Ion Fluxes to Channel Arrays in Monolayers. Computing the Variable Permeability from Currents

Chronoamperometric currents arising from Tl + reduction at a Hg electrode covered with a phospholipid monolayer containing gramicidin monomer ion channels can be quantitatively understood as an interfacial permeation process with a variable local permeability. Any interfacial behavior (described by the permeability) can be combined with the properties of semi-infinite diffusion to yield a simple expression that allows: (a) the computation of the current corresponding to any given variation of the permeability with time and (b) the recovery of the permeability through a semi-integration of the currents. As a result, the diffusion process is accounted for, and one can focus on the obtained permeability, whose variation can, in a further step, be ascribed to phenomena such as a decaying number of active channels, a change in their translocation efficiency, etc. Analysis of the experimental data for the Tl + permeation through gramicidin channels with the derived expression confirms the validity (as a good first approximation within the range of concentrations explored) of considering a simple first-order relaxation process for the gramicidin channel conversion between the conducting and the nonconducting forms coupled with first-order heterogeneous kinetics for the channel crossing.