Linear discriminant analysis-based estimation of the false discovery rate for phosphopeptide identifications

Abstract

The development of liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS) has made it possible to characterize phosphopeptides in an increasingly large-scale and high-throughput fashion. However, extracting confident phosphopeptide identifications from the resulting large data sets in a similar high-throughput fashion remains difficult, as does rigorously estimating the false discovery rate (FDR) of a set of phosphopeptide identifications. This article describes a data analysis pipeline designed to address these issues. The first step is to reanalyze phosphopeptide identifications that contain ambiguous assignments for the incorporated phosphate(s) to determine the most likely arrangement of the phosphate(s). The next step is to employ an expectation maximization algorithm to estimate the joint distribution of the peptide scores. A linear discriminant analysis is then performed to determine how to optimally combine peptide scores (in this case, from SEQUEST) into a discriminant score that possesses the maximum discriminating power. Based on this discriminant score, the p- and q-values for each phosphopeptide identification are calculated, and the phosphopeptide identification FDR is then estimated. This data analysis approach was applied to data from a study of irradiated human skin fibroblasts to provide a robust estimate of FDR for phosphopeptides. The Phosphopeptide FDR Estimator software is freely available for download at http://ncrr.pnl.gov/software/.

Figure 1

Flow chart of the data analysis pipeline used to estimate the FDR of phosphopeptide identifications.

Figure 2

Illustration of the q-value calculation. The red and blue curves denote the pdfs of F that correspond to the incorrect and correct phosphopeptide identifications, respectively. For a given discriminant score f, FDR(f) is the ratio of the red area divided by the blue area. The q-value is then calculated by Eqn. (17).

Figure 3

Histogram of the XCorr rank of the true top hit (blue) and the true second hit (red).

Figure 4

Scatter plots of the SEQUEST search results. The lower-left and upper-right clusters corresponded to the incorrect and correct phosphopeptide identifications, respectively. (A). $\overline{\Delta C{n}^{\prime }}$ vs. $\overline{XCorr}$. (B). $\overline{\Delta C{n}^{\prime }}$ vs. $\overline{Sp}$. (C). $\overline{Sp}$ vs. $\overline{XCorr}$.

Figure 5

Histogram of ΔM. The maximum lower and minimum upper thresholds of the central dense region were 0 and 10 ppm, respectively.

Figure 6

Estimation of the joint pdf of $\overline{XCorr}$, $\overline{Sp}$, and $\overline{\Delta C{n}^{\prime }}$ using EM. The x-axis denotes the indices of iterations and the y-axis denotes the values of the estimated parameters. The parameters that correspond to the incorrect and correct identifications are red and blue, respectively. (A). Convergence of π₀ andπ₁. (B). Convergence of ${\mu }_{0\_\overline{XCorr}}$ and ${\mu }_{1\_\overline{XCorr}}$. (C). Convergence of${\mu }_{0\_\overline{Sp}}$ and ${\mu }_{1\_\overline{Sp}}$. (D). Convergence of ${\mu }_{0\_\overline{\Delta C{n}^{\prime }}}$ and ${\mu }_{1\_\overline{\Delta C{n}^{\prime }}}$. (E) Convergence of $\mathrm{cov}(\overline{XCorr},\overline{\Delta C{n}^{\prime }})$. (F). Convergence of $\mathrm{cov}(\overline{Sp},\overline{\Delta C{n}^{\prime }})$. (G). Convergence of $\mathrm{cov}(\overline{XCorr},\overline{Sp})$. The insets in (B), (C), and (D) are the estimated means of $\overline{XCorr}$, $\overline{Sp}$, and $\overline{\Delta C{n}^{\prime }}$ on a zoomed-in scale.

Figure 7

Determination of the cluster membership using the joint pdf of $\overline{XCorr}$, $\overline{Sp}$, and $\overline{\Delta C{n}^{\prime }}$. The x- and y-axes denote the probability that each phosphopeptide identification belongs to the distribution of incorrect (p-) and correct (p+) identifications, respectively. The identifications in red (below the 45° line) were assigned to cluster 0, and those in blue (above the 45° line) were assigned to cluster 1.

Figure 8

A,B: Histogram of F and the estimated pdf of F. The red and blue curves correspond to the incorrect and correct identifications, respectively. C,D: The p-value (red), q-value (green), and p(+|F) (blue) for each identification. The FNR is shown in cyan. E,F: ROC curves.