Charge Inversion and Calcium Gating in Mixtures of Ions in Nanopores

Calcium ions play important roles in many physiological processes, yet their concentration is much lower than the concentrations of potassium and sodium ions. The selectivity of calcium channels is often probed in mixtures of calcium and a monovalent salt, e.g., KCl or NaCl, prepared such that the concentration of cations is kept constant with the mole fraction of calcium varying from 0 and 1. In biological channels, even sub-mM concentration of calcium can modulate the channels' transport characteristics; this effect is often explained via the existence of high affinity Ca²⁺ binding sites on the channel walls. Inspired by properties of biological calcium-selective channels, we prepared a set of nanopores with tunable opening diameters that exhibited a similar response to the presence of calcium ions as biochannels. Nanopores in 15 nm thick silicon nitride films were drilled using focused ion beam and e-beam in a transmission electron microscope and subsequently rendered negatively charged through silanization. We found that nanopores with diameters smaller than 20 nm were blocked by calcium ions such that the ion currents in mixtures of KCl and CaCl₂ and in CaCl₂ were even ten times smaller than the ion currents in KCl solution. The ion current blockage was explained by the effect of local charge inversion where accumulated calcium ions switch the effective surface charge from negative to positive. The modulation of surface charge with calcium leads to concentration and voltage dependent local charge density and ion current. The combined experimental and modeling results provide a link between calcium ion-induced changes in surface charge properties and resulting ionic transport.