Multi-spectra peptide sequencing and its applications to multistage mass spectrometry

Abstract

Despite a recent surge of interest in database-independent peptide identifications, accurate de novo peptide sequencing remains an elusive goal. While the recently introduced spectral network approach resulted in accurate peptide sequencing in low-complexity samples, its success depends on the chance of presence of spectra from overlapping peptides. On the other hand, while multistage mass spectrometry (collecting multiple MS ³ spectra from each MS ² spectrum) can be applied to all spectra in a complex sample, there are currently no software tools for de novo peptide sequencing by multistage mass spectrometry. We describe a rigorous probabilistic framework for analyzing spectra of overlapping peptides and show how to apply it for multistage mass spectrometry. Our software results in both accurate de novo peptide sequencing from multistage mass spectra (despite the inferior quality of MS ³ spectra) and improved interpretation of spectral networks. We further study the problem of de novo peptide sequencing with accurate parent mass (but inaccurate fragment masses), the protocol that may soon become the dominant mode of spectral acquisition. Most existing peptide sequencing algorithms (based on the spectrum graph approach) do not track the accurate parent mass and are thus not equipped for solving this problem. We describe a de novo peptide sequencing algorithm aimed at this experimental protocol and show that it improves the sequencing accuracy on both tandem and multistage mass spectrometry.

Availability: The open-source implementation of our software is available at http://proteomics.bioprojects.org.

Contact: bandeira@ucsd.edu

Supplementary information:: Supplementary data are available at Bioinformatics online.

1 INTRODUCTION

The coupling of tandem mass spectrometry (MS²) with database search tools (Perkins et al., 1999; Tanner et al., 2005; Yates et al., 1995) is the enabling core behind high-throughput protein identification (Aebersold and Mann, 2003). Unfortunately, this successful strategy is not applicable to unknown protein sequences. Particularly important examples of value derived from initially unknown proteins include antibody drugs such as Herceptin™ or Avastin™ (Haurum, 2006) and drugs derived from venom proteins (Pimenta and De Lima, 2005). Antibodies illustrate the scenario where the universe of possible protein sequences is very large and constantly altered by recombination and somatic hypermutation (Maizels, 2005). Additionally, drugs derived from venom proteins exemplify benefits of exploring the viable proteins already probed by natural biodiversity. Another recently emerged application of de novo peptide sequencing is proteogenomics, using mass spectra to predict new genes and alternatively spliced variants (Edwards, 2007; Gupta et al., 2007; Tanner et al., 2007). Proteogenomics studies would greatly benefit from searching 6-frame translations of entire genomes that amounts to roughly 6 billion amino acids for the mammalian genomes. The database search approaches are impractical for such large searches while de novo-based approaches to protein identifications (e.g. Alves and Yu, 2005) are not seriously affected by the database size.

MS-based studies of unknown proteins rely on de novo peptide sequencing techniques that attempt to recover the peptides directly from the spectra. Unfortunately, despite decades of research, accurate de novo peptide sequencing remains an elusive goal with only 30–40% of all peptides (depending on the sample and peptide size) reconstructed correctly (Pevtsov et al., 2006). While algorithms have been developed to find a best-‘scoring’ peptide for a given spectrum (Bafna and Edwards, 2003; Chen et al., 2001; Dancík et al., 1999; Fischer et al., 2005; Frank and Pevzner, 2005; Ma et al., 2003), their sequencing accuracy is still affected by incomplete fragmentation, noise and ambiguity in ion-type assignments. In abundant, low-complexity samples, these difficulties may be attenuated by generating overlapping peptides and combining the resulting MS² spectra to yield higher accuracy de novo sequences—examples include ¹⁶O/¹⁸O labeling (Shevchenko et al., 1997) or Shotgun Protein Sequencing (Bandeira et al., 2004, 2007a). While Shotgun Protein Sequencing was shown to work well for low-complexity samples it remains unclear how it will scale up for complex samples. Multistage MS (e.g. generating multiple MS³ spectra for each MS² spectrum) could be an ideal method to address the potential limitations of Shotgun Protein Sequencing in a controlled and even experiment-driven fashion. However, while various groups recently demonstrated the advantages of multistage MS for database search (Kalkum et al., 2003; Olsen and Mann, 2004; Ulintz et al., 2008), there are currently no software tools for de novo interpretation of multistage MS data. As a result, the multistage MS data are still manually interpreted, not unlike tandem MS in mid-1990s, before the first de novo peptide sequencing tools were developed.

