HMMatch: Peptide Identification by Spectral Matching

of Tandem Mass Spectra using Hidden Markov Models

Xue Wu1 Chau-Wen Tseng1 Nathan Edwards2∗

1 Department of Computer Science

University of Maryland, College Park

2 Center for Bioinformatics and Computational Biology

University of Maryland, College Park

∗Corresponding author

1

Abstract

Peptide identification by tandem mass spectrometry is the dominant proteomics

workflow for protein characterization in complex samples. The peptide fragmentation

spectra generated by these workflows exhibit characteristic fragmentation patterns that

can be used to identify the peptide. In other fields, where the compounds of interest

do not have the convenient linear structure of peptides, fragmentation spectra are

identified by comparing new spectra with libraries of identified spectra, an approach

called spectral matching. In contrast to sequence based tandem mass spectrometry

search engines used for peptides, spectral matching can make use of the intensities of

fragment peaks in library spectra to assess the quality of a match. We evaluate a hidden

Markov model approach (HMMatch) to spectral matching, in which many examples

of a peptide’s fragmentation spectrum are summarized in a generative probabilistic

model that captures the consensus and variation of each peak’s intensity.

We demonstrate that HMMatch has good specificity and superior sensitivity, com-

pared to sequence database search engines such as X!Tandem. HMMatch achieves

good results from relatively few training spectra, is fast to train, and can evaluate

many spectra per second. A statistical significance model permits HMMatch scores to

be compared with each other, and with other peptide identification tools, on a unified

scale. HMMatch shows a similar degree of concordance with X!Tandem, Mascot, and

NIST’s MS Search, as they do with each other, suggesting that each tool can assign

peptides to spectra that the others miss. Finally, we show that it is possible to ex-

trapolate HMMatch models beyond a single peptide’s training spectra to the spectra

of related peptides, expanding the application of spectral matching techniques beyond

the set of peptides previously observed.

2

Introduction

High-throughput peptide identification using tandem mass spectrometry (MS/MS) is a

widely used technique and an important component of the rapidly growing field of pro-

teomics. The peptide fragmentation spectra generated by these workflows exhibit character-

istic fragmentation patterns that can be used to identify the peptide. The most frequently

observed peptide fragments correspond to cleavage of the peptide backbone, revealing the

amino-acid sequence of the peptide. With sufficient peptide backbone fragments, each back-

bone position is identified and the mass contribution of successive amino-acids can be ob-

served.

The two dominant algorithmic techniques for peptide identification from tandem mass

spectra both rely primarily on the masses of observed peaks. De novo peptide identification

algorithms (Taylor and Johnson, 1997; Dancik et al., 1999; Chen et al., 2000; Bafna and

Edwards, 2003; Ma et al., 2003; Frank and Pevzner, 2005) reconstruct the peptide sequence

directly from the observed fragment ions. This approach works well when each peptide-

backbone bond is represented by a fragment ion in the spectrum. Sequence database search

engines (Yates et al., 1996; Perkins et al., 1999; Craig and Beavis, 2004; Geer et al., 2004;

Tanner et al., 2005) use protein sequence databases to suggest peptide candidates to be

matched to each spectrum. Given a peptide sequence, the masses of its potential fragments

are determined, and candidate sequences may be scored on the basis of matches to the

fragment masses. This approach has been enormously successful, despite the fact that the

popular search engines make no attempt to predict the intensity of observed fragment ions.

Even the search engines, such as SEQUEST, that use a theoretical spectrum to score peptides

typically give all fragment ions the same intensity.

A variety of projects (Bafna and Edwards, 2001; Schutz et al., 2003; Zhang, 2004; Wan

et al., 2006) have sought to predict the probability of observing an ion or to predict its

3

intensity based on intrinsic properties of the peptide or peptide fragment, including the

peptide sequence, the ion cleavage position, the ion-type (chemical bond cleaved), adjacent

amino-acids, peptide charge state, etc. While these techniques show promise, they have

yet to demonstrate a significant increase peptide identification sensitivity or specificity. In

practice, these sophisticated models seem to identify relatively few additional spectra.

In other fields, where the compounds of interest do not have the convenient linear struc-

ture of peptides, fragmentation spectra are identified by comparing new spectra with libraries

of identified spectra, an approach called spectral matching. This approach makes explicit use

of the intensities observed in previously identified spectra. No attempt is made to predict,

a priori, the spectrum of an unknown molecular species, but once observed, identified and

recorded, the time-consuming task of identification need not be repeated. Using mass and

intensity information, spectral matching assigns identifications with higher confidence than

by using mass alone. Even a peptide fragmentation spectrum with only a few peaks might

be strongly characteristic of that peptide, despite insufficient fragmentation to disambiguate

similar peptide sequences.

Traditionally spectral matching approaches utilize a library of spectra and a spectral

similarity measure that evaluates the quality of the spectrum-spectrum match (Stein, 1994;

Stein and Scott, 1994; Stein, 1995). Library spectra may be real spectra, identified using

traditional sequence database search tools, or artificial consensus spectra that summarize the

most important features of spectra from a particular peptide. Spectral comparison functions

have traditionally been based on the dot-product of a vectorized representation of each

spectrum. Recently, a number of groups have described spectral libraries of high-quality real

spectra with high-confidence identifications (Yates et al., 1998; Johnson et al., 2006; Frewen

et al., 2006; Lam et al., 2007) and consensus spectra (Stein et al., 2006; Lam et al., 2006;

Craig et al., 2006). Results indicate spectral matching can be both precise and efficient,

identifying many spectra missed by sequence based search algorithms.

4

We believe that while the dot-product spectral comparison and consensus spectrum tech-

niques are quite effective, significant information contained in the experimental spectra is

being discarded. The dot-product, for example, weights the contribution of each peak of the

experimental mass spectrum only by its intensity (without regard to its consistency), while

the consensus spectrum presumes that a single intensity value is sufficient to represent the

range of intensities observed in the experimental spectra. We propose, instead, employing

a hidden Markov model (HMM) (Rabiner, 1989) approach to spectral matching to resolve

these deficiencies. Using hidden Markov models allow examples of a peptide’s fragmentation

spectrum to be summarized in a generative probabilistic model, making it possible to weight

the contribution of each ion according to its likelihood of observation and intensity variation.

