2.6 Overlap Detection and Deconvolution In the

2.6

Overlap Detection and Deconvolution

In the analysis of real samples examples arise of overlapped peaks that can't be fully resolved either chromatographically or by mass. One such example is a natural variation of hemoglobin B (Hgb). Hgb is expressed from multiple gene copies in individuals. Some of these variants confer resistance to malaria, others are just innocuous amino acid substitutions due to single nucleotide polymorphisms. So any given individual may exhibit two or more natural variants simultaneously. Figure 2.15 shows the mass spectra of a patient with 100% normal (wild-type) Hgb superimposed with that for another patient who has a single amino acid substitution in part of his Hgb complement, imparting an unresolvable 1 Da shift superimposed over the normal Hgb. This mass shift results in the monoisotopic peak of the normal Hgb to be at the same mass as the 13C1 peak of the Hgb variant. With the exception of a slight abundance up shift leading up to, and down shift after, the reference peak, the two spectra are virtually indistinguishable by eye, but not by IVA analysis. Overlap detection by IVA By dividing each peak in the isotopic pattern by the most abundant, the relative abundance of each peak of the isotopic pattern can be determined for several scans and combined to find the average and 95% confidence interval for each peak of the isotopic series (except the reference peak). Using the normal sample (J_25) as the reference vector, we can compare that vector to that of the variant-containing sample (T_23_91). In both vectors (Table 2.5) the reference peak must be removed because its variability is incorporated into that of the other isotopes by virtual of the conversion to relative abundance. The corresponding IVA for the T_23_91 patient sample is 8.4 with confidence intervals of -1.5 and +1.8 (at 95% confidence). Therefore, there is a discernable 8.4% difference between the two isotopic patterns that is statistically different at 95% confidence. Since both vectors carry confidence intervals, the IVA confidence interval is determined by simulation.

Figure 2.15.



Comparison spectra of Hgb (19+ charge state) isolated from a patient (J_25) with a full normal (wild-type) Hgb complement and one (patient T_23_91) carrying at least some of a superimposed natural variant coeluting with the patient's normal Hgb.

Mass (Da) 835.75 835.80 835.85 835.91 835.96 836.02 836.07 836.12 836.17 836.23 836.28 836.33 836.39 836.44 836.49

Table 2.5.

Patient J_25 Relative 95% CI Abundance 0.124303 0.01535 0.221689 0.02943 0.363984 0.05428 0.5666 0.07722 0.775934 0.08694 0.946943 0.12931 1.027397 0.14870 ref peak 0.897635 0.11662 0.735344 0.11150 0.576902 0.08738 0.412447 0.08429 0.298746 0.04784 0.198667 0.03763 0.136464 0.02180

Patient T_23_91 Relative 95% CI Abundance 0.185770 0.143003 0.318644 0.253931 0.520136 0.429174 0.728329 0.628316 0.925572 0.834797 1.043572 0.964078 1.070746 1.001271 ref peak 0.844220 0.775797 0.672271 0.602533 0.501719 0.447884 0.375937 0.332868 0.269843 0.233284 0.186778 0.164959 0.124911 0.109378

Average relative abundance vectors for the 18+ and 19+ charge states of Hgb from both the J_25 and T_23_91 patient samples along with the 95% confidence intervals (CI) for each peak. Conversion to relative abundance incorporates the reference peak errors into all the other isotopic abundances, so this peak is eliminated in the vectors.

Quantitative Deconvolution of the Overlap Hgb has an average mass of 15.1 kDa. Since the charge states of the two Hgb variants are the same, they co-elute in the LC, and the masses are nearly identical, we can assume that any isotopic differences are negligible between the two isoforms. Therefore, the isotopic pattern of the Hgb variant can be approximated by that of the normal Hgb. Since the peaks align, the zero charge mass of the variant must just shifted by one or more Da from that of the normal Hgb. This means that the relative abundance for each isotope of the patient sample that contains the Hgb variant is then the superposition of the two isotopic patterns, where the fractional contribution (ƒ) is undefined (equation 2.3). RAcombined = RAnormal * ƒ + RAvariant * (1-ƒ) Since we know the relative abundances of both the normal and variant are the same, just mass shifted, we can predict a combined theoretical vector for each 1 Da mass shift of the variant as a function of ƒ. The fractional contribution can then be estimated by minimizing the IVA between the theoretical and measured isotopic pattern at each mass shift. The mass shift resulting in the lowest IVA is then the correct mass shift of the Hgb variant and the fractional abundance corresponding to the lowest IVA corresponds to the relative ratio of the two isoforms in the spectrum. We can also carry the 95% confidence intervals along to approximate the 95% confidence intervals on ƒ. Confidence intervals for the fractional contribution can also exhibit non-linear reflections about a minimum attainable value; therefore both the upper and lower limits can be higher than the optimum value based on the average vectors (see section 1.3), at both the low and high ends of the confidence interval range. The results are summarized in Table 2.6.



(2.3)

Zero Charge Mass Shift of Variant Hgb (Da) -4 -3 -2 -1 0 1 2

Table 2.6.



IVA (%) (95% conf. range) 4.4 (3.9 - 6.9) 3.5 (2.9 - 6.5) 2.5 (2.3 - 5.5) 2.3 (2.4 - 4.6) 8.4 (6.9 - 10.1) 8.4 (6.9 - 10.1) 8.4 (6.9 - 10.1)

Fractional Abundance of normal Hgb (95% conf. range) 0.85 (0.85 - 0.95) 0.81 (0.81 - 0.95) 0.72 (0.72 - 0.89) 0.47 (0.50 - 0.73) indeterminate 1.0 (1.0 - 0.9) 1.0 (1.0 - 0.5)

The IVA and fractional contributions of the two Hgb isoforms to the spectrum of patient T_23_91 as a function of the zero charge mass shift of the variant. The most likely solution (red) is the -1 Da mutation in the variant with 43% variant in the mixture. The actual mole ratio of the variant depends on the relative ionization efficiency of the two isoforms.