The arithmetic behind every identity confirmation, worked in full

The commonest arithmetic error in this trade is not a miscalculation. It is a comparison between two figures that were never comparable: an observed monoisotopic mass set against a theoretical average mass, or the reverse. Both numbers are correct. The comparison is meaningless, and it will produce an apparent discrepancy of two to three daltons on an incretin-sized peptide — enough to look like a real finding, enough to start an argument, and entirely an artefact of convention. The Journal has seen this happen three times in correspondence and has done it once itself, which is recorded in the corrections log.

The instrument does not weigh anything

It is worth being exact about what a mass spectrometer does, because the imprecision propagates. The instrument generates ions from a sample, separates them according to the ratio of their mass to their charge, and counts them at a detector. The horizontal axis of every spectrum is mass-to-charge, conventionally written m/z and expressed in thomsons or in dimensionless units depending on the vendor’s software. Nothing is weighed. Nothing is measured against a reference mass in the sense that a balance measures against a calibration weight.

What follows from this is that every molecular weight on every certificate of analysis in this market is a calculated quantity, derived from a measured m/z by assigning a charge and subtracting the mass contribution of whatever adducted to the molecule to give it that charge — usually protons, sometimes sodium, occasionally potassium or ammonium. The assignment is normally straightforward and normally correct. It is nonetheless an assignment, and when it goes wrong it goes wrong by an integer factor, which is the kind of error that produces confident nonsense rather than a plausible discrepancy.

The practical consequence for a reader is a habit: when a mass figure appears, ask what was observed and what was inferred. A report that gives both — the m/z, the charge, and the derived neutral mass — has answered the question before it was asked.

Monoisotopic against average mass, with the numbers

The monoisotopic mass of a molecule is calculated using the exact mass of the most abundant stable isotope of each element: carbon-12 at exactly 12, hydrogen-1 at 1.00783, nitrogen-14 at 14.00307, oxygen-16 at 15.99491. The average mass uses the standard atomic weights, which are abundance-weighted means over the natural isotopic distribution: carbon at 12.011, nitrogen at 14.007, and so on. For a small molecule the two differ negligibly. For a peptide of four thousand daltons containing roughly one hundred and ninety carbon atoms, the difference is on the order of two and a half daltons.

Which one a laboratory should quote depends on what it measured. If the instrument resolved the isotopic envelope, the monoisotopic peak is identifiable and monoisotopic mass is the correct quantity to report. If the envelope was not resolved — which is the ordinary situation on a linear time-of-flight instrument at this molecular weight — the centroid of the unresolved cluster approximates the average mass, and that is what should be quoted.

The error is not in choosing one convention. It is in comparing across them. An observed monoisotopic value set against a theoretical average value will disagree by two to three daltons at incretin molecular weights, and the resulting apparent discrepancy has the size and shape of a real analytical finding. Any identity statement that does not name its convention is one step removed from being uncheckable.¹

The charge-state arithmetic, worked

For a peptide of neutral monoisotopic mass M observed as a protonated ion carrying z protons, the mass-to-charge ratio is (M + z × 1.00728) divided by z, where 1.00728 is the mass of a proton — the mass of a hydrogen atom less the mass of an electron, a distinction that matters at parts-per-million accuracy and not at all below it.

Run this for a peptide of average mass 4113.58. The singly protonated ion appears at 4114.59. The doubly protonated ion appears at 2057.80, the triply at 1372.20, the quadruply at 1029.40 and the quintuply at 823.72. All five describe the same molecule. A reader shown only the fourth of those figures, without a charge assignment, would reasonably conclude the vial contained a peptide of about a thousand daltons.

Inverting the calculation is how the neutral mass is recovered: multiply the observed m/z by the charge and subtract z proton masses. Doing this for two or three charge states from the same spectrum and finding agreement to within the instrument’s stated accuracy is the standard internal consistency check, and it is the check that catches a misassigned charge. A single m/z with a single assumed charge has no such redundancy, which is one reason electrospray with a visible charge-state envelope is more informative than a single MALDI peak even when both instruments are equally well calibrated.

The isotope pattern, and how it declares the charge

Because carbon-13 is present at roughly 1.1% natural abundance, a peptide containing one hundred and ninety carbon atoms will exist substantially as molecules containing one, two or three carbon-13 atoms. In a spectrum this appears as a series of peaks above the monoisotopic peak, separated in mass by approximately 1.00336 daltons and distributed in intensity according to the binomial statistics of the composition.

Two things follow, and both are practically useful. First, the spacing between adjacent isotope peaks in a charge-state cluster is one over the charge: a spacing of 0.5 on the m/z axis means the ion is doubly charged, 0.333 means triply, 0.25 means quadruply. This is the simplest charge assignment available and it requires no assumptions about the sample at all. Second, the relative intensities of the isotope peaks are predictable from the elemental composition, so a cluster whose shape departs markedly from the calculated envelope is evidence that two species are overlapping.

