MixGF: Spectral Probabilities for Mixture Spectra from more than One Peptide

In large-scale proteomic experiments, multiple peptide precursors are often cofragmented simultaneously in the same mixture tandem mass (MS/MS) spectrum. These spectra tend to elude current computational tools because of the ubiquitous assumption that each spectrum is generated from only one peptide. Therefore, tools that consider multiple peptide matches to each MS/MS spectrum can potentially improve the relatively low spectrum identification rate often observed in proteomics experiments. More importantly, data independent acquisition protocols promoting the cofragmentation of multiple precursors are emerging as alternative methods that can greatly improve the throughput of peptide identifications but their success also depends on the availability of algorithms to identify multiple peptides from each MS/MS spectrum. Here we address a fundamental question in the identification of mixture MS/MS spectra: determining the statistical significance of multiple peptides matched to a given MS/MS spectrum. We propose the MixGF generating function model to rigorously compute the statistical significance of peptide identifications for mixture spectra and show that this approach improves the sensitivity of current mixture spectra database search tools by a ≈30–390%. Analysis of multiple data sets with MixGF reveals that in complex biological samples the number of identified mixture spectra can be as high as 20% of all the identified spectra and the number of unique peptides identified only in mixture spectra can be up to 35.4% of those identified in single-peptide spectra.The advancement of technology and instrumentation has made tandem mass (MS/MS)¹ spectrometry the leading high-throughput method to analyze proteins (1, 2, 3). In typical experiments, tens of thousands to millions of MS/MS spectra are generated and enable researchers to probe various aspects of the proteome on a large scale. Part of this success hinges on the availability of computational methods that can analyze the large amount of data generated from these experiments. The classical question in computational proteomics asks: given an MS/MS spectrum, what is the peptide that generated the spectrum? However, it is increasingly being recognized that this assumption that each MS/MS spectrum comes from only one peptide is often not valid. Several recent analyses show that as many as 50% of the MS/MS spectra collected in typical proteomics experiments come from more than one peptide precursor (4, 5). The presence of multiple peptides in mixture spectra can decrease their identification rate to as low as one half of that for MS/MS spectra generated from only one peptide (6, 7, 8). In addition, there have been numerous developments in data independent acquisition (DIA) technologies where multiple peptide precursors are intentionally selected to cofragment in each MS/MS spectrum (9, 10, 11, 12, 13, 14, 15). These emerging technologies can address some of the enduring disadvantages of traditional data-dependent acquisition (DDA) methods (e.g. low reproducibility (16)) and potentially increase the throughput of peptide identification 5–10 fold (4, 17). However, despite the growing importance of mixture spectra in various contexts, there are still only a few computational tools that can analyze mixture spectra from more than one peptide (18, 19, 20, 21, 8, 22). Our recent analysis indicated that current database search methods for mixture spectra still have relatively low sensitivity compared with their single-peptide counterpart and the main bottleneck is their limited ability to separate true matches from false positive matches (8). Traditionally problem of peptide identification from MS/MS spectra involves two sub-problems: 1) define a Peptide-Spectrum-Match (PSM) scoring function that assigns each MS/MS spectrum to the peptide sequence that most likely generated the spectrum; and 2) given a set of top-scoring PSMs, select a subset that corresponds to statistical significance PSMs. Here we focus on the second problem, which is still an ongoing research question even for the case of single-peptide spectra (23, 24, 25, 26). Intuitively the second problem is difficult because one needs to consider spectra across the whole data set (instead of comparing different peptide candidates against one spectrum as in the first problem) and PSM scoring functions are often not well-calibrated across different spectra (i.e. a PSM score of 50 may be good for one spectrum but poor for a different spectrum). Ideally, a scoring function will give high scores to all true PSMs and low scores to false PSMs regardless of the peptide or spectrum being considered. However, in practice, some spectra may receive higher scores than others simply because they have more peaks or their precursor mass results in more peptide candidates being considered from the sequence database (27, 28). Therefore, a scoring function that accounts for spectrum or peptide-specific effects can make the scores more comparable and thus help assess the confidence of identifications across different spectra. The MS-GF solution to this problem is to compute the per-spectrum statistical significance of each top-scoring PSM, which can be defined as the probability that a random peptide (out of all possible peptide within parent mass tolerance) will match to the spectrum with a score at least as high as that of the top-scoring PSM. This measures how good the current best match is in relation to all possible peptides matching to the same spectrum, normalizing any spectrum effect from the scoring function. Intuitively, our proposed MixGF approach extends the MS-GF approach to now calculate the statistical significance of the top pair of peptides matched from the database to a given mixture spectrum M (i.e. the significance of the top peptide–peptide spectrum match (PPSM)). As such, MixGF determines the probability that a random pair of peptides (out of all possible peptides within parent mass tolerance) will match a given mixture spectrum with a score at least as high as that of the top-scoring PPSM.Despite the theoretical attractiveness of computing statistical significance, it is generally prohibitive for any database search methods to score all possible peptides against a spectrum. Therefore, earlier works in this direction focus on approximating this probability by assuming the score distribution of all PSMs follows certain analytical form such as the normal, Poisson or hypergeometric distributions (29, 30, 31). In practice, because score distributions are highly data-dependent and spectrum-specific, these model assumptions do not always hold. Other approaches tried to learn the score distribution empirically from the data (29, 27). However, one is most interested in the region of the score distribution where only a small fraction of false positives are allowed (typically at 1% FDR). This usually corresponds to the extreme tail of the distribution where p values are on the order of 10⁻⁹ or lower and thus there is typically lack of sufficient data points to accurately model the tail of the score distribution (32). More recently, Kim et al. (24) and Alves et al. (33), in parallel, proposed a generating function approach to compute the exact score distribution of random peptide matches for any spectra without explicitly matching all peptides to a spectrum. Because it is an exact computation, no assumption is made about the form of score distribution and the tail of the distribution can be computed very accurately. As a result, this approach substantially improved the ability to separate true matches from false positive ones and lead to a significant increase in sensitivity of peptide identification over state-of-the-art database search tools in single-peptide spectra (24).For mixture spectra, it is expected that the scores for the top-scoring match will be even less comparable across different spectra because now more than one peptide and different numbers of peptides can be matched to each spectrum at the same time. We extend the generating function approach (24) to rigorously compute the statistical significance of multiple-Peptide-Spectrum Matches (mPSMs) and demonstrate its utility toward addressing the peptide identification problem in mixture spectra. In particular, we show how to extend the generating approach for mixture from two peptides. We focus on this relatively simple case of mixture spectra because it accounts for a large fraction of mixture spectra presented in traditional DDA workflows (5). This allows us to test and develop algorithmic concepts using readily-available DDA data because data with more complex mixture spectra such as those from DIA workflows (11) is still not widely available in public repositories.