Food coloring is also listed. Fast, active, fish such as many tetras, danios, damsels, etc., need more protein than do more sedentary fish such as many catfish, hawkfish, etc. Protein is burned up as calories in exercise. Fish also need more protein for egg production. If you want to spawn fish, feed them a high-protein diet.
Temperature plays a large part in how fast a fish metabolizes protein.
Fish kept at higher temperatures need more protein than do the same fish at lower temperatures. You can see why there is really no hard and fast rule here. The number of variables is considerable. Finally on this subject, strictly pisciverous fishes have evolved metabolisms that are more dependent upon animal protein than have omnivorous or herbivorous fishes. That is not to say that plant protein is not important to the omnivores or herbivores.