Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Algorithmic Problems in Peptide Sequencing 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 2/54 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): 325-337, 2001. – Its preliminary version also appears in The 11th Annual SIAM-ACM Symposium on Discrete Algorithms (SODA 2000), page 389-398, 2000. • One of the most-cited algorithm articles in the computational proteomics community. De Novo Sequencing for Peptide Identificaiton 3/54 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 4/54 Anatomy of Protein Molecules • Residue (of the peptides) • Neutral peptide H H O NH C C OH NH Rx H O C C Rx Stable state in nature Basic building blocks De Novo Sequencing for Peptide Identificaiton 5/54 Proteins and Peptides H2 N H O C C 146.19 128.17 R 174.13 156.11 N H R1 K H H H O H H O N C C N C C C C R2 O R3 R4 H H2 N C C R1 C H R5 H H O H H O N C C N C C R3 O N COOH trypsin + H2O arginine (R) or lysine (K) H H R4 H N C H R5 COOH H N H C C OH Rectangles stand for amino acid residues R2 O De Novo Sequencing for Peptide Identificaiton 6/54 Amino Acid Molecules • Please visit http://www.ionsource.com/ for more information. De Novo Sequencing for Peptide Identificaiton 7/54 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 8/54 Tandem Mass Spectrometry • Mass Spectrometers measure the mass of charged ions. – A mass spectrometer has 3 major components. Sample + _ Ionizer Mass Analyzer Detector Adapted from Nathan Edwards’ slides De Novo Sequencing for Peptide Identificaiton 9/54 Proteomics via Mass Spectrometers Enzymatic Digest and Fractionation First stage MS MS/MS Precursor selection and dissociation Adapted from Nathan Edwards’ slides De Novo Sequencing for Peptide Identificaiton 10/54 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 11/54 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 12/54 Peptide Fragmentation Mechanism N-Terminus C-Terminus b-ions y-ions y-ions R E G L b-ions L G E De Novo Sequencing for Peptide Identificaiton R m/z 13/54 Peaks in a Spectrum • Peptide: L – G – E – R Weight Ion Amino Amino Acids Acids 114.2 b1 L 171.2 b2 LG 300.3 b3 LGE Ion Weight GER y3 361.3 ER y2 304.3 R y1 175.2 De Novo Sequencing for Peptide Identificaiton 14/54 Manual De Novo Sequencing 667.27-536.24=131.03 Molecular weight of M 128.09 ≈147.11-19 Molecular weight of K De Novo Sequencing for Peptide Identificaiton 15/54 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 16/54 De Novo Sequencing • 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 17/54 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? M De Novo Sequencing for Peptide Identificaiton 18/54 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. R L y1 E G y2 G E y3 Given only L+ , ER+, LGE+, R+ L R De Novo Sequencing for Peptide Identificaiton m/z 19/54 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. 1. Assume that we want to generate b-ion ladder. 2. If a peak is a b-ion, add the peak value to the list. 3. 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 20/54 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. GER LG Q2 Q4 Q3 0 Q1 Pi: observed peaks Qi: artificial peaks m m/2 P1 P2 P3 P4 L R ER LGE De Novo Sequencing for Peptide Identificaiton 21/54 NC-Spectrum Model • Given a peak list = {P1,P2,P3, … , Pk} • The coordinates of all points along the line: • 1. Pk – 1 Since the ion loses a Hydrogen 2. Qk = M – Pk+1 (why?) (M – (Pk – 1 ) ) - 1 We still have to add two endpoints: 1. 0 2. M – 18 De Novo Sequencing for Peptide Identificaiton 22/54 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. De Novo Sequencing for Peptide Identificaiton 23/54 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 Q4 Q3 0 Q1 m m/2 P1 P2 P3 De Novo Sequencing for Peptide Identificaiton P4 24/54 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 Q4 Q3 0 Q1 m m/2 P1 P2 P3 De Novo Sequencing for Peptide Identificaiton P4 25/54 Dynamic Programming Strategy (Cont’d) • Mass(b-ion) + Mass(y-ion) = PrecursorMass +2 – These b-ion candidates are nested pairs in the spectrum graph. 0 m/2 De Novo Sequencing for Peptide Identificaiton m 26/54 Relabeling the Vertices • To encode the spectrum graph by the nested pairs, we need to relabel the vertex number. 1. {0 = x0, x1, x2, …, xk, yk, …, y2, y1, y0 = m} 2. xi and yi are both generated from the same peak. 3. We go one level further in each iteration. 0 m/2 x0 xk yk De Novo Sequencing for Peptide Identificaiton m y0 27/54 How Dynamic Programming Works We design the |V|×|V| matrix M for representing partial path candidates. • 1. M(i, j) = 1 iff [xo, xi] and [yj, yo] can occur simultaneouly in a legal path. 2. For 1≦ s ≦ i, 1 ≦ s ≦ j, s occurs exactly once in the determined partial path. ? 