1. Algorithmic Problems in Peptide Sequencing

2. De Novo Sequencing for Peptide Identificaiton
Outline
Basics of Proteomics
Roles and Anatomy of Proteins
Tandem Mass Spectrometry
Algorithms for Peptide Identifications
De Novo Sequencing
An Algorithm for Perfect Spectra
Peptide Identification in Real World
Discussions
De Novo Sequencing for Peptide Identificaiton

3. De Novo Sequencing for Peptide Identificaiton
Briefings
We mainly focus on the following result:
Ting Chen, Ming-Yang Kao, Matthew Tepel, John Rush and George Church, A Dynamic Programming Approach to De Novo Peptide Sequencing via Tandem Mass Spectrometry, Journal of Computational Biology, 8(3): , 2001.
Its preliminary version also appears in The 11th Annual SIAM-ACM Symposium on Discrete Algorithms (SODA 2000), page , 2000.
One of the most-cited algorithm articles in the computational proteomics community.
De Novo Sequencing for Peptide Identificaiton

4. De Novo Sequencing for Peptide Identificaiton
Outline
Basics of Proteomics
Roles and Anatomy of Proteins
Tandem Mass Spectrometry
Algorithms for Peptide Identifications
De Novo Sequencing
An Algorithm for Perfect Spectra
An Improved Version
Peptide Identification in Real World
Discussions
De Novo Sequencing for Peptide Identificaiton

5. Anatomy of Protein Molecules
Neutral peptide
Residue (of the peptides) H H O H O NH C C OH NH C C Rx Rx
Stable state in nature
Basic building blocks
De Novo Sequencing for Peptide Identificaiton

6. De Novo Sequencing for Peptide Identificaiton
Proteins and Peptides H O C O N C R4 H O H H H H H2 N C C N C C N C N C
COOH R1 H R2 O R3 H R5
arginine (R) or lysine (K)
trypsin + H2O K
128.17 N
COOH C R5 H R3 O R4 R
156.11
如無意外，應該要切在 K\R N C R1 H2 H O R2 OH
Rectangles stand for amino acid residues
De Novo Sequencing for Peptide Identificaiton

7. De Novo Sequencing for Peptide Identificaiton
Amino Acid Molecules
Please visit for more information.
De Novo Sequencing for Peptide Identificaiton

8. De Novo Sequencing for Peptide Identificaiton
Outline
Basics of Proteomics
Roles and Anatomy of Proteins
Tandem Mass Spectrometry
Algorithms for Peptide Identifications
De Novo Sequencing
An Algorithm for Perfect Spectra
Peptide Identification in Real World
Discussions
De Novo Sequencing for Peptide Identificaiton

9. Tandem Mass Spectrometry
Mass Spectrometers measure the mass of charged ions.
A mass spectrometer has 3 major components.
Ionizer
Sample + _
Mass Analyzer
Detector
Adapted from Nathan Edwards’ slides
De Novo Sequencing for Peptide Identificaiton

10. Proteomics via Mass Spectrometers
Enzymatic Digest
and
Fractionation
First stage MS
Nobel Prize in 2002.
MS/MS
Precursor selection
and dissociation
Adapted from Nathan Edwards’ slides
De Novo Sequencing for Peptide Identificaiton

11. De Novo Sequencing for Peptide Identificaiton
Outline
Basics of Proteomics
Roles and Anatomy of Proteins
Tandem Mass Spectrometry
Algorithms for Peptide Identification
De Novo Sequencing
An Algorithm for Perfect Spectra
Peptide Identification in Real World
Discussions
De Novo Sequencing for Peptide Identificaiton

12. Peptide Identification
Given:
A MS/MS spectrum (m/z, intensity, possibly along with its retention time)
The precursor mass
Output:
The amino-acid sequence of the peptide
Imagine a deck of cards that you can cut many times and obtains the sums of the upper or lower half
De Novo Sequencing for Peptide Identificaiton

13. Peptide Fragmentation Mechanism
N-Terminus
C-Terminus
b-ions
y-ions
B: 1+w(aa), Y = 19+w(aa)
m/z L G E R
b-ions
y-ions
De Novo Sequencing for Peptide Identificaiton

