> Or, more likely, I'm confused by the specialist terminology. Can someone clear up my confusion?

I think you're just reading too much into the problem. The terminology can be a bit daunting and it can be very hard for bioinformatics people to realize just how much specialist terminology we end up using. I mean, we have both computer science and molecular biology jargon that we use every day. It's sometimes hard to recognize just how much assumed knowledge there is in this field.

Unfortunately, bioinformatics is full of edge cases like this.

In this example, if you're talking about the size of a full protein, you need to add the mass of a water (to account for the lack of a bond at the N and C terminus). However, if you're talking about the size of a peptide fragment (a sub-sequence), then you don't need to account for the extra water molecule [0]. And as the explanation says -- peptide identification is the most common use-case for this analysis, so we'll just use that. This is also why the table lists the "residue" weights -- because it's easier to calculate the `sum(residue_weight) + water` as opposed to `sum(amino_acid_weight) - (n-1) * water`.

I think the extra explanation isn't entirely clear, but I wouldn't get hung up on that part or let that bother you too much. The problem really boils down to: calculate a weighted sum of a string using these weights for the letters. That's it... no more, no less.

Congrats on working through the exercise. This is honestly great resource for learning about the field from a coding perspective. As others have mentioned, this is from the people who literally wrote the book about much of the field.

[0] Note: In the protein, you aren't actually adding an intact water molecule itself, but accounting for the extra H at one end, and an extra OH at the other end. Which is the same weight as HOH, or 18.01056 Da.

Think of the normal meaning of the word. The residue is what's left over after whatever was going to happen has finished happening.

For amino acids, the interesting thing is that they get joined into chains that fold up into proteins (which do all the work). The residues after that happens looks like this:

            R   O               R   O
        H   |   ||          H   |   ||            H
  ----- N - C - C --------- N - C - C ----------- N etc
            H                   H

The lines - and | are chemical bonds. The Oxygens are double bonded. N= Nitrogen, C=Carbon, O=Oxygen. The R is one of 20 different chemical groups called side chains that make each amino acid different.

When the amino acids are isolated (not chained) the double-bonded carbon on the right carries an extra OH group. The whole right-hand carbon is often written COOH. The nitrogen on the left hand side of each amino acid carries an extra H. As part of the process that joins the amino acids together, the OH on the left and the H on the right pair off to form water. This is called condensation, and it happens at every junction between two acids. So if there are n amino acids, there are n-1 junctions and n-1 water molecules that were present (in aggregate) in the constituent amino acids that don't make it into the final protein chain.

Note, though, that one of the methods of chopping up protein chains is adding the water molecules back again, so you should know exactly what you're looking if you want to count masses precisely.

Jeez. Didn't mean to write all that. Hope it helps.

Re: the mass of a protein is the sum of all its residues plus the mass of a single water molecule / your second definition, they are equivalent. You could re-write you second version as (sum of all residues minus left and right most) + (sum of left and right residues + two molecules of water) - (one molecule of water) === sum of residues + one water molecule.

(The key is that residues are created whenever a molecule of water is expelled. In theory, you can expel exactly one water molecule from each amino acid to create a residue, with one hydrogen from the amine group and the hydroxl from the carboxylic acid. In reality, it takes two amino acids to start the process of peptide synthesis, and each aa contributes only one part (either the proton or the hydroxl group) of the theoretically expelled water molecule. In reality its not even a single water molecule, as the hydroxyl group is going to pick up a spare proton from solution and the extra proton on the amine will get pick up by gawd knows what) <-- Downright wrong (at least, in regards to its importance to residues.).

The condensation is connected in this instance but not in all instances of residues. I think the usage is more clear if you look at some of the other examples in the biochemistry section of the wiki page "...a residue refers to a specific monomer within the polymeric chain of a polysaccharide, protein or nucleic acid. One might say, "This protein consists of 118 amino acid residues" or "The histidine residue is considered to be basic because it contains an imidazole ring." (https://en.wikipedia.org/wiki/Residue_(chemistry))