Hidden Markov models have proved to be a powerful technique in statistical machine

learning, and have been used extensively in de novo gene finding and protein family cluster-

ing and prediction (Krogh et al., 1994; Eddy, 1998; Finn et al., 2006). In particular, the use of

hidden Markov models for protein families, as in Pfam (Finn et al., 2006), suggests that they

may find application in spectral matching. Given a multiple alignment of protein sequences

known to belong to the same protein family, the Pfam hidden Markov model represents

a statistical consensus for the amino acids observed at each position. Conserved positions

tightly constrain protein family membership, while the contribution of highly variable po-

sitions are down-weighted. The model also permits the insertion or deletion of amino-acids

as necessary to align diverged sequences at positions of significant conservation. The Pfam

hidden Markov model, as a statistical signature of a protein family, is more sensitive than

sequence alignment with any single member of the family, and more specific than aligning

against all protein family members in turn.

[Figure 1 about here.]

Figure 1 summarizes the statistical properties of the low-mass region of a set of spectra

5

with high-confidence identifications to the peptide DLATVYVDVLK. This complex figure

shows the distribution, using a vertical box-plot, of normalized peak intensities before log10

intensity transformation (see Methods section, Spectrum Normalization), for each spectrum,

in various m/z value regions. Regions denoted I0, I1, . . . represent m/z value regions between

singly charged b and y ions of peptide DLATVYVDVLK, while the regions denoted b1, b2, . . .

and y1, y2, . . . represent m/z values within 0.5 Da of the corresponding b and y ions. Above

each box-plot is the average frequency of selected peaks, per spectrum, in each m/z region.

While there is much consistency in the intensity of some ions, others show considerable

variation, and some b and y ions are completely absent. We will use hidden Markov models

to capture this complexity.

We train hidden Markov models on collections of mass spectra confidently assigned to a

specific peptide by the widely used X!Tandem (Craig and Beavis, 2004) sequence database

search engine. The hidden Markov models are then used to evaluate additional mass spectra,

and the results compared with X!Tandem, Mascot (Perkins et al., 1999), another popular

sequence database search engine, and NIST’s MS Search software (Mallard et al., 2005),

a dot-product based spectral matching search engine recently updated to search libraries

of peptide fragmentation spectra (Stein et al., 2006). We point out that this approach is

different from PepHMM (Wan et al., 2006), which uses a single hidden Markov model to eval-

uate the quality of any peptide-spectrum match. Our results show that the HMM MS/MS

Match (HMMatch) approach identifies many mass spectra left unidentified by Mascot and

X!Tandem and is more flexible and robust than MS Search. In the remainder of this paper

we describe the HMMatch design, and then present an experimental evaluation of HMMatch

for peptide identification.

6

Methods

Mass spectra libraries

Public LC-MS/MS datasets derived from human samples are downloaded from their re-

spective data repositories. Sources include PeptideAtlas (Desiere et al., 2006) and Human

Proteome Project (HUPO) Plasma Proteome Project (PPP) (Omenn et al., 2005). In all,

more than 2.3 million spectra are stored locally for searching, representing 722 data files, and

about 33 different labs or projects. Tandem mass spectra are re-searched using conserva-

tive search parameters, such as one missed cleavage, tryptic N and C-terminals, methionine

oxidation and cysteine alkylation modifications only, precursor mass tolerance 2.0 Da, and

fragment mass tolerance 0.4 Da. We use a computational grid of approximately 250 Linux

CPUs managed by the Condor scheduling infrastructure, and the X!Tandem search engine

(Craig and Beavis, 2004) for re-searching public datasets. The Mascot search engine (Perkins

et al., 1999), tied to a single processor, is used for benchmarking, comparison studies, and

to confirm specific identifications.

Training spectra

The results of re-searching public LC-MS/MS spectra are stored in a relational database and

frequently observed peptides are identified. A small set of peptides (in a particular charge

state) with many high-confidence peptide identifications are chosen, and a HMMatch model

is constructed for each such peptide. For each peptide model, we extract the set of MS/MS

spectra with precursors within 2.0 Da of the peptide’s theoretical monoisotopic m/z value.

These spectral sets are partitioned into five classes based on their X!Tandem search

results: High confidence identifications of the model peptide (denoted HC), low confidence

and non-significant identifications of the model peptide (LC), high confidence identifications

of a non-model peptide (HC-Other), low confidence and non-significant identifications of

7

a non-model peptide (LC-Other), and spectra with no peptide identification with E-value

less than 1.0 (Unknown). We use a 10−4 X!Tandem E-value threshold to delineate high-

confidence identifications from other peptide identifications. Approximately half of the model

peptides’ high confidence identifications are selected, at random, for training (HC-Train),

while the remainder are reserved for testing (HC-Test).

E-Value computation

While the E-values of high-scoring peptide identifications of model peptides are easy to

extract from Mascot and X!Tandem search results, E-values from low-scoring and non-

significant scores are more difficult to obtain, as the search engines output only the top

few best scoring peptides for each spectrum. To obtain E-values with respect to the model

peptides of weak identifications, we constructed a special decoy protein sequence database,

following Elias et al. (2005). This sequence database consists of reversed protein sequences

of the IPI-Human (Kersey et al., 2004) protein sequence database, plus (forward) protein

sequences that contain the model peptides. The size of this decoy database is consistent

with IPI-Human, and high-confidence identifications by X!Tandem and Mascot have similar

E-values as for a IPI-Human search (data not shown). We also modified the X!Tandem

source code to output all peptide identifications with hyperscores within 80% of the best

scoring peptide. Lastly, we increased the precursor mass tolerance parameter to 4.5 (6.5) Da

for spectra from charge 2 (3) peptide spectra datasets. Using these techniques, we are able

to obtain valid E-value estimates for many spectra with respect to the model peptides, even

when the identifications are very weak or missing from our original re-search results. We use

these E-value estimates in the Comparative Performance section below.

8

MS Search match factor computation

NIST’s MS Search (Mallard et al., 2005) match factors were computed using the MS Search

search engine DLL via a Python module written to enable convenient command-line script-

ing. We construct a reference library for each model peptide, containing the (single) consen-

sus spectra for the peptide from NIST’s peptide fragmentation library (Stein et al., 2006). A

command-line Python script is used to compute the match factor of all query spectra against

the single peptide consensus spectrum reference libraries. Match factor parameters include

precursor mass tolerance 2.0 Da, and fragment mass tolerance 0.8 Da. OMSSA and Q-tof

scoring were not used. We use these match factor values in the Comparative Performance

section below.

