Final answer:
Voltage-gated sodium channels depolarize the adjacent area during an action potential by allowing an influx of Na+ ions, which triggers the opening of more such channels down the axon.
Step-by-step explanation:
The voltage-gated sodium channels are responsible for depolarizing the adjacent area due to an influx of sodium ions from the current action potential. When the membrane potential increases to the threshold level of about -55 mV, these channels open allowing sodium ions (Na+) to rush into the neuron, which decreases the polarity of the membrane potential. This influx of Na+ causes the membrane potential to further depolarize towards a more positive voltage, triggering adjacent voltage-gated Na+ channels to open, effectively propagating the action potential along the axon. These channels go through a cycle of opening (activation) and then closing (inactivation), which prevents further sodium entry and allows the cell to eventually repolarize through the opening of voltage-gated potassium channels.