The threshold in a membrane potential is reached when there is a significant depolarization which opens the voltage gated Na+ channels a the axon hillock. The diffusion of sodium causes the membrane to have a positive membrane potential. The Nernst potential is then reached at +50 mV, causing the Na channels to inactivate and the K+ voltage gated channels to open as they are triggered by a delayed depolarization. K+ ions will exit until the potential overshoots the resting potential before returning to roughly the K+ Nernst potential.
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