Calcium binding and ionic conduction in single conical nanopores with polyacid chains: model and experiments.

Calcium binding to fixed charge groups confined over nanoscale regions is relevant to ion equilibrium and transport in the ionic channels of the cell membranes and artificial nanopores. We present an experimental and theoretical description of the dissociation equilibrium and transport in a single conical nanopore functionalized with pH-sensitive carboxylic acid groups and phosphonic acid chains. Different phenomena are simultaneously present in this basic problem of physical and biophysical chemistry: (i) the divalent nature of the phosphonic acid groups fixed to the pore walls and the influence of the pH and calcium on the reversible dissociation equilibrium of these groups; (ii) the asymmetry of the fixed charge density; and (iii) the effects of the applied potential difference and calcium concentration on the observed ionic currents. The significant difference between the carboxylate and phosphonate groups with respect to the calcium binding is clearly observed in the corresponding current-voltage (I-V) curves and can be rationalized by using a simple molecular model based on the grand partition function formalism of statistical thermodynamics. The I-V curves of the asymmetric nanopore can be described by the Poisson and Nernst-Planck equations. The results should be of interest for the basic understanding of divalent ion binding and transport in biological ion channels, desalination membranes, and controlled drug release devices.