Mass Spectrometry results question

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The discussion focuses on interpreting mass spectrometry results, specifically analyzing the peaks observed in a peptide spectrum. The major peaks are separated by approximately 1 amu, indicating substitutions of H1 atoms with D2 isotopes. However, the presence of two secondary peaks, 0.058 amu apart, raises questions about the underlying causes, as they suggest significant isotope substitutions that are not supported by the expected abundance of rare isotopes. The analysis concludes that the observed mass differences arise from the combination of non-integer masses and their relative abundances.

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Looking at the graph on the page on "Mass spectrometry" in wikipedia (sorry it didn't let me post the URL), there is something that I do not understand. Easiest to start with what I do understand ...

There are 4 major peaks separated by about 1 amu. OK, so some H1 atoms were substituted by D2 atoms or something similar. That makes sense.

There are secondary peaks around the major peaks. I can see that if one atom was replaced by an isotope 1 lighter and another by an isotope 1 heavier then there would be a slight difference introduced due to the variations in binding energy. E.g. Fe56 - Fe54 = -1.99568 and O18 - O16 = 2.00490 so a change of 0.00922 amu would result. There are many such possible variations but most of them that I can see come out to less than 0.01 amu.

However the third peak in the referenced page has two peaks of almost equal size which are 0.058 amu apart (labeled 862.526 and 862.584). I cannot see any way of getting such a huge difference without many substitutions by rare isotopes. In that case there should be multiple other peaks in between that are much more likely and there are not. Also the substitution of many isotopes by rare ones should produce a much smaller peak than that.

I considered molecular configurations as having binding energy also, but it seems to me these would be of the order of volts or less and not 54,000,000 volts as this difference is.

What is going on here?
 
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The spectrum is of a peptide and therefore only contains C, H, N, O, and S. The mass scale is based on Carbon-12. The other masses relative to this are:

C-13 (13.00335) 1.108% abundant
H-1 (1.007825) 99.984% abundant
H-2 (2.01400) 0.0156% abundant
O-16 (15.99491) 99.759% abundant
O-17 (16.9991) 0.037% abundant
O-18 (17.9992) 0.204% abundant
N-14 (14.00307) 99.635% abundant
N-15 (15.00011) 0.365% abundant
S-32 (31.97207) 95.0% abundant
S-33 (32.97146) 0.76% abundant
S-34 (33.96786) 4.22% abundant
S-36 (35.96709) 0.014% abundant

When you get to masses that are fairly large like this, the combination of non-integer masses and their relative abundances gives you these minor differences.
 

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