Question

What explains the 10,000 to 1 selectivity of the potassium channel for K+ over Na+ considering that the atomic radii of these two ions differ by only 0.4 Angstroms.

Answer 1

K-channels and valinomycin molecules share the exquisite ability to select K⁺ over Na⁺ ions. Highly selective K-channels maintain a special local environment around their binding sites devoid of competing hydrogen bond donor groups, which enables spontaneous transfer of K⁺ from states of low coordinations in water into states of over-coordination by 8 carbonyl ligands. In such a phase-activated state, electrostatic interactions from these 8-fold binding sites, constrained to maintain high coordinations, result in K⁺/Na⁺selectivity with no need for a specific cavity size. Under such conditions, however, direct coordination from 5 or 6 carbonyl ligands does not result in selectivity. Yet, valinomycin molecules achieve selectivity by providing only 6 carbonyl ligands. Does valinomycin use additional coordinating ligands from the solvent or does it have special structural features not present in K-channels? Quantum chemical investigations undertaken here demonstrate that valinomycin selectivity is due to cavity size constraints that physically prevent it from collapsing onto the smaller Na⁺ ion. Valinomycin enforces these constraints using a combination of intra-molecular hydrogen bonds and other structural features, including its specific ring size and the spacing between its connected ligands. Results from these investigations also provide a consistent explanation for the experimental data available for valinomycin’s ion-complexation properties in solvents of varying polarity. Together, investigations on these two systems reveal how nature, despite being popular for its parsimony in recycling functional motifs, can use different combinations of phase, coordination number, cavity size, and rigidity (constraints) to achieve K⁺/Na⁺ selectivity.

Among bio-molecules that differentiate between these two ions, some selectively bind K⁺, while others bind Na⁺. What drives selectivity in favor of a particular ion? Equilibrium thermodynamics dictates that transfer of a particular ion A from one solvation phase m, say water, to another solvation phase p, say protein, is favorable when the ion’s solvation free energy in phase p is lower than its value in phase m,

ΔΔG_A(m → p) = ΔG_A(p)−ΔG_A(m) < 0,

where ΔG_A(m) is the free energy change for ion A in phase m relative to the gas phase.