ArticleJournal of computational physics2010
Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions.
Article in Journal of computational physics, 2010. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 26 papers.
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26 citing papers in PubMed.
- Numerical simulation of PDRN iontophoresis: comparison with passive diffusion and key parameter analysis.Drug delivery · 2026Article
- Multiphysics-guided design of ZIF-67/MWCNT-modified electrodes for highly selective electrochemical detection of sunset yellow in complex food matrices.RSC advances · 2026Article
- How do signals propagate in neuronal compartments? Insights from the Poisson-Nernst Planck model.Frontiers in cellular neuroscience · 2026Article
- Investigate channel rectifications and neural dynamics by an electrodiffusive Gauss-Nernst-Planck approach.PLoS computational biology · 2025Article
- An Algorithm Based on a Cable-Nernst Planck Model Predicting Synaptic Activity throughout the Dendritic Arbor with Micron Specificity.Neuroinformatics · 2023Article
- Co-localization and confinement of ecto-nucleotidases modulate extracellular adenosine nucleotide distributions.PLoS computational biology · 2020Article
- Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model.Entropy (Basel, Switzerland) · 2020Review
- Improved Poisson-Boltzmann Methods for High-Performance Computing.Journal of chemical theory and computation · 2019Article
- An efficient second-order poisson-boltzmann method.Journal of computational chemistry · 2019Article
- Robustness and Efficiency of Poisson-Boltzmann Modeling on Graphics Processing Units.Journal of chemical information and modeling · 2019Article
- Sensitivity analysis of the Poisson Nernst-Planck equations: a finite element approximation for the sensitive analysis of an electrodiffusion model.Journal of mathematical biology · 2019Article
- Frontiers in biomolecular mesh generation and molecular visualization systems.Visual computing for industry, biomedicine, and art · 2018Review
- Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.Journal of chemical theory and computation · 2017Article
- A Continuum Poisson-Boltzmann Model for Membrane Channel Proteins.Journal of chemical theory and computation · 2017Article
- Numerical interpretation of molecular surface field in dielectric modeling of solvation.Journal of computational chemistry · 2017Article
- Calculating protein-ligand binding affinities with MMPBSA: Method and error analysis.Journal of computational chemistry · 2016Article
- Charge Central Interpretation of the Full Nonlinear PB Equation: Implications for Accurate and Scalable Modeling of Solvation Interactions.The journal of physical chemistry. B · 2016Article
- Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smoothed particle hydrodynamics.BMC biophysics · 2015Article
- A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore.Communications in computational physics · 2014Article
- Biophysical significance of the inner mitochondrial membrane structure on the electrochemical potential of mitochondria.Physical review. E, Statistical, nonlinear, and soft matter physics · 2013Article
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4 authors.
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Abstract
In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems.
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