Current transients associated with the ion adsorption on charged membranes: a stochastic model

In this work, we derive an analytic expression for the current transients associated with the absorption of ions by gated pores on biological membranes submitted to voltage-clamped conditions. We focus on the processes that occur on the interface between the membrane and the extra cellular medium, from which the ions are transported toward the membrane. The model accounts for the charge transfer between ion and membrane, responsible for the catalytic reaction that fixes the ion on the electrified surface before its passage through the channels. In order to derive an expression for the current we develop a stochastic model based on a two-stage process, which considers the interplay among diffusion-convection-reaction to define the ions overall kinetics. The solution is explored by changing the relative magnitude of these contributions, so that different current transient behaviors can be identified, in agreement with experimental observation. Comparing theoretical and experimental data, we show that the current is a function of the control parameters, i.e., potential, temperature, ion concentration and the electrical conductivity of the medium.