What is the resting membrane potential?
The resting membrane potential (RMP) is the electrical potential difference across the plasma membrane of a cell in its non-excited state. By convention it is expressed as the voltage inside the cell relative to the outside, so a value of −70 mV means the interior is 70 mV more negative than the extracellular fluid.
Every cell has one, but it matters most in excitable cells — neurons and skeletal, cardiac and smooth muscle — because these cells depart from rest to fire action potentials. Na+ and K+ dominate the RMP; large intracellular anions (proteins, organic phosphates) that cannot cross the membrane also contribute.
How is the resting membrane potential generated?
Two conditions are needed: (1) a concentration gradient for an ion, and (2) selective permeability of the membrane to that ion. The Na+/K+-ATPase sets up the gradients (high K+ inside, high Na+ outside). At rest, many K+ leak channels (two-pore domain K+ channels) are open, so K+ diffuses out down its concentration gradient. Each K+ that leaves takes a positive charge with it and leaves an unpaired negative anion behind — the inside becomes negative.
As the inside grows more negative, it pulls K+ back. When the electrical force inward exactly balances the chemical force outward, net K+ movement stops — that voltage is the K+ equilibrium potential. Only a tiny number of ions need to move to create this voltage, so the bulk concentrations hardly change.
What is the Nernst equation and what are the equilibrium potentials?
The Nernst equation gives the equilibrium potential of one ion — the membrane voltage at which that ion has no net movement.
E(ion) = (RT / zF) × ln([ion]out / [ion]in) ≈ (61.5 / z) × log10([ion]out / [ion]in) mV at 37 °C
R = gas constant, T = absolute temperature, z = valence (+1 for K+ and Na+, −1 for Cl−, +2 for Ca2+), F = Faraday's constant.
| Ion | Inside (mM) | Outside (mM) | Equilibrium potential | Direction at rest |
|---|---|---|---|---|
| K+ | 120 | 4 | about −90 mV (−85 mV in some sources) | Leaks out; RMP lies close to EK |
| Na+ | 14 | 140 | about +60 to +65 mV | Tends to enter; permeability at rest is low |
| Cl− | Low | High | Close to the RMP in skeletal muscle | Little net movement at rest in muscle |
What is the Goldman-Hodgkin-Katz equation?
A real membrane is permeable to several ions at once, so the RMP is not equal to any single equilibrium potential. The Goldman-Hodgkin-Katz (GHK) equation extends Nernst to multiple monovalent ions (K+, Na+, Cl−), weighting each by its permeability:
Vm = 61.5 × log10( (PK[K+]o + PNa[Na+]o + PCl[Cl−]i) / (PK[K+]i + PNa[Na+]i + PCl[Cl−]o) )
Note that Cl− concentrations are inverted (inside on top) because it carries a negative charge.
- The more permeable the membrane is to an ion, the closer the RMP lies to that ion's equilibrium potential.
- At rest, Na+ permeability is about 5% of K+ permeability or less, so the RMP sits close to EK (−90 mV) but is pulled slightly positive — to about −70 to −80 mV in a typical neuron.
- During the action potential upstroke, Na+ permeability rises sharply, and the membrane potential swings towards ENa — the same equation, different permeabilities.
What does the Na+/K+-ATPase contribute?
The Na+/K+-ATPase pumps 3 Na+ out and 2 K+ in for each ATP used. It maintains the Na+ and K+ gradients that the leak channels depend on. Because it moves one net positive charge out per cycle, it is electrogenic — it adds a small extra negativity directly.
- Indirect role (major) — building and maintaining the ionic gradients. Without the pump, gradients run down and the RMP slowly collapses.
- Direct electrogenic role (minor) — a few millivolts. In cultured rat skeletal myotubes, blocking the pump with ouabain depolarised the membrane by 5–8 mV within 30 seconds.
- The pump contributes to the RMP in probably all cells, including skeletal, cardiac and smooth muscle and neurons.
