Figure A2.

The free energy vs. position curves for 12, 14, 16, and 18 oxygen molecules. There is a large barrier to getting to the center of the cavity with 12 or 14 molecules, but much less with 16 or 18 water molecules in the cavity. It is possible that the ion pushes out one or two water molecules as it moves up, or that the water content is affected by the presence of an ion at the gate, as suggested in Figure 6. The free energy calculated here does not include a second ion; the interaction of a second ion with the ion calculated here would raise the energy by a decreasing amount as the water moves up, for any number of water molecules. The calculation is corrected for the free energy of the appropriate number of water molecules, compared to bulk solution. The energy of the system was calculated, as in Figure A1, with the ion in each of the following positions: M (middle of cavity), M + 2, M + 4, M + 5, and M + 6, where the last is the lowest position of the selectivity filter:numbers of water molecules: circles, 12; squares, 14; triangles, 16; diamonds, 18.