Given a spectrum s, de novo peptide sequencing algorithms attempt to find a peptide π that best ‘explains’ the spectrum (e.g. maximizes the probability of generating the spectrum s). In multi-spectra peptide sequencing, one attempts to find a peptide π that best explains multiple spectra s¹, … ,s^k at once. Multistage MS is an example of the multi-spectra peptide sequencing problem. In certain aspects, interpretation of multistage MS data is more challenging than interpretation of multiple tandem mass spectra (as in Bandeira et al., 2007a) since MS³ spectra typically have lower quality than MS² spectra. The manual usage of MS³ spectra as an aid to de novo sequencing dates back to a decade ago (Lin and Glish, 1998). To the best of our knowledge, the only automated approach to multistage MS is a heuristic approach proposed by Zhang and McElvain (2000). However, the sequencing accuracy of this approach remains unknown since Zhang and McElvain were limited to only 42 sets of multistage spectra and the accuracy gains from the proposed heuristics were described qualitatively rather than quantitatively. Moreover, this approach has not enthused further MS²/MS³ sequencing efforts because no implementation is publicly available. Our multi-spectra peptide sequencing algorithm was benchmarked on a set of 602 MS² spectra with varying numbers of dependent MS³ spectra (yeast dataset). To further evaluate our algorithm we also tested it on 10 517 MS² spectra for which spectra from overlapping prefix/suffix peptides were available.

Sequencing an MS² spectrum in conjunction with k dependent MS³ spectra entails searching for the best-scoring peptide while considering every possible combination of fragment types for the MS³ spectra (i.e. was the MS³ generated from a b- or a y-ion). Our approach explores this search space by using dynamic programming to find the best peptide for each of 2^k possible MS³ fragment-type assignments. We build on a probabilistic model (Frank and Pevzner, 2005) to score peptide-spectrum matches and extend it to include the particularities of MS²/MS³ sequencing. By incorporating these readily available experimental capabilities into a rigorous algorithmic framework, we show that overlapping spectra can significantly increase de novo sequencing accuracy and even make it almost error free when enough ‘usable’ MS³ spectra are available. As an addition (or alternative) to overlapping spectra, we also propose an efficient dynamic programming algorithm for de novo peptide sequencing with accurate peptide masses and evaluate the resulting contribution to de novo sequencing accuracy.

2 METHODS

Datasets The yeast dataset was acquired from a trypsin digestion of a yeast whole-cell lysate on a Thermo LTQ-FT instrument configured for the acquisition of up to five MS³ spectra from each MS² spectrum with a doubly charged precursor; precursor masses for the MS³ spectra were restricted to masses higher than the MS² precursor mass. As a result, we obtained a total of 3184 MS² spectra with 15 770 dependent MS³ spectra. These spectra were searched against a yeast database using InsPecT (details are provided in Supplementary Materials) and resulted in the identification of 890 out of all 3148 MS² spectra (28%), having a total of 4447 dependent MS³ spectra.¹. In general, we observed that MS³ spectra tend to have less explained intensity and less b/y-ion peaks than MS² spectra (details shown in Table 1). The shewanella dataset was acquired on Thermo LTQ instruments over many LC/MS/MS runs with different multi-dimensional separation techniques (Gupta et al., 2007). For the purpose of this study we arbitrarily selected 34 326 MS² spectra from different peptides, resulting in 10 517 MS² spectra with between one and five other MS² spectra from prefix/suffix peptides. From a computational perspective, this shewanella MS² dataset mimics the yeast MS²/MS³ dataset with unrealistically high quality of MS³ spectra and thus allows one to establish an upper bound on the performance of our multistage MS approach.

Table 1.

Spectrum ion statistics for the yeast dataset

	Type of spectra	Number of spectra	Intensity (%)				Number of peaks	p (b)	p (y)
			b	y	Satellite	Unexplained
a)	MS/MS (MS2)	890	13	30	20	37	542	0.81	0.84
	MS/MS/MS (MS3)	4447
	from y-ions	2592	11	17	23	49	62	0.41	0.51
	from b-ions	1039	11	1	25	64	47	0.27	0.09
b)	Scored MS2	890	28	28	23	31	80	0.81	0.81
	Scored MS3	4447
	from y-ions	2592	20	20	16	44	41	0.53	0.53
	from b-ions	1039	14	3	22	61	36	0.30	0.12
c)	Merged (MS2 + MS3)	602	66	8	7	19	83	0.89	0.77
d)	Merged + sequenced	602	92	1	1	6	11	0.82	0.01

a) Ion statistics for RAW spectra. b) Ion statistics after replacing each peak's raw intensity with a likelihood score (Frank and Pevzner, 2005). c) Ion statistics of the consensus spectra obtained by merging each MS² spectrum with its dependent MS³ spectra (after scoring). This category has less spectra (602) than the others (890) mainly because not all MS² spectra had at least one ‘usable’ MS³ spectrum (details in main text). d) Ion statistics for the peaks selected by de novo sequencing on the merged spectra.