Spectrum normalization

While the fragmentation spectra of peptides subject to collisionally induced dissociation

are widely believed to be reproducible under a variety of experimental and instrumental

conditions, this reproducibility is difficult to observe without considerable normalization of

each spectrum. For a spectrum represented by a list of peaks, positive real-valued (m/z,int)

pairs, ordered by m/z, the techniques described in Stein (1994); Stein and Scott (1994);

Yates et al. (1998); Wan et al. (2006); Craig et al. (2006); Frewen et al. (2006); Lam et al.

(2006); Stein et al. (2006); Lam et al. (2007) include intensity normalization relative to the

base peak or rank, m/z binning and blurring, transformations such as the square root or

logarithm of peak intensity, and elimination of insignificant ions by intensity or ranking.

There seems little consensus, to date, on spectrum normalization techniques for spectral

matching, although the work of Wolski et al. (2005) provides some basis for evaluating the

many possibilities.

We have tested a number of normalization procedures and have selected an approach

9

that seems to give good results in our experiments. We do not claim a comprehensive or

exhaustive examination of the possibilities, but we plan to revisit these issues in future work.

We have restricted ourselves to spectrum normalization techniques that can be carried out

without knowledge of the model peptide or global properties of the training spectra, with

the hope that our techniques might be useful in other settings.

Intensity normalization

The absolute value of peak intensities varies significantly between mass spectra of the same

peptide, due to peptide abundance variation and different instrument technologies. We

normalize the intensity of each peak in the peak list by the 3rd most intense peak. The

normalized intensity of the first and second peaks are reset to 100%. We use the third

most intense peak, rather than the base peak, to avoid creating spurious variation due to a

non-reproducible base peak (often the precursor ion).

Peak selection

To ensure that only the most informative peaks are used in HMMatch training, we keep

only the top ten peaks with normalized intensity at least 1.0%. The selection of a small

number of peaks ensures that the significant variation in the number of small, insignificant,

“grass” peaks in each spectrum is eliminated. The resulting fixed length peak list ensures

that HMMatch scores for different spectra are consistent in magnitude. We have found that

this aggressive peak selection does not compromise HMMatch’s performance.

Intensity transformation

Normalized intensities are transformed using the base ten logarithm, which helps to mod-

erate the larger variance observed in more intense peaks. After transformation, retained

normalized intensity values range from 0.0 to 2.0.

10

Spectrum Discretization

Normalized spectra are discretized for use with the discrete-valued HMMatch hidden Markov

model, described next.

Normalized peak intensities are discretized with respect to four equal-sized bins between

the minimum and maximum normalized intensity values. For the spectrum normalization

described above, normalized intensities range from [0.0, 2.0], resulting in normalized intensity

bins [0.0, 0.5], (0.5, 1.0], (1.0, 1.5], and (1.5, 2.0]. We denote these intensity bins I.

Each m/z value in the peak list is transformed from a positive real-valued number to a

symbol describing a region of the m/z axis. Let M = (m1, . . . , mk) be an ordered sequence

of the theoretical m/z values of expected or commonly observed ions of a peptide and ε be

a suitable mass tolerance for matching observed peaks with the elements of M . We add the

values m0 = −ε and mk+1 = +∞ to M for notational convenience. The m/z axis is then

partitioned into 3k + 1 regions: RLj = [mj − ε, mj] for j = 1, . . . , k, RH

j = (mj , mj + ε] for

j = 1, . . . , k, and Rj,j+1 = (mj + ε, mj+1 − ε) for j = 0, . . . , k. Figure 2 shows these regions

on the m/z axis. We use ε = 0.5 Da throughout. We denote the set of all such regions R.

[Figure 2 about here.]

Hidden Markov model

The HMMatch hidden Markov model for peptide fragmentation spectra is based on the

protein family hidden Markov model used by the Pfam database, and is shown in Figure 3.

[Figure 3 about here.]

Hidden States

The hidden Markov model represents each of a peptide’s commonly observed or expected

ions, with m/z value mj ∈ M , by a hidden state Sj. We use states representing singly

11

charged b and y ions for 2+ peptides, but find that adding some doubly charged b and y ions

and dropping rarely observed ions improves predictive performance for 3+ peptides. These

hidden states, represented by squares in Figure 3, are ordered as in M . Insertion states

Ij,j+1 (diamonds in Figure 3) represent additional, unexpected, or unmodeled ions between

expected m/z values mj , mj+1 ∈ M . The absence of expected m/z values is modeled by silent

delete states, represented by circles in Figure 3. The silent begin and end states conceptually

represent the minimum and maximum m/z values, 0.0 (m0 ∈ M) and +∞ (mk+1 ∈ M),

respectively.

Emission Probabilities

Each non-silent state emits a discrete valued m/z value-intensity pair (m/z, int) from R ×

I. We model the m/z value and intensity emission probabilities as independent, so that

PS(m/z, int) = PS(m/z)PS(int) for each non-silent state S. Each ion state Sj, for mj ∈ M ,

emits peaks such that m/z ∈ {RLj , RH

j }. Similarly, each insertion state Ij,j+1 between states

Sj and Sj+1, for mj , mj+1 ∈ M emits peaks such that m/z ∈ {RHj , Rj,j+1, R

Lj+1}. Figure 2

shows the valid m/z regions that may be output by each non-silent state.

Transition Probabilities

Non-zero transition probabilities are shown as directed edges in Figure 3.

Model Training

We train the hidden Markov model using the Baum-Welch (Baum, 1972) algorithm, as imple-

mented in the LAMP_HMM package (DeMenthon and Vuilleumier, 2003), applied to discretized,

normalized spectra from HC-Train. Intensity emission probabilities for expected m/z value

and insertion states are initialized according to peaks from the training spectra in the m/z

regions RLj ∪ RH

j and Rj,j+1, respectively, with small pseudo-counts added for unobserved

12

intensity values. Non-zero m/z value emission probabilities are initialized with probabilities

proportional to the size of the m/z value region they represent. All transition probabilities

from state S in Figure 3 are initialized to 1/degree(S).

