  We use Brownian dynamics simulations to study the permeation properties of a
generic electrostatic model of a biological ion channel as a function of the
fixed charge $Q_f$ at its selectivity filter. We reconcile the
recently-discovered discrete calcium conduction bands M0 ($Q_f$=1e), M1 (3e),
M2 (5e) with the set of sodium conduction bands L0 (0.5-0.7e), L1 (1.5-2e)
thereby obtaining a completed pattern of conduction and selectivity bands v
$Q_f$ for the sodium-calcium channels family. An increase of $Q_f$ leads to an
increase of calcium selectivity: L0 (sodium selective, non-blocking channel) ->
M0 (non-selective channel) -> L1 (sodium selective channel with divalent block)
-> M1 (calcium selective channel exhibiting the anomalous mole fraction
effect). We create a consistent identification scheme where the L0 band is
identified with the eukaryotic (DEKA) sodium channel, and L1/L2 (speculatively)
with the bacterial NaChBac channel. The scheme created is able to account for
the experimentally observed mutation-induced transformations between
non-selective channels, sodium-selective channels, and calcium-selective
channels, which we interpret as transitions between different rows of the
identification table. By considering the potential energy changes during
permeation, we show explicitly that the multi-ion conduction bands of calcium
and sodium channels arise as the result of resonant barrier-less conduction.
Our results confirm the crucial influence of electrostatic interactions on
conduction and on the Ca/Na valence selectivity of calcium and sodium ion
channels. The model and results could be also applicable to biomimetic
nanopores with charged walls.
