Membrane Potential Calculators

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Membrane potential is the electrical potential difference across the cell membrane, measured in millivolts (mV), with the inside of the cell as reference (negative inside for resting cells). The resting membrane potential of a typical neuron is approximately −70 mV, maintained by the Na⁺/K⁺-ATPase pump and differential ion permeability (mainly K⁺ leak channels). The Nernst equation calculates the equilibrium potential for a single ion; the Goldman-Hodgkin-Katz (GHK) equation integrates multiple ions and their permeabilities to predict the actual resting potential. Changes in membrane potential (depolarization, hyperpolarization) drive action potentials and synaptic signaling.

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Resting Membrane Potential

Typical values: neurons ~−70 mV; cardiac muscle ~−90 mV; skeletal muscle ~−80 mV; red blood cells ~−10 mV. Set by: (1) Ion concentration gradients maintained by Na⁺/K⁺-ATPase (3 Na⁺ out / 2 K⁺ in per cycle — electrogenic). (2) Differential membrane permeability: K⁺ leak channels are open at rest → K⁺ diffuses out → negative charge inside. (3) Impermeant anions (proteins, organic phosphates) inside the cell contribute to intracellular negativity.

Nernst Equation (Single Ion)

E_ion = (RT/zF) × ln([ion]_out / [ion]_in)

At 37°C: E_ion = (61.5 mV / z) × log₁₀([ion]_out / [ion]_in).

E_K = (61.5/1) × log(5/140) = 61.5 × (−1.447) = −89 mV. E_Na = 61.5 × log(145/15) = +61 mV.

Goldman Equation (Multiple Ions)

V_m = (RT/F) × ln [(P_K[K]_o + P_Na[Na]_o + P_Cl[Cl]_i) / (P_K[K]_i + P_Na[Na]_i + P_Cl[Cl]_o)].

At rest: P_K : P_Na : P_Cl ≈ 1 : 0.04 : 0.45 → V_m ≈ −70 mV. During action potential: P_Na increases 500–1000× → V_m → +40 mV.

Action Potential Phases

Resting (−70 mV) → Threshold (−55 mV) → Rapid depolarization (Nav opens) → Overshoot (+40 mV) → Repolarization (Nav inactivates, Kv opens) → Hyperpolarization → Return to resting.

Glossary

Resting Membrane Potential
The stable electrical potential across a resting cell membrane (~−70 mV in neurons); set by K⁺ leak channels, ion concentration gradients, and the Na⁺/K⁺-ATPase pump.
Nernst Equation
E_ion = (RT/zF) × ln([out]/[in]); calculates equilibrium potential for a single ion; E_K ≈ −89 mV; E_Na ≈ +61 mV; the Goldman equation generalizes to multiple ions.
Depolarization
A decrease in membrane potential toward 0 mV or positive values; caused by Na⁺ or Ca²⁺ influx; drives the action potential upstroke; threshold ≈ −55 mV for neuron firing.

Frequently Asked Questions

Membrane potential (V_m) is the electrical voltage across the cell membrane (inside relative to outside). Three factors determine resting V_m: (1) Ion concentration gradients: K⁺ is high inside (~140 mM) and low outside (~5 mM); Na⁺ is high outside (~145 mM) and low inside (~15 mM); maintained by Na⁺/K⁺-ATPase. (2) Differential membrane permeability: at rest, K⁺ channels (leak channels) are open; K⁺ flows outward down its concentration gradient, carrying positive charge out → inside becomes negative. (3) Fixed negative charges inside (large anions like proteins that cannot cross the membrane) contribute to intracellular negativity. Result: V_m ≈ −70 mV at rest.

The Nernst equation gives the membrane voltage at which there is no net flow of a specific ion (electrochemical equilibrium): E_ion = (RT/zF) × ln([ion]_outside/[ion]_inside). R = 8.314 J/mol/K; T = 310 K (37°C); F = 96,485 C/mol; z = charge. At 37°C: E_ion = (25.7 mV/z) × ln([out]/[in]) = (61.5 mV/z) × log₁₀([out]/[in]). E_K = (61.5/1) × log(5/140) = −89 mV. E_Na = 61.5 × log(145/15) = +61 mV. The resting V_m (−70 mV) lies between E_K and E_Na, weighted toward E_K by the higher K⁺ permeability.

The negative resting V_m arises from two main mechanisms: (1) Selective K⁺ permeability: at rest, K⁺ leak channels are the dominant open channels. K⁺ moves outward down its concentration gradient (high inside, low outside). As positive K⁺ ions leave, negative charge builds up inside — creating an electrical gradient opposing further K⁺ exit. Equilibrium: when electrical force = concentration force; V_m = E_K ≈ −89 mV (but partial Na⁺ and Cl⁻ permeability pulls V_m to ~−70 mV). (2) Na⁺/K⁺-ATPase: electrogenic pump exports 3 Na⁺ and imports 2 K⁺ per cycle → net outward positive charge → contributes ~−5 mV to V_m.

Depolarization: V_m becomes less negative (moves toward 0 mV or even positive). Caused by: Na⁺ or Ca²⁺ influx; K⁺ efflux reduction; Cl⁻ efflux. Example: action potential upstroke (Nav opens → Na⁺ rushes in → V_m goes from −70 to +40 mV). Hyperpolarization: V_m becomes more negative (moves away from 0 mV). Caused by: K⁺ efflux increase; Cl⁻ influx; GABA_A receptor activation (Cl⁻ influx). Example: afterhyperpolarization following an action potential (Kv channels slow to close → K⁺ efflux continues after Nav inactivation → V_m dips below −70 mV). Resting potential: the stable V_m maintained between stimuli (−70 mV in neurons). Threshold: ~−55 mV — the V_m at which enough Nav channels open to create positive feedback → action potential.