Abstract
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
ɛ
p
. 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 Ca
2+
) are computed in concentrations as low as 10
−5
M Ca
2+
. In general, small
R
reduces ion occupancy and favors Na
+
over K
+
because of steric repulsion. Small
ɛ
p
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
ɛ
p
; charge selectivity depends on both
R
and
ɛ
p
. Thus, small
R
and
ɛ
p
make an efficient Na channel that excludes K
+
and Ca
2+
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.
