There also seems to be a few migraine-reducing interactions for other ingredients like glutamate and unsaturated fats which are not well understood. Food cravings during the prodrome phase of a migraine may be related to this(!)

Specific ketogenic diets (low carb, high polyunsaturated fat diets) are known to have have a high degree of success in reducing seizures. The same also is true for migraines.

The pathophysiological relationship between migraines and seizures isn't particularly well understood either, so unfortunately I don't have any cool facts to share about how any of this actually works.