Solution (source code)

= Solution

An <ion channel> is a selective permeation pathway, not simply an aqueous hole of fixed diameter. A hydrated <ion> entering a narrow <selectivity filter> must lose or reorganize some hydration water. The energetic cost can be offset by interactions with charged or polar groups in the pore. Different ionic radii, valences, hydration <free energies>, and coordination geometries therefore produce different permeation barriers and binding affinities.

A classical <potassium> <selectivity filter> presents oxygen ligands that stabilize relatively dehydrated <potassium> in configurations resembling its aqueous coordination. Smaller <sodium> does not automatically pass more easily: its hydration is stronger and the filter need not provide a compensating configuration at equally low <free energy>. Filter flexibility and multi-ion occupancy matter, so the explanation is an energetic balance, not the assertion that a rigid hole simply blocks every larger or smaller sphere. Ion-ion interactions and coupled displacement can permit rapid conduction while maintaining selectivity.<The structure of the potassium channel: molecular basis of K+ conduction and selectivity by Declan A. Doyle and others>[Science 280 (1998), pp. 69–77: structural basis of potassium coordination and selective permeation]{ref}

Other <ion channels> use different arrangements. Fixed negative groups can strongly favor divalent <calcium> over monovalent <ions>; occupancy and competition then influence both selectivity and throughput. Selectivity is distinct from activation or <ion-channel inactivation>, which control access or availability. Selective passive flux follows an <electrochemical potential> gradient; it does not by itself pump <ions> uphill. Selectivity allows cells to establish particular <membrane potentials>, generate <action potentials>, regulate <calcium> signals, and control solute balance without dissipating every ionic gradient whenever one pathway opens.