Nernst Equation for Membrane Potential
Calculate the equilibrium potential across a cell membrane for a specific ion using the Nernst equation.
Essential for neuroscience.
The Formula
The Nernst equation calculates the equilibrium potential (also called the reversal potential) for a single ion species across a biological membrane. At this voltage, the electrical force pulling the ion in one direction exactly balances the concentration gradient pushing it the other way, resulting in zero net ion flow.
Walther Nernst, a German physical chemist, derived this equation in 1889. While originally developed for electrochemistry, it became one of the most important equations in neuroscience and cell biology. Every neuron in your body relies on ion concentration gradients to generate electrical signals, and the Nernst equation predicts the voltage each ion "wants" to establish.
In practice, biologists often use a simplified version at body temperature (37 degrees Celsius or 310 K). At this temperature, RT/F equals approximately 26.7 mV. For a monovalent positive ion like sodium or potassium (z = +1), the equation simplifies to approximately 61.5 mV times the log base 10 of the concentration ratio.
The Nernst equation is limited to one ion at a time. Real cell membranes are permeable to multiple ions simultaneously. For a more complete picture of membrane potential, scientists use the Goldman-Hodgkin-Katz equation, which accounts for the relative permeabilities of all major ions. However, the Nernst equation remains essential as a building block and for understanding each ion's individual contribution.
Typical resting membrane potential of a neuron is about -70 mV. This is close to the Nernst potential for potassium (-90 mV) because the resting membrane is most permeable to potassium ions.
Variables
| Symbol | Meaning |
|---|---|
| Eion | Equilibrium potential for the ion (in volts) |
| R | Universal gas constant (8.314 J/(mol·K)) |
| T | Absolute temperature (in Kelvin) |
| z | Valence of the ion (+1 for K⁺, +2 for Ca²⁺, -1 for Cl⁻) |
| F | Faraday constant (96,485 C/mol) |
| [ion]outside | Ion concentration outside the cell |
| [ion]inside | Ion concentration inside the cell |
Example 1
Find the equilibrium potential for potassium (K⁺) at 37°C. [K⁺]outside = 5 mM, [K⁺]inside = 140 mM.
Use the simplified form at 37°C: E = (61.5 mV / z) × log₁₀([outside] / [inside])
E = (61.5 / 1) × log₁₀(5 / 140)
E = 61.5 × log₁₀(0.0357) = 61.5 × (-1.447)
EK ≈ -89.0 mV
Example 2
Find the equilibrium potential for sodium (Na⁺) at 37°C. [Na⁺]outside = 145 mM, [Na⁺]inside = 12 mM.
E = (61.5 / 1) × log₁₀(145 / 12)
E = 61.5 × log₁₀(12.083) = 61.5 × 1.082
ENa ≈ +66.6 mV
When to Use It
The Nernst equation is used whenever you need to find the equilibrium voltage for a single ion across a membrane.
- Calculating resting membrane potential contributions of K⁺, Na⁺, and Cl⁻ in neurons
- Understanding action potential generation and ion channel behavior
- Predicting electrode potentials in electrochemistry experiments
- Designing biosensors and ion-selective electrodes
- Studying cardiac muscle cell electrophysiology
- Analyzing synaptic transmission and neurotransmitter effects