Donnan Membrane Equilibrium
When two solutions are separated by a membrane permeable to both water and small ions, but one of the compartments contains non-diffusible ions like proteins, the distribution of permeable ions reaches an equilibrium known as the Donnan Equilibrium. This equilibrium state is governed by the principles of electroneutrality and the conservation of mass.
In the figure, the left compartment contains the salt NaR, which dissociates into the diffusible ion Na⁺ and the non-diffusible ion R⁻. The right compartment contains NaCl, which dissociates into the diffusible ions Na⁺ and Cl⁻.
At equilibrium, the key principle of the Donnan effect states that the product of the concentrations of the diffusible electrolytes in both compartments will be equal. This can be expressed as:
[Na⁺]L × [Cl⁻]L = [Na⁺]R × [Cl⁻]R
Using the hypothetical values from the figure, the product of the ion concentrations in the left compartment (9 × 4 = 36) equals the product in the right compartment (6 × 6 = 36), thus satisfying the Donnan equation.
Additionally, two other conditions must be met at equilibrium:
Electroneutrality: Each compartment must remain electrically neutral. The total positive charge must equal the total negative charge within each compartment.
In the left compartment: [Na⁺]L = [R⁻]L +[Cl⁻]L
Substituting the values: 9 = 5 + 4
In the right compartment: [Na⁺]R = [Cl⁻]R
Substituting the values: 6 = 6
Conservation of Mass: The total number of each type of diffusible ion remains constant throughout the process.
Initial total Na⁺: 5 (from NaR) + 10 (from NaCl) = 15
Final total Na⁺: 9 (left) + 6 (right) = 15
Initial total Cl⁻: 10 Final total Cl⁻: 4 (left) + 6 (right) = 10
Clinical and Biological Applications
The Donnan effect is crucial for understanding various physiological processes:
Osmotic Pressure: Plasma proteins, which are non-diffusible anions, cause a net osmotic gradient across capillary walls. This results in the total concentration of solutes in plasma being higher than in the interstitial fluid, influencing fluid movement.
pH and Ion Distribution: The presence of negatively charged proteins inside cells (e.g., hemoglobin in red blood cells) causes an unequal distribution of ions, including H⁺. This leads to a slightly lower pH inside the cell compared to the surrounding plasma, as more H⁺ ions are drawn into the cell to balance the negative protein charges.
Chloride Shift: The movement of chloride ions into or out of red blood cells to maintain electroneutrality during carbon dioxide transport is a classic example of the Donnan effect.
Ion Regulation: The principles of Donnan equilibrium are also relevant to the distribution of ions like sodium across biological membranes and in different body fluid compartments.
Test Your Knowledge
1. Which of the following ions is non-diffusible and causes the Donnan effect in biological membranes?
a) Na⁺
b) Cl⁻
c) Proteins or large anions (R⁻)
d) K⁺
View Answer
c) Proteins or large anions (R⁻)
2. According to the Donnan equilibrium, which condition must be satisfied at equilibrium across a semipermeable membrane?
a) The sum of positive charges equals sum of negative charges in the entire system.
b) The concentration of all ions is equal on both sides.
c) The product of concentrations of diffusible cations and anions is equal on both sides.
d) The concentration of non-diffusible ions is zero on both sides.
View Answer
c) The product of concentrations of diffusible cations and anions is equal on both sides.
3. In the Donnan equilibrium example, if R⁻ is trapped on the left side, what happens to the concentration of Na⁺ on that side at equilibrium?
a) It decreases compared to the initial concentration.
b) It remains unchanged.
c) It increases to balance the negative charge of R⁻.
d) It moves out completely to the other side.
View Answer
c) It increases to balance the negative charge of R⁻.
4. Why does the Donnan equilibrium lead to an osmotic pressure difference across the membrane?
a) Because water moves towards the compartment with lower ion concentration.
b) Because non-diffusible ions create unequal ion distributions that cause water to move.
c) Because ions pass freely across the membrane.
d) Because both compartments have the same concentration of impermeant ions.
View Answer
b) Because non-diffusible ions create unequal ion distributions that cause water to move.
5. What is the main physiological significance of the Donnan effect in capillaries?
a) It causes the capillary walls to become impermeable.
b) It helps regulate osmotic pressure and fluid balance across capillary membranes.
c) It prevents protein molecules from entering the bloodstream.
d) It increases the rate of diffusion of ions across membranes.
View Answer
b) It helps regulate osmotic pressure and fluid balance across capillary membranes.