Building upon local alignments

We have thus far worked with local alignments with a linear gap penalty and global alignments with affine gap penalties (see "Local alignment with scoring matrix¹" and "Global alignment with scoring matrix and affine gap penalty²").

It is only natural to take the intersection of these two problems and find an optimal local alignment given an affine gap penalty.

Assignment

Write a function localAlignmentScore that takes two protein strings $$s$$ and $$t$$. The function must return the maximum local alignment score of $$s$$ and $$t$$. To align the two given DNA strings, the function must use the BLOSUM62 scoring matrix, a gap open penalty equal to 11 and a gap extension penalty equal to 1.
Write a function localAlignment that takes two protein strings $$s$$ and $$t$$. The function must return a tuple containing two substrings $$r$$ and $$u$$ of $$s$$ and $$t$$, respectively, that correspond to an optimal local alignment of $$s$$ and $$t$$. To align the two given DNA strings, the function must use the BLOSUM62 scoring matrix, a gap open penalty equal to 11 and a gap extension penalty equal to 1. If multiple optimal alignments exist, the function may return any one.

Example

In the following interactive session, we assume the FASTA file data.faa³ to be located in the current directory.

        >>> from Bio import SeqIO

>>> localAlignmentScore('PLEASANTLY', 'MEANLY')
12
>>> localAlignmentScore(*SeqIO.parse('data.faa', 'fasta'))
230

>>> localAlignment('PLEASANTLY', 'MEANLY')
('LEAS', 'MEAN')
>>> localAlignment(*SeqIO.parse('data.faa', 'fasta'))
('IGSWGACF-------IH-SFRNRG---CILY-----HIGY------SAIQCT-----AFFMGP-------YKDSLNN---------GISDTWD-----RMSRQY--TC--PAHKFG-------MF---AQEDG---FSNHG---HLVY----NSKL---QLDHQELT---IYMH-PC-HN---TFRNLNIIV-------ERFALIQNFNI---------KC-QGID-PN-YPHEA', 'IGSWGACSDKNFILQIHASFIRRGNQNCSIWLDYYCHIGYLGSDAASPIQCKWSTTIAFFMGKPQGSNIYYKDSLNECSNMSGILISVCDTWDMRMQSRAARQYYTECLGPAHKHDKAEFPGCMFICCAQEDYDYYFSNHGPIFHLVEYVLNQSKLHKRQLDHQEMSLTQIYMHFPCMHNDTYTFRNLRNVISIHVYDNERFALDLNFNICITINLVHVKCVQGIDHPNIYPHEA')