Spectrum identification Similar to the protocol used for the identification of spectra in the shewanella dataset (Gupta et al., 2007), InsPecT (Tanner et al., 2005) was used to search a database containing 7517 Saccharomyces cerevisiae protein sequences (SwissPROT, October 8, 2006) and sequences of common contaminant proteins. The database additionally contained 7517 decoy protein sequences used to enforce the selected 5% false-discovery rate. InsPecT was configured to allow for 0.5 Da fragment mass tolerance and 2.5 Da precursor mass tolerance; the high accuracy of the experimental precursor masses was used to confirm identifications rather than to restrict the space of possible peptides. The set of allowed modifications was oxidation (M), phosphorylation (S, T and Y), acetylation (N-term), deamidation (Q) and ¹³C₆¹⁵N₂ SILAC label (K). Since our approach does not address sequencing with post-translational modifications, we discarded all modified peptides with a single exception of the abundant SILAC-K whose mass was added as a 21st amino acid.

The search identified 890 out of all 3148 MS² spectra (28%). However, only 1282 MS³ spectra out of 15 770 (8%) resulted in a significant match to the database. To further increase the number of annotated MS³ spectra, we matched each MS³ precursor mass to the theoretical fragment masses from the peptide assigned to the parent MS² spectrum. Note that this procedure does not increase the number of identified peptides, but rather allows us to better characterize the data and evaluate the algorithms described below. The selection of unambiguous MS³ precursor mass matches resulted in 1039 MS³ spectra annotated as prefix fragments (b-ions), 2592 MS³ spectra annotated as suffix fragments (y-ions) and 320 spectra annotated as prefix/suffix fragments after loss of H₂O or NH₃. All dependent MS³ spectra from all identified MS² spectra were used for de novo sequencing.

The ion statistics for all identified yeast spectra (shown in Table 1) allow us to quantify the differences between MS² and MS³ spectra. In general, the latter tend to have less explained intensity and less b/y-ion peaks. Note that these observations are not entirely surprising, because we only consider the MS² spectra that had a strong match to the database while most MS³ spectra were identified only by their precursor mass.

We note that the different number of spectra in Table 1(b, c) stems from the fact that 202 MS² spectra did not generate any usable MS³ spectrum and also because 86 MS² spectra contained modified residues not considered for our current de novo sequencing purposes. The only exception to the latter was SILAC-labeled Lysine because of the high number of peptides containing this modification.

De novo-peptide sequencing problem The best de novo sequencing algorithms use probabilistic models that capture multiple features such as peak intensities and expected propensities of the different ion types (Dancík et al., 1999; Fischer et al., 2005; Frank and Pevzner, 2005; Ma et al., 2003). We start by introducing a model that seemingly has nothing to do with de novo peptide sequencing, but rather describes a very general probabilistic process that transforms one Boolean string into another. We will show later that this process not only generalizes the probabilistic model from (Dancík et al., 1999) but also allows one to study de novo peptide sequencing from multiple spectra.

Let s=s₁, … ,s_n be a Boolean string called a spectrum and π=π₁, …,π_n be a Boolean string called a peptide. The probability of peptide π generating spectrum s is defined as P(s∣π)=Π_i=1ⁿ P(s_i∣π_i), where P(x∣y) is a 2 × 2 matrix.

Given a spectrum s and a set of strings Π, we are interested in solving the optimization problem of finding max_π∈Π P(s∣π). Below we focus on the sets Π that are relevant in the context of tandem MS. Let V={1, …, n} and G(V,E) be a topological ordering of a Directed Acyclic Graph (DAG) such that i<j for every directed edge (i,j) in E. Every path from 1 to n in graph G corresponds to a G-peptide π=π₁, …,π_n such that π_i=1 iff vertex i belongs to the path. We are interested in the following peptide sequencing (PS) problem.

PS problem Given a spectrum s and a DAG G, find a G-peptide Π maximizing P(s∣ π) over all G-peptides.

