Equilibrium potentials and what sets the resting voltage
An ion's equilibrium potential depends on its charge, temperature and concentrations inside and outside the cell. A typical resting neurone lies near the potassium equilibrium potential because its membrane is highly permeable to potassium. Other ion currents and the sodium-potassium pump also contribute.
What a learner can do afterwards
- Calculates an equilibrium potential from inside and outside concentrations.
- Predicts how the resting voltage shifts when external potassium is raised.
- Explains why the resting membrane sits near the potassium value but not exactly at it.
1 · Read
You have met a neurone's resting voltage. Membrane voltage means inside relative to outside. An ion's equilibrium potential, E_ion, is the voltage where its concentration gradient and electrical force balance. Its net passive flow through open channels is zero, though individual ions can cross both ways. For K+ concentrated inside, diffusion favours outward movement while a negative inside attracts it inward.
The sodium-potassium pump uses one ATP to move three Na+ out and two K+ in, against their concentration gradients. It maintains high sodium outside and high potassium inside. Each cycle also exports one net positive charge, tending to make the inside more negative. Pumps maintain gradients over time; channels allow the fast passive ion flows that change voltage.
At 37°C, use E_ion = (61.5 mV/z) log10(c_out/c_in). This Nernst equation uses concentrations to approximate ion activities. c_out and c_in are outside and inside concentrations in matching units. z is signed ion charge: +1 for K+ or Na+, -1 for Cl-. Divide outside by inside, take the base-10 logarithm with a calculator, then multiply by 61.5/z. The coefficient changes with temperature.
A typical resting neurone is more permeable to K+ than to Na+, so its voltage, V_m, lies near E_K. Sodium entry usually shifts V_m toward the more positive E_Na. Other ion currents and pump current also contribute, so V_m need not equal E_K. With no applied current, a steady V_m means total membrane current, including pump current, is zero. Individual ion currents can still flow.
Keep inside K+, temperature, other ion concentrations and permeabilities fixed. Raising outside K+ increases c_out/c_in, making a negative E_K less negative. A potassium-dominated resting voltage also becomes less negative. At 37°C, doubling outside K+ raises E_K by 61.5 log10(2), about 18.5 mV. V_m need not rise by exactly that amount. Lowering outside K+ shifts E_K in the negative direction.
Permeability means how readily an ion crosses the membrane. It affects V_m but is not an input to the Nernst equation. With concentrations and temperature fixed, opening more K+ channels leaves E_K unchanged while shifting V_m toward E_K. Increasing Na+ permeability shifts V_m toward E_Na. These predictions give a direction; they do not calculate an arithmetic average of equilibrium potentials.
Calculate an ion's equilibrium potential from charge, temperature and its concentration ratio. Resting voltage also depends on permeability, other ion currents and pump current.
Lesson, questions and flashcards written for this dataset.
Readings and flashcards written for this dataset. Linked videos: Khan Academy, "Neuron resting potential description" and "Sodium potassium pump". Video licensing terms have not been verified.
More to read
What balances at an equilibrium potential?
A membrane voltage compares the cell's inside with its outside. A negative value means the inside is at a lower electrical potential.
Take a cell with more K+ inside than outside. Through an open potassium channel, diffusion favours outward movement. A negative inside attracts the positively charged potassium inward. These influences oppose each other.
At the potassium equilibrium potential, E_K, their effects balance. Equal average flows in opposite directions give no net passive potassium flow. Individual ions do not have to stop moving.
This balance applies to potassium under the stated conditions. A whole resting neurone can carry sodium, potassium and other currents at the same time, so its voltage need not equal E_K.
Setting up the Nernst calculation
At 37°C, use E_ion = (61.5 mV/z) log10(c_out/c_in). The result is inside voltage relative to outside. The equation uses concentration as an approximation to ion activity.
First check that both concentrations use the same units. Divide the outside concentration by the inside concentration, then take the base-10 logarithm of the ratio. Finally multiply by 61.5/z.
The signed charge z matters. It is +1 for K+ and Na+, but -1 for Cl-. For a positive ion, an outside-to-inside ratio below 1 gives a negative equilibrium potential. A negative ion reverses that sign through z.
For the lesson's K+ example, 1 mM outside divided by 100 mM inside gives 0.01. The logarithm is -2, so E_K = -123 mV.
The factor 61.5 mV applies at 37°C. A calculation at another temperature needs a different factor.
Changing channels without changing E_K
Suppose potassium concentrations and temperature stay fixed while more potassium channels open. The membrane becomes more permeable to K+, but E_K does not change. The Nernst calculation has no permeability input.
Membrane voltage, V_m, can change in this situation. The extra potassium pathways give potassium more influence, shifting V_m toward E_K.
The same distinction applies to sodium. If sodium concentrations and temperature stay fixed, E_Na stays fixed. Increasing sodium permeability shifts V_m toward E_Na.
In a typical resting neurone, potassium has the largest permeability and keeps V_m near E_K. Sodium and other currents still contribute. These facts predict the direction of a voltage change. They do not provide an arithmetic averaging rule for calculating V_m.
When outside potassium doubles
Keep inside K+ and temperature fixed. Doubling outside K+ doubles the ratio c_out/c_in in the Nernst equation.
A logarithm turns that doubling into an added log10(2). At 37°C, the change in E_K is therefore 61.5 log10(2), about +18.5 mV. A negative E_K becomes less negative. This is a change in voltage, not the new voltage itself.
For a potassium-dominated resting membrane, raising outside K+ also makes V_m less negative when other ion concentrations and permeabilities stay fixed. Its change need not be exactly 18.5 mV because potassium is not the only influence.
Lowering outside K+ reduces the concentration ratio and shifts E_K in the negative direction.
Stable voltage with continuing ion movement
A steady resting voltage does not mean that every ion is at equilibrium. With no applied current, the total membrane current is zero, but individual currents can continue in opposite directions.
The sodium-potassium pump is part of that current balance. Each cycle uses one ATP to export three Na+ and import two K+. Exporting one net positive charge tends to make the inside more negative.
The pump also maintains the concentration differences used by passive channels. Its gradient-maintaining role continues over time. Channels allow the fast passive flows that change membrane voltage.
Keeping these roles separate avoids treating the pump as the mechanism that directly performs each rapid voltage reset after an action potential. A cell can have a stable resting voltage while continuing to move ions and use ATP.
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