# Structural Biochemistry/Enzyme Catalytic Mechanism/Integral Membrane Protein/Potassium Channel
## Potassium Channels

Potassium channels are numerous and are found in almost all sorts of organisms. They play an important role in regulating the influx of K$^+$ ions, which creates an electrical gradient that the cell needs to create action potentials. Note that when we talk of "influx" of ion, we mean the net flux because the ions can flow in both directions.
The channel, which is an integral protein, is a tetramer, able to bind four ligands, although not simultaneously. It is conical in shape, and the wide "opening" begins inside of the cell, and toward the outside of the cell where the selectivity filter is located, the channel narrows down. There is water lining only the outside cavity and around the "opening" inside the channel.

### Mechanism

Inside the cell, there are K$^+$ ions that enter the wide opening of the pump. When they come in, they usually come in pairs, with a water molecule sandwiched in-between them (#1 in Mechanism figure). In order to move through the channel, they must pass through the selectivity filter, which houses the four binding sites (able to hold on to two K$^+$ ions). The binding site is lined with TVGYG amino acid sequence, which has carbonyl groups that contain oxygen used to dehydrate the ion. Dehydration of the K$^+$ ions is necessary to establish an efficient interaction with the binding sites. The selectivity filter will undergo conformation and bind the K$^+$ tightly, stabilizing the binding sites (#2). This allows the K$^+$ ion to move on ahead to the next binding site, which is in a similar free energy state as the one before it (#3). However, once it reaches near the exit, complete expulsion does not just happen because it is energetically unfavorable (still #3). It is only when the second K$^+$ ion enters the first binding site that the electrostatic forces between the two ions will expel the first K$^+$ (#4-5). This occurs very rapidly.

### Selectivity

Both outside and inside the cell, K$^+$ and Na$^+$ are present. Therefore theoretically, the channel can be permeable to either one. However, the selectivity of the potassium channel arises from the difference in the ions' free energy cost of dehydration. It costs more to dehydrate a Na$^+$ ion (72 kcal/mol) than to dehydrate K$^+$ (55 kcal/mol).
Furthermore, the difference in radius of the two ions affects the binding affinity of the binding site to the ions. Na$^+$, is a smaller ion than K$^+$. Because of its smaller radius of about 0.95 Angstrom, the bond it creates with the Oxygen (1.4 Angstrom) will result in 2.35 Angstrom bond--too close for optimal interaction. In contrast K$^+$ has a radius of 1.33 Angstrom and creates a bond length of 2.73 Angstrom with oxygen. This is a good length and can allow for a better interaction. Therefore Na$^+$ ions cannot dehydrate and is therefore impermeable to the channel.

### Cooperativity

The four binding sites made up of TVGYG sequence in the selectivity filter operate in negative cooperativity. This gives the channel high selectivity on the ions it can pass through, and allows for a very rapid diffusion via electrostatic repulsion.

## References

Berg, J., Tymoczko, J., Stryer, L. (2002). Biochemistry (5th ed.) New York: W. H. Freeman and Company.
Grigoryan, G., Moore, D., DeGrado, W. (2011, May 3). Transmembrane Communication: General Principles and Lessons from the Structure and Function of the M2 Proton Channel, K$^+$ Channels, and Integrin Receptors. Retrieved from Annual Review of Biochemistry.