2.1. Principles of Chimera Spectra Detection within 2D-PC-MS
As a direct consequence of mass and charge conservation in the course of the peptide decomposition, the 2D-PC-MS correlation signals of the pairs of complementary terminal fragment ions (e.g., b
/y
fragments in the collision-induced dissociation (CID) measurements [
15]) can be easily identified as lying on the primary mass conservation lines, see Equation (
2). The equations of all the possible primary mass conservation lines for a parent ion of molecular mass
and charge
can be expressed as:
where the complementary fragment ion charges
and
are constrained by
(to avoid double counting) and
. Therefore, provided knowledge of the charge state and
of a parent ion, it is possible to define all the primary mass conservation lines for its decomposition products a priori, without any assumption on the peptide sequence or the type of the decomposition products (e.g., b/y vs. c/z). As a result, all the measured pairs of complementary ions can be read directly from the 2D-PC-MS map, assumption-free. This unique feature of the 2D-PC-MS is key to the proposed method of the chimera diagnostics.
In what follows, we shall distinguish between three distinct scenarios leading to chimera spectra:
- Scenario 1
co-fragmented parent ions have different charges, but arbitrarily close ;
- Scenario 2
co-fragmented parent ions have the same charge, while their masses are close, but distinguishable within the mass resolution of the MS equipment; and
- Scenario 3
co-fragmented parent ions have the same charge and either indistinguishable (within the mass resolution of the equipment) or exactly the same masses.
Under
Scenario 1, i.e., if the co-isolated parent ions have a different charge state, Equation (
4) dictates that their fragment ions will fall on two different sets of the primary mass conservation lines, characterized by different
slopes and
y-axis intercepts. As demonstrated in Reference [
13], this enables immediate identification of the chimera spectrum, as well as its in silico deconvolution. Under
Scenario 2, i.e., if the co-isolated parent ions have the same charge state, but the
tolerance of the fragment ion detector is sufficient to resolve the difference in the sums of their masses, the complementary ions from the different co-isolated parents are separated by virtue of falling on primary mass conservation lines with the same slopes, but different y-axis intercepts,
, see Equation (
4). It is only left, therefore, to consider the most challenging
Scenario 3, under which the 2D-PC-MS correlations between the complementary fragment ions of the co-fragmented peptides will fall on exactly the same primary mass conservation lines (for isomers) or on the primary conservation lines indistinguishable within the instrumental mass resolution. This scenario is considered in detail below.
Without loss of generality, consider the complementary fragment ions formed in CID, i.e., b
/y
. Within this series of complementary pairs, each successive b-ion or y-ion is separated from the next one of the same type by the mass of the next amino acid residue. The amino acid residue of the lowest mass (57 Da) is glycine, where the functional R-group is a single H atom. Looking at the 2D-PC-MS correlation signals of the pairs of complementary fragments on all the primary mass conservation lines, we do not know whether any particular fragment within a pair is of b- or y-type. Therefore, if three or more fragment ions forming correlations which are found on a mass conservation diagonal within a mass interval of 57 Da or less, there must exist at least two b-ions or y-ions in the fragment spectrum which are within less than 57 Da mass of each other. In this case, either all three ions are of the same type, or one is a b-(y-)ion, and the other two are y-(b-)ions. Since the minimum mass by which two consecutive b- or y-ions from the same sequence can be separated is the mass of glycine residue (57 Da), two b- or y-ions separated by less than 57 Da cannot come from the same parent sequence; therefore, we observe a chimera spectrum. In this line of reasoning, we take into account that the charge states of the fragments are known, either via isotopic envelope measurement, or (within 2D-PC-MS) via the measurement of the slope of the primary mass conservation line to which their correlation belongs, as was done in Reference [
13].
