Final answer:
Neuromuscular blocking agents manipulate the somatic portion of the motor branch of the peripheral nervous system to induce muscle paralysis for surgical procedures or ventilation.
Step-by-step explanation:
The portion of the nervous system that is manipulated by neuromuscular blocking agents to induce paralysis in surgical procedures or during mechanical ventilation is the somatic portion of the motor branch. Neuromuscular blocking agents work by interfering with the transmission of nerve impulses in the neuromuscular junction, leading to paralysis of the skeletal muscles. This is part of the peripheral nervous system and more specifically, the somatic nervous system (SNS), which is responsible for controlling the body's skeletal muscles.