HMMatch Scores

Once trained, the HMMatch hidden Markov model is used to assess the extent that unknown

spectra are consistent with the training spectra. Unknown spectra are normalized and dis-

cretized, as above, and the Viterbi algorithm is used to compute the probability of the most

likely path through the hidden Markov model consistent with the unknown spectrum. We

report the Viterbi distance: − log10(p), where p is the probability of the Viterbi path, as the

HMMatch score.

Statistical Significance of HMMatch Scores

While we observe good separation between the HMMatch scores of spectra from the model

peptide of interest and spectra from other peptides, the magnitude of the Viterbi distance

changes with the training set, normalization procedure, model parameters, and model pep-

tide, which makes comparison of HMMatch scores impossible. To normalize the Viterbi

distance scores, we construct a statistical significance model by comparison to the distribu-

tion of HMMatch scores of “random” spectra. Once determined, for each HMMatch model,

this null-model is used to transform HMMatch scores to p-values.

Random spectra

Generating random spectra for statistical significance models must be done with care. Naively

generated random spectra are so unlike peptide MS/MS spectra that even poor HMMatch

scores appear statistically significant. We require that the random spectra look enough like

13

true peptide fragmentation spectra that poor HMMatch scores are not statistically signifi-

cant, while ensuring that good HMMatch scores are still unlikely to be observed.

We extract the intensity and m/z value properties of discretized, normalized training

spectra independently. Each peak list contains ten peaks, three of which have normalized

intensity 100%, by construction. The discrete intensities of the remaining peaks in each

training spectrum are tabulated to construct an empirical probability density for peak in-

tensity.

The probability density of the discretized training spectra m/z values is determined from

the m/z values of the top N most intense peaks in each spectrum, for some N ≥ 10. As

with the intensities, the m/z regions are tabulated to construct an empirical probability

density. For small N , the probability density strongly favors m/z regions corresponding to

very abundant ions, while for large N , the probability density weights m/z regions according

to their size. If the probability density favors abundant ions from the training set too heavily,

even for large N , we add pseudo-counts to the m/z regions. As the pseudo-counts increase,

the m/z regions are sampled according to their size and all information about the m/z values

of the abundant ions in the training spectra is lost.

Once the empirical distribution of m/z values and intensities from the training spectra are

established, random spectra are generated by choosing ten peaks according to the discrete

intensity and m/z region probability densities. Three peaks are assigned intensity 100%, with

the rest drawing their intensity independently from the empirical intensity distribution. Each

of the peaks draws their m/z value from the empirical m/z value distribution independently

of each other, and their intensity values.

The parameters of this random spectrum generation technique serve to favor, or discount,

the selection of abundant training spectra m/z values. We initially set the pseudo-counts to

zero and adjust the parameter N until the distribution of the HMMatch scores of random

spectra matches the distribution of the HMMatch scores of HC-Other spectra. Pseudo-counts

14

are used if no value of N is sufficient.

Score Distribution

We find that the normal distribution, with appropriately chosen mean and variance, is a

good fit to the empirical shape of the HMMatch scores from random spectra. The mean and

variance of HMMatch scores of 1000 random spectra are easily computed, and are used to

transform HMMatch scores to normal distribution z-scores to estimate p-values.

Results and Discussion

Peptide and Spectra Dataset Selection

We select eight peptide/charge state combinations from the relational database of identified

spectra (see Methods section). The peptides, their m/z value, and the number of spectra

in each category is shown in Table 1. Peptides were selected from those with the most

high-confidence identifications in the relational database.

[Table 1 about here.]

Training and Performance Evaluation

After training the HMMatch models using the Baum-Welch algorithm (see Methods section)

we evaluate the performance of each model on each spectrum class. Given the relatively

small number of training examples for each peptide, we must be sensitive to the possibility

of over-fitting the model. We carefully considered this issue in the hidden Markov model

design, particularly in the spectrum discretization and emission probability independence

assumption, and in our initialization of intensity emission probability distributions. Plotting

the distribution of HMMatch scores (Figure 4) for the HC-Train and HC-Test spectra shows

15

that there is no evidence of over-fitting. In each case, the distribution of training scores match

the distribution of testing scores. Furthermore, we see that there is excellent separation

between the HMMatch scores of the spectra with high-confidence identifications to the model

peptide (HC-Test) compared with that of other peptides (HC-Other). This implies that

HMMatch has similar specificity as X!Tandem with respect to spectra with high-confidence

identifications.

[Figure 4 about here.]

The time to train each HMMatch model varies depending on the number of states, the

number of training spectra, and the number of Baum-Welch iterations required for conver-

gence. Table 2 shows these statistics for each model. Most of the HMMatch models were

trained in less than ten seconds, with the longest training time less than one minute.

[Table 2 about here.]

Computation of the HMMatch score is also quite fast. Table 3 shows the time to com-

pute HMMatch scores for each peptide’s spectra. Viterbi distance evaluation time depends

primarily on the number of states in the hidden Markov model. While more time-consuming

than the sequence and dot-product based search engines, the time to compute HMMatch

scores is not prohibitive, even for very large spectral datasets, despite the use of a generic

hidden Markov model codebase that does not take advantage of our model’s sparsity.

[Table 3 about here.]

We evaluate the sensitivity of HMMatch by plotting the distribution of HMMatch score

p-values for spectra with weak or no identifications (Figure 5). A large proportion of the

spectra with weak identifications to the model peptide (LC) have very small p-values, demon-

strating higher confidence than X!Tandem for these peptides. A few weak identifications to

16

other peptides (LC-Other) have quite significant HMMatch scores which suggests the weak

X!Tandem identifications are incorrect. Lastly, a considerable fraction of the spectra with

no identification with E-value ≤ 1.0 (Unknown) have significant HMMatch scores. We have

manually examined a number of these cases and discuss them below. In each case we find

that spectra with significant HMMatch scores are an excellent match to high confidence

spectra from the model peptide.

[Figure 5 about here.]

We also test the performance of HMMatch as the number of training spectra is re-

duced. We construct HMMatch models for the peptides LNDLEDALQQAK and DFLAG-

GIAAAISK using training sets consisting of 5, 10, 20, and 40 randomly selected HC spectra.