We impose no restrictions on the graph G(V,E), but in practical applications it is usually assumed that (i,j)∈E iff (j−i) equals the integer mass of an amino acid. Such graphs are referred to as spectrum graphs (Bartels, 1990; in MS, they usually encode all peptides of a given parent mass n).

The relation between this abstract Boolean strings model and de novo peptide sequencing is straightforward. In reality, an MS/MS spectrum can be represented as a string of ones (peak present) and zeros (no peak present), with a 0/1 for every consecutive 1 Da interval. Similarly, sequences of amino acid masses (peptides) can also be represented as strings of zeros and ones. Every amino acid can be represented as a string of α−1 zeros followed by a single one, where α is the integer amino acid mass. Then, a peptide is simply a concatenation of Boolean strings corresponding to its amino acids. In this context, θ≈0.05 (probability of observing a noise peak) and ρ≈0.7 (probability of observing a b-ion) represent typical values of θ and ρ for ion-trap MS/MS spectra (see table in Fig. 1A). This somewhat simplistic Boolean string model can be modified for any mass resolution, peptide-fragmentation rules and peak intensities (Bafna and Edwards, 2003; Chen et al., 2001; Frank and Pevzner, 2005). Moreover making this model more realistic typically does not affect the algorithmic solution. In particular, (Bandeira et al., 2007b) recently showed how spectral alignment can be used to separate between b/y-ions and thus generate strings as in this model.

Fig. 1.

(A) Probability P(x∣y) of a peptide symbol y generating a spectrum symbol x. Thus, the probability of a spectrum s=s₁, … ,s_n being generated by a peptide π=π₁, …,π_n is defined as P(s∣π)=Π_i=1ⁿP(s_i∣π_i). (B) Construction of a HMM 𝒢 for a graph G. The bold (hidden) path corresponds to the 𝒢-peptide 10101001.

The PS Problem has an easy solution first described by (Dancík et al., 1999). We will find it convenient to cast the approach in (Dancík et al., 1999) as an application of the Viterbi algorithm (Durbin et al., 1999; Viterbi, 1967) in an appropriately constructed hidden Markov model (HMM) 𝒢. Figure 1 shows a graph G with every edge (i,j) substituted by a path with new j−i−1 traversal vertices that starts at i and ends at j. The resulting graph with vertex set V∪T (where V={1, …, n} and T is the set of all traversal vertices) represents the hidden states of the HMM 𝒢 and all possible transitions between the states. The emission probabilities of the HMM are defined by the matrix P(x∣y) with P(x∣y=0) for T states and P(x∣y=1) for all other states (see Fig. 1A). The transition probabilities of all edges in this HMM are defined to be 1.² Finding an optimal path in this HMM is a straightforward application of the Viterbi algorithm.

The model above does not capture the fact that MS/MS spectra represent both prefix ions (b-ions series) and suffix ions (y-ions series). To reflect this we represent peptides as strings in 3-letter alphabet: 1 (theoretical b-cut), −1 (theoretical y-cut) and 0 (no cut). Given a peptide π=π₁, …,π_n, we define its reverse as the peptide π^*=−π_n, …,−π₁, i.e. . We now redefine the probability of peptide π generating spectrum as s as , where Prob(x∣y) is a 2 × 3 matrix. In general, k ions can be modeled by k+1 parameter columns in this matrix; note that using additional ion-types only changes the emission probabilities but not the construction of the HMM.

However, this and other formulations of the peptide sequencing problem encode a particular bias toward peptides that have b-ions b_i, b_j such that b_i and b_j add up to the peptide mass. In these cases, both ions use the same masses in the spectrum to artificially increase the score of the peptide but do so with conflicting ion type assignments (because b_i=y_j and b_j=y_i). Peptides that do not have such pairs of b-ions are referred to as anti-symmetric peptides and efficient algorithms are available to find the maximum scoring anti-symmetric peptide for any given spectrum (Bafna and Edwards, 2003; Chen et al., 2001).³ Nevertheless, ambiguous b/y-ion assignments remain one of the main sources of de novo sequencing errors. We show below how MS³ spectra can help resolve these ambiguities.

Although this model still essentially amounts to maximizing the weighted number of matched masses between a spectrum and a peptide, it already captures enough detail to allow us to describe the proposed extensions for combining MS²/MS³ spectra. In practice, this same framework is used to model more elaborate events to take into consideration the intensity of the peaks in the spectrum and to account for the presence/absence of other ion types (e.g. b−H_2O ions). As shown in Table 1, using more elaborate scoring from (Frank and Pevzner, 2005), one can replace raw intensities with peak scores to significantly increase the signal-to-noise ratio over all collected spectra. The resulting scored spectra have more intensity assigned to true fragment masses and feature a much smaller number of noise peaks while simultaneously retaining almost all b/y-ions.

