Part II. Molecular Dynamics Calculations

Potassium Ions

Ions in electrolyte solutions are not free but hydrated with the first shell relatively firmly bound, followed by a more loosely bound second shell.

For potassium ions, there are on average about 7 water molecules in the first hydration shell, lying at around 2.8 angstrom from the ion centre. Each of these waters stabilizes the ion by approximately 24 kT.

Thus, the apparent radius of a potassium ion is far too large to pass across the selectivity filter unless the water-ion geometry is re-arranged.

As the ion enters the selectivity filter, some of the tightly bound water molecules are stripped off. To prevent the insurmountable energy cost involved with this loss, the carbonyl oxygen atoms play the role of the water molecules by forming temporary bonds with the potassium ion.

The ion-water geometry can be deduced more rigorously by examining what is commonly known as the radial distribution function. Here, the probability of finding oxygen atoms is plotted against the distance from the centre of the potassium ion.

The peak in the radial distribution function due to water contributions, shown here in pink, is becoming smaller as water molecules become less accessible, while the peak corresponding to carbonyl oxygens, shown here in orange, is approaching and becoming larger as the ion enters the selectivity filter.

Through most of the selectivity filter, the potassium ion in surrounded by carbonyl oxygen atoms and water molecules such that the two peaks in the radial distribution function are roughly superimposed. This demonstrates how well the carbonyl groups are able to emulate water molecules.

The perfectly overlapping electron clouds of the potassium ion and carbonyl oxygens explains how this ion is able to traverse the narrow segment of the potassium channel.

Sodium Ions

Consider now a sodium ion attempting to traverse the selectivity filter. As it enters, waters are stripped away, as they are for potassium.

However, due to the smaller ion size, the carbonyl oxygen atoms are unable to replace water molecules as effectively. As a result the sodium ion is ejected from the filter. Observe the two peaks in the radial distribution function as we push a sodium ion through.

Carbonyl oxygens are unable to come close enough to the sodium ion to behave as water molecules. The oxygens are held away from the ion by the molecular springs created by interactions with external protein sidechains. Observe the poor fit of oxygen atoms around the ion.

When we compare to the potassium ion we can understand how this channel discriminates between these two ions. Clearly the protein cannot admit the passage of a sodium ion due to the energy barrier faced as a result of solvation losses.

The channel therefore relies on the differing sizes of the potassium and sodium ions to obtain selectivity. The dimensions of the selectivity filter have been perfectly optimised by nature to achieve this outcome.


Last modified: Fri Nov 20 13:47:28 "EST 1998