PNP Equations with Steric Effects: A Model of Ion Flow through Channels

Horng, Tzyy Leng; Lin, Tai-Chia; Li, Chun; Eisenberg, Robert S.

doi:10.1021/jp305273n

Cited by 177 publications

(186 citation statements)

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“…It is essentially a system coupling diffusion and electrostatics, and the nonlinearity comes from the drift effect of electric field on ions. Such a system and its variants have found extensive and successful applications in biological systems, in particular in the description of ion transport through cells and ion channels [1,2]. It has also been applied to many industrial fields, such as the semiconductor devices [3] and the detection of poisonous lead by ion-selective electrode [4].…”

Section: Introductionmentioning

confidence: 99%

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Electroneutral models for dynamic Poisson-Nernst-Planck systems

2018

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The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layers poses both modelling and computational challenges. In this paper, we derive simplified electro-neutral (EN) models where the thin boundary layers are replaced by effective boundary conditions. There are two major advantages of EN models. First of all, it is much cheaper to solve them numerically. Secondly, EN models are easier to deal with compared with the original PNP, therefore it is also easier to derive macroscopic models for cellular structures using EN models.Even though the approach is applicable to higher dimensional cases, this paper mainly focuses on the one-dimensional system, including the general multi-ion case. Using systematic asymptotic analysis, we derive a variety of effective boundary conditions directly applicable to EN system for the bulk region. This EN system can be solved directly and efficiently without computing the solution in the boundary layer. The derivation is based on matched asymptotics, and the key idea is to bring back higher order contributions into effective boundary conditions. For Dirichlet boundary conditions, the higher order terms can be neglected and classical results (continuity of electrochemical potential) are recovered. For flux boundary conditions, however, neglecting higher contribution leads to physically incorrect solutions since they account for accumulation of ions in boundary layer. The validity of our EN model is verified by several examples and numerical computation. In particular, our EN model is much more efficient than the original PNP model when applied to the computation of membrane potential. Implemented with the Hodgkin-Huxley model, the computational time for solving the EN model is significantly reduced without sacrificing the accuracy of the solution due to the fact that it allows for relatively large mesh and time step sizes.

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Section: Introductionmentioning

confidence: 99%

“…Appendix A: The functions Fi, fi in Theorems 1,2 We show that the functions F i , f i are well defined. We take F i for example, and recall that…”

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confidence: 99%

Electroneutral models for dynamic Poisson-Nernst-Planck systems

2018

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“…There are a number of excellent works that have explored the e ects of nite ion size on transport (including PNP) [4,10,11,22,24,29,36,37,39,42,46]. The steric Poisson-Nernst-Planck [17] is one of typical models accounting for the nite-size e ects of ions formulated by the energetic variational approach [12]. It has been observed that the 1D computational results of steric Poisson-Nernst-Planck greatly enhances the selectivity of the ion channel.…”

Section: Discussionmentioning

confidence: 99%

“…It has been observed that the 1D computational results of steric Poisson-Nernst-Planck greatly enhances the selectivity of the ion channel. In the near future, another improvement of the Poisson-NernstBrought to you by | HEC Bibliotheque Maryriam ET J. Authenticated Download Date | 6/11/15 7:56 PM Planck model is to implement the 3D computations of steric Poisson-Nernst-Planck [17] taking into account the critical nite-size e ects of mobile ions moving through the narrow channel.…”

Section: Discussionmentioning

confidence: 99%

Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores

Chen

Majd

et al. 2014

Computational and Mathematical Biophysics

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Gramicidin A is a small and well characterized peptide that forms an ion channel in lipid membranes. An important feature of gramicidin A (gA) pore is that its conductance is a ected by the electric charges near the its entrance. This property has led to the application of gramicidin A as a biochemical sensor for monitoring and quantifying a number of chemical and enzymatic reactions. Here, a mathematical model of conductance changes of gramicidin A pores in response to the presence of electrical charges near its entrance, either on membrane surface or attached to gramicidin A itself, is presented. In this numerical simulation, a two dimensional computational domain is set to mimic the structure of a gramicidin A channel in the bilayer surrounded by electrolyte. The transport of ions through the channel is modeled by the Poisson-Nernst-Planck (PNP) equations that are solved by Finite Element Method (FEM). Preliminary numerical simulations of this mathematical model are in qualitative agreement with the experimental results in the literature. In addition to the model and simulations, we also present the analysis of the stability of the solution to the boundary conditions and the convergence of FEM method for the two dimensional PNP equations in our model.

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“…The differential capacitance plays an important role in modelling a wide variety of processes, such as the motion of colloidal particles in an applied electric field [1] and the behavior electro-osmotic pumps [2], including the phenomena of flow reversal in AC electro-osmosis [3], and the regulation of ion transfer and ion selectivity across cell membranes [4] and nanoporous channels [5,6]. It is relevant to the fields of biology, materials science, colloid science and the study of nano-fluidic devices.…”

Section: Introductionmentioning

confidence: 99%

The influence of excluded volume and excess ion polarisability on the capacitance of the electric double layer

Minton

Lue

2016

Molecular Physics

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This version is available at https://strathprints.strath.ac.uk/55894/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. We apply a modified Poisson-Boltzmann theory which permits ions of different sizes and excess polarizabilities to the study of these properties' effects on the differential capacitance of the electric double layer. For a planar electrode, we find an analytical expression for the differential capacitance, which is examined in the limits of low and high applied potential. In the low potential limit, a reduction of the solution relative permittivity caused by the ion polarizability causes the differential capacitance to decrease above a certain concentration, relative to the Gouy-Chapman-Stern theory. A similar effect is observed for the excluded volume, but only if the ions are of different sizes. In the high potential limit, the differential capacitance decreases inversely with the square root of the applied voltage. In a mixed electrolyte, asymmetries in both ion size and excess polarizability alter the surface adsorption of species: at high potentials, smaller ions displace larger ions and less polarizable ions displace more polarizable ions. The extent of the displacement agrees favorably with experimental data. A further consequence of this displacement is the appearance of a second peak in the differential capacitance, which is enhanced by excess ion polarizability.

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PNP Equations with Steric Effects: A Model of Ion Flow through Channels

Cited by 177 publications

References 258 publications

Electroneutral models for dynamic Poisson-Nernst-Planck systems

Electroneutral models for dynamic Poisson-Nernst-Planck systems

Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores

The influence of excluded volume and excess ion polarisability on the capacitance of the electric double layer

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