Monte Carlo simulations of equilibrium selectivity of Na channels with a DEKA locus are performed over a range of radius R and protein dielectric coefficient εp. Selectivity arises from the balance of electrostatic forces and steric repulsion by excluded volume of ions and side chains of the channel protein in the highly concentrated and charged (∼30 M) selectivity filter resembling an ionic liquid. Ions and structural side chains are described as mobile charged hard spheres that assume positions of minimal free energy. Water is a dielectric continuum. Size selectivity (ratio of Na + occupancy to K+ occupancy) and charge selectivity (Na+ to Ca2+) are computed in concentrations as low as 10-5 MCa2+. In general, small R reduces ion occupancy and favors Na+ over K+ because of steric repulsion. Small εp increases occupancy and favors Na+ over Ca 2+ because protein polarization amplifies the pore's net charge. Size selectivity depends on R and is independent of εp; charge selectivity depends on both R and εp. Thus, small R and εp make an efficient Na channel that excludes K+ and Ca2+ while maximizing Na+ occupancy. Selectivity properties depend on interactions that cannot be described by qualitative or verbal models or by quantitative models with a fixed free energy landscape.
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