For peptide LNDLEDALQQAK, the distribution of HMMatch scores for HC-Test and HC-

Other overlap a little for five training spectra, but are completely separated for 10, 20, and

40 training spectra. For peptide DFLAGGIAAAISK, the HC-Test and HC-Other scores are

well separated for all training set sizes from 5 to 40. As with all machine-learning techniques,

HMMatch training is more effective as the number of training examples increases, however,

these experiments demonstrate that good performance is possible even with a relatively small

number of training spectra per peptide.

Comparative Performance

In the absence of a sufficiently rich dataset with known correct peptide identifications to

establish performance in terms of sensitivity and specificity, we compare HMMatch to se-

quence database search engines X!Tandem and Mascot, and spectral matching search engine

MS Search from NIST with consensus spectra from the NIST library of peptide fragmenta-

tion spectra. We use precision-recall statistics to compare the tools’ peptide identification

17

scores, and manually examine some of the cases where HMMatch is able to confidently

identify spectra the other tools cannot.

Comparative Precision-Recall Curves

Each tool orders the spectra in each dataset according to some spectrum-peptide match score.

For X!Tandem and Mascot, this is the E-value, for NIST’s MS Search this is the match factor,

and for HMMatch this is the HMMatch score described above. Given a reference labeling as

positive or negative with respect to the model peptide, we can evaluate, with respect to any

spectrum-peptide match score threshold, the extent to which the partition of the spectra

using this threshold is consistent with the reference labels. The spectrum-peptide match

score and threshold and the reference labels partition the spectra into true-positive (TP ),

false-positive (FP ), false-negative (FN), and true-negative (TN) sets. Precision, then, is

defined as |TP |/(|TP | + |FP |), while recall is defined as |TP |/(|TP | + |FN |). Perfect

correspondence with the reference labels, for a particular match score and threshold, results

in 100% precision and 100% recall. The precision-recall curve, which plots the precision-

recall statistics for all thresholds, captures the extent to which the ranking of spectra by

some match score is consistent with the reference partition of the spectra into positive and

negative examples. Perfect correspondence with the reference labels results in a square

precision-recall curve.

We compare each tool to the others by using each tool and some spectrum-peptide score

threshold, in turn, to construct synthetic reference labels. As such, these precision-recall

statistics and curves do not represent true measures of sensitivity and specificity, instead

they capture the extent that each tool’s spectrum-peptide match score ranks the spectra in

an order that is consistent with the synthetic reference. We show a complete set of precision-

recall curves for the synthetic reference based on X!Tandem E-value and significance thresh-

old 0.01 in Figure 6. To summarize the comparative behavior more comprehensively, we

18

show the % recall at 99% precision for each tool averaged across the eight datasets, with

respect to synthetic reference labels derived from each tool’s spectrum-peptide match score

in Table 4.

[Figure 6 about here.]

[Table 4 about here.]

The precision-recall curves and statistics show only a moderately good correspondence

between the ranking imposed by any pair of tools. From Table 4 we see that for high precision

identification, the HMMatch score is more like X!Tandem and Mascot than MS Search, par-

ticularly for the smaller E-value synthetic label thresholds. For spectral matching synthetic

labels from MS Search, HMMatch shows a similar degree of correspondence as Mascot, with

X!Tandem showing quite a bit less. The precision-recall curves in Figure 6 show there is no

tool that is uniformly more consistent with X!Tandem than the others. For four of the eight

datasets, the HMMatch score recalls the most spectra at 100% agreement with X!Tandem,

Mascot and MS Search recall the most for two each of the remaining datasets. Peptide SH-

CIAEVENDEMPADLPSLAADFVESK shows considerable disagreement between the search

engine tools and the spectral matching based tools, with strong agreement between the spec-

tral matching based tools. On the other hand, peptide AVM∗DDFAAFVEK shows consid-

erable difference between the spectra matching based tools, as compared to X!Tandem. On

the strength of the precision-recall curves and statistics, we can conclude that HMMatch

shows a similar level of concordance with the other tools as they do to each other. We can

also observe, again, that HMMatch does not seem to be overtrained or biased towards the

X!Tandem identifications, despite the use of these identifications in HMMatch training.

19

Comparative Case-Study Spectra

Our datasets contain many spectra with highly significant HMMatch scores but with poor

scores from X!Tandem and Mascot. HMMatch confidently identifies, with HMMatch score

p-value < 10−5, 3537 spectra with both Mascot and X!Tandem E-values greater than 0.05.

By way of comparison, NIST’s MS Search confidently identifies, with match factor threshold

0.9, only 673 spectra with both Mascot and X!Tandem E-values greater than 0.05. We

examined a number of these spectra manually to determine whether or not HMMatch was

likely correct and to try to explain the poor scores from other tools.

A considerable proportion (∼ 350) of the spectra were correctly identified by HMMatch

and misidentified by the search engines due to peptide candidate selection issues. We ob-

served a large number of misidentified spectra with precursor molecular weight outside of

the allowed search engine precursor tolerance of 2.0 Da. The spectral matching techniques

also use a precursor tolerance of 2.0 Da, but it is applied to the m/z value of the precursor.

When the search engine parameter is increased to 4.0 Da (6.0 Da) for charge 2 (charge 3)

peptides, these spectra are usually confidently identified as the corresponding model-peptide

by X!Tandem and Mascot. So, while these spectra are confidently identified by HMMatch,

they are not a good demonstration of the strength of HMMatch scores as compared to the

peptide sequence based scoring. However, it does suggest that the usual 2.0 Da precursor

tolerance used for sequence searching is perhaps too aggressive. Nevertheless, increasing the

precursor tolerance increases Mascot and X!Tandem E-values by a similar factor, further

reducing their sensitivity.

Another class of spectra correctly assigned by HMMatch, but with poor X!Tandem and

Mascot scores, are noisy spectra with many extraneous peaks, as in the fragmentation spec-

trum of peptide DLATVYVDVLK in Figure 7(a). This spectrum, confidently identified by

HMMatch with p-value 7.341×10−12 has Mascot E-value 1.07 and X!Tandem E-value 0.0013.

While X!Tandem’s E-value is less than typical significance thresholds, the E-value does not

20

indicate the same degree of confidence as HMMatch. The sequence database search engines

have trouble with these spectra as the extra peaks tend to match fragment ions whether or

not the correct peptide is being evaluated. The MS Search spectral matching search engine

computes a match factor of 0.844 for this spectrum-peptide combination, well below match

factors for other high-confidence peptide identifications. The dot-product based match factor

is affected by noisy spectra, as documented by Mallard et al. (2005). We believe that the ag-

gressive peak selection strategy used for spectrum normalization makes the HMMatch robust

with respect to the presence of extraneous noise peaks, without compromising identification

performance.

