Is the appearance of a single peak in gel filtration chromatography when purifying an enzyme with several isoenzymes necessary, or is it possible that more than one peak appears?
Multiple peaks could occur if the protein exists in different stable oligomeric forms, e.g. monomer, dimer, etc. Also, if there is a large aggregate of the protein, that will appear as a peak at the void volume.
When there are multiple possible isoenzymes, several peaks can result. Sometimes the peaks merge and resulting shoulder peaks if the isoenzymes are not separated properly.
If the isoenzymes have a similar molecular weight, but just different amino acid sequences but still similar structure because proteins with 20% sequence identity can have similar 3D structure in terms of helices and beta sheets being in similar places but just with different amino acid compositions then you probably won't see different peaks ... which I think is likely.
If you are recombinantly expressing and purifying an enzyme then there is only one isoenzyme which is the one you are purifying so the separate peaks are due to oligomerization or in the unlucky event proteolysis of your enzyme, or in the even more unlucky event an impure purification with native proteins of whatever host expression cell you are using.