skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: A Poisson-Nernst-Planck single ion channel model and its effective finite element solver
A single ion channel is a membrane protein with an ion selectivity filter that allows only a single species of ions (such as potassium ions) to pass through in the “open” state. Its selectivity filter also naturally separates a solvent domain into an intracellular domain and an extracellular domain. Such biological and geometrical characteristics of a single ion channel are novelly adopted in the construction of a new kind of dielectric continuum ion channel model, called the Poisson-Nernst-Planck single ion channel (PNPSIC) model, in this paper. An effective PNPSIC finite element solver is then developed and implemented as a software package workable for a single ion channel with a three-dimensional X-ray crystallographic molecular structure and a mixture of multiple ionic species. Numerical results for a potassium channel confirm the convergence and efficiency of the PNPSIC finite element solver and demonstrate the high performance of the software package. Moreover, the PNPSIC model is applied to the calculation of electric current and validated by biophysical experimental data.  more » « less
Award ID(s):
2153376
PAR ID:
10413417
Author(s) / Creator(s):
;
Publisher / Repository:
Elsevier
Date Published:
Journal Name:
Journal of Computational Physics
Volume:
481
Issue:
C
ISSN:
0021-9991
Page Range / eLocation ID:
112043
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. (, Journal of Computational Physics)
    In this paper, a nonuniform size modified Poisson-Boltzmann ion channel (nuSMPBIC) model is presented as a nonlinear system of an electrostatic potential and multiple ionic concentrations. It mixes nonlinear algebraic equations with a Poisson boundary value problem involving Dirichlet-Neumann mixed boundary value conditions and a membrane surface charge density to reflect the effects of ion sizes and membrane charges on electrostatics and ionic concentrations. To overcome the difficulties of strong singularities and exponential nonlinearities, it is split into three submodels with a solution of Model 1 collecting all the singular points and Models 2 and 3 much easier to solve numerically than the original nuSMPBIC model. A damped two-block iterative method is then presented to solve Model 3, along with a novel modified Newton iterative scheme for solving each related nonlinear algebraic system. To this end, an effective nuSMPBIC finite element solver is derived and then implemented as a program package that works for an ion channel protein with a three-dimensional molecular structure and a mixture of multiple ionic species. Numerical results for a voltage-dependent anion channel (VDAC) in a mixture of four ionic species demonstrate a fast convergence rate of the damped two-block iterative method, the high performance of the software package, and the importance of considering nonuniform ion sizes. Moreover, the nuSMPBIC model is validated by the anion selectivity property of VDAC. 
    more » « less
  2. ; ; ; (, Journal of Computational Chemistry)
    ABSTRACT Voltage‐dependent anion channel (VDAC) is the primary conduit for regulated passage of ions and metabolites into and out of a mitochondrion. Calculating the solvation free energy for VDAC is crucial for understanding its stability, function, and interactions within the cellular environment. In this article, numerical schemes for computing the total solvation free energy for VDAC—comprising electrostatic, ideal gas, and excess free energies plus the nonpolar energy—are developed based on a nonuniform size modified Poisson–Boltzmann ion channel (nuSMPBIC) finite element solver along with tetrahedral meshes for VDAC proteins. The current mesh generation package is also updated to improve mesh quality and accelerate mesh generation. A VDAC Solvation Free Energy Calculation (VSFEC) package is then created by integrating these schemes with the updated mesh package, the nuSMPBIC finite element package, the PDB2PQR package, and the OPM database, as well as one uniform SMPBIC finite element package and one Poisson–Boltzmann ion channel (PBIC) finite element package. With the VSFEC package, many numerical experiments are made using six VDAC proteins, eight ionic solutions containing up to four ionic species, including ATP4−and Ca2+, two reference states, different boundary values, and different permittivity constants. The test results underscore the importance of considering nonuniform ionic size effects to explore the varying patterns of the total solvation free energy, and demonstrate the high performance of the VSFEC package for VDAC solvation free energy calculation. 
    more » « less
  3. (, Journal of Computational Physics)
    This paper presents an efficient finite element iterative method for solving a nonuniform size- modified Poisson-Nernst-Planck ion channel (SMPNPIC) model, along with an SMPNPIC program package that works for an ion channel protein with a three-dimensional crystallographic structure and an ionic solvent with multiple ionic species. In particular, the SMPNPIC model is constructed and then reformulated by novel mathematical techniques so that each iteration of the method only involves linear boundary value problems and nonlinear algebraic systems, circumventing the numerical difficulties caused by the strong nonlinearities, strong asymmetries, and strong differential equation coupling of the SMPNPIC model. To further improve the method’s efficiency, an efficient modified Newton iterative method is adapted to the numerical solution of each related nonlinear algebraic system. In addition, a uniform SMPNPIC model is introduced and solved, numerically, as a special case of the SMPNPIC model. Numerical results for a voltage-dependent anion channel (VDAC) and two mixture solutions of four ionic species, including ATP4− ions, demonstrate the method’s convergence, the package’s high performance, and the importance of considering nonuniform ion size effects. They also partially validate the SMPNPIC model by the anion selectivity property of VDAC. 
    more » « less
  4. ; ; ; ; (, Science Advances)
    Reproducing the exquisite ion selectivity displayed by biological ion channels in artificial nanopore systems has proven to be one of the most challenging tasks undertaken by the nanopore community, yet a successful achievement of this goal offers immense technological potential. Here, we show a strategy to design solid-state nanopores that selectively transport potassium ions and show negligible conductance for sodium ions. The nanopores contain walls decorated with 4′-aminobenzo-18-crown-6 ether and single-stranded DNA (ssDNA) molecules located at one pore entrance. The ionic selectivity stems from facilitated transport of potassium ions in the pore region containing crown ether, while the highly charged ssDNA plays the role of a cation filter. Achieving potassium selectivity in solid-state nanopores opens new avenues toward advanced separation processes, more efficient biosensing technologies, and novel biomimetic nanopore systems. 
    more » « less
  5. ; ; ; ; ; (, Chemical Science)
    Potassium channels modulate various cellular functions through efficient and selective conduction of K + ions. The mechanism of ion conduction in potassium channels has recently emerged as a topic of debate. Crystal structures of potassium channels show four K + ions bound to adjacent binding sites in the selectivity filter, while chemical intuition and molecular modeling suggest that the direct ion contacts are unstable. Molecular dynamics (MD) simulations have been instrumental in the study of conduction and gating mechanisms of ion channels. Based on MD simulations, two hypotheses have been proposed, in which the four-ion configuration is an artifact due to either averaged structures or low temperature in crystallographic experiments. The two hypotheses have been supported or challenged by different experiments. Here, MD simulations with polarizable force fields validated by ab initio calculations were used to investigate the ion binding thermodynamics. Contrary to previous beliefs, the four-ion configuration was predicted to be thermodynamically stable after accounting for the complex electrostatic interactions and dielectric screening. Polarization plays a critical role in the thermodynamic stabilities. As a result, the ion conduction likely operates through a simple single-vacancy and water-free mechanism. The simulations explained crystal structures, ion binding experiments and recent controversial mutagenesis experiments. This work provides a clear view of the mechanism underlying the efficient ion conduction and demonstrates the importance of polarization in ion channel simulations. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email