William Kern had been a bio-chemistry professor in the Science department at University of Washington, and appears in the series only as Kyle recovers his memory.
As soon as Kyle is living with the Tragers, and Nicole suggests trying to draw to begin recovering his memory, Kyle draws an area of woods near Victor Falls. One night during a rain storm, he is startled awake by a vision of a hooded man looking in a vehicle window during a thunderstorm. He is able to draw a portrait of the vision to show Nicole.
Detective Breen calls Nicole about a skeleton found in the woods, and a Professor Kern is reported missing. Kyle connects the missing professor with his dreams, and finds out more about him.
After the bones in the woods are confirmed as being those of Kern, Kyle has another dream of Kern and Foss fighting in the rain. Kern seems to be aiming a gun at Tom, who throws him down and picks up a gun. Foss shoots Kern.
Desperate to help Kyle remember before the Petersons take him away, Tom takes him back to the original place in the woods. It is raining again, and Kyle does remember seeing Prof. Kern pointing a pistol at Tom, saying "Zzyzx ordered you to exterminate him, I can't let either of you walk away. Baylin gave up any claim on the boy when he turned his back on the company. They want the boy dead." At that, Foss saved Kyle's life again by killing Kern with Kern's pistol.
While living with Adam Baylin, Kyle learns about the experiment by Adam and Kern at Zzyzx that produced him as 781227. Going on Lori's hiking trip to the Zzyzx site in the woods, while trying to find her in the bombed complex Kyle has detailed recall of Kern expelling Adam from the company and the experiment.
Kern was using 781227 as a bio-computer, and Foss was working at Zzyzx as a security guard. Kern objected to Tom playing classical music when he was in the room with 781227, saying "I don't know why you insist on playing that, it can't comprehend it," and turns off the tape player. He tells Tom "I'm prepping for a data input retention test, don't let anyone through the door." Tom makes a disparaging comment, and Kern turns to him to say "Do your job." Tom advises him "You know, one of these days, he's going to tell you what you can do with your tests."
When 781227 refuses to process military information, Kern says "It can't make judgement calls, that's like my saying my toaster has a conscience." He makes a phone call to report "781227 is no longer cooperating." Called to the room again, Kern is told "The whole memory matrix. The entire database -- all the research we've ever done, or recorded -- has been copied" by 781227. Kern says "It can't do that. It can't make decisions and act on its own." When the technician says "That's what it's doing, sir." Kern hollers "Well then disconnect it, now!" As other staff pull life-support tubing, Kern says "Begin protocols for termination." As Kern urgently leaves, Foss says "I won't let you do this, Kern."
With that part of the story told, we do not see anything more about Kern.
All appearances were as Kyle's memory, Kern was dead before the episodes begin.