ArticleEuropean journal of applied mathematics2008
Singular perturbation analysis of the steady-state Poisson-Nernst-Planck system: Applications to ion channels.
Article in European journal of applied mathematics, 2008. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 13 papers.
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13 citing papers in PubMed, 115 citations in OpenAlex.
- Competition between Cations via Classical Poisson-Nernst-Planck Models with Nonzero but Small Permanent Charges.Membranes · 2021Article
- Selecting ions by size in a calcium channel: the ryanodine receptor case study.Biophysical journal · 2014Article
- Multiscale Multiphysics and Multidomain Models I: Basic Theory.Journal of theoretical & computational chemistry · 2013Article
- Interacting ions in biophysics: real is not ideal.Biophysical journal · 2013Review
- Quantum dynamics in continuum for proton transport--generalized correlation.The Journal of chemical physics · 2012Article
- Variational multiscale models for charge transport.SIAM review. Society for Industrial and Applied Mathematics · 2012Article
- Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids.The Journal of chemical physics · 2010Article
- Enhancement of charged macromolecule capture by nanopores in a salt gradient.The Journal of chemical physics · 2009Article
- Intracellular calcium release channels mediate their own countercurrent: the ryanodine receptor case study.Biophysical journal · 2008Article
- The anomalous mole fraction effect in calcium channels: a measure of preferential selectivity.Biophysical journal · 2008Article
- Synthetic nanopores as a test case for ion channel theories: the anomalous mole fraction effect without single filing.Biophysical journal · 2008Article
- Energetics of divalent selectivity in a calcium channel: the ryanodine receptor case study.Biophysical journal · 2008Article
- Singular perturbation analysis of the steady-state Poisson-Nernst-Planck system: Applications to ion channels.European journal of applied mathematics · 2008Article
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Authors and funding
4 authors at 3 institutions in 2 countries.
Funding
Abstract
Ion channels are proteins with a narrow hole down their middle that control a wide range of biological function by controlling the flow of spherical ions from one macroscopic region to another. Ion channels do not change their conformation on the biological time scale once they are open, so they can be described by a combination of Poisson and drift-diffusion (Nernst-Planck) equations called PNP in biophysics. We use singular perturbation techniques to analyse the steady-state PNP system for a channel with a general geometry and a piecewise constant permanent charge profile. We construct an outer solution for the case of a constant permanent charge density in three dimensions that is also a valid solution of the one-dimensional system. The asymptotical current-voltage (I-V ) characteristic curve of the device (obtained by the singular perturbation analysis) is shown to be a very good approximation of the numerical I-V curve (obtained by solving the system numerically). The physical constraint of non-negative concentrations implies a unique solution, i.e., for each given applied potential there corresponds a unique electric current (relaxing this constraint yields non-physical multiple solutions for sufficiently large voltages).
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