Optimal kmer superstrings for peptide identification from tandem mass spectra

1
Optimal k-mer superstrings for peptide
identification from tandem mass spectra

• Nathan Edwards
• Center for Bioinformatics and Computational
  Biology

2
Proteomics

• Study of observed proteins
• How much of each?
• What protein is it?
• Usually a combination of
• Wet-lab biological sample manipulation
• Mass spectrometry
• Data analysis

3
Sample Preparation
4
(Single Stage) Mass Spectrometry
MS
5
Tandem Mass Spectrometry
MS/MS
6
Peptide Fragmentation
Peptide S-G-F-L-E-E-D-E-L-K
7
Peptide Fragmentation
100
Intensity
0
m/z
250
500
750
1000
8
Peptide Fragmentation
1166
1020
907
778
663
534
405
292
145
88
b ions
S
K
L
E
D
E
E
L
F
G
147
260
389
504
633
762
875
1022
1080
1166
y ions
100
Intensity
0
m/z
250
500
750
1000
9
Peptide Fragmentation
1166
1020
907
778
663
534
405
292
145
88
b ions
S
K
L
E
D
E
E
L
F
G
147
260
389
504
633
762
875
1022
1080
1166
y ions
y6
100
y7
Intensity
y5
b3
b4
b5
y2
y3
y8
y4
b8
b6
b7
b9
y9
0
m/z
250
500
750
1000
10
Peptide Identification

• Given
• The mass of the parent ion
• The MS/MS spectrum
• Output
• The amino-acid sequence of the peptide

11
Sequence Database Search

• Compares peptides from a protein sequence
  database with spectra
• Filter peptide candidates by
• Parent mass
• Digest motif
• Score each peptide against spectrum
• Generate all possible peptide fragments
• Match putative fragments with peaks
• Score and rank

12
Peptide Candidates

• Parent ion
• Typically lt 3000 Da
• Tryptic Peptides
• Cut at K or R
• Search engines
• Dont handle gt 4 well
• Long peptides dont fragment well
• of distinct 30-mers (N30) upper bounds total
  peptide content

13
de Bruijn Sequences

• de Bruijn sequences represent all words of length
  k from some alphabet A.
• A 0,1, k 3 s 0001110100
• A 0,1, k 4 s 0000111101011001000

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de Bruijn Graph A 0,1, k 4
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
15
de Bruijn Sequences Graphs

• de Bruijn graphs (k,A)
• Edges represent length k words from A
• Each node has
• in degree A
• out degree A
• Eulerian tour constructs de Bruijn sequence.

16
Sequence Database Compression

• Construct sequence database / superstring that is
  
• Complete
• All 30-mers are present
• Correct
• No other 30-mers are present
• Compact
• No 30-mer is present more than once

17
SBH-graph
ACDEFGI, ACDEFACG, DEFGEFGI
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Compressed SBH-graph
ACDEFGI, ACDEFACG, DEFGEFGI
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Sequence Databases CSBH-graphs

• Original sequences correspond to paths

ACDEFGI, ACDEFACG, DEFGEFGI
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Sequence Databases CSBH-graphs

• Complete
• All edges are on some path
• Correct
• Output path sequence only
• Compact
• No edge is used more than once
• C3 Path Set uses all edges exactly once.

21
Sequence Databases CSBH-graphs

• Use each edge exactly once

ACDEFGEFGI, DEFACG
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Size of C3 Path Set for k-mers

• Each path costs
• (k-1)-mer path sequence EOS
• Sequence database with p paths
• Nk p k
• Minimize sequence database size by minimizing
  number of paths
• subject to C3 constraints

23
Best case senario

• if CSBH-graph admits an Eulerian path.
• Sequence database size
• (k-1) Nk 1
• How many paths are required if the CSBH-graph is
  not Eulerian?

24
Non-Eulerian Components

• Net degree
• b(v) in edges - out edges
• Total degree surplus
• B ?b(v)gt0 b(v)
• For each path
• Start nodes net degree 1
• End nodes net degree -1
• Otherwise, net degree no change
• To reduce all nodes to net degree 0, must have at
  least B paths.

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Components w/ B(C) 0

• Balanced component must have Eulerian tour, so
  require exactly one path.
• m balanced components

26
Paths Lower Bound

• The C3 path set must containat least B m
  paths.
• This lower bound is achievable!
• Just add (B - 1) restart edges to non-Eulerian
  components

27
Achieving Path Lower Bound
28
k-mer superstrings

• Solution is optimal, for C3 constraints
• Polynomial time algorithm in length of original
  sequences
• General superstring problem
• Requires completeness only
• NP-hard Garey Johnson 79
• Approximable within a factor of 2.5
• MAX-SNP hard

29
AA Sequence Databases
30
Minimum Size C3 Sequence Database
31
Relative Search Time
SP
UP
IPI-H
SP-VS
UP-VS
32
Constraint Relaxation

• Why insist on compactness?
• What about 29-mers?
• Can we compress still further?
• Complete, Correct (C2)
• Use edges more than once, if helpful!
• How could this possibly help?

33
C2 Superstring

• Sequence set with p paths Nk p k
• Costs k to use restart edges
• Restart edges from nodes v s.t. b(v) gt 0 to v
  s.t. b(v) lt 0
• Reuse edges instead! provided the path length
  is lt k
• Transportation problem!