14. De Novo Sequencing for Peptide Identificaiton
Peaks in a Spectrum
Peptide: L – G – E – R
Weight
Ion
Amino
Acids
114.2 b1 L
GER y3
361.3
171.2 b2 LG ER y2
304.3
300.3 b3
LGE R y1
175.2
De Novo Sequencing for Peptide Identificaiton

15. Manual De Novo Sequencing
=131.03
Molecular weight of M ≈
Molecular weight of K
De Novo Sequencing for Peptide Identificaiton

16. De Novo Sequencing for Peptide Identificaiton
Outline
Basics of Proteomics
Roles and Anatomy of Proteins
Tandem Mass Spectrometry
Algorithms for Peptide Identification
De Novo Sequencing
An Algorithm for Perfect Spectra
Peptide Identification in Real World
Discussions
De Novo Sequencing for Peptide Identificaiton

17. De Novo Sequencing for Peptide Identificaiton
De Novo: From the beginning in Latin.
Database search tools match against known peptides.
Problem Definitions:
Given a spectrum ( a set of real intervals ),
a mass value M,
compute a sequence P, ( a set of real number with specific order)
s.t. m(P)=M, and the matching score is maximized.
m(P) is the sum of residue mass. M
De Novo Sequencing for Peptide Identificaiton

18. De Novo Sequencing: An Ideal Case
An ideal tandem mass spectrum is noise-free and contains only b- and y-ions, and every mass peak has the same height.
The task is to find paths connecting two endpoints on a directed acyclic graph.
The problem is : how to construct the ion ladder?
We can model this problem as a partial digest problem. M
De Novo Sequencing for Peptide Identificaiton

19. Ion Ladders in an Ideal Case
Based on an ideal ion ladder, we can determine the sequence by concatenating prefixes (or suffixes) in order.
However, we cannot determine the ion type of a peak before identifying it.
m/z y1 y2 y3 L G E R
Given only
L+ , ER+,
LGE+, R+
De Novo Sequencing for Peptide Identificaiton

20. De Novo Sequencing for Peptide Identificaiton
NC-Spectrum Model
We generate a (superset of ) ladder of ions.
A Trick: Even if we cannot determine the ion types, we know that an ion is either b-ion or y-ion.
Assume that we want to generate b-ion ladder.
If a peak is a b-ion, add the peak value to the list.
If a peak is a y-ion, add the complementary b-ion value to the list.
This phase doubles the number of peaks.
De Novo Sequencing for Peptide Identificaiton

21. De Novo Sequencing for Peptide Identificaiton
NC-Spectrum Model
For the peptide sequence LGRE, we construct all possible b-ions with respect to current spectrum.
{P1, Q3, P4} or {P2, P3, Q1} are both complete ladders. m P1 P2 P3 P4 L R ER
LGE Q2 Q1 Q4 Q3
m/2 LG
GER
Pi: observed peaks
Qi: artificial peaks
De Novo Sequencing for Peptide Identificaiton

22. De Novo Sequencing for Peptide Identificaiton
NC-Spectrum Model
Given a peak list = {P1,P2,P3, … , Pk}
The coordinates of all points along the line:
Pk – 1
Qk = M – Pk+1 (why?)
We still have to add two endpoints:
M – 18
Since the ion loses a Hydrogen
(M – (Pk – 1 ) ) - 1
Please recall peptide fragmentation mechanism
De Novo Sequencing for Peptide Identificaiton

23. NC Spectrum Model: A Summary
We are given k peaks.
Now we have at most 2k+2 vertices.
Two vertices are adjacent if their coordinates differ by the weight of some amino acid.
The spectrum graph can be constructed in O(n2). (Why?)
The de novo sequencing is to search a path (or paths) representing a good path from coordinate 0 to M-18.
Such a path is not necessarily an ion ladder, though.
我們只能說， prefix 中間攙雜 suffix 或 suffix 摻雜 prefix 的話，成功接起來成為一條 path 的機會比較不那麼高。但也不能避免歪打正著。
De Novo Sequencing for Peptide Identificaiton

24. Dynamic Programming Strategy
Dynamic Programming can solve this problem efficiently.
Uni-directional (forward) DP does not work since it could produce a solution containing both candidates for each peak. Q2 Q1 Q4 Q3 m
m/2 P1 P2 P3 P4
De Novo Sequencing for Peptide Identificaiton

25. Dynamic Programming Strategy (Cont’d)
Dynamic Programming can solve this problem efficiently using a different encoding scheme.
We approach the middle part from both end sides. Q2 Q1 Q4 Q3 m
m/2 P1 P2 P3 P4
De Novo Sequencing for Peptide Identificaiton

