Understanding Equilibrium Potentials and Nernst Equation

Aug 31, 2024

Lecture Notes on Equilibrium Potentials

Introduction to Equilibrium Potentials

  • Discussion of equilibrium potentials, focusing on ion diffusion across cell membranes.
  • Equilibrium Potential: A voltage that opposes further movement of an ion.
  • Ion Diffusion: Occurs when the concentration of an ion like X is higher outside the cell and the membrane is permeable.

Membrane Permeability and Ion Movement

  • Ion Movement: Positive ions entering a small cell significantly increase internal positivity.
  • Charge Repulsion: Like charges repel, making it harder for additional positive ions to enter.
  • Stalemate: When internal voltage opposes ion diffusion, equilibrium potential is achieved.

The Nernst Equation

  • Used to calculate equilibrium potential.
  • Equation Breakdown:
    • E_x: Equilibrium potential for ion X.
    • RT/ZF: Represents cell constraints.
      • R: Gas constant.
      • T: Temperature (constant in mammalian cells).
      • Z: Valence of the ion.
      • F: Faraday constant (96,000 coulombs per mole).
    • Ln: Natural log of concentration ratios (outside/inside).

Simplified Nernst Equation

  • Simplified Equation: 61 millivolts divided by the valence of the ion, using log base 10.
  • Application: Calculate potential for any permeable ion across the membrane.

Example Calculations

Potassium (K+)

  • Concentration: Higher inside (140 mM) vs. outside (4 mM).
  • Calculation Steps:
    • Use modified Nernst equation: 61 divided by valence (1) = 61.
    • Calculate log(4/140) = -1.54.
    • Result: Equilibrium Potential = -94 mV.

Sodium (Na+)

  • Concentration: Higher outside (142 mM) vs. inside (14 mM).
  • Calculation Steps:
    • Use modified Nernst equation: 61 divided by valence (1) = 61.
    • Calculate log(142/14) = 1.06.
    • Result: Equilibrium Potential = 61.4 mV.

Conclusion

  • Equilibrium Potentials: Positive inside needed for sodium, negative inside for potassium to maintain concentration differences.
  • Discussion: Encourage reviewing the equation and further discussion in groups.

These notes capture the core ideas and calculations related to equilibrium potentials, focusing on the concept of ion diffusion and how the Nernst equation is used to calculate equilibrium potentials for different ions.