On the basis of the above, we define a 2D-PC-MS chimera `tag’ as a single set of 3 complementary fragment ions of mass within 57 Da of each other (`3-57 chimera tag’). It is possible for a chimera spectrum to contain multiple such tags (see
Section 2.3); however, even a single chimera tag is sufficient to identify co-fragmentation of multiple parent ions with mathematical certainty, purely on the basis of the geometrical positions of the fragment-fragment correlations on the 2D-PC-MS map, prior to any attempt of the sequence assignment. It is important to point out that the 3-57 Da chimera tag is straightforwardly applicable only when the MS/MS spectrum features complementary ion pairs of a single type only, such as b
/y
under positive ion mode CID. This may not always be the case in ECD, where b/y complementary fragments can be observed (see, e.g., Reference [
16]), despite the general dominance of the c/z fragment ions [
17], as well as in the certain types of sequences under negative ion CID, where formation of c/z complementary pairs is possible alongside the dominant backbone fragmentation leading to the b/y ions [
18]. In such uncommon cases, 3-57 chimera tags featuring fragments with certain characteristic mass differences (e.g., b-c mass difference of 15 Da) should be disregarded as not necessarily informative of multiple peptide co-fragmentation.
2.2. Experimental Demonstration of 3-57 Tags
We demonstrate the principle of operation of the 2D-PC-MS 3-57 chimera tag experimentally using mixtures of palindromic (i.e., fully isomeric) sequences GSNKGAIIGLM (
I1) and MLGIIAGKNSG (
I2). The 3D view of the 2D-PC-MS maps of the pure ions [
I1 + 2H]
2+ and [
I2 + 2H]
2+ are shown in
Figure 1. The specific choice of the doubly charged states of the peptides in the experimental investigation of the chimera spectra was motivated by the fact that the two-fold chimera spectra of doubtly charged ioan is the most challenging case within the presented approach, with the highest possible probability of false-negative result, see Figure 3. The maps were obtained using a linear ion trap LTQ-XL mass spectrometer (Thermo Fischer Scientific, San Jose, CA, USA ) under CID conditions in the positive ion mode. The details of the experimental procedure are as in Reference [
9]; details can also be seen in Materials and Methods.
The 2D view of the 2D-PC-MS map of the co-isolated ions [
I1 + 2H]
2+ and [
I2 + 2H]
2+ at a relative molar concentration of 1:499 is shown in
Figure 2. The complementary fragment correlations among the top 50 2D-PC-MS features ranked according to their correlation score (Equation (
3)) were queried for 3-57 chimera tags. In
Figure 2, the top 50 2D-PC-MS correlation score-ranked features are plotted for the 1:499 mixture, and the their scores are coded in the color map. The two chimera tags identified even at this extremely low abundance of one of the precursor ions are annotated in
Figure 2. The two 3-57 tags clearly indicate that the fragment ion spectrum has resulted from the fragmentation of more than one parent ion.
Table 1 shows the growth of the number of the identified 3-57 tags at progressively higher relative concentrations of the isomer
I1.
2.3. Estimation of the False-Negative Rate of Chimera Spectra Detection Using 3-57 Tags within 2D-PC-MS
The TIC-based self-correcting partial covariance (see Equation (
1)) has been shown to be false-positive-free [
9]. Therefore, the chimera spectra diagnostics using the 2D-PC-MS 3-57 tags presented above is false-positive-free by construction, provided that no double series of complementary ion pairs arise (as, for example, in References [
16,
18]) or that false tags stemming from such double series can be efficiently rejected on the basis of their characteristic mass difference. However, no chimera diagnostic method, whether 1D MS or 2D-PC-MS based, can be 100% free of false-negatives. Indeed, conditions can always be devised, under which the decompositions of one or more of the co-fragmented peptides will not show strongly enough in the spectrum, therefore suppressing the possible chimera tags. Factors adversely affecting the detection of the chimera tags include relative concentrations of the co-fragmented isomeric or isobaric sequences and sequence-dependent fragmentation efficiency. It is, therefore, left to investigate the rate of false-negatives for the 2D-PC-MS chimera spectra detection based on the 3-57 chimera tags. Here, we perform such an investigation for the positive ion mode CID decompositions by applying numerical simulations to the peptide sequences derived from the UniProt/Swiss-Prot database [
19].
The false-negative identifications of chimera spectra using the 2D-PC-MS 3-57 tags could arise only from the lack of formation or detection of the correlations between the complementary ion pairs that could have given rise to the 3-57 tags, such as those in
Figure 2. Therefore, the key question for the estimation of the false positive rate is what percentage of the complementary fragment ion correlations is detected by 2D-PC-MS under certain fragmentation conditions. In Reference [
9], we performed 2D-PC-MS measurements on 35 various peptide ions under positive ion mode CID (see Table 1 in Reference [
9]), which is the most common fragmentation technique in proteomic MS. Statistical analysis of these measurements shows that the obtained 2D-PC-MS maps feature
of all the theoretically possible b/y complementary pairs for 2+ parent ions and
of all the theoretically possible b/y complementary ion pairs for the 3+ parent ions. In what follows, we will adopt these detection rates as representative of 2D-PC-MS measurements within the positive ion mode CID.
