

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?

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

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.

Peptide Sequencing Problem
Goal: Find a peptide with maximal match between
an experimental and theoretical spectrum.
Input:
Output:
• A peptide whose theoretical spectrum
matches the experimental S spectrum the best

Peptide Identification Problem
Goal: Find a peptide from the database with
maximal match between an experimental and
theoretical spectrum.
Input:
• database of peptides
Output:
• A peptide from the database whose theoretical
spectrum matches the experimental S
spectrum the best

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.

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

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.

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.

Peptide Masses
415
486
301
154
57
71
185
332
429

Peptide Masses: Modification +16 on N
415
486
301
154
57
71
185
332
429
+16
+16
+16
+16
+16
+16

Reconstructing Modified Peptides
(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

Reconstructing Modified Peptides
(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

Peptide Identification Problem Revisited
Goal: Find a peptide from the database with
maximal match between an experimental and
theoretical spectrum.
Input:
Output:
• A peptide from the database whose theoretical
spectrum matches the experimental S
spectrum the best

Modified Peptide Identification Problem
Goal: Find a modified peptide from the database with maximal
match between an experimental and theoretical spectrum.
Input:
• 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

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.

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.

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.

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

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.

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.

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

Spectral Convolution
)0)((
))((
,
12
12
122211
22111212
:
SS
xSS
ssSsSs
}S,sS:ss{sSS
x
:peak)(SPCcountpeakssharedThe
withpairsofNumber

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

1
2
3
4
5
0
-150 -100 -50 0 50 100
150
x
Spectral Convolution: An Example

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.

Spectral Comparison: Difficult Case
S S’
S S’’

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.

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).

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
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.

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
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)?

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

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

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!

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

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
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

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.

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+ }

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)

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.

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!

Spectral Product
A={a1,…., an} and B={b1,…., bn}
SpectralproductA 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+ )

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.

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

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

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

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
jijiifkD
kD
ji
ji
jiji
ij
,1)1(
),(~)','(,1)(
max)(
''
''
),()','(
{
)(max)( kDkD ij
ij

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

Fast Spectral Alignment Algorithm
1)1(
1)(
max)(
1,1
),(
kM
kD
kD
ji
jidiag
ij
)(max)( ''
),()','(
kDkM ji
jiji
ij
)(
)(
)(
max)(
1,
,1
kM
kM
kD
kM
ji
ji
ij
ij
Running time: O(n2 k)

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.

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

MS/MS and East-West Traveling Salesman Problem

EE SE E SE D E SE D T E S
129
244
345
47487
216
317
432
E D T
ES
S
E S
T D E
E
S
Anti-symmetric paths
E D T
ES
S
E S
T D E
E
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 SETDEwould be
missed and the algorithm would output a symmetric peptide:
ESESE
Why?
De-novo problem
Input: Spectrum graph
Output: Anti-symmetric longestpath

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)

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 - Oxidation
14 on K - Methylation
22 - Sodium
32 on M - Double oxidation
28 on K - Dimethylation

Filtration in Similarity Searches
Scoring
Protein Query
SequenceAlignment – Smith-Waterman Algorithm
Sequence matches
Filtration
SequenceAlignment: – 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

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

Filtration in MS/MS Sequencing
• Filtration in MS/MS is more difficult than in BLAST.
• Early approaches using Peptide Sequence Tags were
not able to substitute the complete database search.
• Can we design a filtration based search that can replace
the database search, and is orders of magnitude faster?

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

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!

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:

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.

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.

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
DW
L
P
T
L
T
AVGELTK
TAG Prefix Mass
AVG 0.0
VGE 71.0
GEL 170.1
ELT 227.1
LTK 356.2

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
DW
L
P
T
L T
TAG Prefix Mass
AVG 0.0
WTD 120.2
PET 211.4

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.

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

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
DW
L
P
T
L T
W
R
A
C
V
G
K
DW
L
P
T
L T
W
R
A
C
V
G
K
DW
L
P
T
L T
E
W
W
R
A
C
V
G
K
D
L
P
T
L T

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

Experimental Results
Length 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

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

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

Keyword Trees
Y A K
SN
N
F
F
AT
YFAK
YFNS
FNTA
…..Y F R A Y F N T A…..

Tag Extension
Filter SignificanceScoreExtension
De novo
Db
55M
peptides
Candidate
Peptides
(700)

• 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>

Scoring Modified Peptides
Filter SignificanceScoreExtension
De novo
Db
55M
peptides

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

Assessing Reliability of Identifications
Filter SignificanceScoreextension
De novo
Db
55M
peptides

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

Separating power of features

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

Distribution of Quality Scores

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)

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

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

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

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

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

Database Candidate
• 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

Database Candidate
• 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

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

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

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.

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)

Solving Mass-Alignment Problem
])[,()])1..([),((min
)])1..([,(
])..[),((min
min])..[,(
jZydistjiZymm
indeljiZm
indeljiZymm
jiZm
y
y

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.

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

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

Bioalgo 2012-03-massspec

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Bioalgo 2012-03-massspec