A model framework for ion channels with selectivity filters based on continuum non-equilibrium thermodynamics

Abstract

A mathematical model framework to describe ion transport in nanopores is presented. The model is based on non-equilibrium thermodynamics and considers finite size effects, solvation phenomena as well as the electrical charges of membrane surfaces and channel proteins. Par- ticular emphasis is placed on the consistent modelling of the selectivity filter in the pore. It is treated as an embedded domain in which the constituents can change their chemical properties. The diffusion process through the filter is governed by an independent diffusion coefficient and at the interfaces, de- and resolvation reactions are introduced as Neumann interface conditions. The evolution of the molar densities is described by drift-diffusion equations, where the fluxes depend on the gradient of the chemical potentials and the electric force. The chemical potentials depend on the molar fractions and on the pressure in the electrolyte and accounts for solvation effects. The framework allows the calculation of current-voltage relations for a variety of chan- nel properties and ion concentrations. We compare our model framework to experimental results for calcium-selective ion channels and show the general validity of our approach. Our parameter studies show that calcium and sodium currents are proportional to the surface charge in the se- lectivity filter and to the diffusion coefficients of the ions. Moreover, they show that the negative charges inside the pore have a decisive influence on the selectivity of divalent over monovalent ions.