26. Dynamic Programming Strategy (Cont’d)
Mass(b-ion) + Mass(y-ion) = PrecursorMass +2
These b-ion candidates are nested pairs in the spectrum graph. m
m/2
De Novo Sequencing for Peptide Identificaiton

27. Relabeling the Vertices
To encode the spectrum graph by the nested pairs, we need to relabel the vertex number.
{0 = x0, x1, x2, …, xk, yk, …, y2, y1, y0 = m}
xi and yi are both generated from the same peak.
We go one level further in each iteration.
另一個好處是，你只要避免在內縮的過程中同時選到 xk 和 yk, 就可以滿足一對只取一個的條件了。 m
m/2 x0 xk yk y0
De Novo Sequencing for Peptide Identificaiton

28. How Dynamic Programming Works
We design the |V|×|V| matrix M for representing partial path candidates.
M(i, j) = 1 iff [xo, xi] and [yj, yo] can occur simultaneouly in a legal path.
For 1≦ s ≦ i, 1 ≦ s ≦ j, s occurs exactly once in the determined partial path. ? xi yj m
m/2
De Novo Sequencing for Peptide Identificaiton

29. How Dynamic Programming Works (Cont’d)x0 x1 x2 x3 x4 y4 y3 y2 y1 y0
m/2 m
M(0,0) = 1 x0 y0
M(0,1) = 1 x0 y1 y0
M(1,0) = 1 x0 x1 y0
De Novo Sequencing for Peptide Identificaiton

30. How Dynamic Programming Works (Cont’d)x0 x1 x2 x3 x4 y4 y3 y2 y1 y0
m/2 m x0 y0 y1 x1
M(0,1) = 1
M(1,0) = 1
M(2,0) = 0 x0 x1 x2 y0
M(1,0) =1 , but we cannot reach x2 from x0 nor x1.
M(2,1) = 1 x0 x2 y1 y0
M(0,1) =1 , and we can reach x2 from x0.
De Novo Sequencing for Peptide Identificaiton

31. How Dynamic Programming Works (Cont’d)x0 x1 x2 x3 x4 y4 y3 y2 y1 y0
m/2 m x0 y0 y1 x1
M(0,1) = 1
M(1,0) = 1
M(0,2) = 0 x0 y2 y1 y0
M(0,1) =1 , but we cannot reach y2 from y0 nor y1.
M(1, 2) = 1 x0 x1 y2 y0
M(1,0) =1 , and we can reach y2 from y0.
De Novo Sequencing for Peptide Identificaiton

32. Dynamic Programming: Preview
In the i-th iteration, we determine and record all possible (partial) paths in [0, xi] and [ yi, m].
m/2 m
第 j 個 iteration 等於把所有邊界為 xj 或者 yj 的 path 都檢查一次 … … x0
xi-1 yt y0
xi or yi?
t < i-1 … … x0
xi-1 yt y0 xi yi
De Novo Sequencing for Peptide Identificaiton

33. Dynamic Programming: Preview(Cont’d) Path extension
How can we reach yi?
To calculate M(xj, yi) for all j < i,
For every j < i, check if yi is adjacent to yt and M(xj, yt) = 1, for some t < i
Then M(xj, yi) = 1. Otherwise, it is 0. … … x0 xj yi yt y0 … … x0 xj yi yt y0
De Novo Sequencing for Peptide Identificaiton

34. Dynamic Programming: Preview(Cont’d) Path extension
Similarly, how can we reach xi?
To calculate M(xi, yj) for all j < i,
For every j < i, check if xi is adjacent to xt and M(xt, yj) = 1, for some t < i
Then define M(xi, yj) =1. … … x0 xt xi yj y0 … … x0 xt xi yj y0
De Novo Sequencing for Peptide Identificaiton

35. De Novo Sequencing for Peptide Identificaiton
Dynamic Programming
m/2 m x0 x1 x2 x3 x4 y4 y3 y2 y1 y0 M y0 y1 y2 y3 y4 x0 x1 x2 x3 x4
De Novo Sequencing for Peptide Identificaiton

36. Dynamic Programming: Initializationx0 x1 x2 x3 x4 y4 y3 y2 y1 y0 M y0 y1 y2 y3 y4 x0 1 x1 x2 x3 x4
De Novo Sequencing for Peptide Identificaiton

