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Human Physiology I · Cellular Physiology

Resting Membrane Potential

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On this page 7 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Worked example
  6. Key takeaway
  7. Study tools

In 30 seconds

is the steady voltage across a resting cell membrane, about −70 mV in neurons (inside relative to outside). It exists because the membrane is far more permeable to potassium than to sodium, so potassium leaks out through down its , leaving negative charge behind. The pumps potassium back in and sodium out to sustain the gradients. This voltage is the baseline for all electrical signaling.

Why this matters

Resting membrane potential underlies recordings such as ECGs and EEGs. In the lab it is measured with a microelectrode and compared with Nernst/GHK predictions to judge whether gradients or channels are normal. Electrolyte shifts change excitability: low blood potassium can hyperpolarize excitable cells, high potassium can depolarize them. Clinical values, diagnostic criteria, and protocols vary by institution and jurisdiction; these notes support education and do not replace clinical instruction or supervision. Concerning symptoms require evaluation by qualified clinicians or local emergency services.

The college version

1. Chemical, electrical, and electrochemical gradients

A chemical gradient is a concentration difference; ions move high to low. An is a charge (voltage) difference; ions move away from like charges and toward opposite ones. Their sum is the , which sets net movement. For sodium, both gradients point inward. For potassium, the chemical gradient points out and the electrical gradient points in; at rest they nearly balance. Chloride is higher outside; calcium is kept at very low free concentration inside.

2. Channels, selectivity, and permeability

is how easily each ion crosses compared with others, set mainly by which channels are open. means a channel admits almost only one ion species. At rest most sodium channels are closed while many potassium leak channels are open, so the membrane is 25–50 times more permeable to potassium than sodium.

3. Equilibrium potential and membrane voltage

The (E_ion) is the voltage at which one ion's gradients cancel, so that ion has no net flow. (V_m) is the actual measured potential. Resting membrane potential is V_m with no signal passing — not one ion's E_ion but a permeability-weighted compromise nearest to E_K.

How it works

  1. The Na⁺/K⁺ pump builds steep Na⁺ and K⁺ gradients using ATP.
  2. K⁺ leak channels let potassium exit, making the inside negative.
  3. The negative interior opposes further K⁺ exit (electrical gradient).
  4. Net K⁺ movement stops near E_K (≈ −90 mV).
  5. A small sodium leak shifts V_m to ≈ −70 mV.
  6. The pump restores gradients, keeping the potential stable.

Common confusions

Do not confuseWithDifference
Chemical gradientElectrical gradientConcentration vs. charge difference
Equilibrium potentialResting membrane potentialOne ion's balance point vs. the cell's permeability-weighted voltage
Nernst equationGoldman-Hodgkin-Katz equationSingle ion vs. multiple ions weighted by permeability
DepolarizationHyperpolarizationV_m toward zero vs. more negative
Potassium leak channelVoltage-gated potassium channelAlways open vs. opens on depolarization

Memory aids

"K leaks, Na sneaks, the pump restores." Potassium leak channels make the inside negative, a little sodium sneaks in to hold −70 mV instead of −90 mV, and the Na⁺/K⁺ pump restores the gradients so the system never runs down.

Quick review

Topic Recap

Resting membrane potential (≈ −70 mV) is a steady voltage set by ion gradients and membrane permeability. Potassium leak channels dominate, so V_m sits near E_K; a small sodium leak and the continuous Na⁺/K⁺ pump refine and sustain it. Nernst gives each ion's equilibrium potential, and GHK combines them to predict the real voltage.

Knowledge Check

  1. Why is resting membrane potential closer to E_K than to E_Na?
  2. A K⁺-only neuron has 150 mM inside and 5 mM outside. Estimate E_K at 37 °C.
  3. What two gradients act on an ion, and how are they combined?
  4. What does the sodium-potassium ATPase contribute, and what happens if it stops?
  5. Distinguish from .

Answers and Rationales

  1. Resting membranes are far more permeable to K⁺ than Na⁺, so potassium dominates the GHK average. Rationale: permeability, not concentration alone, sets V_m.
  2. E_K ≈ 61 × log₁₀(5/150) ≈ −90 mV. Rationale: apply the 37 °C cation form with [out]/[in].
  3. Chemical (concentration) and electrical (charge) gradients; their sum is the electrochemical gradient. Rationale: ions respond to both forces.
  4. It builds and holds the gradients and exports 3 Na⁺/imports 2 K⁺ per ATP; if it stops, gradients run down and V_m slowly decays. Rationale: the pump is upkeep, not the source, of the voltage.
  5. Depolarization makes V_m less negative; hyperpolarization more negative. Rationale: both are relative to rest.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

A ball rolls downhill because of gravity. Ions "roll" two ways at once: if one side has more of an ion, they spread toward even concentration (the chemical gradient), and because ions are charged, opposite charges attract and like charges repel (the electrical gradient). Together these form the electrochemical gradient that decides which way an ion moves.

