Poisson–Nernst–Planck equations for simulating biomolecular diffusion–reaction processes I: Finite element solutions

Lu, Benzhuo; Holst, Michael; McCammon, J. Andrew; Zhou, Y. C.

doi:10.1016/j.jcp.2010.05.035

Cited by 157 publications

(148 citation statements)

References 51 publications

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“…In addition to the BL analysis, many (conservative) numerical schemes have been developed for PNP systems, such as finite element method [17], finite difference scheme [18] and finite volume method [19,20], in one or high-dimensional spaces [21,22]. Due to the presence of BL, computation of the PNP system needs to accurately capture the behaviour of solution in BL.…”

Section: Introductionmentioning

confidence: 99%

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%

Electroneutral models for dynamic Poisson-Nernst-Planck systems

2018

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“…Another example is the electrodiffusion-controlled reaction that enables ligand-enzyme complexion. (55) In fact, in these biological processes, the rates and orders of the reactions are mainly dependent on progressive electrodiffusion of charged particles or complexes through the transport medium. Particle-based computational models such as Langevin and Brownian dynamics (LD and MD) and the Monte Carlo (MC) method are widely used to predict reaction rates and constants for biological processes.…”

Section: Macroscale Analysis Of Bioelectronic Devicesmentioning

confidence: 99%

“…Mass transfer through electrochemical bioelectronic devices can be considered to be governed by the Nernst-Planck equation that characterizes the fluxes of mobile solutes. The molar flux of species, ϕ i , is described as (55) …”

Section: Macroscale Analysis Of Bioelectronic Devicesmentioning

confidence: 99%

A Short Review of the Architecture and Computational Analysis in the Design of Graphene Based Bioelectronic Devices

2018

Sensors and Materials

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Graphene possesses a high surface-to-volume ratio, which enables biomolecules to attach to it for bioelectronic applications. In this article, first, the classification and applications of bioelectronic devices are briefly reviewed. Then, recent work on real fabricated graphenebased bioelectronic devices as well as the analysis of their architecture and design using a computational approach to their charge transport properties are presented and discussed. A comparison to nongraphitic bioelectronic devices is also given. On the macroscale level, the design of devices is elaborated on the basis of a finite element analysis (FEA) approach, and the impact of design on the performance of the devices is discussed. On the nanoscale level, transport phenomena and their mechanisms for different design categories are elaborated on the basis of the density functional theory (DFT) and other quantum chemistry calculations. The calculated and measured charge transport properties of graphene-based bioelectronic devices are also compared with those of other available bioelectronic devices.

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“…In this work, we propose an alternative formulation of governing equations by introducing the Slotboom variables [25,27] (transformed concentrations) according to…”

Section: Slotboom Variablesmentioning

confidence: 99%