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This is pretty vexing: I got asked to explain the meaning of the match line in a blastp output, especially the subtle difference between a blank and plus. E.g.:

 Query  181  NHIEEL...
             N I+EL...
 Sbjct  181  NQIKEL...

For me this is under the "everyone knows this" category, but I wanted to have an authoritative reference I could cite.

Alas, none of the documents on the BLAST help page seems to have this information. My Google fu also failed as I was not able to find an authoritative source which I could cite.

Also, I'm not sure whether BLAST introduced this notation or it simply picked it up somewhere else.

Any pointers appreciated.

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The reference that is mentioned when I run a BLASTP search using NCBI's web service is this one. Here's some relevant text from the caption of Figure 3 of that paper:

On the central lines of the alignment, identities are echoed and substitutions to which the BLOSUM-62 matrix (18) gives a positive score are indicated by a ‘+’ symbol.

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I think gringer is correct to say this is because of the BLOSUM62 matrix and a ‘+’ symbol inidcating a positive score for a mismatch but here is a little more explanation.

BLASTP looks for (nearly) identical short protein matches pairwise, called seeds, and then extends the seeds in each direction one residue at a time using arbitrary gap penalties for indels and a matrix for substitutions. Based on some thresholds and more, the highest scoring alignments are kept and ultimately reported.

The default choice of matrix for BLASTP is BLOSUM62, which looks like this. Obviously matches have high positive scores, but also mismatches have varying positive or negative scores.

If you look up your changes:

H -> Q; ; score 0

E -> K; +; score 1

Note that this matrix is symmetric so the scores for H -> Q == Q -> H and E -> K == K -> E.

In terms of why E -> K has a positive score, well not all amino acid changes are viewed equally. BLOSUM matrices are not based on any biological theory but instead use the log-odds ratio, a likelihood approach, that estimates from real sequence alignments how frequently different amino acid changes occur. The more often E -> K substitutions are observed in these alignments, the higher the substitution will score in the derived matrix.

Hopefully these scores are intupretable based on the biochemical properties of the amino acids. For example, R -> K scores 2, a high score for a mismatch, but both amino acids are basic and so share a similar structure, presumably making a change more likely to occur and/or more likely to maintain the protein function and so not be harmful.

For your case, I don't have a good biological explanation for why E -> K scores positive, another author notes this is surprising, but ultimately the reason it is given a positive score is just because regardless of why, E -> K does apparently frequently occur, at least in the alignment data used to derive this scoring matrix. Incidentally, BLOSUM matrices are pretty ancient and based on few alignments by modern standards, but nonetheless appear to work quite well.

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