For the estimation of the false-negative rate of chimera spectra detection by 2D-PC-MS 3-57 chimera tag, we subjected all sequences in the UniProt/Swiss-Prot database [
19] to an in silico tryptic digestion (no missed cleavages), omitting the 0.47% of protein sequences with ambiguous amino acid residue coding. From the resultant digestion products, five different sets of 5000 peptide sequences of length between 5 and 15 residues were selected at random. All combinations of such sequences which produce, at a given positive charge state, two parent ions falling within a typical ion trap isolation width of 2.5 Da were identified. From each pool, sets of possible two-fold, three-fold, and four-fold mixtures of peptides with a risk of being co-isolated and co-fragmented were drawn without replacement at random.
Each set of potentially co-isolated sequences was co-fragmented in silico, and the resultant b-ion/y-ion complementary correlations were then assumed to be `measured’ with the experimentally determined average detection probability as reported above, i.e., 69% for doubly charged parent ions and 74% for the triply charged parent ions. To account for experimental inaccuracies, the in silico `measurement’ incorporated a random deviation from the theoretical
which was uniformly distributed across
, with
the specified instrumental
accuracy (here, 0.8 Da as in the linear ion trap 2D-PC-MS measurements [
9]). For 3+ parents, which generate a 2+/1+ complementary pair, the 2+ fragment was specified to be the longest (in terms of number of residues) of the two, and if the fragments had equal numbers of residues the extra charge was attributed to the y-ion. The resultant b/y complementary pairs measured in silico for each two-, three-, or four-fold chimera spectrum were then queried to identify all 3-57 chimera tags, i.e., all sets of of three or more consecutive complementary ions falling within
of each other for 2+ parent ions, or
for 3+ parent ions. The subtraction of the factors
or
accounts for the finite accuracy of the detector. The appearance of a two-, three-, or four-fold chimera spectrum with zero 3-57 tags was then counted as a false negative result.
For triply charged ions, the numerical simulations involving five different sets of 5000 randomly selected peptides produced the false negative result in
% of the two-fold chimera spectra,
false negatives for the three-fold chimera spectra, and
false negatives for the four-fold chimera spectra. The analogous calculations for the doubly charged parent ions produced false negative rates of
,
and
for the two-, three-, and four-fold chimera spectra, respectively.
Figure 3 shows the histograms of the numbers of 3-57 chimera tags estimated to be produced in the positive ion mode CID 2D-PC-MS measurement of two-, three-, and four-fold chimera spectra of doubly and triply charged peptides. In the case of two-fold chimera spectra of the triply charged peptide ions, for example, altogether,
simulated chimera spectra were used to create the corresponding histogram, resulting in the average number of tags produced across the various simulated two-fold mixtures to be ≈5.
The strong modulation in favor of an even number of detected tags revealed by
Figure 3 is readily explained by the symmetry of the 2D-PC-MS map with respect to the autocorrelation diagonal. Indeed, all of the b-(y-)ions contributing to a given 3-57 chimera tag will have complementary y-(b-)ions, whose mass is the difference between the parent molecule and its complementary b-(y-)ion. Given the parent masses of all co-fragmented ions are constrained to be similar (isolation width 2.5 Da in our numerical simulation), and most of the theoretically possible correlations are assumed to be detected (69% or 74% depending on the parent charge state), in the majority of the 3-57 tags the three b- or y-ions within 57 Da mass will have three respective complementary ions which also fall within 57 Da of each other, producing their own, symmetrical chimera tag. This symmetry between the chimera tags produced by the complementary ions can be seen in
Figure 2. As a test of our numerical method, we have also simulated complementary ion spectra for 50,000 pure peptides, assuming 100% detection probability for all possible complementary b-ion/y-ion pairs. The simulation produced zero 3-57 chimera tags, as expected of a false-positive-free technique.