Understanding Ion Equilibrium and Membrane Mechanics

Sep 12, 2024

Lecture Notes on Ion Equilibrium and Membrane Permeability

Initial Setup

  • Two compartments with sodium chloride (NaCl) initially in equal amounts on both sides.
  • Both sides are electrically neutral.
  • Membrane is permeable to both sodium (Na) and chloride (Cl).
  • Expectation: Movement of Na and Cl to reach diffusional equilibrium (equal concentration on both sides).

Modified Setup

  • NaCl initially only on the left side.
  • Membrane only permeable to Na, not to Cl.
  • Reflection Coefficient:
    • Na: 0 (membrane permeable)
    • Cl: 1 (membrane impermeable)

Chemical and Electrical Gradients

  • Chemical gradient for Na and Cl: From left to right, Cl cannot move.
  • Movement Outcome:
    • Na moves right leaving negative charge behind (due to immobile Cl).
    • Development of diffusion potential (charge separation).

Electrochemical Gradient

  • As Na moves, an electrical gradient develops opposing further Na movement.
  • Equilibrium: Electrical force equals chemical gradient.
  • Equilibrium Potential:
    • At equilibrium, the electrochemical gradient is zero.

Nernst Equation

  • Used to calculate the equilibrium potential (Nernst Potential) for an ion.
  • Formula:
    • Equilibrium potential = Z (valence) × 60 mV × log(concentration outside/concentration inside)
    • Z: Valence of the ion.

Relative Ion Concentrations

  • Sodium (Na): More concentrated outside the cell.
  • Potassium (K): More concentrated inside the cell.

Equilibrium Potentials for Ions

  • Sodium (Na): Approx. +60 mV
  • Potassium (K): Approx. -90 mV
  • These are reference values for simplicity.

Key Takeaways

  • Equilibrium Potential:
    • Represents the electrical force that counterbalances the chemical force for an ion.
    • Specific to individual ions.
    • Magnitude of electrical force equals the chemical gradient.