Multi-spectra peptide sequencing problem The simultaneous sequencing of spectra from multiple peptides (e.g. PEPTIDE, PEPTID and EPTIDE) requires solving two problems: (i) finding the correct multiple alignment between all spectra (described in the next subsection) and (ii) reconstructing a maximal-scoring peptide from the aligned spectra. In the following we assume that the spectra are already aligned (as shown in Fig. 2) and describe the problem of peptide sequencing from multiple aligned spectra. We do not limit ourselves to MS²/MS³ (when all MS³ spectra correspond to prefixes or suffixes of the peptide corresponding to MS² spectrum), but rather consider arbitrary sets of overlapping peptides.

Fig. 2.

Conceptual illustration of peak scoring on an MS² spectrum (e.g. from PEPTIDE) aligned with its dependent MS³ spectra (e.g. S₁ from PEPTID and S₂ from EPTIDE). Since the correct alignment between MS²/MS³ spectra is not known a priori, our algorithm finds the highest scoring peptide over all possible alignments. M indicates the parent mass of the MS² spectrum and complementary masses (e.g. b/y-ions whose masses add up to the corresponding parent mass) are connected by arcs under each spectrum. Colors indicate the sets of masses accounted for when scoring different peaks; the colored squares in the equations represent the summed scores of all peaks of the same color; violet peaks indicate the b-ion masses dictated by the parent masses of the MS³ spectra. Intuitively, the score of a mass m summarizes all corroborating evidence for it being generated from a prefix fragment. The red and blue peaks illustrate the contribution of the MS³ spectra to the separation of b/y-ions in the MS² spectrum—intuitively, if m is a b-ion and M−m is not then the red peaks should be more prominent than the blue peaks.

MS³ spectra contain additional information in the form of corroborating fragmentation peaks at the expected fragment masses in the MS² and all MS³ spectra. When the MS³ spectra are aligned with the MS² spectrum, the corroborating b-ions match ‘vertically’ while the matching y-ions are found at different positions depending on the parent mass of each MS³ spectrum (Fig. 2). As such, we now consider the problem of finding the most probable peptide π=π₁, …,π_n for a set of multiple (possibly overlapping) spectra s¹, …,s^k. Thus, the alignment between the MS²/MS³ spectra defines a substring mapping where is the sequence of consecutive numbers from to () such that the substring generates the spectrum sⁱ.

We now consider the following Multi-spectra peptide sequencing (MSPS) problem.

MSPS problem Given spectra s¹, …,s^k and a substring mapping φ, find a G−peptide Π maximizing .

It is easy to see that the HMM constructed for the PS Problem (described above) can also solve the MSPS problem. The only difference between the two HMMs resides in the types of symbols emitted by the hidden states. Let S(i) be the set of all spectrum values generated from π_i (defined by spectra s¹, … ,s^k and the mapping φ). Then, each hidden state now emits a set of independent values S(i)={v_j}, with P(v_j∣π_i) given by the table in Figure 1 as before: P(x∣y=0) for T states and P(x∣y=1) for all other states. Assuming all v_j are independent observations, the probability of observing any given set S(i) is ∏_vj∈S(i) P(v_j,π_i). Once again, the MSPS problem can be solved by an anti-symmetric sequencing algorithm on 𝒢 (Bafna and Edwards, 2003; Chen et al., 2001). We note that although multiple ion-type assignments can be avoided in the MS² spectrum, the resulting peptide may be somewhat biased by conflicting ion-type assignments in the MS³ spectra. While these conflicts could be readily avoided when only one overlapping spectrum is available (as described in Bandeira et al., 2007b), extending the algorithm to more overlapping spectra would lead to a significant computational burden unlikely to result in relevant gains in terms of sequencing accuracy.

A possible change to the MSPS problem would be to require the start/end positions of each spectrum as mandatory 1s in the returned peptide Π. This modified problem can also be solved using the strategy described above if we modify the HMM 𝒢 by removing all T states at the start/end positions of every spectrum. As such, every path through this modified HMM 𝒢 will be forced to use the states corresponding to these start/end positions and thus results only in peptides that are consistent with the alignment of MS³ spectra.

