M04.04.003 Equilibrium Potential

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Learning Objective: The objective of this topic is to help the learner understand the concept of equilibrium potential, explain how it is calculated using the Nernst equation, describe how ions move to bring membrane potential toward their equilibrium potential, and apply these principles to predict changes in membrane potential during depolarization and hyperpolarization based on ion permeability.

Equilibrium Potential

Equilibrium potential (E<sub>X</sub>) is the membrane potential at which the electrical driving force exactly balances the chemical (concentration) gradient for a specific ion. At this voltage, net ionic movement = 0, even though channels may be open.

Activity

The Nernst Equation

The Nernst equation calculates the equilibrium potential of any ion based on concentration gradients across the membrane.

E_\text{ion} = \frac{61.5}{z} \log \left( \frac{[X^+]_\text{out}}{[X^+]_\text{in}} \right)

Where:

Symbol Meaning
E<sub>X</sub> equilibrium potential of ion X
[X⁺]ₒ extracellular concentration
[X⁺]ᵢ intracellular concentration
z ionic charge (e.g., K⁺ = +1, Cl⁻ = –1)

Key Points About Equilibrium Potential

1. Ions diffuse in a way that drives Em toward their Ex.

  • If E<sub>K</sub> = –90 mV and Em = –60 mV → K⁺ leaves the cell to make Em more negative.
  • If E<sub>Na</sub> = +60 mV and Em = –60 mV → Na⁺ enters the cell to make Em more positive.

2. Net ionic current depends on:

  • Driving force (difference between Em and E<sub>X</sub>)
  • Conductance (how many channels of that ion are open)

Current∼(Em−EX)×conductance\text{Current} \sim (\text{Em} – E_X) \times \text{conductance}

3. Em is pulled toward the equilibrium potential of the most permeable ion.

  • Resting membrane potential is close to E<sub>K</sub> (~ –90 mV) because the membrane is mostly K⁺ permeable at rest.
  • During depolarization, Na⁺ permeability ↑ → Em shifts toward E<sub>Na</sub> (+60 mV).

4. Only a tiny number of ions move to change Em.

  • Opening ion channels changes voltage, not bulk concentrations.
  • Intracellular and extracellular ion concentrations remain essentially unchanged.

Activity

Typical Equilibrium Potentials

Ion Approximate E<sub>X</sub>
K⁺ –90 mV
Na⁺ +60 mV
Cl⁻ –70 mV
Ca²⁺ +120 mV

(Values vary by tissue and exact concentrations.)

Depolarization and Hyperpolarization

Depolarization:

Em becomes less negative (moves toward 0).
Often due to Na⁺ or Ca²⁺ entry.

Hyperpolarization:

Em becomes more negative (moves further from 0).
Often due to K⁺ efflux or Cl⁻ influx.

Activity

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