How to unlock: The quest will activate when after teleporting to the Institute - The Molecular Level quest - you will become the enemy of the Institute faction.
The quest is an alternative path to ending the storyline. The plot will start when you will become an enemy of the Institute, for example by killing an important member of the organization. You can start this quest in the time frame between starting The Molecular Level quest and before completing The Nuclear Option quest that ends the story.
Revealing yourself before the Institute will automatically end all the quests that you started for them. Your objective is to return to Desdemona and report to her. She will tell you that the faction has no other ways of helping you in fighting the Institute and she will point you to Preston, the leader of the Minutemen. In this way, you will switch the story plot to quests for Minutemen faction.
Quest rewards: experience points, continuing the game in other storyline (Minutemen faction).