In what stage of sleep do you experience a high level of motor cortex activity (the part of the brain involved in the planning, control, and execution of voluntary movements) that is blocked by the brainstem, leaving you more-or-less temporarily paralyzed?

REM

Explanation:

There are four stages, 3 of them are non-REM stages, (or NREM) and obviously, the other is the REM stage.

We are looking for a stage where your body becomes "paralyzed".

This would be the REM sleep stage.

This is the stage where most of your dreams happen, and that is why your body is more-or-less paralyzed, so you do not move while dreaming.

There are other characteristics, like irregular (and faster) breathing and an increase in blood pressure and heart rate.

cell regulation is conducted by special proteins.

the cell cycle is the final answer! : )