The Nernst Equation

Core Idea

The Nernst equation predicts the equilibrium potential for a single ion: V = (RT/zF) × ln([out]/[in]). It quantifies the voltage at which that ion has no net electrochemical drive.

Explainer

From your study of cell membrane structure, you know that the lipid bilayer is selectively permeable — ions can only cross through specific channel proteins, and different ions are distributed unevenly across the membrane. Potassium (K⁺) is concentrated inside the cell, sodium (Na⁺) and calcium (Ca²⁺) are concentrated outside, and chloride (Cl⁻) is mostly extracellular. The Nernst equation answers a deceptively simple question: if the membrane were permeable to only one ion, what voltage would develop across it?

The answer emerges from a tug-of-war between two forces. Consider potassium: because K⁺ is more concentrated inside the cell, there is a concentration gradient driving it outward. But as K⁺ ions leave, they carry positive charge with them, making the inside of the cell progressively more negative. This growing voltage difference creates an electrical gradient that opposes further K⁺ efflux — the negative interior starts pulling positive ions back in. At some voltage, these two forces exactly balance: the concentration gradient pushing K⁺ out equals the electrical gradient pulling it back in. That voltage is the equilibrium potential (E) for potassium, and it is the value the Nernst equation calculates.

The equation itself is E = (RT/zF) × ln([ion]outside/[ion]inside), where R is the gas constant, T is absolute temperature, z is the ion's charge (including sign), and F is Faraday's constant. At body temperature (37°C), this simplifies to approximately E = (61.5 mV / z) × log₁₀([out]/[in]) when using base-10 logarithms. For K⁺ with typical concentrations of 5 mM outside and 140 mM inside, you get E_K ≈ (61.5/1) × log(5/140) ≈ −89 mV. For Na⁺ (145 mM outside, 12 mM inside), E_Na ≈ +67 mV. Notice that the sign of the equilibrium potential depends on which side of the membrane has the higher concentration and on the charge of the ion — this is captured automatically by the math.

The Nernst equation gives you the equilibrium potential for one ion at a time, which is a simplification — real membranes are permeable to multiple ions simultaneously. That is why the resting membrane potential (around −70 mV in a typical neuron) does not exactly equal E_K or E_Na but falls between them, weighted by relative permeabilities. The Goldman equation, which you will encounter next, handles this multi-ion case. But the Nernst equation remains indispensable because it tells you the driving force on any individual ion: the difference between the actual membrane potential and that ion's equilibrium potential (V_m − E_ion). If V_m is more positive than E_K, potassium will flow outward; if V_m is more negative than E_Na, sodium will flow inward. This concept of electrochemical driving force is the foundation for understanding every electrical event in neurons — from resting potentials to action potentials to synaptic currents.