Nernst Potential in Physiology: Why K+ Sets the Resting Membrane Potential

The Nernst potential for an ion is the membrane voltage at which its electrical and chemical driving forces cancel. In physiology, that single number tells you which way an ion will move when its channels open, and it explains why a neuron at rest sits close to the potassium equilibrium potential. At body temperature the equation simplifies to E_ion = (61.5 / z) log([ion]_out / [ion]_in) mV, where z is the ion's charge. The core derivation is in the <a href="nernst-equation-equilibrium-potential-mcat">Nernst equation note</a>. This note applies it.

Typical mammalian values

Check the sign pattern: cations that are more concentrated outside have positive E, and cations that are more concentrated inside have negative E. Anions flip the sign through z.

Why the resting potential is near E(K)

At rest the membrane has many open K⁺ leak channels and few open Na⁺ channels. Each ion pulls the membrane toward its own equilibrium potential in proportion to its permeability, which is the idea behind the <a href="goldman-equation-resting-membrane-potential-mcat">Goldman equation</a>. K⁺ dominates, so the resting potential is around -70 mV, near E_K = -90 mV but nudged upward by a small Na⁺ leak. The Na⁺/K⁺ ATPase does not create the resting voltage directly. It maintains the concentration gradients that the Nernst potentials depend on.

Driving force and direction of flow

The driving force on an ion is V_m - E_ion. Positive driving force on a cation means it exits, and negative means it enters.

At V_m = -70 mV:

• Na⁺: -70 - 60 = -130 mV, a large inward push when channels open, which depolarizes the cell.
• K⁺: -70 - (-90) = +20 mV, a small outward push.
• Cl^-: depends on the sign convention, but E_Cl is close to rest, so there is little net movement.

An action potential upstroke is Na⁺ entry pushing V_m toward E_Na. The downstroke is K⁺ exit pushing it back toward E_K. See <a href="action-potential-phases-ion-channels">action potential phases</a> for the sequence.

Worked example 1: hyperkalemia

Serum K⁺ rises from 5 to 8 mM, while intracellular K⁺ stays 140 mM. The new E_K is 61.5 log(8/140) = 61.5 × (-1.24) = about -76 mV. The resting potential moves from near -70 mV (set by a balance with Na⁺) to a less negative value, so it is closer to threshold. Initially, cells become more excitable. With prolonged depolarization, voltage-gated Na⁺ channels inactivate and cells become harder to excite, which is why severe hyperkalemia causes muscle weakness and cardiac arrhythmias.

Worked example 2: hypokalemia

Serum K⁺ falls to 3 mM. E_K = 61.5 log(3/140) = 61.5 × (-1.67) = about -103 mV. The membrane hyperpolarizes, so it is farther from threshold and harder to excite, which fits the cramping and weakness of hypokalemia.

Worked example 3: a tenfold gradient

If a cation with z = +1 is 10 times more concentrated outside, E = 61.5 log 10 = +61.5 mV. For a divalent cation (z = +2) with the same ratio, E is half as large, about +31 mV. Each tenfold change in the concentration ratio shifts E by 61.5/z mV.

When Nernst does not apply

The Nernst equation describes one ion at equilibrium. A real cell at rest is not at equilibrium for Na⁺ or K⁺, because ions keep leaking and the pump keeps restoring them. Use Goldman when more than one ion contributes, and Nernst when asked about a single ion or a driving force.

Common traps

• Using ln instead of log. The 61.5 mV form uses log₁₀ (at 37 °C).
• Flipping the ratio. Use outside over inside for the sign convention above.
• Ignoring z. Divalent ions such as Ca²⁺ have half the slope.
• Saying the pump sets the resting voltage. The leak channels set it, and the pump maintains the gradients.
• Assuming any rise in extracellular K⁺ raises excitability forever. Prolonged depolarization inactivates Na⁺ channels.

One-minute recap

E_ion = (61.5/z) log(out/in). K⁺ is about -90 mV, Na⁺ about +60 mV, Cl^- about -64 mV, and Ca²⁺ about +130 mV. Resting potential sits near E_K because K⁺ leak channels dominate. Driving force is V_m - E_ion. Raising extracellular K⁺ depolarizes the cell, and lowering it hyperpolarizes it.

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