There are five Rat Man dens in the game. They appear as scribbling and handprints on the wall.
1: Test Chamber Sixteen:
After you pass three turrets and you’ll find a platform with two cubes stacked on top of each other. Move the two cubes, duck down, and go into the space behind them. You’ll find the writing on the wall to the left.
2: Test Chamber Seventeen:
Once you’ve passed by the two energy balls, fall over the edge and shoot a portal behind the projecting wall panel. Shoot the other portal on the wall next to the portal and pass through to find the writing on the wall.
3: Test Chamber Eighteen:
Use the portals to get onto the platform across from the first one. Once there, crouch down and slip into the alcove on the left. You’ll find the writing on the wall.
4: Test Chamber Nineteen:
Fall down the deep pit that you crossed on a giant pipe earlier and then go right into an alcove.
5: Test Chamber Nineteen:
After the fourth Rat Man’s Den, you’ll find three turrets. Pass them and then go into an alcove to access another room with a turret. When you dispose of the turret, walk to the back of the room and look to your right to find the alcove with the den.
Below is a video showing the location of all five Rat Man Dens: