Gibbs-Donnan Equilibrium

History

Donnan equilibrium which is also called Gibbs-Donnan effect, Donnan’s effect, Donnan law or Gibbs-Donann equilibrium is named after an American physicist Josiah Willard Gibbs who proposed it in 1878 and Frederick George Donnan, a British chemist who, in 1911, first measured the changes brought about by adding an impermeant substance to one side of a divided solution at equilibrium.

Definition

The membrane potential at which the movement into the cell is equal to the movement outside of the cell is known as Donnan Equlibrium.

                                     Figure: Na⁺ movement across semi permeable membrane

According to the above figure, due to higher sodium ions concentration, sodium ions move across the membrane to the right side. After some time the reverse movement of sodium ions occur due to the increase in charge at the right side. Both movements then become equal leading to the Donnan Equilibrium.

The Donnan Equilibrium for sodium ion is approximately 58 mV. If for example the membrane potential is not equal to the Donnan Equlibrium potential then it is going to cause a Driving Force. Due to this driving force the ions will move to the direction to attain equilibrium.

Impermeant ions and Donnan Equilibrium

In the presence of impermeant ions, there is an unequal distribution of permeant ions on either side of a semi permeable membrane which is known as Donnan Equilibrium.

Due to permeant ions the distribution between both sides across the semi permeable membrane which changes the osmolarity between both sides. After attaining equilibrium, both sides become electrically neutral because at equilibrium become equal.

Figure: Back and forth movement of ions in Donnan Equilibrium

The concentration gradient and electrical gradient causes the movement of potassium and chloride ions across the semi permeable membrane to attain equilibrium and stability. When equilibrium is attained, both compartments become electrically neutral and movements of opposite charges become equal.

 The presence of non-diffusible ions on one side of the membrane affects the distribution of diffusible ions on both sides of a semi-permeable membrane.

Mathematical Equation

  The mathematical derivation is explained in many areas on the internet but the final and decision making equation as called Donnan membrane equation is as under;

       

“i” stands for inside while “o” stands for outside of the cell. Using this equation we can calculate the quantity of drugs to be used for better absorption of drugs in the body.

Consequences of Donnan Equilibrium

There are six consequences of the Donnan Equilibrium in which three are equalities and the rest three are inequalities. All of them are discussed below;

·         Concentration gradient for one ion is equal to the Electrical gradient of the same ion.

·         In Donnan Equilibrium, positive charge of one side is equal to the negative charge of the other.

·         The product of diffusible ions in impermeant compartment is equal to the product of ions in the non-impermeant compartment.

·         Osmotic pressure in the impermeant compartment is greater than the osmotic pressure In the non-impermeant compartment.

·         The sum of diffusible ions in impermeant compartment is greater than the sum of ions in the non-impermeant compartment.

·         Water shift from impermeant compartment to the non-impermeant compartment.

Donnan Equilibrium Vs Donnan Effect

Some physiological sources consider the Donnan effect and Donnan equilibrium as similar terms but there is a difference between them. Donnan effect can be harmful to the cell and cell has to perform strategies to overcome this effect while Donnan equilibrium can be very useful.

To explain this with an example lets imagine a unicellular organism in the ocean. According to Evolutionary biology life is evolved from unicellular cells in the ocean. The unicellular cell contain a membrane which was permeable to outside (ocean) and has Na⁺ and Cl^- ions. The cell than starts lying down the proteins and other macromolecules with the passage of time. These organic ions are large and cannot cross the membrane and they are negative charged molecules. These impermeant ions increase negativity and Cl^- ions will be pushed to outside along its electrical gradient but there will also be pull of chloride ions into the cell along its concentration gradient. Due to increased negativity in the cell, the electrical gradient for sodium ions increase and the sodium Na+ ions will move into the cell to balance the negative charge. At a certain level the electrical gradient (positive charge) for sodium will be balnced with its concentration gradient (amount of sodium ions). Due to these changes the total solute concentration in the cell is now greater than outside ocean which will cause water entry into the cell. Water will move towards the region with higher solute concentration. Water entry will try to dilute the solutes in the cell to possible extent which will again cause solute movement into the cell followed by water entry and will start a cycle which will result in the swelling of cell and if not prevented, lysis will occur and cell will burst. This is the possible outcome of the Donnan Effect.

The phenomenon of water entry into a compartment which has an impermeant ion is referred to as Donnan effect.

Countering Donnan Effect

If water entry can be prevented then an equilibrium state can be achieved which is referred to as Donnan Equilibrium. Both plants and animal cells adopt certain strategies to cope with water entry;

The plants strategy is very simple which is the presence of CellWall which is rigid and prevents more water entry into the cell by generating hydrostatic pressure and hence, will not allow more entry of water.

Animal cells do not have cell walls. Animal cells perform strategies to maintain an impermeant ion outside the cell, so that water entry due to impermeant ion can be balanced by water exit due to impermeant ion outside the cell. The most abundant impermeant is that of sodium ions which are pushed out of cells through sodium pumps (active transport) against the concentration gradient to maintain them as impermeant ion. In exchange of sodium, potassium are moved into the cell through potassium pumps in place of Na⁺ ions, hence, used sodium-potassium pumps in the activity. The accumulation of Na⁺ ions outside as impermeant ion helps in water exit from cell and prevent cell from swelling and lysis.

Applications of Donnan Equilibrium

The important applications of Donnan Equilibrium are;

• The principle and equation of Donnan effect can be used in drug administration to get higher degree absorption of drugs in the body.
• Donnan hydrolysis systems generally affect the internal environment for the weathering of rocks.
• Donnan equilibrium is used to cope with Donnan effect to prevent cell from swelling and bursting.