= Solution
An <ion channel> supplies a water-accessible pathway through the otherwise strongly insulating, <hydrophobic> <lipid bilayer>. Moving a hydrated <ion> directly into that low-<permittivity> region is energetically expensive. The channel's polar pore and coordinating groups reduce the barrier while retaining selectivity. Transport is passive: the <electrochemical potential> difference drives net movement, and the channel does not itself pump an <ion> uphill. For an ideal species of charge number $z$,
$$
\Delta\widetilde\mu_{\rm out\to in}=RT\ln\frac{c_{\rm in}}{c_{\rm out}}+zFV.
$$
The net <electric current> of a pathway permeable only to that species reverses at its <Nernst equilibrium potential>. An open channel can carry zero net <electric current> at that voltage even while individual <ions> cross both ways.
The <selectivity filter> balances loss of the hydration shell against favorable coordination within the pore. In a typical <potassium> channel, backbone carbonyl oxygen atoms create appropriately arranged binding sites for a substantially dehydrated <potassium> <ion>. The smaller <sodium> <ion> is not automatically preferred simply because it fits geometrically: its hydration is stronger and the filter does not compensate its dehydration in the same way. Geometry, flexibility, coordination chemistry and ion occupancy all matter. <Sodium>-selective and <calcium>-selective channels use different arrangements, often involving charged side chains; a single rigid-sieve explanation is inadequate.
Rapid passage coexists with transient binding because several nearby sites have comparable <free energies> and relatively low barriers between them. Multiple <ions> occupying a pore influence one another through <electrostatic interactions>, enabling correlated exchange and displacement rather than irreversible trapping at one deep site. High throughput therefore requires favorable passage kinetics as well as strong discrimination against unwanted species. A more tightly bound species can even block a pathway instead of being its fastest permeant.
Gating and selectivity are distinct. A <voltage-sensing domain> couples <membrane potential> to activation-gate conformation; <ligand-gated ion channels> couple binding to opening; <mechanosensitive ion channels> couple membrane stress to opening. <Ion-channel inactivation> introduces additional unavailable states. None of these mechanisms alone identifies which <ion> the open pore prefers.
For $N$ similar independent channels, a local Ohmic approximation with outward-positive <electric current> is
$$
\boxed{I=Np_O\gamma(V-E_{\rm rev}).}
$$
Here open <probability> controls availability, single-channel <electrical conductance> controls current per open pore, and $V-E_{\rm rev}$ is the electrical driving factor in this approximation. Nonlinear current-voltage relations and mixed-ion permeation may require a fuller model. <Single-channel recording> resolves discrete openings; reversal shifts when ionic <concentrations> change test selectivity; gating <electric currents> test sensor motion; structural evidence identifies the pore and its coordinating groups. Together these distinguish rapid selective permeation from the separate process of opening the gate.
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