How resting membrane potentials are established

Membrane potential

Membrane potential refers to the net difference in charge on each side of a selectively permeable membrane  due to an imbalance of cations and anions. This difference has the potential to become electrical energy (current) which is produced when ions move down an electrochemical gradient. 

In the body, a membrane potential exists between the intracellular fluid and the extracellular fluid (ie almost all cells and the extracellular fluid surrounding it). Membrane potential is measured in milivolts (mV) in the body. It is always measured with the inside (ICF) relative to the outside (ECF). 

Equilibrium potentials 

Membrane potentials are formed when cations are split from their anions across the permeable membrane causing there to be more positive ions on one side compared to the other. In the body, the 2 main ions which contribute to membrane potential are potassium (K+) and sodium (Na+). imbalances of each ion across the membrane contributes to the membrane potential. 

If we looked at each ion seperately, given the concentrations of the ion found on each side of the membrane, each would form an electrochemical gradient. 

For example, given that there is a higher concentration of sodium in the extracellular fluid, that there is initially no net imbalances in charge (no potential present) and that there is free permeablity to sodium, sodium would move down the concentration gradient into the intracellular space. 

The movement of sodium into the cell would cause a net increase in positive ions in the cell, producing an electrical gradient. This would increase as the concentration of sodium in the cell increases, and thus the sodium outside the cell and the concentration gradient decreases. The electrical gradient causes the ions to exit the cell, and at the point of equilibrium, the amount of ions entering the cell due to the concentration gradient and the ions exiting the cells due to the electrical gradient will balance out. 

This hypothetical point is known as the equilibrium potential. Each ion has its own equilibrium potential, which may be calculated with the nernst equation given the relative concentrations of the ion at equilibrium. 

E represents the equilibrium potential in mV, [ion]o and [ion] i the concentration of ion on the outside and the inside respectively and z the charge of the ion (which for Na+ and K+ is 1). 

The equilibrium potential for sodium is about +60 mV, and the one for potassium is about -90mV.

In the body, as both ions form opposite electrical gradients which cancel each other out, the actual membrane potential is dependent on the permeability of the membrane to each ion. The membrane potential of an actual cell can therefore be calculated from the concentrations of each ion inside and outside the cell, and the relative permeability via the goldman-hodgkin-katz equation. 

Establishing a resting membrane potential

In the body, the sodium-potassium pump actively pumps sodium ions out of the cell and potassium ions into the cell. This produces a concentration gradient such that potassium tends to flow out of the cell, and sodium into the cell. The sodium potassium pump also creates a slight electrical gradient as it pumps out 3 sodium ions for every 2 potassium ions pumped in. There would therefore be less positive ions overall in the cell. However, the difference in ions produced by the pump is so small it only produces 2-3mV of electrical potential. 

 The plasma membrane of cells also have a number of potassium and sodium ion leak channels. This allows the ions to leak out back to the other side. The permeability of the membrane to potassium ions is about 20 times greater than that of sodium, therefore, more potassium ions flow back out than sodium ions flowing in. This produces a net increase in positive ions on the outside producing a negative membrane potential . The membrane potential is driven towards the equilibrium potential of potassium as it's flow is dominant. However, it never reaches the equilibrium potential as sodium flows in the opposite direction cancelling out the charge of the excess potassium. The resting membrane potential is therefore at around -70mV. 

sodium and potassium would continue to flow out if there were no sodium potassium pumps. However, these pumps pump continuously maintaining the concentration gradient which allows the electrical gradient to be formed. 

Anions in the cell are mainly made up of large protein molecules which cannot exit the cell. Chloride ions flow down the electrical gradient produced by excess potassium ions to the outside of the cell. The membrane is freely permeable to it and it therefore distributes itself in the presence of a membrane potential. 

The net increase of positive ions on the outside compared to the inside also attracts the negative ions to the inner surface of the membrane, which in turn attracts the positive ions towards the membrane on the outside.