= Solution
The hydrophobic core of a <lipid bilayer> makes transfer of a hydrated <ion> into bare lipid energetically costly. An <ion channel> supplies a water-accessible route across that barrier. Its narrow <selectivity filter> presents coordinating chemical groups that compensate for loss or rearrangement of the <ion>'s <hydration shell>. Selectivity depends on the <free energy>[free-energy] balance of hydration, coordination, <electrostatics> and geometry, rather than a sieve that passes all smaller <ions>.
A <potassium>-channel filter presents backbone carbonyl oxygens in a geometry favourable for <potassium>; smaller <sodium> does not automatically gain the same energetic compensation. <Sodium> and <calcium> channels use different filter architectures: charged side chains and their coordination environments favour particular <ions>, with <ion> occupancy and competing species also affecting permeation. In canonical vertebrate <voltage-gated sodium channels>, the DEKA selectivity ring illustrates chemical discrimination distinct from <potassium>-channel carbonyl coordination. The precise mechanism therefore depends on the channel family.
Rapid flux requires low \i[successive] <free energy>[free-energy] barriers, not permanent binding of the preferred <ion>. Several occupied sites, nearby water and <ion>–<ion> interactions can facilitate passage without requiring the <ion> to cross the lipid. For scale, a $100\,\mathrm{pS}$ open channel driven by $100\,\mathrm{mV}$ carries $10\,\mathrm{pA}$, approximately $6\times10^7$ monovalent <ions> per second. A nanometre-scale route with favourable coordination can support such rapid, thermally driven motion. An <ion channel> is not an <ATP>-driven pump: net flux follows the <electrochemical potential> difference,
$$
\boxed{\Delta\mu= k_BT\ln\frac{c_{\rm in}}{c_{\rm out}}+ze(V_{\rm in}-V_{\rm out}),}
$$
which vanishes at the species' <Nernst equilibrium potential>. <ATP>-consuming pumps maintain the <gradients> that make sustained channel currents possible.
Permeation selectivity and opening <probability> are separate properties. Voltage-sensor movement, <ligand> binding or mechanical tension can regulate access to the pore, while <ion-channel inactivation>[inactivation] can terminate conduction during a maintained stimulus. <patch clamp>[Patch-clamp] unitary currents establish discrete conducting states; reversal potentials under changed ionic compositions quantify selectivity. Structure determination locates the filter and gates, and <mutations> or specific blockers test their functional roles. Agreement between these measurements is stronger evidence than structure or current shape alone.
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