Aligning MS²/MS³ spectra Under common experimental conditions, the highest intensity peaks in MS² spectra typically correspond to y- and, to a lesser extent, b-ions. Another common source of high-intensity peaks are doubly charged ions. However, on MS² from doubly charged peptides one can avoid doubly charged fragment ions by considering only peaks with a mass higher than that of the precursor ion. By restricting the selection of MS³ precursor ions to this high-mass region our experimental setup (i) implicitly selected singly charged MS³ precursors from doubly charged MS² precursors and (ii) biased toward MS³ spectra generated from b/y-ions.

As such, determining the correct alignment between an MS³ spectrum and its parent MS² spectrum essentially reduces to determining the b/y-ion type of the MS³ precursor ion.

Given an MS² spectrum from a particular peptide (e.g. PEPTIDE), the generation of an MS³ spectrum from one of its b-ions yields additional information about the corresponding prefix peptide (e.g. PEPTID). The converse reasoning applies to MS³ spectra from y-ions and suffix peptides (e.g. PTIDE). As such, the assignment of an MS³ spectrum to the correct ion type allows one to match the corroborating fragmentation from the same peptide regions and thus reinforce the confidence in co-occurring fragment masses. Since the correct ion-type assignments are not known in advance, one needs to explore 2^k possible combinations of assignments—an easy task since k is usually small. Using the set of peaks with matching masses between the MS² and MS³ spectrum (in either ion-type assignment), we define an MS³ spectrum as usable if the summed scores of the matched peaks include at least 25% of the total summed peak scores (in each spectrum).

Using the peptide sequencing framework described here, our approach explores all 2^k possible ion-type assignments for an MS² spectrum with k usable dependent MS³ spectra and selects the combination of assignments resulting in the highest scoring peptide. The same algorithm was used for the case of overlapping MS² spectra, with the peptide dependencies (but not the b/y-ion assignments) determined from InsPecT identifications (see Bandeira et al., 2007b; for a blind approach to the detection of spectra from overlapping peptides).

De novo-peptide sequencing with accurate parent masses Nearly all de novo peptide sequencing algorithms use spectrum graphs (Bartels, 1990; Chen et al., 2001; Dancík et al., 1999; Fernández-de Cossío et al., 1995; Frank and Pevzner, 2005) for interpreting the spectra. The spectrum graph approach, while very useful, has an important (and often overlooked) shortcoming when it comes to handling the parent-mass tolerance. Indeed, due to errors in mass measurements, the lengths of edges in the spectrum graph may deviate from the exact masses of amino acids by as much as 0.5 Da for ion-trap instruments. In the case when all errors are +0.5 Da (unlikely but possible case), this can result in 0.5 × n error in the parent mass for a peptide of length n. Such large deviations may result in optimal but inadequate solutions thus reducing the accuracy of de novo peptide sequencing. While such inconsistent solutions represent a minor nuisance in the low-accuracy setting, they turn into a major problem in the case of highly accurate parent mass measurements. Indeed, in this case it becomes necessary to find the best solution with a given parent mass rather than the best solutions among all peptides encoded by the spectrum graph.

The accurate handling of accurate parent masses (with tolerances of 0.05 Da or lower) can be achieved by adding a third dimension to the standard anti-symmetric recursion (Chen et al., 2001; Dancík et al., 1999) to keep track of the cumulative mass errors (Fig. 3).

Fig. 3.

Dynamic programming recursion for de novo peptide sequencing of a spectrum S with accurate parent mass M. The variable S[u,v,k] represents the maximum gapped-peptide score over all anti-symmetric gapped-peptides with a prefix ending at peak u, a suffix starting at peak v and with cumulative mass error k; a gapped-peptide at position S[u,v,k] is defined as a (possibly incomplete) peptide consisting of a prefix peptide ending at peak u, a gap of mass m(v)−m(u) and a suffix peptide starting at peak v. Used notation: m(x)—mass of peak x; s(x)—score of peak x; 𝒜—set of amino acid masses; δ is the mass error incurred by modeling the peak mass difference m(x)−m(x′) with the amino acid mass a. In reality, user-specified fragment mass tolerances are allowed when appropriate. Also, the set of amino acid masses 𝒜 may include summed masses of pairs of amino acids (to allow for missing ions in the spectrum).

In practical terms, the memory requirements for the third dimension spanned by k can be controlled by binning the cumulative mass errors at a chosen resolution r. For typical values of t=0.5 Da, r=0.01 Da and T≪t this results in a need for 100× more memory than would have otherwise been needed. The memory requirements are on the order of O(m²/r), where m is the number of peaks in the spectrum. Since m is usually ≤100, these requirements can be easily met on any current desktop computer.⁵ We further note that the mass-error tolerances can easily be adjusted for each individual peak by varying the allowed range for k. In particular, peaks derived from the parent masses of overlapping peptides may be set to much lower mass tolerances than peaks from fragment masses.

