Energetics of double-ion occupancy in the gramicidin a channel
To understand the energetics of double-ion occupancy in gramicidin A (gA) channels, the 2D potential of mean force (PMF) is calculated for two ions at different positions along the channel axis. The cross sections of this 2D PMF are compared with available one-ion PMFs to highlight the effect of one ion on the permeation dynamics of the other. It is found that, if the first ion stays on one side in the channel, the second ion has to pass over an additional barrier to move into the outer binding site. At the same time, both outer and inner binding sites for the second ion become shallower than those in the one-ion PMF. The calculated ion-ion repulsion for a doubly occupied channel is about 2 kcal/mol, in good agreement with previous experimental estimates. The number of water molecules inside the channel and their dipole moment are calculated to interpret the energetics of double-ion occupancy. As the first ion moves into the outer binding site and then further into the channel, the oxygen atoms of the single-file water column in the channel are oriented to point toward the ion. The observed dipole moment distribution of a singly occupied channel has only one sharp peak, and the water alignment is essentially perfect once the ion is in the inner binding site. For this reason, there is an energy penalty to accommodate a second ion at the opposite end of the channel.