Picture the membrane as a wall with a few "potassium-only" doors. Potassium wanders out because there is more inside than outside (chemical gradient); each potassium that leaves takes positive charge with it, making the inside negative (electrical gradient pulling potassium back in). The voltage where push-out and pull-in cancel is the resting membrane potential.

Where it stops being exact: the ball picture has one force, but ions feel two forces at once that must be added. Real cells also have several ion types and doors, so the resting voltage is a permeability-weighted average, not one ion's balance point.

Simple Example

A cell permeable only to potassium (150 mM inside, 5 mM outside) leaks potassium out until the negative interior pulls it back as fast as the gradient pushes it out — about −90 mV, potassium's equilibrium potential.

Worked example

  1. The sodium-potassium ATPase (Na⁺/K⁺ pump) uses ATP to move 3 Na⁺ out and 2 K⁺ in per cycle, building the gradients (high Na⁺ and Cl⁻ outside; high K⁺ inside). It sets up the "batteries" but adds little directly to the voltage.
  2. Open potassium leak channels let K⁺ flow out down its chemical gradient; each exit removes positive charge, so the inside turns negative.
  3. Outward flow slows as the interior goes negative, because the electrical gradient now opposes further loss; net K⁺ movement stops near −90 mV.
  4. A small inward sodium leak pulls V_m slightly positive of −90 mV. The GHK equation combines these effects to give ≈ −70 mV.
  5. The pump keeps re-exporting leaked Na⁺ and re-importing leaked K⁺, so the gradients and resting potential persist.

Equations

Nernst (single ion): Eion = RTzFln[ion]out[ion]in R = gas constant, T = absolute temperature (K), z = ion valence (+1 K⁺/Na⁺, −1 Cl⁻, +2 Ca²⁺), F = Faraday constant, [ion]_out and [ion]_in = outside/inside concentrations. At 37 °C, a monovalent cation gives E_ion ≈ 61 mV × log₁₀([ion]_out/[ion]_in); anions invert the ratio.

Goldman-Hodgkin-Katz (membrane voltage from multiple ions): Vm = RTFlnPK[K+]o + PNa[Na+]o + PCl[Cl-]iPK[K+]i + PNa[Na+]i + PCl[Cl-]o P_K, P_Na, P_Cl are permeabilities; chloride is inverted (anion). Assumptions: uniform membrane, independent ions, only these ions matter. Limits: ignores the pump's direct current and Ca²⁺, and describes a steady state only.

Key takeaways

  • High yield: Resting potential is a permeability-weighted compromise of ion equilibrium potentials, dominated by K⁺.
  • High yield: A K⁺-only cell rests at E_K ≈ −90 mV; the Na⁺ leak explains why neurons sit near −70 mV.
  • Depolarization = less negative V_m; hyperpolarization = more negative V_m.
  • The pump sets up gradients but adds little direct current; removing it causes slow run-down.
  • Nernst ratio is [out]/[in] for cations, [in]/[out] for anions.
  • At 37 °C, E_ion ≈ 61 mV × log₁₀([ion]_out/[ion]_in) for a monovalent cation.

Keep learning

Ready to build on this? Continue to the next lesson.

Study tools & related lessonsYou’ll learn to · Key vocabulary · Related

You’ll learn to

  • Distinguish chemical, electrical, and electrochemical gradients for a given ion.
  • Use the Nernst equation to find an ion's equilibrium potential and explain its meaning.
  • Use the Goldman-Hodgkin-Katz (GHK) equation to explain why resting membrane potential sits near the potassium equilibrium potential.
  • Relate potassium leak channels and the sodium-potassium ATPase to the maintenance of resting membrane potential.

Key vocabulary

Resting membrane potential
Steady voltage across a resting membrane (≈ −70 mV)
Chemical gradient
Concentration difference across a membrane
Electrical gradient
Voltage difference across a membrane
Electrochemical gradient
Sum of chemical and electrical forces
Sodium (Na⁺)
Main extracellular cation
Potassium (K⁺)
Main intracellular cation
Chloride (Cl⁻)
Main extracellular anion
Calcium (Ca²⁺)
Divalent cation, very low inside
Equilibrium potential
Voltage where one ion's gradients cancel
Nernst equation
Computes E_ion from concentrations
Goldman-Hodgkin-Katz equation
Computes V_m from permeabilities and concentrations
Relative membrane permeability
How easily each ion crosses vs. others
Potassium leak channels
Always-open K⁺-selective channels
Sodium-potassium ATPase
Pump moving 3 Na⁺ out / 2 K⁺ in per ATP
Membrane voltage
Actual potential difference across the membrane
Depolarization
V_m becomes less negative
Hyperpolarization
V_m becomes more negative
Ion-channel selectivity
A channel's preference for one ion species

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