3 RESULTS

When analyzed in isolation, individual MS³ spectra are less useful than individual MS² spectra. Lower amounts of substrate, low charge and a bias toward shorter peptides result in spectra with generally inferior-ion statistics (Table 1) and consequently a much smaller percentage of identified spectra—8% of all MS³ spectra versus 28% of all MS² spectra in the yeast dataset (using traditional database search). However, the combination of dependent MS³ spectra with the parent MS² spectrum promptly reveals matching peaks from true peptide fragments and non-matching peaks from unexplained noise masses. Capitalizing on this corroborating fragmentation leads to a significant increase in signal-to-noise ratio with 19% intensity in non-explained peaks versus 31%/49% in MS²/MS³ spectra. Also, the distinct locations of b/y-ions in the aligned MS²/MS³ spectra (Fig. 2) allow one to separate between these ion types. Separating b/y-ions alleviates the uncertainties in peak ion-type assignments and thus reduces the probability of high-scoring incorrect peptide identifications. Furthermore, the parent masses of the MS³ spectra create a strong bias toward the corresponding b-ion masses. Since the overwhelming majority of all usable MS³ spectra come from true fragment masses, the resulting set of essentially mandatory b-ions significantly reinforces the score of the correct peptide, while severely reducing the probability of an incorrect high-scoring peptide match (see Fig. S1 Supplementary Materials). This feature is very important for de novo-based approaches to peptide identifications (like RAId-DbS, Alves and Yu, 2005). The main bottleneck of such approaches is a large set of full-length suboptimal peptides that need to be generated to ensure that the correct peptide is searched against a database. As shown in Figure S1, multistage mass spectrometry has a potential to reduce the number of such peptides by several orders of magnitude. The gains obtained from merging MS³ spectra with the corresponding parent MS² spectra are summarized in Table 1c.

Our analysis revealed that scored MS³ spectra sometimes have b/y-ions absent in MS² spectra. Such additional fragmentation is especially important in a de novo sequencing context because one implicity searches for the best peptide match over the space of all possible peptides of the observed parent mass. The combined contributions of the factors described above results in a strong bias toward the correct peptide sequence reflected in a significant increase in the average percentage of correctly predicted amino acids (from 85.7 to 90.7%, Fig. 4). Moreover, we note that this increase in sequencing accuracy is not achieved at the cost of making less predictions—sequencing MS²/MS³ spectra resulted in 4922 amino acid predictions versus 4772 for MS² spectra only. As expected, having more usable MS³ spectra results in increasing de novo sequencing accuracy, generating almost-error-free sequences as soon as four usable MS³ spectra are available.

Fig. 4.

Improvements in de novo peptide sequencing from overlapping spectra and accurate parent masses. (A) Changes in amino acid prediction accuracy, defined as percentage of correct amino acids out of all amino acid predictions; (B) Changes in number of spectra yielding a correct tag of six amino acids or longer (see Bandeira et al., 2007b, for a discussion of how these long tags could suffice for peptide identification). Four different scenarios were found to result in significantly different sequencing results (shown in four different colors), with the yeast dataset mostly resembling the blue subset of the shewanella dataset (charge two precursors with average peptide length ≈11.5). Values for single spectra are marked with triangle and the corresponding de novo sequencing gains (from additional overlapping spectra) are marked with a diamond of the same color and in the same column; values from the same peptide subset are connected by either dashed (single spectra) or full (multiple spectra) lines. The plots for the single peptides are not perfectly horizontal since there are small variations in the spectral quality of subsets of MS² spectra with i dependent MS³ spectra (for 1≤i≤5).

