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A stabilized finite volume element method for solving Poisson-Nernst-Planck equations.

Jiao Li1, Jinyong Ying2

  • 1School of Mathematics and Statistics, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, Hunan, China.

International Journal for Numerical Methods in Biomedical Engineering
|October 30, 2021
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Summary

A new stabilized finite volume method addresses convection dominance in Poisson-Nernst-Planck (PNP) equations for ion transport. This robust solver yields more accurate ion concentration values in channel proteins.

Keywords:
Poisson-Nernst-Planck equationsfinite volume element methodstabilized technique

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Area of Science:

  • Computational Biology
  • Biophysics
  • Numerical Analysis

Background:

  • Solving Poisson-Nernst-Planck (PNP) equations is crucial for understanding ion transport in biological channels.
  • A key challenge is the convection-dominant problem within the Nernst-Planck equations, affecting accuracy.
  • Existing methods struggle with general mixed boundary conditions at interfaces.

Purpose of the Study:

  • To propose a novel stabilized finite volume element method for solving steady-state PNP equations.
  • To overcome the convection-dominant issue in Nernst-Planck equations.
  • To handle general mixed boundary conditions for ion concentration functions.

Main Methods:

  • Developed a stabilized finite volume element method based on a standard weak formulation.
  • Applied the method to solve the steady-state Poisson-Nernst-Planck equations.
  • Incorporated general mixed boundary conditions at interfaces.

Main Results:

  • The proposed method significantly improves the robustness of the PNP solver.
  • Numerical tests on four ion-channel proteins demonstrate enhanced performance.
  • Computed ion concentration values, particularly maximal concentrations, are more reasonable and accurate.

Conclusions:

  • The novel stabilized finite volume element method effectively resolves the convection-dominant problem in PNP equation solvers.
  • This technique enhances the reliability and accuracy of ion transport simulations in channel proteins.
  • The improved solver provides more biologically relevant concentration predictions.