The best solution is to use the already mentioned chdir Perl built-in to get into the right default directory. But if you want to do it in shell, you could issue two shell commands within the same exec or system shell command string, for example;

my $home='~/bin/MIReNA-2.0';
system("cd $home; ./MIReNA.sh");
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An example Perl one-liner on my system:

$ perl -e ' exec "cd ./Matt; ls -l"'
total 11756
drwxr-xr-x+ 1 Laurent None        0 27 juin  19:26 appartement
-rwxr-xr-x  1 Laurent None 12038144 27 juin  22:27 appartement.tar
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In the latest example above, I used exec because I did not care that the program would die immediately after having displayed the content of the directory. I would use system if I wanted the Perl program to do other things after having run the shell command. And if I wanted to retrieve the data in Perl (which is probably the most common use of shelling out calls to the OS), say to format the output of the ls command with line numbers, then I would use backticks instead of exec or system:

$ perl -E ' my @content = `cd ./Matt; ls -l`; print ++$i, ": $_"  for 
+@content'
1: total 11756
2: drwxr-xr-x+ 1 Laurent None        0 27 juin  19:26 appartement
3: -rwxr-xr-x  1 Laurent None 12038144 27 juin  22:27 appartement.tar
[download]