Self-organized models of selectivity in calcium channels

The role of flexibility in the selectivity of calcium channels is studied using a simple model with two parameters that accounts for the selectivity of calcium (and sodium) channels in many ionic solutions of different compositions and concentrations using two parameters with unchanging values. We compare the distribution of side chains (oxygens) and cations (Na⁺ and Ca²⁺) and integrated quantities. We compare the occupancies of cations Ca²⁺/Na⁺ and linearized conductance of Na⁺. The distributions show a strong dependence on the locations of fixed side chains and the flexibility of the side chains. Holding the side chains fixed at certain predetermined locations in the selectivity filter distorts the distribution of Ca²⁺ and Na⁺ in the selectivity filter. However, integrated quantities—occupancy and normalized conductance—are much less sensitive. Our results show that some flexibility of side chains is necessary to avoid obstruction of the ionic pathway by oxygen ions in 'unfortunate' fixed positions. When oxygen ions are mobile, they adjust 'automatically' and move 'out of the way', so they can accommodate the permeable cations in the selectivity filter. Structure is the computed consequence of the forces in this model. The structures are self-organized, at their free energy minimum. The relationship of ions and side chains varies with an ionic solution. Monte Carlo simulations are particularly well suited to compute induced-fit, self-organized structures because the simulations yield an ensemble of structures near their free energy minimum. The exact location and mobility of oxygen ions has little effect on the selectivity behavior of calcium channels. Seemingly, nature has chosen a robust mechanism to control selectivity in calcium channels: the first-order determinant of selectivity is the density of charge in the selectivity filter. The density is determined by filter volume along with the charge and excluded volume of structural ions confined within it. Flexibility seems a second-order determinant. These results justify our original assumption that the important factor in Ca²⁺ versus Na⁺ selectivity is the density of oxygen ions in the selectivity filter along with (charge) polarization (i.e. dielectric properties). The assumption of maximum mobility of oxygens seems to be an excellent approximate working hypothesis in the absence of exact structural information. These conclusions, of course, apply to what we study here. Flexibility and fine structural details may have an important role in other properties of calcium channels that are not studied in this paper. They surely have important roles in other channels, enzymes, and proteins.