This website has a description for how to get a Midisport 1×1/2×2/etc MIDI box going with Linux.
But it’s old and outdated! Don’t click that link! 🙂
This package on Sourceforge is what you want! usb-midi-fw contains up to date firmware for Midisport devices. It appears to be semi-endorsed by M-Audio, as their names are referenced in some of the copyrights. Yay.