the easiest way is to take the existing filters off the 50g and put them directly on the new setup 220g.
the bacterial population in the filters are keeping up with the load in the 50g, so they will easily handle the same load in the new tank with 4x the amount of water.
the bacteria in the filter will seed the gravel etc and the new tank will be fine.
what I have done in the past was given the filters a clean a week or two before im ready to make the transfer, so they have good flow when you put them on the new tank and they are not clogged. the week in between the filter clean and the transfer over allows any disturbance to the bacterial population to go away (repopulate), so the filter is full of good bacteria AND has great flow through when its time to make the switch.
just make sure the new tank is up to temperature and dechlorinated properly before you make the switch
good luck and enjoy your new tank.