Mining documents for nucleotide and peptide sequences
I am not sure there is a state of the art for that.
Some possible strategies I can think of:

Applying a dictionary to identify language words and discard these.
Using some context information like identifying some words in the same sentence than the sequence.
I guess the format in papers for sequences will not be the same as for text. Maybe you can find a pattern.

I would use an incremental strategy. Use the simplest algorithm then see what it recovers. If there is garbage, find a strategy to remove some garbage with a common pattern. Repeat until you are happy with the result.
Disclaimer: I have some experience in Natural Language Processing.