ArticleBiophysical journal2011
Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes II: size effects on ionic distributions and diffusion-reaction rates.
Article in Biophysical journal, 2011. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 18 papers.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
18 citing papers in PubMed, 135 citations in OpenAlex.
- Nanoporous Carbon Coating of Separator Boosts Rate Capability of Cathodes in Lithium-Ion Batteries.Advanced materials (Deerfield Beach, Fla.) · 2026Article
- Electrodiffusion dynamics in the cardiomyocyte dyad at nano-scale resolution using the Poisson-Nernst-Planck (PNP) equations.PLoS computational biology · 2025Article
- A Computational Model of Protein Induced Membrane Morphology with Geodesic Curvature Driven Protein-Membrane Interface.Journal of computational physics · 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
- 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
- A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore.Communications in computational physics · 2014Article
- Exploring accurate Poisson-Boltzmann methods for biomolecular simulations.Computational & theoretical chemistry · 2013Article
- Ionic Size Effects: Generalized Boltzmann Distributions, Counterion Stratification, and Modified Debye Length.Nonlinearity · 2013Article
- A molecular level prototype for mechanoelectrical transducer in mammalian hair cells.Journal of computational neuroscience · 2013Article
- Electrostatic forces in the Poisson-Boltzmann systems.The Journal of chemical physics · 2013Article
- Interacting ions in biophysics: real is not ideal.Biophysical journal · 2013Review
- Progress in developing Poisson-Boltzmann equation solvers.Molecular based mathematical biology · 2013Article
- Exploring a charge-central strategy in the solution of Poisson's equation for biomolecular applications.Physical chemistry chemical physics : PCCP · 2013Article
- Modeling and simulation of ion channels.Chemical reviews · 2012Review
- Competitive adsorption and ordered packing of counterions near highly charged surfaces: From mean-field theory to Monte Carlo simulations.Physical review. E, Statistical, nonlinear, and soft matter physics · 2012Article
- MEAN-FIELD THEORY AND COMPUTATION OF ELECTROSTATICS WITH IONIC CONCENTRATION DEPENDENT DIELECTRICS.Communications in mathematical sciencesArticle
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
2 authors at 2 institutions in 2 countries.
Funding
No grant is acknowledged in the PubMed record.
Abstract
The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations.
Indexed as
Identifiers
What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.