As illustrated by the blue lines in Figure 4, the gain in de novo sequencing accuracy is considerably higher when combining multiple MS² spectra from overlapping peptides (shewanella dataset). The larger gains seem to be due to two distinct factors—(i) the lower average quality of MS² spectra not yielding MS³ spectra (as compared to yeast MS² spectra) and (ii) the better ion statistics of the MS² spectra from overlapping peptides (as compared to yeast MS³ spectra). These two factors are clearly illustrated in Figure 4 by the differences between the blue/green dashed (case i) and full (case ii) lines. Nevertheless, increasing numbers of overlapping spectra also resulted in the the same trend of better sequencing accuracy.⁶ In addition to these blue/green cases where the peptides from the yeast and shewanella datasets were most similar, we also observed significant improvements in the traditionally difficult de novo sequencing of long peptides (13+ amino acids). Since these peptides tend to generate less singly charged b/y-ion fragments in the MS² spectrum (especially for triply charged precursors), these cases gain the most from the additional fragmentation in the additional spectra from overlapping peptides. Thus, the sequencing accuracy of long peptides becomes essentially indistinguishable from that of short peptides and doubly charged precursors. Also, while the sequencing accuracy on MS² spectra from triply charged precursors still remains slightly inferior, it roughly approaches (or exceeds, when accurate parent masses are available) the sequencing accuracy previously achievable only for spectra from doubly charged precursors.

The higher sequencing accuracy in combined MS²/MS³ spectra increases the number of spectra for which one can recover long subsequences (i.e. tags) of at least six consecutive amino acids. The availability of MS³ ameliorates but does not completely eliminate the difficulties in de novo sequencing of complete peptides caused by missing fragment masses and high-intensity noise peaks. Nevertheless, one is often able to confidently recover tags that may uniquely identify the peptide using a simple (and very efficient) text-based database search. Even when these long tags happen to match multiple locations in larger databases, the number of possibilities tends to be very small and can be quickly resolved by matching the N/C-terminal masses (tags are usually recovered from the middle of the spectrum) and additional peaks not included in the tag. These factors are especially relevant when de novo sequencing is followed by homology-tolerant searches such as those enabled by MS-Alignment (Tsur et al., 2005). In these cases, the tag-based efficiency gains (Bandeira et al., 2007b; Tanner et al., 2005) should combine with the improved ion statistics shown in Table 1d to simultaneously deliver faster and more accurate results.

4 CONCLUSION

High-throughput studies of unknown proteins such as recombinant (Pham et al., 2006) or venom (Birrell et al., 2007) proteins remain burdened by low-throughput experimental procedures such as Edman sequencing and the limited accuracy of de novo sequencing of individual tandem mass spectra. While related approaches increase the sequencing accuracy by combining multiple MS² spectra from overlapping peptides (Bandeira et al., 2004; Bandeira et al., 2007a; Shevchenko et al., 1997), the experimental setup described here requires fewer sample handling steps (no need to digest with multiple enzymes) and should thus be applicable to smaller amounts of substrate.

We have demonstrated the utility of MS³ spectra for de novo peptide sequencing and compared the resulting gains with those obtainable from overlapping MS² spectra. Although the ion statistics in individual MS³ spectra are usually too weak to allow reliable identification via database searching, the combination of multiple MS³ spectra with the parent MS² spectrum results in higher signal-to-noise ratios and much improved separability of b/y-ions. By combining the corroborating fragmentation in multiple spectra our approach leads to increasing accuracy with higher numbers of usable MS³ spectra and even achieves almost error-free sequencing as soon as four usable MS³ spectra are available. The algorithmic incorporation of accurate parent masses was also shown to contribute to higher sequencing accuracy.

When applied to sets of overlapping MS² spectra, the approach described here also resulted in sequencing accuracy improvements and practically erased the distinction between de novo sequencing of short and long peptides. These gains were even more pronounced for spectra of long peptides, including the traditionally difficult case of spectra from triply charged precursors.

The major reason why database search is more accurate than de novo sequencing is that the former only matches each spectrum to a relatively small number of peptides in the database, while the latter searches the space of all possible peptides. This distinction is especially relevant because peptide fragmentation is usually incomplete and generally confounded by noise peaks. Rather than requiring an a priori guess of the set of possible peptides, the simultaneous analysis of sets of spectra from distinct fragments of the same peptide provides an independent experimental bias toward the correct peptide and largely reduces the set of possible high-scoring alternatives. Since more spectra lead to increasingly restricted sets of high-scoring peptides, it follows that increasing the number of usable MS³ spectra should result in yet higher sequencing accuracy. Experimentally, higher fragment mass accuracy would significantly reduce the chances of spurious peak matches and should seamlessly increase the percentage of usable MS³ spectra. Alternatively, more elaborate statistical models could be used to predict the ion-types of MS³ precursor ions and eventually allow the utilization of MS³ spectra from doubly charged precursor ions. We further note that the approach described here is applicable to peptides of any length and could, in principle, be used in the context of top-down or middle-down (via limited proteolysis) proteomics experiments. However, algorithmic extensions may be necessary to account for MS³ spectra of internal peptide fragments.