# Part III. Electrostatic Calculations

 When an ion in water approaches a low dielectric boundary, such as a protein wall, it experiences electrostatic repulsion due to induced charges at the boundary. Thus, an ion entering the channel will experience a repulsive force and faces an energy barrier. As a potassium ion move along the central axis of the channel, it encounters a huge, insurmountable energy barrier. The channel is impermeable to ions. It is the dipoles on the protein wall that renders the channel permeable to potassium ions. First, lining the wall of the selectivity filter are 16 carbonyl carbon atoms, each of which carries a partial negative charge. These dipoles transforms an energy barrier in the selectivity filter into an energy well. Secondly, there are four helix dipoles, with their negative poles pointing the inner, oval chamber. These dipoles transforms an energy barrier in the wide section of the channel into an energy well. Finally, there is a ring of dipoles at each end of the channel. These 3 sets of dipoles - helix dipoles, carbonyl oxygens and mouth dipoles - transform the insurmountable energy barrier into an attractive energy well of about 30 kT in depth. A potassium ion outside the channel is attracted to this deep well and quickly occupies the region where the energy is the minimum. The presence of the first ion in the well drastically alters the energy profile seen by a second ion. To this ion, another energy well appears some distance from the first ion, and this well is now occupied by the second ion. The presence of the second ion in the channel shifts the position of the energy minimum for the first ion. Through successive adjustments, the two ions come to occupy the positions at which the axial component of the force experienced by the ions is zero. In the energy profile seen by a third ion, there is a shallow energy well near the entrance of the channel. The ion in this well needs to gain a sufficient kinetic energy to climb out of it. Once the third ion climbs out of the well, the repulsive Coulomb force exerted by it disrupts the stable equilibrium established by the two ions in the selectivity filter.