The fragmentation spectrum, also of peptide DLATVYVDVLK, in Figure 7(b) represents

another interesting failed identification by Mascot and X!Tandem that is correctly identified

by HMMatch. The HMMatch score has significance 1.738 × 10−12, while MS Search com-

putes a match factor of 0.994. Mascot, on the other hand, computes an E-value of 5.7 and

X!Tandem an E-value of 0.16, neither of which is statistically significant. Close examination

of the search engine results revealed that the spectrum received poor scores due to the frag-

ment ion mass tolerance parameter. The X!Tandem and Mascot searches were conducted

using a fragment ion match tolerance of 0.4 Da, a relatively conservative fragment tolerance

appropriate for the ion trap spectra that makes up the majority of publicly available MS/MS

spectra. However, for the spectrum of Figure 7(b), b4 and y3 ions, amongst others, were ob-

served more than 0.4 Da from their theoretical value, which was sufficient to drive down

the search engine scores. Increasing the fragment tolerance increases Mascot and X!Tandem

E-values, further reducing their sensitivity. HMMatch uses a fragment tolerance of 0.5 Da,

and matched b4, but didn’t even use the peak that matched y3 as it was outside of the ten

most intense peaks. The MS Search match factor was computed using the default bin-size

of 0.8 Da, so the measurement error apparent in these fragment ions did not affect its score.

We believe that the use of peak intensity by HMMatch makes it possible to use a larger

21

fragment ion tolerance and more aggressive peak selection, without sacrificing identification

performance.

[Figure 7 about here.]

Model Extrapolation

Traditional spectral matching, which uses dot-product based similarity scores, essentially

treats the reference spectra as bitmapped images with no semantic content. The use of

artificial consensus spectra, which implicitly encodes semantics by retaining only frequently

observed or expected peaks and permits asymmetric variants of the dot-product based sim-

ilarity measures, is the approach adopted by NIST for its GC/MS (Stein and Scott, 1994)

and peptide fragmentation spectral libraries, as well as the MS Search spectral matching

search engine.

The construction of a probability model, such as HMMatch, to abstract and semanti-

cally summarize the behavior of a set of peptide fragmentation spectra makes it possible to

extrapolate the model to spectra from other, related, peptides. Two peptides that differ by

a single amino-acid or by the addition or removal of a post-translational modification will,

in many cases, have similar normalized intensities, once an appropriate offset is applied to

some of the ions. For example, the peptides DFLAGGVAAAISK and DFLAGGIAAAISK

differ by a Val to Ile substitution, a mass shift of +14.02 Da, which affects the m/z value of

all the fragment ions that contain the changed residue, including b7, . . . , b12 and y7, . . . , y12,

and of course the precursor. Other than this mass shift, however, the peptide fragmentation

spectra of these peptides are very similar. Figure 8 shows the spectral box-plot of HC-Train

spectra, defined as for Figure 1, for each of these peptides. This figure, which plots the

distribution of intensities in each of the discrete m/z regions of R, abstracts away the shift

introduced by the amino-acid substitution and makes the similarity apparent.

22

[Figure 8 about here.]

Given the semantic abstraction of our trained HMMatch model, it is straightforward

to compute the HMMatch scores of spectra of one peptide using the HMMatch model of

the other. Our set of spectra includes three such pairs: DFLAGGVAAAISK and DFLAG-

GIAAAISK, AVMDDFAAFVEK and AVM∗DDFAAFVEK; and SHCIAEVENDEMPADLP-

SLAADFVESK and SHCIAEVENDEM∗PADLPSLAADFVESK. The last two pairs differ by

an oxidized methionine (+15.99), indicated by ∗, while the first pair has an amino-acid sub-

stitution, as already described. For each peptide, we compute the p-value of the HMMatch

score of HC-Test spectra using both the original HMMatch model and the extrapolated

model of its twin. Figure 9 plots the original p-value vs the extrapolated p-value for each of

the six paired peptides. The line y = x is added to provide a visual aid for estimating the

number of HC-Test spectra with increased or decreased significance.

[Figure 9 about here.]

We see that while the p-values are somewhat scattered, most spectra with statistically

significant HMMatch scores computed using the correct model are still statistically significant

with respect to the extrapolated twin peptide’s HMMatch model. In fact, a good number

of the HC-Test spectra are more significant (lie above the y = x line) when scored using the

twin’s model. The success of this model extrapolation suggests that HMMatch models may

be created and used to identify peptides from a specific isoform or modification, even when

their spectra have not previously been identified by other tools. Similarly, it may be possible

to train a single HMMatch model using fragmentation spectra from two related peptides,

useful when there are too few high-confidence training spectra for each individual peptide.

While many related peptides have similar (up to mass shift) spectra, this is clearly not

true for all amino-acid substitutions (in particular, the insertion of a basic residue) and post-

translational modifications. While we cannot necessarily predict which related peptides will

23

have similar spectra, the statistical significance computation ensures that we do not accept

extrapolated model assignments when they are unlikely to be correct.

A larger problem for HMMatch is the linear, ordered, structure of the expected ion hidden

states. If the masses of expected or common fragments ions after the mass shift is applied

are no longer correctly ordered, then it is unclear how we should adjust the hidden Markov

model’s transition probabilities to compensate. For each of the peptide pairs above, the mass

shift is small enough that this is not an issue.

Conclusions

In this paper we have demonstrated a novel approach, HMMatch, to peptide identification,

using a hidden Markov model to summarize the statistical variation and consensus in a

peptide’s fragmentation spectra and applying this model to the identification of unassigned

spectra. Our results indicate that HMMatch has good specificity and superior sensitivity,

compared to sequence database search engines such as X!Tandem. The HMMatch design

achieves good results from relatively few training spectra, is fast to train, and can evaluate

many spectra per second. A statistical significance model permits HMMatch scores to be

compared with each other (and with other peptide identification tools) on a unified scale.