37. Dynamic Programming: 1st iteraton
We then compute M(1,0) and M(0,1).
m/2 m x0 x1 x2 x3 x4 y4 y3 y2 y1 y0 M y0 y1 y2 y3 y4 x0 1 x1 x2 x3 x4
Check the arcs (x0, x1) and (y1, y0)
De Novo Sequencing for Peptide Identificaiton

38. Dynamic Programming: Recursion (a)
For j = 2 to k
For i = 0 to j-2
(a) If M(i, j-1) = 1 and edge(Xi, Xj) = 1, then M(j, j-1) = 1.
m/2 m x0 x1 x2 x3 x4 y4 y3 y2 y1 y0
從 y-ion 那邊的觀點，逐一檢查能不能把 x 那一端的界線拉到 (j) M y0 y1 y2 y3 y4 x0 1 x1 x2 x3 x4
Can we adjust the leftmost endpoint to xj?
De Novo Sequencing for Peptide Identificaiton

39. Dynamic Programming: Recursion (b)
For j = 2 to k
For i = 0 to j-2
(b) If M(i, j-1) = 1 and edge(Yj, Yj-1) = 1, then M(i, j) = 1.
m/2 m x0 x1 x2 x3 x4 y4 y3 y2 y1 y0
從 y-ion 那邊的觀點，逐一檢查能不能把 y 那一端既有的界線從 j-1 拉到 (j) M y0 y1 y2 y3 y4 x0 1 x1 x2 x3 x4
Can we adjust the rightmost endpoint to yj?
De Novo Sequencing for Peptide Identificaiton

40. Dynamic Programming: Recursion (c)
For j = 2 to k
For i = 0 to j-2
(c) If M(j-1,i) = 1 and edge(Xj-1, Xj) = 1, then M(j, i) = 1.
m/2 m x0 x1 x2 x3 x4 y4 y3 y2 y1 y0
從b-ion 那邊的觀點，逐一檢查能不能把 b 這一端既有的界線自 j-1 拉到 (j) M y0 y1 y2 y3 y4 x0 1 x1 x2 x3 x4
Can we adjust the leftmost endpoint to xj?
De Novo Sequencing for Peptide Identificaiton

41. Dynamic Programming: Recursion (d)
For j = 2 to k
For i = 0 to j-2
(d) If M(j-1, i) = 1 and edge(Yi, Yj) = 1, then M(j-1, j) = 1.
m/2 m x0 x1 x2 x3 x4 y4 y3 y2 y1 y0
從 b-ion 那邊的觀點，逐一檢查能不能把 y 那一端的界線拉到 (j) M y0 y1 y2 y3 y4 x0 1 x1 x2 x3 x4
Can we adjust the rightmost endpoint to yj?
De Novo Sequencing for Peptide Identificaiton

42. Dynamic Programming (Cont’d)
Now for j = 3
m/2 m x0 x1 x2 x3 x4 y4 y3 y2 y1 y0
從 y-ion 那邊的觀點，逐一檢查能不能把 x 那一端的界線拉到 (j) M y0 y1 y2 y3 y4 x0 1 x1 x2 x3 x4
De Novo Sequencing for Peptide Identificaiton

43. Dynamic Programming (Cont’d)
Now for j = 4
m/2 m x0 x1 x2 x3 x4 y4 y3 y2 y1 y0
從 y-ion 那邊的觀點，逐一檢查能不能把 x 那一端的界線拉到 (j) M y0 y1 y2 y3 y4 x0 1 x1 x2 x3 x4
De Novo Sequencing for Peptide Identificaiton

44. Dynamic Programming: Constructing the Answer
Legal path: Starting our search from the outermost regions ( the last row/column):
[x4, y4] -> [x3, y3] -> [x2, y2] ->[x1, y1]
We backtrack M to search each edge corresponding to the feasible solution
m/2 m x0 x1 x2 x3 x4 y4 y3 y2 y1 y0
如果 M(k,k-1) = 1, 向上找 M(i, k-1) =1 的最大 I; 如果 M(k, j) 才等於1, j < k-1, 請記得，從 k 到 j 之間這些層還是要走的，所以：先退一圈。M(k-1, j) = 1 M y0 y1 y2 y3 y4 x0 1 x1 x2 x3 x4
De Novo Sequencing for Peptide Identificaiton

