This quest will automatically trigger shortly after Father names as you as the successor in the quest “Mankind Redefined”.
Talk to Newton Oberly to update this quest. You'll be requested to try talking to the protesting scientists first before resorting to violence. Follow the quest marker and take out the synths and turrets. Once you've reached the laboratory, talk to Dr. Higgs. This is your only chance to resolve the conflict peacefully. You can save the dialogue screen right before selecting a speech check option. Try to talk him out; if that fails, access the terminal nearby and load the BioScience Systems Access holotape.
Once loaded, you have the option to disable the turrets, release the specimens, or unlock the door. At this point, you'll have no choice but to kill him and his comrade. Once killed, get the Bioscience Security Override holotape, insert it on a terminal, and cancel the security override.