HMMatch shows a similar degree of concordance with X!Tandem, Mascot, and NIST’s MS

Search, as they do with each other, suggesting that each tool can assign peptides to spectra

that the others miss. Finally, we have shown that it is possible to extrapolate HMMatch

models beyond a single peptide’s training spectra to the spectra of related peptides, expand-

ing the application of spectral matching techniques beyond the set of peptides previously

observed.

We believe that as the popularity of protein characterization by tandem mass spectrom-

etry grows and the public repositories of peptide fragmentation spectra to increase in size,

24

covering a larger proportion of more organisms’ proteomes with more examples of mass spec-

tra from a variety of instruments, the hidden Markov model approach to spectral matching

will become increasingly useful in the analysis of peptide fragmentation spectra.

Acknowledgments

This work is supported by NIH/NCI Grant CA126189 and USDA cooperative agreement

5812757342. The authors are grateful for the open source search engine X!Tandem and

the public release of LC-MS/MS datasets via the PeptideAtlas and HUPO PPP projects,

without which this work would not have been been possible.

25

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30

List of Tables

Table 1 Model peptides and spectral dataset sizes. Cysteines alkylated with iodoac-

etamide. * indicates oxidized methionine.

Table 2 Time (in seconds) for HMMatch training.

Table 3 Time (in seconds) to compute HMMatch scores.

Table 4 Average % recall at 99% precision for eight model-peptide spectrum datasets

with respect to various synthetic reference labels. Training spectra and spectra with no

reference score excluded.

Peptidem/z z HC-Train HC-Test LC HC-Other LC-Other Unknown

DFLAGGVAAAISK610.34 2 36 23 59 48 879 22481

DFLAGGIAAAISK617.35 2 33 36 14 113 804 5001

DLATVYVDVLK618.35 2 36 40 61 159 772 4615

AVMDDFAAFVEK671.82 2 110 82 143 205 820 5543

LNDLEDALQQAK679.35 2 28 28 45 169 741 7591

AVM*DDFAAFVEK679.82 2 56 50 52 116 723 7585

SHCIAEVENDEMPADLPSLAADFVESK992.12 3 27 25 140 162 1317 6208

SHCIAEVENDEM*PADLPSLAADFVESK997.45 3 40 40 125 128 1192 6074

Table 1: Model peptides and spectral dataset sizes. Cysteines alkylated with iodoacetamide.* indicates oxidized methionine.

PeptideTime (s) Iterations States Spectra

DFLAGGVAAAISK6 2 81 36

DFLAGGIAAAISK5 2 81 33

DLATVYVDVLK4 2 69 36

AVMDDFAAFVEK16 2 75 110

LNDLEDALQQAK3 2 75 28

AVM*DDFAAFVEK8 2 75 56

SHCIAEVENDEMPADLPSLAADFVESK16 2 120 27

SHCIAEVENDEM*PADLPSLAADFVESK44 2 141 40

Table 2: Time (in seconds) for HMMatch training.

PeptideTime (s) Spectra Spectra/s

DFLAGGVAAAISK586 23526 36.47DFLAGGIAAAISK

143 6001 41.11DLATVYVDVLK

90 5683 62.46AVMDDFAAFVEK

137 6903 48.96LNDLEDALQQAK

175 8602 48.87AVM*DDFAAFVEK172 8582 48.49

SHCIAEVENDEMPADLPSLAADFVESK629 7879 13.33

SHCIAEVENDEM*PADLPSLAADFVESK919 7599 8.45

Table 3: Time (in seconds) to compute HMMatch scores.

Reference Threshold Pos./Neg. X!Tandem Mascot MS Search HMMX!Tandem 0.1 93 / 12 - 59% 54% 53%(E-value) 0.05 90 / 15 - 56% 54% 54%

0.01 79 / 26 - 48% 37% 43%0.001 61 / 44 - 38% 14% 32%

Mascot 0.1 38 / 67 38% - 33% 40%(E-value) 0.05 34 / 71 42% - 35% 34%

0.01 26 / 79 45% - 26% 33%MS Search 0.8 52 / 63 46% 61% - 60%

(Match Factor) 0.9 62 / 53 36% 55% - 49%0.95 72 / 43 32% 42% - 46%

Table 4: Average % recall at 99% precision for eight model-peptide spectrum datasets withrespect to various synthetic reference labels. Training spectra and spectra with no referencescore excluded.

List of Figures

Figure 1 Normalized intensity distribution (before log10 transformation) of low-mass

peaks in m/z regions between (I0, . . .) and near singly charged b (b1, . . .) and y (y1, . . .)

ions from training spectra for peptide DLATVYVDVLK. Average peak frequency, per spec-

trum, in each m/z region is indicated above each normalized intensity box-plot.

Figure 2 Discretization of m/z axis into regions. Valid m/z region emissions, for each

non-silent HMM hidden state, also shown.

Figure 3 The HMMatch hidden Markov model for peptide fragmentation mass spectra.

Figure 4 HMMatch scores for spectra with high-confidence identifications (X!Tandem E-

value < 10−4). High-Confidence Train (HC-Train) ⋆; High-Confidence Test (HC-Test) ◦;

High-Confidence Other (HC-Other) ♦.

Figure 5 HMMatch p-values of low-confidence and unknown spectra (X!Tandem E-value

> 10−4). Low-Confidence (LC) ⋆; Low-Confidence Other (LC-Other) ◦; Unknown ♦.

Figure 6 Precision-recall curves for Mascot ( ), MS Search ( ), and HMMatch ( )

for synthetic reference labels defined by X!Tandem E-value threshold 0.01. Training spectra

and spectra with no X!Tandem E-value for the model peptide are excluded.

Figure 7 Case-study fragmentation spectra of peptide DLATVYVDVLK. (a) Mascot E-

value: 1.07, X!Tandem E-value: 0.0013, MS Search match factor: 0.844, HMMatch p-value:

7.341 × 10−12; (b) Mascot E-value: 5.7, X!Tandem E-value: 0.16, MS Search match factor:

0.994, HMMatch p-value: 1.738 × 10−12.

Figure 8 Normalized intensity boxplots for peaks in each m/z value region from HC-Train

spectra of DFLAGGVAAAISK and DFLAGGIAAAISK.

Figure 9 Comparison of p-values of HC-Test spectra scored with the peptide’s HMMatch

model and the extrapolated HMMatch model of its related “twin” peptide.