34
C2 Superstring
S vb(v)gt0
Tvb(v)lt0
Cost k
35
C2 Superstring
S vb(v)gt0
Tvb(v)lt0
Cost 0
Cost 0
Cost k
36
C2 Superstring
S vb(v)gt0
Tvb(v)lt0
4
10
Shortcut paths
7
37
C2 Superstring
S vb(v)gt0
Tvb(v)lt0
Cost 0
Cost 0
Cap 1
Cost 0
38
C2 Superstring
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Extensions and Futher Work

• Better compression
• Enumerate tryptic peptides only
• Relax correctness constraint
• Other uses of CSBH graphs
• Compact representation of mer counts
• Implicit set operations on mers
• Structural graph properties

40
Thanks

• Informatics Research _at_ ABI Celera
• Ross Lippert, Clark Mobarry, Bjarni Halldorsson
• UMIACS _at_ University of Maryland, CP
• V.S. Subrahmanian, Fritz McCall, Doan Pham

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Swiss-Prot
42
Swiss-Prot Variant Annotations
43
Swiss-Prot Variant Annotations
44
Swiss-Prot Sequence
45
Swiss-Prot

• VarSplic enumerates all variants, conflicts,
  isoforms
• Swiss-Prot sequence size
• 60 Mb
• VarSplic sequence size
• 95 Mb
• How many more peptide candidates?

46
Swiss-Prot Variant Annotations
Feature viewer
Variants
47
Swiss-Prot VarSplic Output
P13746-00-01-00 MAVMAPRTLLLLLSGALALTQTWAGSHSM
RYFYTSVSRPGRGEPRFIAVGYVDDTQFVRF P13746-01-01-00
MAVMAPRTLLLLLSGALALTQTWAGSHSMRYFYTSVSRPGRGEPRFI
AVGYVDDTQFVRF P13746-00-00-00
MAVMAPRTLLLLLSGALALTQTWAGSHSMRYFYTSVSRPGRGEPRFIAVG
YVDDTQFVRF P13746-00-03-00
MAVMAPRTLLLLLSGALALTQTWAGSHSMRYFYTSVSRPGRGEPRFIAVG
YVDDTQFVRF P13746-01-03-00
MAVMAPRTLLLLLSGALALTQTWAGSHSMRYFYTSVSRPGRGEPRFIAVG
YVDDTQFVRF P13746-00-04-00
MAVMAPRTLLLLLSGALALTQTWAGSHSMRYFYTSVSRPGRGKPRFIAVG
YVDDTQFVRF P13746-01-04-00
MAVMAPRTLLLLLSGALALTQTWAGSHSMRYFYTSVSRPGRGKPRFIAVG
YVDDTQFVRF P13746-00-05-00
MAVMAPRTLLLLLSGALALTQTWAGSHSMRYFYTSVSRPGRGEPRFIAVG
YVDDTQFVRF P13746-01-05-00
MAVMAPRTLLLLLSGALALTQTWAGSHSMRYFYTSVSRPGRGEPRFIAVG
YVDDTQFVRF P13746-01-00-00
MAVMAPRTLLLLLSGALALTQTWAGSHSMRYFYTSVSRPGRGEPRFIAVG
YVDDTQFVRF P13746-00-02-00
MAVMAPRTLLLLLSGALALTQTWAGSHSMRYFYTSVSRPGRGEPRFIAVG
YVDDTQFVRF P13746-01-02-00
MAVMAPRTLLLLLSGALALTQTWAGSHSMRYFYTSVSRPGRGEPRFIAVG
YVDDTQFVRF


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Swiss-Prot VarSplic Output
P13746-00-01-00 SSQPTIPIVGIIAGLVLLGAVITGAVVAA
VMWRRKSS------DRKGGSYTQAASSDSAQ P13746-01-01-00
SSQPTIPIVGIIAGLVLLGAVITGAVVAAVMWRRKSSGGEGVKDRKG
GSYTQAASSDSAQ P13746-00-00-00
SSQPTIPIVGIIAGLVLLGAVITGAVVAAVMWRRKSS------DRKGGSY
TQAASSDSAQ P13746-00-03-00
SSQPTIPIVGIIAGLVLLGAVITGAVVAAVMWRRKSS------DRKGGSY
TQAASSDSAQ P13746-01-03-00
SSQPTIPIVGIIAGLVLLGAVITGAVVAAVMWRRKSSGGEGVKDRKGGSY
TQAASSDSAQ P13746-00-04-00
SSQPTIPIVGIIAGLVLLGAVITGAVVAAVMWRRKSS------DRKGGSY
TQAASSDSAQ P13746-01-04-00
SSQPTIPIVGIIAGLVLLGAVITGAVVAAVMWRRKSSGGEGVKDRKGGSY
TQAASSDSAQ P13746-00-05-00
SSQPTIPIVGIIAGLVLLGAVITGAVVAAVMWRRKSS------DRKGGSY
TQAASSDSAQ P13746-01-05-00
SSQPTIPIVGIIAGLVLLGAVITGAVVAAVMWRRKSSGGEGVKDRKGGSY
TQAASSDSAQ P13746-01-00-00
SSQPTIPIVGIIAGLVLLGAVITGAVVAAVMWRRKSSGGEGVKDRKGGSY
TQAASSDSAQ P13746-00-02-00
SSQPTIPIVGIIAGLVLLGAVITGAVVAAVMWRRKSS------DRKGGSY
SQAASSDSAQ P13746-01-02-00
SSQPTIPIVGIIAGLVLLGAVITGAVVAAVMWRRKSSGGEGVKDRKGGSY
SQAASSDSAQ


49
Peptide Candidates

• At most 1 additional peptides in 1.6 times as
  much sequence

50
Mascot Running Time
51
Total Search Time
UniProt
SwissProt
UniProt-VS
IPI-HUMAN
SwissProt-VS