Dr. Brian Virgil was a member of the Institute at some point before 2287. He was in charge of a project involving the Forced Evolutionary Virus and the creation of super mutants in the BioScience Division. Virgil took control of the program after his predecessor, Dr. Syverson, passed away. Overcome with guilt from the pain and suffering he had inflicted on so many innocent people, he decided to leave the Institute. Virgil destroyed the lab equipment and all of the research, which is logged as "Incident V" in terminal entries. He then escaped to the Glowing Sea and infected himself with a unique strain of FEV to survive the high levels of radiation.
The Glowing Sea: After heading through the Glowing Sea and being asked by the Sole Survivor for information on the Institute, Virgil will ask the Sole Survivor to recover an experimental serum that he claims will make him a human again, but isn't sure if it exists or not. The player character must agree to this if they want to complete the quest and continue the main story line. The player character will have to go to the FEV labs in the Institute to retrieve the serum.
After getting the serum, the player character has two options:
They can simply give Virgil the serum, and certain companions will react differently to this choice. For example, John Hancock, Piper, Nick Valentine, Codsworth, Deacon and Curie like the player's choice to cure Virgil, but Danse won't like it at all; this is due to what happened to his friend Cutler. Strong also won't like it as he prefers being a Super Mutant and is angry with the doctor's ambitions to cure the others.
They can also lie to Virgil through a sequence of three speech checks, claiming that the serum wasn't there. The checks' difficulty increases with each one. After the first two checks the player character still has the option to give the serum to Virgil through breaking and reinitiating dialog with him. After the third speech check Virgil requests the player character to kill him and Virgil's Cure will fail. If the player has visited Swan's Pond, and read the notes there, they can ask Virgil if he remembers Edgar Swan after the first speech check. This will lead to a medium speech check to convince him to end his life (bypassing the hard check).
If the player character gives Virgil the serum and waits three days, they can go back and see that Virgil is now a normal human. After this, all the items inside the cave become available for looting.
If the player character is wearing a power armor helmet with a Targeting HUD mod when returning to complete the quest The Glowing Sea, the Sole Survivor will immediately fail the quest upon re-entering rocky cave with the serum. Remove the helmet before entering the cave.
If upon first entering and leaving the Institute, even if the player does not get the serum, the player character waits before bringing the serum to Virgil for around a week, Virgil is then found completely turned hostile and the quest "The Glowing Sea" will immediately fail upon re-entering rocky cave.
If the Sole Survivor destroys the Institute, Virgil will confront them about it the next time they enter his cave. No matter how the Sole Survivor responds, he states that "innocents died," and replies that they have nothing more to speak about, and tells them to leave his cave. The Sole Survivor can stay however long they want, regardless of what Virgil says, as he will not turn hostile.
If the Sole Survivor tells Virgil his research needs to stop, Virgil will become hostile. Strong will like this action.
Even though X6-88 ordered Kellogg to kill Virgil, he will dislike it if the player allows Virgil to let them kill him.
Despite being from the Bioscience division, Virgil's mutant form will wear rags in the Robotics division's orange color and a blue Advanced Systems lab coat as a human. This may be explained by his escape from the the Institute, as he could have stolen supplies before leaving.
He will mention the Sole Survivor's Pip-Boy having a radio installed even in situations where he can't possibly know about them possessing such a device, such as the Survivor wearing a full suit of power armor.
Triggering the Evacuation signal before destroying the Institute will not affect Virgil's behavior if the player destroyed the Institute.
Recruiting Madison Li from the Institute to the Brotherhood will allow Virgil to send a note about his cure. Madison accepts the note, but it does not change her mind about the Brotherhood.
The third entry on Virgil's terminal suggests that he is losing his memory, and as a result his sanity, because of being a mutant.
It is possible that the reason he has retained his sanity and mental state for so long is because he is a human of significantly pure DNA, which may hint at a connection to the Mariposa FEV strain.
Even if the player becomes Director of the Institute AND gives Virgil the serum, there is no option via dialogue to have the now-human Virgil return to the Institute.
If the Sole Survivor travels to his laboratory at the beginning of the game he will simply not be there.
The following is based on unverified behind the scenes information and has not been confirmed by canon sources.
Virgil could be a name reference to the Divine Comedy, a XIV century epic poem by Dante Alighieri, who, as its protagonist, is guided through Hell and Purgatory by Virgil. Similarly, the Sole Survivor is guided by Brian Virgil into the Institute (which is situated underground).
End of information based on unverified behind the scenes information.