Statistical significance of pairwise protein sequence alignment

Question

I have identified a conserved region in a protein I'm studying, by doing multiple sequence alignments against a dozen of its orthologs. I've then found that this region also aligns relatively well with a functional region (binding motif) in a completely unrelated protein, and I'm trying to estimate whether it's reasonable to believe the two regions might be bound by the same protein. blastp doesn't identify this match, would I then assume that this is insignificant?

Let's say I have a 15 aa long peptide sequence X, which I align against a longer 200 aa protein sequence Y. I find some best match (gaps allowed).

What statistical test could I now perform to answer the question:

Is the match I found for sequence X in sequence Y significantly better than what I would expect to find between X and a random 200 aa sequence Z?

Answer 1

Just formalise the answer, its a straight use of the Blast E-value and I wouldn't personally advise against anything beyond that (explained below) within molecular evolution.

So the Google gives the definition

The BLAST E-value is the number of expected hits of similar quality (score) that could be found just by chance. E-value of 10 means that up to 10 hits can be expected to be found just by chance, given the same size of a random database.

Thus the smaller the E-value the better the hit.

Using a local blast server will provide a specific query verse reference E-value.

blastp -query gene.fa -subject genome.fa 

The broader question concerns the whether the Blast hit is a genuine homology and that is very complicated. This is simply because amino acid loci could have arisen by convergent evolution rather than direct descendancy which are homologues and this can become controversial.

When trying to assign a function to a amino acid locus this starts becoming relevant because e.g. the selection pressures of convergence could very difference.

Identifying homologues would require a phylogenetic tree which is compatible with the established phylogenetic tree, e.g. for house-keeping genes as a starting point. It gets complex quickly beyond that. Functional domains within the Blast variant (Blast-Psi) could be of use, its field specific however.

Thus the simple answer is to use Blast E-value (bit-score) and it is a universally recognised metric, the reader can then make up their own mind what the value represents. You could simply simple state the definition of the E-value in the report.