0

20

40

60

80

100

11%

17%

6%

94%

8%

0%

11%

86%

17%

0%

6%

92%

19%

3%

3% 3%

0%

I0 I1 I2 I3 I4 I5 I6 I7 I8b1 b2 b3 b4y1 y2 y3 y4

Figure 1: Normalized intensity distribution (before log10 transformation) of low-mass peaksin m/z regions between (I0, . . .) and near singly charged b (b1, . . .) and y (y1, . . .) ions fromtraining spectra for peptide DLATVYVDVLK. Average peak frequency, per spectrum, ineach m/z region is indicated above each normalized intensity box-plot.

Figure 2: Discretization of m/z axis into regions. Valid m/z region emissions, for eachnon-silent HMM hidden state, also shown.

Figure 3: The HMMatch hidden Markov model for peptide fragmentation mass spectra.

0 50 100 1500

5

10

15

20

25DFLAGGVAAAISK

Spec

tra

HMMatch Score0 50 100 150

0

5

10

15

20

25

30

35DFLAGGIAAAISK

Spec

tra

HMMatch Score

0 20 40 60 800

20

40

60

80DLATVYVDVLK

Spec

tra

HMMatch Score0 20 40 60 80 100

0

10

20

30

40

50AVMDDFAAFVEK

Spec

tra

HMMatch Score

0 20 40 60 800

10

20

30

40

50

60LNDLEDALQQAK

Spec

tra

HMMatch Score0 20 40 60 80

0

10

20

30

40

50AVM∗DDFAAFVEK

Spec

tra

HMMatch Score

0 20 40 60 80 1000

20

40

60

80SHCIAEVENDEMPADLPSLAADFVESK

Spec

tra

HMMatch Score0 20 40 60 80 100 120

0

10

20

30

40SHCIAEVENDEM∗PADLPSLAADFVESK

Spec

tra

HMMatch Score

Figure 4: HMMatch scores for spectra with high-confidence identifications (X!Tandem E-value < 10−4). High-Confidence Train (HC-Train) ⋆; High-Confidence Test (HC-Test) ◦;High-Confidence Other (HC-Other) ♦.

10 20 30 40

20

40

60

80

100

− log10(p-value)

DFLAGGVAAAISK

DD

FA

AFV

EK

AD

LP

SLA

AD

FV

ESK

Spec

tra

10 20 30 40 50 60 70

20

40

60

80

100

− log10(p-value)

DFLAGGIAAAISK

Spec

tra

4 6 8 10 12 14

20

40

60

80

100

− log10(p-value)

DLATVYVDVLK

Spec

tra

4 5 6 7 8

20

40

60

80

100

− log10(p-value)

AVMDDFAAFVEK

Spec

tra

4 6 8 10 12

20

40

60

80

100

− log10(p-value)

LNDLEDALQQAK

Spec

tra

4 5 6 7 8 9

20

40

60

80

100

− log10(p-value)

AVM∗DDFAAFVEK

Spec

tra

4 6 8 10 12

20

40

60

80

100

− log10(p-value)

SHCIAEVENDEMPADLPSLAADFVESK

Spec

tra

4 6 8 10 12

20

40

60

80

100

− log10(p-value)

SHCIAEVENDEM∗PADLPSLAADFVESK

Spec

tra

Figure 5: HMMatch p-values of low-confidence and unknown spectra (X!Tandem E-value> 10−4). Low-Confidence (LC) ⋆; Low-Confidence Other (LC-Other) ◦; Unknown ♦.

0 0.2 0.4 0.6 0.8 10.9

0.92

0.94

0.96

0.98

1DFLAGGVAAAISK

LN

DLE

DA

LQ

QA

KD

DF

0 0.2 0.4 0.6 0.8 10.94

0.95

0.96

0.97

0.98

0.99

1DFLAGGIAAAISK

0 0.2 0.4 0.6 0.8 10.88

0.9

0.92

0.94

0.96

0.98

1DLATVYVDVLK

0 0.2 0.4 0.6 0.8 10.75

0.8

0.85

0.9

0.95

1AVMDDFAAFVEK

0 0.2 0.4 0.6 0.8 10.88

0.9

0.92

0.94

0.96

0.98

1LNDLEDALQQAK

0 0.2 0.4 0.6 0.8 10.5

0.6

0.7

0.8

0.9

1AVM∗DDFAAFVEK

0 0.2 0.4 0.6 0.8 10.5

0.6

0.7

0.8

0.9

1SHCIAEVENDEMPADLPSLAADFVESK

0 0.2 0.4 0.6 0.8 10.65

0.7

0.75

0.8

0.85

0.9

0.95

1SHCIAEVENDEM∗PADLPSLAADFVESK

Figure 6: Precision-recall curves for Mascot ( ), MS Search ( ), and HMMatch ( ) forsynthetic reference labels defined by X!Tandem E-value threshold 0.01. Training spectraand spectra with no X!Tandem E-value for the model peptide are excluded.

a)

b)

Figure 7: Case-study fragmentation spectra of peptide DLATVYVDVLK. (a) Mascot E-value: 1.07, X!Tandem E-value: 0.0013, MS Search match factor: 0.844, HMMatch p-value:7.341 × 10−12; (b) Mascot E-value: 5.7, X!Tandem E-value: 0.16, MS Search match factor:0.994, HMMatch p-value: 1.738 × 10−12.

1.5

2

b3 b4 b5 b6 b7 b8 b9 b10 b11y2 y3 y4 y5 y6 y7 y8 y9 y10 y11

DFLA

DFLAGGVAAAISK

1.5

2

b3 b4 b5 b6 b7 b8 b9 b10 b11y2 y3 y4 y5 y6 y7 y8 y9 y10 y11

DFLAGGIAAAISK

Figure 8: Normalized intensity boxplots for peaks in each m/z value region from HC-Trainspectra of DFLAGGVAAAISK and DFLAGGIAAAISK.

0 10 20 30 400

10

20

30

40DFLAGGVAAAISK

GG

IAA

AIS

K

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10AVMDDFAAFVEK

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10AVM∗DDFAAFVEK

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20SHCIAEVENDEMPADLPSLAADFVESK

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Figure 9: Comparison of p-values of HC-Test spectra scored with the peptide’s HMMatchmodel and the extrapolated HMMatch model of its related “twin” peptide.