OE

Week 3 ELM 6: The Nernst Equation

The Nernst Equation

  • The Nernst equation helps determine the equilibrium potential for a specific ion.

Ion Gradients in Cells

  • Ions have different concentrations inside and outside the cell, creating concentration gradients.
  • Examples of ion concentrations (mM): Na^+ (150 outside, 15 inside), K^+ (5 outside, 100 inside), Ca^{2+} (2 outside, 0.0002 inside), Cl^- (150 outside, 13 inside).
  • Typical concentration ratios: Na^+ (10:1), K^+ (1:20), Ca^{2+} (10000:1), Cl^- (11.5:1).
  • The cell interior is negatively charged, around -70 to -60 mV relative to the outside.

Forces Acting on Ions

  • Ions are influenced by both concentration gradients and electrical gradients.
  • Concentration gradients drive ions to move from areas of high to low concentration.
  • Electrical gradients are due to the membrane potential.

Determining Ion Movement

  • To predict ion movement, we need to consider both electrical and concentration gradients.
  • This requires mathematical analysis.

Energy Due to Electrical Gradient

  • Work (energy) required to move an ion across an electrical gradient is given by: Work = z \cdot F \cdot V
    • z = valence of the ion
    • F = Faraday constant (96500 Coulombs/mol)
    • V = membrane potential (Volts)
  • Definition of a Volt: 1 Volt is the potential that requires 1 Joule of work to move 1 Coulomb of charge.
  • To move 1 mole of z-valent ions across a membrane potential of Vm Volts requires z \cdot F \cdot Vm Joules.

Energy Due to Concentration Gradient

  • Work required to move 1 mole of substance from concentration ci (inside) to co (outside) is: Work = R \cdot T \cdot ln(ci/co)
    • R = gas constant
    • T = temperature in Kelvin
    • ln = natural logarithm
  • If ci = co, then ln(1) = 0, and no work is required.

Total Work and Ion Movement

  • Total work to move an ion across the membrane is the sum of work due to electrical and concentration gradients:
    • Total Work = z \cdot F \cdot V + R \cdot T \cdot ln(ci/co)
  • Three possible cases:
    • Work > 0: Energy is needed (active transport).
    • Work < 0: Energy is released (spontaneous movement