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1. An efficient finite element solver for a nonuniform size-modified Poisson-Nernst-Planck ion channel model

   https://doi.org/10.1016/j.jcp.2024.113393  

   Xie, Dexuan (December 2024, 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. 

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2. VDAC Solvation Free Energy Calculation by a Nonuniform Size Modified Poisson–Boltzmann Ion Channel Model

   https://doi.org/10.1002/jcc.70003  

   Jemison, Liam; Stahl, Matthew; Dash, Ranjan_K; Xie, Dexuan (December 2024, 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. 

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3. A Poisson-Nernst-Planck single ion channel model and its effective finite element solver

   https://doi.org/10.1016/j.jcp.2023.112043  

   Xie, Dexuan; Chao, Zhen (May 2023, Journal of Computational Physics)

   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. 

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4. Integral equation method for the 1D steady-state Poisson-Nernst-Planck equations

   https://doi.org/10.1007/s10825-023-02092-y  

   Chao, Zhen; Geng, Weihua; Krasny, Robert (September 2023, Journal of Computational Electronics)

   Abstract An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. The differential equations are recast as integral equations using Green’s 3rd identity yielding a fixed-point problem for the electric potential gradient and ion concentrations. The integrals are discretized by a combination of midpoint and trapezoid rules, and the resulting algebraic equations are solved by Gummel iteration. Numerical tests for electroneutral and non-electroneutral systems demonstrate the method’s 2nd order accuracy and ability to resolve sharp boundary layers. The method is applied to a 1D model of the K$$^+$$ ${}^{+}$ ion channel with a fixed charge density that ensures cation selectivity. In these tests, the proposed integral equation method yields potential and concentration profiles in good agreement with published results. 

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5. Enzymatic Noncovalent Synthesis for Mitochondrial Genetic Engineering of Cancer Cells

   https://doi.org/10.1016/j.xcrp.2020.100270  

   He, Hongjian; Lin, Xinyi; Wu, Difei; Wang, Jiaqing; Guo, Jiaqi; Green, Douglas R.; Zhang, Hongwei; Xu, Bing (December 2020, Cell Reports Physical Science)

   Since mitochondria contribute to tumorigenesis and drug resistance in cancer, mitochondrial genetic engineering promises a new direction for cancer therapy. Here, we report the use of the perimitochondrial enzymatic noncovalent synthesis (ENS) of peptides for delivering genes selectively into the mitochondria of cancer cells for mitochondrial genetic engineering. Specifically, the micelles of peptides bind to the voltage-dependent anion channel (VDAC) on mitochondria for the proteolysis by enterokinase (ENTK), generating perimitochondrial nanofibers in cancer cells. This process, facilitating selective delivery of nucleic acid or gene vectors into mitochondria of cancer cells, enables the mitochondrial transgene expression of CRISPR/Cas9, FUNDC1, p53, and fluorescent proteins. Mechanistic investigation indicates that the interaction of the peptide assemblies with the VDAC and mitochondrial membrane potential are necessary for mitochondria targeting. This local enzymatic control of intermolecular noncovalent interactions enables selective mitochondrial genetic engineering, thus providing a strategy for targeting cancer cells. 

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