A dynamic mass-transport method is proposed for approximately solving the Poisson–Nernst–Planck (PNP) equations. The semi-discrete scheme based on JKO type variational formulation naturally enforces solution positivity and energy law as continuous PNP system. fully discrete further formulated a constrained minimization problem, shown to be solvable, satisfy all three properties (mass conservati...

This work is aimed to give an electrochemical insight into the ionic transport phenomena in cellular environment of organized brain tissue. The Nernst–Planck–Poisson (NPP) model presented, and its applications description electrodiffusion relevant nanoscale neurophysiology are reviewed. These include: signal propagation neurons, liquid junction potential extracellular space, ion channels, elect...

Continuum theories of electrolytes are widely used to describe physical processes in various biological systems, even when the system dimensions are comparable to the Debye length. We test the validity of the mean field approximation in Poisson–Boltzmann and Poisson–Nernst–Planck theories by contrasting their predictions with those of Brownian dynamics simulations in cylindrical pores of varyin...

We propose an anomalous diffusion approach to analyze the electrical impedance response of electrolytic cells using time-fractional derivatives. establish, in general terms, conservation laws connected a modified displacement current entering fractional formulation Poisson–Nernst–Planck (PNP) model. In this new formalism, we obtain analytical expressions for case blocking electrodes and presenc...

A composite continuum theory for calculating ion current through a protein channel of known structure is proposed, which incorporates information about the channel dynamics. The approach is utilized to predict current through the Gramicidin A ion channel, a narrow pore in which the applicability of conventional continuum theories is questionable. The proposed approach utilizes a modified versio...

We study the charging dynamics of a long electrolyte-filled slit pore in response to suddenly applied potential. In particular, we analytically solve Poisson–Nernst–Planck (PNP) equations for which λD≪H≪L, with λD Debye length and H L pore’s width length. For small potentials, find time-dependent potential drop between surface its center be complete agreement prediction celebrated transmission ...

The recent Perspectives on Ion Permeation have brought the debate about the applicability of the Poisson-Nernst-Planck (PNP) theory in ion channels to a sharp focus. Despite the differences in opinion, all sides of the debate agree that the mean field approximation in PNP theory needs to be checked by comparison with a more accurate theory; e.g., Brownian dynamics (BD). Clearly, for such a test...

We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively stud...

We study global asymptotic behavior of Poisson-Nernst-Planck (PNP) systems for flow of two ion species through a narrow tubular-like membrane channel. As the radius of the cross-section of the three-dimensional tubular-like membrane channel approaches zero, a one-dimensional limiting PNP system is derived. This one-dimensional limiting system differs from previously studied one-dimensional PNP ...