Question

the manner in which potassium ions are transported across the membrane by the potassium channel.

a. Provide an explanation as to why potassium cannot cross the plasma membrane without the aid of a potassium channel.

b. Provide an protein structure based explanation as to how the potassium channel is able to transport potassium ions through the membrane at a high rate while at the same time preventing the transport of sodium ions which have a smaller ionic radium than potassium ions.

Answer 1

Ions can't cross this lipid bilayer on their own: they must be carried across by special proteins. Potassium channels are designed to allow the flow of potassium ions across the membrane, but to block the flow of other ions--in particular, sodium ions. These channels are typically composed of two parts: the filter, which selects and allows potassium but not sodium to pass, and the gate, which opens and closes the channel based on environmental signals.

Channel proteins are transport proteins that move ions across the cell membrane with a chemical gradient or electrical potential. This means that the ions are already chemically or electrically attracted to the place they're going -- the channel protein simply opens a gate so they can get there. Potassium channels are the most common and are almost always open because they're part of the sodium potassium pump -- the mechanism that keeps cell membranes intact. Channels for other elements open in response to specific biochemical signals.

Potassium channels allow potassium ions to pass, but block smaller sodium ions. Potassium channels allow K+ ions to easily diffuse through their pores while effectively preventing smaller Na+ ions from permeation. The ability to discriminate between these two similar and abundant ions is vital for these proteins to control electrical and chemical activity in all organisms. Selectivity is thought to arise because smaller ions such as Na+ do not bind to these K+ sites in a thermodynamically favorable way.

Potassium channels are 100-fold as permeable to K+ as to Na+. The narrow diameter (3 Å) of the selectivity filter of the potassium channel enables the filter to reject ions having a radius larger than 1.5 Å. However, a bare Na+ is small enough to pass through the pore. Indeed, the ionic radius of Na+ is substantially smaller than that of K+. We need to consider the free-energy cost of dehydrating the Na+ and K+ ions, given that they cannot pass through this part of the channel bearing a retinue of water molecules. The key point is that the free-energy costs of dehydrating these ions are considerable [Na+, 72 kcal mol-1 and K+, 55 kcal mol-1]. The channel pays the cost of dehydrating K+ by providing compensating interactions with the carbonyl oxygen atoms lining the selectivity filter. However, these oxygen atoms are positioned such that they do not interact very favorably with Na+, because it is too small. The higher cost of dehydrating Na+ would be unrecovered, and so Na+ would be rejected.