45. Dynamic Programming: Review
Chen et al. create a new NC-specturm graph G=(V, E), where V=2k+2 and k is the number of mass peaks (ions).
Given the NC-spectrum graph, we can solve the ideal de novo peptide sequencing problem in O(|V|2) time and O(|V|2) space.
M construction : O(|V|2) time
Constructing a feasible solution : O(|V|) time
Therefore we find a feasible solution in O(|V|2) time and O(|V|2) space.
De Novo Sequencing for Peptide Identificaiton

46. De Novo Sequencing for Peptide Identificaiton
Outline
Basics of Proteomics
Roles and Anatomy of Proteins
Tandem Mass Spectrometry
Algorithms for Peptide Identification
De Novo Sequencing
An Algorithm for Perfect Spectra
Peptide Identification in Real World
Discussions
De Novo Sequencing for Peptide Identificaiton

47. De Novo Sequencing for Peptide Identificaiton
Noises in Real Spectra
The de novo strategy is too fragile to handle frequent errors.
False negative peaks
Missing ions will break the path. The algorithms may find wrong paths by concatenating two partial paths.
False positive peaks
The main critique of de novo strategy
Peak value is not the ion mass
Peak values represent the mass over charge value of ions.
It relies on the vendor. (Applied Biosystem)
De Novo Sequencing for Peptide Identificaiton

48. False Positives in Real Spectra
Different types of ions
a-x, b-y, c-z
Internal fragments/immonium ions
Neutral losses
Neutral loss of water (~18Da)
Neutral loss of ammonia (~17Da)
PTM (like adding new letters)
Phosphorylation, glycopeptides
Isotopes
Unpurified samples
前幾點或許還可以靠信號處理幫忙。但最後一點真的很麻煩。
De Novo Sequencing for Peptide Identificaiton

49. De Novo Sequencing for Peptide Identificaiton
Database Search Tools
MASCOT:
The de facto identification tool
De Novo Sequencing for Peptide Identificaiton

50. Database Search Tools (Cont’d)
Brian Searle of Proteome Software informs us:
De Novo Sequencing for Peptide Identificaiton

51. Peptide and Protein Identification
A brief comparison of popular tools
Scoring Strategy
Representatives
Correlation, Z-score, posterior probabilities
SEQUEST, MS-Tag, Scope, CIDentify, Popitam, ProbID, and PepSearch
Statistical significance: E-values or P- values
Mascot, Sonar, InsPecT,
OMSSA, and X!Tandem
De Novo Sequencing
Pseudo-peaks
PEAKS
Spectrum graphs
Lutefisk, PepNovo, AUDENS
Statistical models
NovoHMM
De Novo Sequencing for Peptide Identificaiton

52. De Novo Sequencing for Peptide Identificaiton
Outline
Basics of Proteomics
Roles and Anatomy of Proteins
Tandem Mass Spectrometry
Algorithms for Peptide Identification
De Novo Sequencing
An Algorithm for Perfect Spectra
An Improved Version
Peptide Identification in Real World
Discussions
De Novo Sequencing for Peptide Identificaiton

53. De Novo Sequencing for Peptide Identificaiton
Wrap Up
The MS/MS measures the mass of fragment ions.
A single stage MS measures a collection of peptide.
We generate ion ladders to reconstruct peptide sequence.
Masses are more reliable than intensities.
De novo sequencing is an elegant strategy, but not robust.
We need some signal preprocessing strategies.
Database search tools cannot handle novel proteins, and results from different tools are often inconsistent.
Integration of the two above methods may be a possible way.
De Novo Sequencing for Peptide Identificaiton

54. Some Guys You May Wish to Know
Affiliation
Principal Investigators
Topics
ETH at Zurich
Ruedi Aebersold
Peptide-atlas, statistical significance estimation
UCSD
Pavel Pevzner, Vineet Bafna
De novo sequencing: Multi-spectra alignment
Waterloo
Bin Ma
De novo sequencing: SPIDER, PEAKS
NIH
Yi-Kuo Yu
Signal calibration, statistical significance estimation
Xerox
Andrew Goldberg, Marshall Bern
PTM
Georgetown
Nathan Edwards
Peptide identification
USC
Tim Chen
De Novo Sequencing
De Novo Sequencing for Peptide Identificaiton