A Model Framework for Ion Channels with Selectivity Filters Based on Non-Equilibrium Thermodynamics.

A thermodynamically consistent model framework to describe ion transport in nanopores is presented. The continuum model unifies electro-diffusion and selective ion transport and extends the classical Poisson-Nernst-Planck (PNP) system for an idealized incompressible mixture by including finite ion size and solvation effects. Special emphasis is placed on the consistent modeling of the selectivity filter within the pore. It is treated as an embedded domain in which the constituents can change their chemical properties and mobility. Using this framework, we achieve good agreement with an experimentally observed current-voltage (IV) characteristic for an L-type selective calcium ion channel for a range of ion concentrations. In particular, we show that the model captures the experimentally observed anomalous mole fraction effect (AMFE). As a result, we find that calcium and sodium currents depend on the surface charge in the selectivity filter, the mobility of ions and the available space in the channel. Our results show that negative charges within the pore have a decisive influence on the selectivity of divalent over monovalent ions, supporting the view that AMFE can emerge from competition and binding effects in a multi-ion environment. Furthermore, the flexibility of the model allows its application in a wide range of channel types and environmental conditions, including both biological ion channels and synthetic nanopores, such as engineered membrane systems with selective ion transport.