What are the typical resting potentials in different cells?
| Cell | Typical RMP | Key point |
|---|---|---|
| Neuron | About −70 mV (range −70 to −80) | Some Na+ leak pulls it positive to EK |
| Skeletal muscle fibre | About −90 mV | High Cl− conductance (ClC-1) — about 80% of resting conductance — stabilises the RMP |
| Ventricular myocyte (phase 4) | About −90 mV | Stable; passively open K+ channels let K+ flow out, and the Na+/K+ pump maintains the gradients |
| SA node pacemaker cell | No true rest; phase 4 starts near −60 mV | Phase 4 begins at about −60 mV with mainly Na+ influx → spontaneous depolarisation (automaticity) |
The cardiac ventricular action potential then runs: phase 0 rapid depolarisation (voltage-gated Na+ influx), phase 1 brief repolarisation (K+ out), phase 2 plateau (Ca2+ in balanced by K+ out), phase 3 repolarisation (K+ out) back to the phase 4 resting level of about −90 mV.
How do hyperkalaemia and hypokalaemia change the RMP and excitability?
Because the RMP sits close to EK, changes in extracellular K+ move it directly. Intracellular K+ is so large that clinically relevant shifts are driven by the plasma level.
| State | K+ gradient | Effect on RMP | Effect on excitability |
|---|---|---|---|
| Hypokalaemia | Steeper (less K+ outside) | Hyperpolarised (more negative) | A larger stimulus is needed to reach threshold; delayed ventricular repolarisation favours re-entrant arrhythmias |
| Hyperkalaemia | Shallower (more K+ outside) | Depolarised (less negative) | Sustained depolarisation inactivates voltage-gated Na+ channels and prolongs the refractory period → conduction block and major arrhythmias |
How do you solve resting potential calculation questions?
Calculation MCQs almost always reduce to the simplified Nernst form for a monovalent ion: E = 61.5 × log10([out]/[in]) mV, with the sign flipped for an anion. Work out the ratio, take the log, multiply — and then check that the sign makes physiological sense.
| Gradient (out : in) | log10 of ratio | Equilibrium potential | Sense check |
|---|---|---|---|
| 1 : 10 (cation higher inside) | −1 | about −61 mV | Cation concentrated inside → inside negative at equilibrium |
| 4 : 120 (K+) | about −1.5 | about −90 mV | Matches the textbook EK |
| 140 : 14 (Na+) | +1 | about +61 mV | Matches the textbook ENa of +60 to +65 mV |
| 10 : 1 (cation higher outside) | +1 | about +61 mV | Cation concentrated outside → inside positive at equilibrium |
- Doubling the valence halves the potential for the same gradient — a 10-fold Ca2+ gradient gives about 30 mV, not 61 mV.
- Equal concentrations on both sides → log 1 = 0 → equilibrium potential of 0 mV, whatever the ion.
- Permeability does not appear in Nernst. If a question gives permeabilities, it wants the Goldman equation or a qualitative answer ('closer to the ion with higher permeability').
- Driving force on an ion = membrane potential minus its equilibrium potential. At an RMP of −70 mV, Na+ (ENa about +60 mV) has a large inward driving force, while K+ (EK about −90 mV) has a small outward one.
How does the resting potential link to the action potential?
The RMP is the starting point. A graded depolarisation (for example from synaptic input) moves the membrane towards threshold. If threshold is crossed, voltage-gated Na+ channels open, Na+ rushes in and the membrane swings towards ENa. Voltage-gated K+ channels then open and Na+ channels inactivate, returning the membrane to rest. Not every depolarisation produces an action potential — only those large enough to reach threshold.
- Depolarisation = membrane potential becomes less negative (more positive).
- Hyperpolarisation = membrane potential becomes more negative.
- Most non-excitable cells keep a constant RMP; only excitable cells generate action potentials.
