Mass to Sequence Estimator

Reversing a mass into a sequence is an underdetermined problem, and it is worth being blunt about that before anything else on the page. A mass is one number. A sequence is a run of choices, one per residue. The number of sequences consistent with any particular measured mass is enormous, and no amount of arithmetic converts one into the other. What this page returns is therefore an estimate of length, not a candidate molecule, and a length is a far weaker claim than it can appear to be when it sits in a column of numbers.

There are two independent sources of the ambiguity, and keeping them apart makes the whole problem easier to reason about. The first is order. Every rearrangement of the same multiset of residues has an identical mass, because mass is a sum and a sum does not care what order the terms arrived in. So even if the composition were somehow pinned down exactly, the sequence itself would still be undetermined, and no amount of care in the arithmetic would change that. A ten residue chain of ten different residues has more than three million arrangements sharing one mass, before composition is even raised as a question.

The second is composition. Different multisets of residues can add up to the same mass without being the same multiset at all, so the mass does not pin down the composition either. These two ambiguities multiply rather than merely add, which is why the space of possibilities is not simply large but unbounded by anything a single mass measurement is capable of telling you. Every method that appears to narrow it is adding something you supplied, or guessing. This is why any list of matches from any database is a list of what the mass does not exclude, not a list of what it establishes, and the distinction is usually blurred by how the output happens to be arranged.

The estimate is built from exactly one number: the average of the twenty average residue masses, which is about 118.9 and belongs to no actual peptide. Subtract the single water a chain adds and divide the remainder by that average, and you get a length in the right neighbourhood. The entire method therefore rests on an assumption that the composition is unbiased, and that is the assumption real peptides break most often, since many are enriched in one or two residues deliberately. Nothing in the estimate can detect its own failure, because a chain built almost entirely from glycines and a chain with a typical residue mix return the same length while differing by nearly a factor of three in what they actually weigh.

How badly it breaks is clearer at the extremes than at the middle. Glycine is the lightest residue at about 57.05 and arginine the heaviest at about 156.19, a ratio of nearly three. Take a target of 1000 Da, subtract the water and divide by the heaviest residue, and the shortest chain that could possibly weigh that much is six residues. Divide by the lightest instead and the longest is seventeen. One measured mass is consistent with anything from six residues to seventeen, and the estimate of eight sits inside that range without being distinguished within it.

A factor of nearly three in possible chain length, from a single number, is a property of the problem rather than a defect of the estimate, and no reporting convention changes it. The peptide length calculator and the average molecular weight calculator are the pair that genuinely link a sequence to a length, in that order, while the mass difference calculator is the one to reach for when the question is about material added to or lost from a chain rather than read off one. Run in the opposite direction the same pair of pages is fully determined, and that asymmetry is what makes this page a generator of hypotheses rather than a solution to one.

Some of the ambiguity is much sharper than the general case, because certain residue combinations share a mass exactly rather than approximately. Leucine and isoleucine are the standard example: both carry a residue mass of 113.08406, so no mass measurement at any achievable precision can separate them. Two glycines come to 114.04292 against asparagine at 114.04293, and alanine plus glycine comes to 128.05857 against glutamine at 128.05858. Those are identities in the masses themselves, not rounding coincidences that better equipment would resolve. Any sequence containing a leucine also has an isobaric twin in which every leucine is swapped for an isoleucine, with identical monoisotopic mass as well as identical average mass.

That is the sharpest available statement of why the problem cannot be solved from a mass alone. An errorless exact mass measurement, correct to as many decimal places as the instrument can report, still leaves whole families of sequences indistinguishable from one another. The monoisotopic mass calculator will give you that exact figure to as much precision as it can, and it will still leave the ambiguity in place. A more accurate instrument narrows the tolerance and shortens the list without ever reducing it to a single entry. What closes the gap is a different kind of measurement, not a better resolution of the same one.

The consequence for anyone reading a list of candidates is direct. The order of such a list is not a likelihood ranking, and the first entry is not the answer. Treating a mass match as an identification means accepting the first thing that fits, which is precisely the definition of a guess dressed up as a result. It is tempting to do exactly that precisely because a long list looks like evidence and no line of an output says otherwise, while the ordering reflects how the search was built rather than anything about the sample.

So what is a mass good for? It rules things out, cheaply and immediately. A chain of a given length cannot have a mass falling outside the range its residues can produce, and a mass far above the target immediately contradicts any estimate of length below the one this page produces. It can also support a hypothesis about size, which is the job this page is built for. Beyond that it is a constraint, and a constraint becomes evidence only when something independent is added to it. That is a genuinely useful job even though it sounds modest, because a wrong expectation about size is one of the easier errors to make and one of the more expensive to discover downstream.

Establishing identity takes a second, independent observation: a pattern of fragments from a digest, a second mass from a different ionisation or derivatisation, retention time against material already authenticated, or a direct sequence measurement. Any one of those turns a mass into real evidence, and none of them is performed here or anywhere else on this site. When a sequence is already in your hands and you want to know what it should weigh, the molecular weight from sequence guide runs that arithmetic in the direction which is actually determined, and monoisotopic against average mass explains which convention to enter first.