Modeling Ion Transport and Selectivity via a Lennard-Jones Modified Poisson-Nernst-Planck Approach

Ion transport across membranes plays a vital role in both the central nervous system and the maintenance of normal human physiological activities. Classical Poisson-Nernst-Planck (PNP) model fails to accurately capture the non-Coulombic interactions, such as short-range repulsion and long-range attraction, and thus cannot discriminate between ion species like Na+ and K+ based on their inherent properties. Here, we proposed a three-dimensional computable PNP model modified with the Lennard-Jones (LJ) potential, which incorporates the influence of different LJ parameters on ion concentration distributions. The estimated Na+/K+ selectivity ratio of the sodium ion channel protein using this model agreed well with molecular dynamics simulations. Furthermore, the effects of various nanochannel and ionic parameters on transmembrane transport are systematically elucidated. Analysis using an axisymmetric model reveals that the LJ effect, set by its energy and distance parameters (ϵ,δ), dictates the sign (enhancement or suppression) of its influence on ion current, while the channel geometry determines its amplitude. We present a phase diagram that directly correlates these (ϵ,δ) parameters with the resultant current modulation. This structure-property relationship may provide valuable insights for designing selective nanopores.