Deconvolution: Why the Mass on a Certificate Was Calculated, Not Measured

A mass spectrum of a peptide rarely shows the peptide’s mass. It shows a series of ions at various m/z values, and the mass on the certificate was calculated from that series by software. Knowing how that calculation works tells you what can go wrong with it.

Why one molecule gives several peaks

Electrospray ionisation works by adding protons. A peptide with several basic sites — lysines, arginines, histidines, the N-terminus — can accept more than one, and in a population of molecules different numbers get added.

The instrument measures mass-to-charge, not mass. A molecule of neutral mass M carrying n protons appears at m/z equal to (M + n × 1.00728) divided by n. Each value of n gives a different peak, and the set of them is the charge envelope.

Working it backwards by hand

Two adjacent peaks in the envelope are enough to solve for both the charge and the mass, because they differ by exactly one proton.

Take a peptide giving peaks at m/z 1123.6 and 843.0. If the first is n-plus and the second is (n+1)-plus, then n × 1123.6 minus n × 1.00728 equals (n+1) × 843.0 minus (n+1) × 1.00728. Solving gives n = 3, and the neutral mass comes out near 3367.9 daltons. Every other peak in the envelope should then fall where that mass predicts, which is the check that the assignment was right.

Software does this across the whole envelope at once and produces a single reconstructed spectrum on a neutral mass axis. That reconstruction is what a certificate usually reports.

A deconvoluted mass is a calculated number

This is the point worth holding on to. The deconvoluted mass was not measured; it was derived from measurements by an algorithm operating on assumptions — that the peaks belong to one species, that the spacing is protons, that the envelope is complete enough to constrain the answer.

When those assumptions hold, the result is more accurate than any single measurement, because it averages several. When they do not, the algorithm still returns a number, and the number looks exactly as authoritative as a correct one.

The failure modes

• Two species, one envelope. If a sample contains the peptide and a closely related impurity, their envelopes interleave. Deconvolution may report one mass between the two, or split them incorrectly, depending on the algorithm and the settings.
• Adducts read as charge states. Sodium and potassium adducts add 22 and 38 daltons to the neutral species and appear at predictable offsets. An algorithm that does not account for them can produce artefact peaks in the reconstructed spectrum that look like real related species.
• Truncated envelopes. If the scan range cuts off part of the charge distribution, fewer peaks constrain the answer and the uncertainty rises without any visible indication.
• Over-smoothing. Aggressive parameter settings produce clean-looking reconstructions by suppressing real minor components.

How charge state is actually read

Not from position. From isotope spacing. Carbon-13 gives every organic molecule an isotope cluster whose peaks are separated by about 1.0033 daltons in mass, which appears as 1.0033 divided by the charge on the m/z axis.

So a singly charged ion shows isotope peaks about 1.0 apart, a doubly charged ion 0.5 apart, a triply charged ion 0.33 apart, and so on. This is unambiguous and it requires no assumptions — but it requires enough resolution to see the isotope peaks at all. A low-resolution instrument cannot do it, which is why charge assignment on such instruments depends on the spacing between charge states instead.

Monoisotopic or average

Which mass a deconvolution reports depends on whether the isotope envelope was resolved. If it was, the software can report the monoisotopic mass, the one calculated from the lightest isotope of every element. If it was not, the reconstruction gives an average mass, weighted across the natural isotope distribution.

The two differ by roughly one dalton per thousand, so on a 3,000 dalton peptide they are about two daltons apart. Comparing a reported figure against the wrong calculated value produces an apparent error of exactly that size. The distinction is covered in monoisotopic versus average mass.

What a report should show

Ideally the raw spectrum alongside the deconvoluted one. The raw spectrum shows the envelope, lets a reader check that the charge states are sensibly spaced, and reveals adducts and second species that the reconstruction may have absorbed.

A deconvoluted mass presented alone, with no raw data and no statement of whether it is monoisotopic or average, is a single number standing in for a calculation nobody can check. It is usually right. It is not verifiable.

What this means when reading a certificate

A stated mass should say which kind it is and should be accompanied by the spectrum it came from. Where only a number is given, it is worth knowing that it is the output of a model rather than a direct reading of an instrument, and that the model had settings. Related reading: MALDI versus ESI and mass accuracy in parts per million.