0 xi yj m/2 De Novo Sequencing for Peptide Identificaiton m 28/54 How Dynamic Programming Works (Cont’d) x0 x1 x2 x3 x4 y4 y3 y2 y1 y0 m/2 m 0 M(0,0) = 1 x0 M(0,1) = 1 x0 M(1,0) = 1 x0 y0 y1 x1 De Novo Sequencing for Peptide Identificaiton y0 y0 29/54 How Dynamic Programming Works (Cont’d) x0 x1 x2 x3 x4 y4 y3 y2 y1 y0 m/2 m 0 M(0,1) = 1 x0 M(1,0) = 1 x0 M(2,0) = 0 x0 y1 x1 x1 y0 y0 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 30/54 How Dynamic Programming Works (Cont’d) x0 x1 x2 x3 x4 y4 y3 y2 y1 y0 m/2 m 0 M(0,1) = 1 x0 M(1,0) = 1 x0 M(0,2) = 0 y1 x1 x0 y0 y0 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 31/54 Dynamic Programming: Preview • In the i-th iteration, we determine and record all possible (partial) paths in [0, xi] and [ yi, m]. 0 m m/2 x0 x0 … xi-1 yt xi or yi? … xi-1 xi t < i-1 yi De Novo Sequencing for Peptide Identificaiton yt … … y0 y0 32/54 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 x0 … xj yi yt … y0 – Then M(xj, yi) = 1. Otherwise, it is 0. x0 … xj yi De Novo Sequencing for Peptide Identificaiton yt … y0 33/54 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 x0 … xt xi yj … y0 – Then define M(xi, yj) =1. x0 … xt xi De Novo Sequencing for Peptide Identificaiton yj … y0 34/54 Dynamic Programming m/2 m 0 x0 x1 x2 x3 x4 y4 M y3 y0 y2 y1 y1 y2 y3 y0 y4 x0 x1 x2 x3 x4 De Novo Sequencing for Peptide Identificaiton 35/54 Dynamic Programming: Initialization m/2 m 0 x0 x1 x2 x3 x4 y4 y3 M y0 x0 1 y2 y1 y0 y1 y2 y3 y4 x1 0 0 0 0 x2 0 0 0 0 x3 0 0 0 0 x4 0 0 0 0 De Novo Sequencing for Peptide Identificaiton 36/54 Dynamic Programming: 1st iteraton We then compute M(1,0) and M(0,1). m/2 m 0 x0 x1 x2 x3 x4 Check the arcs (x0, x1) and (y1, y0) y4 y3 y2 M y0 y1 x0 1 1 x1 1 y1 y0 y2 y3 y4 0 0 0 0 x2 0 0 0 0 x3 0 0 0 0 x4 0 0 0 0 De Novo Sequencing for Peptide Identificaiton 37/54 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 0 x0 x1 x2 x3 x4 y4 y3 y1 M y0 y1 x0 1 1 x1 1 0 y0 y2 y3 y4 0 0 0 x3 0 0 0 x4 0 0 0 x2 Can we adjust the leftmost endpoint to xj? y2 De Novo Sequencing for Peptide Identificaiton 1 38/54 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 0 x0 x1 x2 x3 x4 y4 y3 y1 M y0 y1 y2 x0 1 1 0 x1 1 0 y0 y3 y4 0 0 0 x3 0 0 0 x4 0 0 0 x2 Can we adjust the rightmost endpoint to yj? y2 De Novo Sequencing for Peptide Identificaiton 1 39/54 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 0 x0 x1 x2 x3 x4 y4 Can we adjust the leftmost endpoint to xj? y3 y2 y1 M y0 y1 y2 x0 1 1 0 x1 1 0 x2 0 1 y0 y3 y4 0 0 0 x3 0 0 0 x4 0 0 0 De Novo Sequencing for Peptide Identificaiton 40/54 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 0 x0 x1 x2 x3 x4 y4 Can we adjust the rightmost endpoint to yj? y3 y2 y1 M y0 y1 y2 x0 1 1 0 x1 1 0 1 x2 0 1 y0 y3 y4 0 0 0 x3 0 0 0 x4 0 0 0 De Novo Sequencing for Peptide Identificaiton 41/54 Dynamic Programming (Cont’d) Now for j = 3 m/2 m 0 x0 x1 x2 x3 x4 y4 y3 y2 y1 y0 M y0 y1 y2 y3 x0 1 1 0 0 x1 1 0 1 1 x2 0 1 0 1 0 x3 0 0 1 0 0 0 0 0 x4 De Novo Sequencing for Peptide Identificaiton y4 42/54 Dynamic Programming (Cont’d) Now for j = 4 m/2 m 0 x0 x1 x2 x3 x4 y4 y3 y2 y1 y0 M y0 y1 y2 y3 y4 x0 1 1 0 0 0 x1 1 0 1 1 0 x2 0 1 0 1 0 x3 0 0 1 0 0 x4 0 0 0 1 0 De Novo Sequencing for Peptide Identificaiton 43/54 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 0 x0 x1 x2 x3 x4 y4 y3 y2 y1 y0 M y0 y1 y2 y3 y4 x0 1 1 0 0 0 x1 1 0 1 1 0 x2 0 1 0 1 0 x3 0 0 1 0 0 x4 0 0 0 1 0 De Novo Sequencing for Peptide Identificaiton 44/54 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 45/54 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 46/54 Noises in Real Spectra • The de novo strategy is too fragile to handle frequent errors. 1. False negative peaks • Missing ions will break the path. The algorithms may find wrong paths by concatenating two partial paths. 2. False positive peaks • The main critique of de novo strategy 3. 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 47/54 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 De Novo Sequencing for Peptide Identificaiton 48/54 Database Search Tools • MASCOT: http://www.matrixscience.com/ • The de facto identification tool De Novo Sequencing for Peptide Identificaiton 49/54 Database Search Tools (Cont’d) • Brian Searle of Proteome Software informs us: De Novo Sequencing for Peptide Identificaiton 50/54 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 Pvalues 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 51/54 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 52/54 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 53/54 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 54/54