Both observations require an instrument capable of resolving the isotope peaks at the relevant m/z, which is where resolving power stops being a specification-sheet number and becomes the thing that determines whether a spectrum can be interpreted at all. Below roughly ten thousand resolving power, a multiply charged peptide envelope collapses into a single broad hump that carries neither the spacing nor the shape information.

The instrument classes, and what each can support

A single quadrupole mass filter provides unit resolution and mass accuracy of a few tenths of a dalton. It is entirely adequate to confirm that a sample is broadly the compound expected and to detect large modifications, and it is the analyser in most low-cost LC-MS systems. It cannot resolve an isotopic envelope at peptide molecular weights and therefore cannot assign charge from spacing.

Time-of-flight analysers separate ions by the time they take to traverse a flight tube. A linear tube gives modest resolving power; adding a reflectron and delayed extraction raises it into the tens of thousands, and modern quadrupole time-of-flight hybrids achieve low single-figure parts-per-million accuracy with routine calibration. Orbital trapping instruments measure the frequency of ion oscillation in an electrostatic field and convert it by Fourier transform, delivering resolving powers from sixty thousand to several hundred thousand and sub-part-per-million accuracy with internal calibration. Fourier-transform ion cyclotron resonance remains the highest-performing class and the least common outside academic facilities.

What this hierarchy means for a reader of certificates is that the instrument named on the document sets a ceiling on what the document can claim, independent of the laboratory’s competence. An unnamed instrument leaves that ceiling unknown, which is why the Journal now treats the absence of an instrument name as a material omission rather than a stylistic one.

The inversion that weighs nothing

Amino acids other than glycine are chiral, and peptide synthesis is performed with L-configured building blocks. Racemisation during synthesis — most commonly at cysteine, histidine and aspartate residues, and promoted by prolonged base exposure during coupling and deprotection — produces a peptide containing one or more D residues. The resulting molecule has the same elemental composition, the same monoisotopic mass, the same average mass, and the same fragmentation masses as the intended product.

Mass spectrometry cannot detect it. This is not a limitation of any particular instrument; it is a consequence of what the technique measures. Reversed-phase chromatography sometimes separates diastereomeric peptides, and where it does the epimer appears as a shoulder or a satellite peak of unassigned identity — which is one reason a chromatogram with an unexplained minor peak deserves more attention than a purity percentage does. Where the epimer co-elutes, no routine analysis in this market would find it.

Deliberate detection requires chiral amino-acid analysis after total hydrolysis, or digestion with a stereospecific protease that fails to cleave across a D residue, or in some cases ion-mobility separation. None of these is offered as a standard service to private buyers by any of the four testing services this market relies on, and the Journal’s position is that this is a genuine gap rather than a failing on their part: nobody has ever been asked to price it.

The standing rule in this department

This publication applies one rule to every identity claim it reports, and it is worth stating in isolation because it governs the rest. A mass measurement supports a statement about composition. Only a fragmentation or mapping experiment supports a statement about sequence. Where a source says identity was confirmed, we report that a mass was measured, unless we have seen evidence of the second kind.

The rule has consequences we accept. It makes our coverage read as more sceptical than the underlying documents, because the documents claim more than they establish. It occasionally irritates laboratories which have in fact done sequence-level work and have simply not printed it, and the remedy there is a two-line email which we are glad to receive. And it means we cannot describe any research-grade vial in this market as sequence-confirmed, because on the evidence available to us almost none are.

What the rule is not is an accusation. Nothing in this article suggests that vendors are selling material other than what they label, and the Journal has no evidence of that in respect of any company it covers. The claim is narrower and, we think, harder to argue with: the documentation in general circulation does not have the discriminating power that the language on it implies, and the gap between the two is where every avoidable dispute in this market begins.

A short glossary, because the terms are used loosely

m/z — mass-to-charge ratio, the quantity a mass spectrometer actually measures. Monoisotopic mass — mass calculated using the lightest stable isotope of each element. Average mass — mass calculated using standard atomic weights. Nominal mass — the integer sum of integer isotope masses; adequate for small molecules, useless here.

Resolving power — m divided by peak width at half height; the ability to separate nearby masses. Mass accuracy — deviation of a measurement from the true value, in parts per million. Mass defect — the difference between an exact mass and its nominal value, and the property that makes near-isobars separable.

Adduct — an ion formed by association with something other than a proton, commonly sodium or potassium. Charge-state envelope — the family of differently charged ions from one compound. Isobaric — of identical mass at the achieved precision. Isomeric — of identical composition and different structure. b and y ions — the complementary fragment series produced by amide-bond cleavage.

Precision in these terms is not decoration. Several disputes this department has been asked to adjudicate turned out, on inspection, to be disagreements about whether the word mass meant monoisotopic or average.

The uncomfortable conclusion of all this is not that identity testing in this market is worthless. It is that identity testing here is doing considerably less work than the language attached to it suggests, and that the shortfall is documentary rather than analytical. The instruments are capable. The laboratories are competent. What is missing is six lines on a page, and the reason they are missing is that nobody has ever declined a purchase for want of them.