Question 1

What is the difference between the Nernst equation and the Goldman-Hodgkin-Katz (GHK) equation?

Accepted Answer

The Nernst equation E_ion = (RT/zF)×ln([ion]_out/[ion]_in) gives the equilibrium potential when only a single ion can permeate the membrane. In real cell membranes multiple ions permeate simultaneously, so the Goldman-Hodgkin-Katz (GHK) equation, which weights each ion by its permeability (P), is used to calculate the resting membrane potential. The resting potential of a neuron (≈ −70 mV) is dominated by K⁺ permeability (P_K >> P_Na) and lies close to the K⁺ Nernst potential (≈ −90 mV).

Question 2

What drives each phase of an action potential (depolarization, repolarization, hyperpolarization)?

Accepted Answer

When the threshold potential (≈ −55 mV) is exceeded, voltage-gated Na⁺ channels open rapidly, causing massive Na⁺ influx and depolarization (up to about +40 mV). Na⁺ channels then inactivate while delayed-rectifier K⁺ channels open, allowing K⁺ efflux and repolarization. Before K⁺ channels fully close, hyperpolarization (undershoot) occurs, and the Na/K pump restores the resting potential. Due to the all-or-none law, stimuli below threshold do not generate an action potential.

Question 3

What is the role of the Na/K pump?

Accepted Answer

The Na/K-ATPase pump uses ATP to transport 3 Na⁺ ions out of and 2 K⁺ ions into the cell per cycle, maintaining the high intracellular K⁺ and low Na⁺ concentration gradients. The actual ion flux per action potential is very small (equal to the charge needed to charge the membrane capacitor), so concentration changes accumulate only after tens of thousands of action potentials; however, the pump is essential for long-term maintenance of the gradients.

Question 4

How is this tool applied in biomedical and neural engineering?

Accepted Answer

Key applications: ① Threshold current evaluation for deep brain stimulation (DBS) and cochlear implant parameter design ② Cardiomyocyte modeling and arrhythmia research (cardiac electrophysiology) ③ Pre-analysis and model validation for patch-clamp experiments ④ Signal processing design for neural interfaces (BCI). The GHK model directly corresponds to the equivalent circuit (conductance model) used in circuit simulators such as LTSpice.

Membrane Potential, Nernst Equation & Action Potential Simulator

Governing Equations