Do you have Perl 5.14 (or later) for "Non-destructive substitution"? If so:

$ perl -E '
    use v5.14;
    my $seq = "UUUIUUIMUUMOUUOPUUPBUUBUUU";
    my $exp = "IIIIIIIMMMMOOOOPPPPBBBBBBB";
    say $seq;
    say $seq =~ s/^(U+)(.)/$2 x length($1) . $2/er
             =~ s/(.)(U+)/$1 . $1 x length($2)/egr;
    say $exp;
'
UUUIUUIMUUMOUUOPUUPBUUBUUU
IIIIIIIMMMMOOOOPPPPBBBBBBB
IIIIIIIMMMMOOOOPPPPBBBBBBB
[download]