Final answer:
The glossopharyngeal nerve runs lateral of the tongue and supplies the anterior two-thirds. It conveys taste information, relays pharyngeal sensations, and stimulates the gag reflex. The vagus nerve controls the motor response of the pharyngeal muscles.
Step-by-step explanation:
The nerve that runs lateral of the tongue and supplies the anterior two-thirds is the glossopharyngeal nerve. This nerve is responsible for conveying gustatory (taste) information to the brain and relaying general sensations from the pharyngeal walls. It also plays a role in stimulating the gag reflex. The motor response of the pharyngeal muscles involved in swallowing and speech functions is mediated through the vagus nerve.