The hunt is intensifying for new treatments for migraines, the common and debilitating headaches that have confounded scientists for decades.

Of greatest focus for researchers is a brain chemical known as CGRP, which appears to play a role in the transmission of pain, but not in other brain functions, such as cognition or mood. Researchers are trying a variety of experimental drugs to stop CGRP from working by blocking its receptors in the brain. Others are working on artificial antibodies that could soak up the chemical in...