Cell Transport

Master answer

Equilibrium Potential

Nernst Equation

The potential difference generated by a permeable ion in electrochemical equilibrium when there are different concentrations on either side of the cell can be calculated via the Nernst Equation:

Goldman-Hodgkin-Katz Equation

The Nernst equation describes the equilibrium potential for a single ion, and assumes that the membrane is completely permeable to that ion.

However, calculation of membrane potential requires examining the effects of many different ions with different permeability. This can be performed with the Goldman-Hodgkin-Katz equation:

where,
P_x is the permeability constant for the ion, x
If the membrane is impermeable to x, then Px = 0

Note that:
This model does not consider valency
The concentrations of negative ions are reversed relative to positive ions

Resting Membrane Potential

• Definition: The potential difference (units volts) that exists across the cell membrane (i.e. between the intracellular and extracellular environment) when the cell is in a unexcited state, where the reference voltage is the extracellular environment.
• Resting Membrane Potential (RMP) is the result of two key properties of cells:
  • the cell membrane is semi-permeable, that is it has variable permeability to different species in solution.
  • differing concentration gradients exist across the semi-permeable cell membrane for different ions in solution, the most important determinant of these gradients being the Na⁺-K⁺-ATPase.
• At rest, membranes are:
  • Permeable to potassium
  • Impermeable to other ions
• Generation of membrane potential:
  • Intracellular potassium concentration is much higher than extracellular potassium concentration – Due to the action of the Na⁺-K⁺pump.
  • As the membrane is permeable to potassium, potassium will attempt to diffuse down this gradient, generating a negative intracellular charge which opposes further diffusion
• At some point, an electrochemical equilibrium is reached between:
  • The concentration gradient dragging potassium out of the cell
  • Negative electrical charge pulling it in

Determinants of RMP

1. K⁺ Diffusion Potential
   • From the Nernst equation above we can see that the normal RMP of most tissue is relatively close to the K⁺ equilibrium potential (-94mV). From this (and the Goldman equation) we can infer that the membrane is likely to be most permeable to K⁺ at rest. Indeed the primary determinant of the RMP is K⁺. Relative permeability of the membrane to K⁺ vs Na⁺ is 100:1.
   • This has the corollary that changes in K⁺ concentration will have the most major effect on RMP. This is particularly the case with [K⁺]_o due to its low value – small absolute changes in [K⁺]_o are a relatively large proportion of [K⁺]_o.
   • Note that while the RMP is as close (or closer) to the equilibrium potential for Cl^–, Cl^– is not the primary determinant of the RMP as the concentration gradient for Cl^– is largely the passive result of the electrochemical gradient created by the Na⁺-K⁺-ATPase.
2. Na⁺ Influx
   • While the resting membrane is very impermeable to Na⁺ the electrochemical gradient for its movement into the cell is so large that there is a small ‘leak current’ of Na⁺ into the cell.
   • This Na⁺ leak is the single factor responsible for most of the deviation of the RMP from the equilibrium potential for K⁺ (contributes roughly +8mV to the RMP).
3. Na⁺-K⁺-ATPase
   • As noted there is a constant slow leak of Na⁺ into the cell. Because of the deviation away from the K⁺ equilibrium potential that this causes, there is also an electrochemical gradient to cause a slow leak of K⁺ out of the cell. As such the Na⁺-K⁺-ATPase is essential to maintain the relative concentration gradients of these ions and thus the RMP.
   • In addition the Na⁺-K⁺-ATPase itself is electrogenic, transferring as it does 3 Na⁺ out for every 2 K⁺ pumped in, leaving a net negative charge balance on the inside of the cell membrane. This contributes roughly -4mV to the RMP.
4. Gibbs-Donnan Effect
   • The Gibbs-Donnan effect accounts for the effect of non-diffusible ions on the RMP. In vivo the high concentration of negatively charged intracellular proteins has a small but significant effect on RMP. The presence of this net fixed negative charge on the inside of the cell effects the distribution of permeable ions across the membrane.

Resting Membrane Potential in Different Tissues

Typical values of RMPs:

• Ventricular Myocyte: -90mV
• Cardiac Pacemaker cell: -60mV
• Skeletal Muscle cell: -80mV
• Myelinated Axon: -70mV

Gibbs – Donnan Effect

• Describes the tendency of diffusable ions to distribute themselves such that the ratios of the concentrations are equal when they are in the presence of non-diffusable ions.
• Occurs when:
  • A semi-permeable membrane separates two solutions
  • At least one of those solutions contains a non-diffusable ion
• The distribution of permeable charged ions will be influenced by both their valence and the distribution of uncharged ions, such that at equilibrium the products of the concentrations of paired ions on each side of the membrane will be equal:
  

• The two main contributors to the Gibbs-Donnan effect in the body are sodium and protein. This occurs because cell membranes:
  • Are impermeable to protein
    Intracellular protein concentration is high.
  • Effectively impermeable to sodium
    Due to the Na⁺-K⁺ ATP-ase pump.
• Changing Gibbs-Donnan equilibriums also change the tonicity on each side of the cell membrane, causing movement of water which then upsets the Gibbs-Donnan effect – therefore there is no stable state.
• The Gibbs-Donnan Effect is important for:
  • Maintenance of cell volume
    Na⁺ acts as an effective osmole, reducing cellular swelling.
  • Plasma oncotic pressure
    Increased plasma ion concentration increases oncotic pressure.
  • Resting Membrane Potential

JC 2019

Answer by JC