The Application of Gaussian Mixture Models for Signal Quantification in MALDI-ToF Mass Spectrometry of Peptides

<div><p>Matrix assisted laser desorption/ionization time-of-flight (MALDI-TOF) coupled with stable isotope standards (SIS) has been used to quantify native peptides. This peptide quantification by MALDI-TOF approach has difficulties quantifying samples containing peptides with ion currents in overlapping spectra. In these overlapping spectra the currents sum together, which modify the peak heights and make normal SIS estimation problematic. An approach using Gaussian mixtures based on known physical constants to model the isotopic cluster of a known compound is proposed here. The characteristics of this approach are examined for single and overlapping compounds. The approach is compared to two commonly used SIS quantification methods for single compound, namely Peak Intensity method and Riemann sum area under the curve (AUC) method. For studying the characteristics of the Gaussian mixture method, Angiotensin II, Angiotensin-2-10, and Angiotenisn-1-9 and their associated SIS peptides were used. The findings suggest, Gaussian mixture method has similar characteristics as the two methods compared for estimating the quantity of isolated isotopic clusters for single compounds. All three methods were tested using MALDI-TOF mass spectra collected for peptides of the renin-angiotensin system. The Gaussian mixture method accurately estimated the native to labeled ratio of several isolated angiotensin peptides (5.2% error in ratio estimation) with similar estimation errors to those calculated using peak intensity and Riemann sum AUC methods (5.9% and 7.7%, respectively). For overlapping angiotensin peptides, (where the other two methods are not applicable) the estimation error of the Gaussian mixture was 6.8%, which is within the acceptable range. In summary, for single compounds the Gaussian mixture method is equivalent or marginally superior compared to the existing methods of peptide quantification and is capable of quantifying overlapping (convolved) peptides within the acceptable margin of error.</p></div

A MALDI-TOF mass spectrum from the analysis of Ang I extracellular breakdown [2] by rat glomeruli in the presence of amastatin (APA inhibitor) and thiorphan (NEP inhibitor) at 60 minutes.

<p>The sample contains a mixture of Ang-(2–10), Ang-(1–9), and SIS-Ang-(2–10) that overlap forming one cluster. These peaks are fit and the individual areas for each isotopic cluster can be decomposed from the spectrum.</p

Two way ANOVA with pairwise testing.

<p>The Two-way ANOVA analysis takes into account that several samples are replicates of a single mixture of peptides (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0111016#pone.0111016.s004" target="_blank">Material S1</a>) and that there may be differences between peptides used and not just the methods of peak quantifcation. All standard errors for the mean estimates were equal (0.01159).</p><p>Two way ANOVA with pairwise testing.</p

A MALDI-TOF mass spectrum of a known ratio of 1∶1∶1∶1 peptides consisting of 300 nM Ang-(2–10), Ang-(1–9), SIS-Ang-(2–10) and SIS-Ang-(1–9).

<p>The spectrum has been fit using GMM and the figure shows how each estimated peptides contributes to the whole spectrum. Since all peptides are estimated simultaneously, each peptide is presented here separately to illustrate the individual contribution of each peptide to the spectrum as a whole. (A) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0111016#pone-0111016-g003" target="_blank">Figure 3a</a> shows the entire estimation as a whole, preformed as a single fit to a single cluster of four overlapping peptides. The data is shown in black with the estimated peaks superimposed in red. (B) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0111016#pone-0111016-g003" target="_blank">Figure 3b</a> shows the estimated contribution of Ang-(2–10) to the spectra superimposed in blue. (C) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0111016#pone-0111016-g003" target="_blank">Figure 3c</a> shows the estimated contribution of Ang-(1–9) to the spectra superimposed in green. (D) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0111016#pone-0111016-g003" target="_blank">Figure 3d</a> shows the estimated contribution of SIS-Ang-(2–10) to the spectra superimposed in dark yellow. (E) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0111016#pone-0111016-g003" target="_blank">Figure 3e</a> shows the estimated contribution of SIS-Ang-(1–9) to the spectra superimposed in dark purple.</p

Correlation plots showing the difference in estimation error of the peak ratio for a given spectrum when different methods of peak ratio measurement.

<p>The red line denotes a correlation of ρ = 1 and the blue lines denote 0% error in ratio estimation for that given method. Here we see that the Peak intensity and Riemann sum AUC methods of quantification correlate more highly with one another than with the Gaussian mixture method. Note that the GMM estimates tend to cluster closer to the blue line suggesting lower error.</p

Method Comparison Summary.

<p>The mean percent error (MPE), MSE, Variance and bias of each method’s percent error of the peptide ratio for various methods of ratio quantification. While all methods fall within the error parameters of the SIS method The Gaussian mixture model produces estimates in both single and convolved peptides while the peak intensity and Riemann sum methods of estimation cannot be used in convolved peptides.</p><p>Method Comparison Summary.</p

Different methods used for fitting a single peptide isotopic cluster to a MALDI-TOF spectrum of unlabeled Angiotensin II.

<p>The inclusion of a slope-intercept form baseline (red estimation) increases the fit over a flat baseline (blue estimation). Both of which are better than not including a baseline (green estimation).</p

Secondary peptide ratio estimation.

<p>Here the Gaussian mixture method is used to recover the peptide ratio of the second peptide in a convolved set. The error in the estimation of an Ang-(1–9) peak ratio against its corresponding SIS peptide when convolved with various amounts of Ang-(2–10) and its corresponding SIS is used to test the Gaussian mixture method. The initial concentration of 300 nM of each peptide (for a 1∶1∶1∶1 ratio of peptides, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0111016#pone.0111016.s005" target="_blank">Material S2</a>) is modified by changing the amount of Ang-(2–10). Here we see that the Gaussian mixture method can recover the second peptide from a series of different peptide ratios.</p><p>Secondary peptide ratio estimation.</p